%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW314+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n029.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 12:25:56 EDT 2023

% Result   : Theorem 1.71s 2.43s
% Output   : Proof 1.71s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SWW314+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Thu May 18 22:45:43 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 1.71/2.43  
% 1.71/2.43  /export/starexec/sandbox/benchmark/theBenchmark.p is a Theorem
% 1.71/2.43  Start of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.71/2.43  %-----------------------------------------------------
% 1.71/2.43  ncf(matrix, plain, [(52791 ^ _782464) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)], (2 ^ _782464) ^ [_782494] : [-(_782494 = _782494)], (4 ^ _782464) ^ [_782517, _782519] : [_782519 = _782517, -(_782517 = _782519)], (10 ^ _782464) ^ [_782590, _782592, _782594] : [-(_782594 = _782590), _782594 = _782592, _782592 = _782590], (20 ^ _782464) ^ [_782727, _782729, _782731, _782733, _782735, _782737, _782739, _782741, _782743, _782745, _782747, _782749] : [-(c_Predicate_Oinv__imagep(_782747, _782743, _782739, _782735, _782731, _782727)), c_Predicate_Oinv__imagep(_782749, _782745, _782741, _782737, _782733, _782729), _782749 = _782747, _782745 = _782743, _782741 = _782739, _782737 = _782735, _782733 = _782731, _782729 = _782727], (50 ^ _782464) ^ [_783272, _783274, _783276, _783278, _783280, _783282] : [-(c_Orderings_Oorder__class_Ostrict__mono(_783280, _783276, _783272)), c_Orderings_Oorder__class_Ostrict__mono(_783282, _783278, _783274), _783282 = _783280, _783278 = _783276, _783274 = _783272], (68 ^ _782464) ^ [_783541, _783543, _783545, _783547, _783549, _783551, _783553, _783555, _783557, _783559, _783561, _783563] : [-(c_Nitpick_Ofold__graph_H(_783561, _783557, _783553, _783549, _783545, _783541)), c_Nitpick_Ofold__graph_H(_783563, _783559, _783555, _783551, _783547, _783543), _783563 = _783561, _783559 = _783557, _783555 = _783553, _783551 = _783549, _783547 = _783545, _783543 = _783541], (98 ^ _782464) ^ [_784086, _784088, _784090, _784092, _784094, _784096, _784098, _784100] : [-(c_Partial__Function_Omk__less(_784098, _784094, _784090, _784086)), c_Partial__Function_Omk__less(_784100, _784096, _784092, _784088), _784100 = _784098, _784096 = _784094, _784092 = _784090, _784088 = _784086], (120 ^ _782464) ^ [_784439, _784441, _784443, _784445, _784447, _784449, _784451, _784453] : [-(c_Finite__Set_Ofolding__idem(_784451, _784447, _784443, _784439)), c_Finite__Set_Ofolding__idem(_784453, _784449, _784445, _784441), _784453 = _784451, _784449 = _784447, _784445 = _784443, _784441 = _784439], (142 ^ _782464) ^ [_784792, _784794, _784796, _784798, _784800, _784802, _784804, _784806, _784808, _784810, _784812, _784814] : [-(c_Finite__Set_Ofolding__image__simple(_784812, _784808, _784804, _784800, _784796, _784792)), c_Finite__Set_Ofolding__image__simple(_784814, _784810, _784806, _784802, _784798, _784794), _784814 = _784812, _784810 = _784808, _784806 = _784804, _784802 = _784800, _784798 = _784796, _784794 = _784792], (172 ^ _782464) ^ [_785337, _785339, _785341, _785343, _785345, _785347] : [-(c_Big__Operators_Osemilattice__big(_785345, _785341, _785337)), c_Big__Operators_Osemilattice__big(_785347, _785343, _785339), _785347 = _785345, _785343 = _785341, _785339 = _785337], (190 ^ _782464) ^ [_785606, _785608, _785610, _785612, _785614, _785616, _785618, _785620, _785622, _785624] : [-(c_Big__Operators_Ocomm__monoid__big(_785622, _785618, _785614, _785610, _785606)), c_Big__Operators_Ocomm__monoid__big(_785624, _785620, _785616, _785612, _785608), _785624 = _785622, _785620 = _785618, _785616 = _785614, _785612 = _785610, _785608 = _785606], (216 ^ _782464) ^ [_786051, _786053] : [-(class_Rings_Odivision__ring__inverse__zero(_786051)), _786053 = _786051, class_Rings_Odivision__ring__inverse__zero(_786053)], (226 ^ _782464) ^ [_786176, _786178] : [-(class_Rings_Odivision__ring(_786176)), _786178 = _786176, class_Rings_Odivision__ring(_786178)], (236 ^ _782464) ^ [_786301, _786303] : [-(class_Fields_Ofield(_786301)), _786303 = _786301, class_Fields_Ofield(_786303)], (246 ^ _782464) ^ [_786426, _786428] : [-(c_Nat__Transfer_Ois__nat(_786426)), _786428 = _786426, c_Nat__Transfer_Ois__nat(_786428)], (256 ^ _782464) ^ [_786551, _786553] : [-(class_Fields_Olinordered__field__inverse__zero(_786551)), _786553 = _786551, class_Fields_Olinordered__field__inverse__zero(_786553)], (266 ^ _782464) ^ [_786676, _786678, _786680, _786682] : [-(c_Int_Oiszero(_786680, _786676)), c_Int_Oiszero(_786682, _786678), _786682 = _786680, _786678 = _786676], (280 ^ _782464) ^ [_786869, _786871] : [-(class_Fields_Ofield__inverse__zero(_786869)), _786871 = _786869, class_Fields_Ofield__inverse__zero(_786871)], (290 ^ _782464) ^ [_786994, _786996, _786998, _787000] : [-(c_Nitpick_Orefl_H(_786998, _786994)), c_Nitpick_Orefl_H(_787000, _786996), _787000 = _786998, _786996 = _786994], (304 ^ _782464) ^ [_787187, _787189, _787191, _787193, _787195, _787197] : [-(c_Orderings_Oorder__class_Omono(_787195, _787191, _787187)), c_Orderings_Oorder__class_Omono(_787197, _787193, _787189), _787197 = _787195, _787193 = _787191, _787189 = _787187], (322 ^ _782464) ^ [_787456, _787458, _787460, _787462] : [-(c_FunDef_Oreduction__pair(_787460, _787456)), c_FunDef_Oreduction__pair(_787462, _787458), _787462 = _787460, _787458 = _787456], (336 ^ _782464) ^ [_787649, _787651, _787653, _787655] : [-(c_Nitpick_Owf_H(_787653, _787649)), c_Nitpick_Owf_H(_787655, _787651), _787655 = _787653, _787651 = _787649], (350 ^ _782464) ^ [_787842, _787844] : [-(c_Nitpick_Ounknown(_787842)), _787844 = _787842, c_Nitpick_Ounknown(_787844)], (360 ^ _782464) ^ [_787967, _787969, _787971, _787973] : [-(c_Wellfounded_OwfP(_787971, _787967)), c_Wellfounded_OwfP(_787973, _787969), _787973 = _787971, _787969 = _787967], (374 ^ _782464) ^ [_788160, _788162, _788164, _788166] : [-(c_Relation_Oirrefl(_788164, _788160)), c_Relation_Oirrefl(_788166, _788162), _788166 = _788164, _788162 = _788160], (388 ^ _782464) ^ [_788353, _788355, _788357, _788359, _788361, _788363] : [-(c_Relation_Ototal__on(_788361, _788357, _788353)), c_Relation_Ototal__on(_788363, _788359, _788355), _788363 = _788361, _788359 = _788357, _788355 = _788353], (406 ^ _782464) ^ [_788622, _788624, _788626, _788628, _788630, _788632] : [-(c_Relation_Osingle__valued(_788630, _788626, _788622)), c_Relation_Osingle__valued(_788632, _788628, _788624), _788632 = _788630, _788628 = _788626, _788624 = _788622], (424 ^ _782464) ^ [_788891, _788893, _788895, _788897, _788899, _788901, _788903, _788905] : [-(c_Finite__Set_Ofolding(_788903, _788899, _788895, _788891)), c_Finite__Set_Ofolding(_788905, _788901, _788897, _788893), _788905 = _788903, _788901 = _788899, _788897 = _788895, _788893 = _788891], (446 ^ _782464) ^ [_789244, _789246, _789248, _789250, _789252, _789254] : [-(c_Finite__Set_Ofolding__one__idem(_789252, _789248, _789244)), c_Finite__Set_Ofolding__one__idem(_789254, _789250, _789246), _789254 = _789252, _789250 = _789248, _789246 = _789244], (464 ^ _782464) ^ [_789513, _789515, _789517, _789519, _789521, _789523] : [-(c_Finite__Set_Ofolding__one(_789521, _789517, _789513)), c_Finite__Set_Ofolding__one(_789523, _789519, _789515), _789523 = _789521, _789519 = _789517, _789515 = _789513], (482 ^ _782464) ^ [_789782, _789784, _789786, _789788, _789790, _789792, _789794, _789796, _789798, _789800, _789802, _789804] : [-(c_Finite__Set_Ofolding__image__simple__idem(_789802, _789798, _789794, _789790, _789786, _789782)), c_Finite__Set_Ofolding__image__simple__idem(_789804, _789800, _789796, _789792, _789788, _789784), _789804 = _789802, _789800 = _789798, _789796 = _789794, _789792 = _789790, _789788 = _789786, _789784 = _789782], (512 ^ _782464) ^ [_790327, _790329] : [-(class_Rings_Oinverse(_790327)), _790329 = _790327, class_Rings_Oinverse(_790329)], (522 ^ _782464) ^ [_790452, _790454, _790456, _790458, _790460, _790462] : [-(c_Nitpick_Oless__frac(_790460, _790456, _790452)), c_Nitpick_Oless__frac(_790462, _790458, _790454), _790462 = _790460, _790458 = _790456, _790454 = _790452], (540 ^ _782464) ^ [_790721, _790723, _790725, _790727, _790729, _790731] : [-(c_Nitpick_Oless__eq__frac(_790729, _790725, _790721)), c_Nitpick_Oless__eq__frac(_790731, _790727, _790723), _790731 = _790729, _790727 = _790725, _790723 = _790721], (558 ^ _782464) ^ [_790990, _790992] : [-(c_Nat__Transfer_Onat__set(_790990)), _790992 = _790990, c_Nat__Transfer_Onat__set(_790992)], (568 ^ _782464) ^ [_791115, _791117, _791119, _791121, _791123, _791125, _791127, _791129] : [-(c_List_Olistrelp(_791127, _791123, _791119, _791115)), c_List_Olistrelp(_791129, _791125, _791121, _791117), _791129 = _791127, _791125 = _791123, _791121 = _791119, _791117 = _791115], (590 ^ _782464) ^ [_791468, _791470] : [-(class_Lattices_Oab__semigroup__idem__mult(_791468)), _791470 = _791468, class_Lattices_Oab__semigroup__idem__mult(_791470)], (600 ^ _782464) ^ [_791593, _791595, _791597, _791599, _791601, _791603] : [-(c_Finite__Set_Ofun__left__comm__idem(_791601, _791597, _791593)), c_Finite__Set_Ofun__left__comm__idem(_791603, _791599, _791595), _791603 = _791601, _791599 = _791597, _791595 = _791593], (618 ^ _782464) ^ [_791862, _791864, _791866, _791868, _791870, _791872, _791874, _791876, _791878, _791880] : [-(c_Typedef_Otype__definition(_791878, _791874, _791870, _791866, _791862)), c_Typedef_Otype__definition(_791880, _791876, _791872, _791868, _791864), _791880 = _791878, _791876 = _791874, _791872 = _791870, _791868 = _791866, _791864 = _791862], (644 ^ _782464) ^ [_792307, _792309, _792311, _792313, _792315, _792317] : [-(c_Finite__Set_Ofun__left__comm(_792315, _792311, _792307)), c_Finite__Set_Ofun__left__comm(_792317, _792313, _792309), _792317 = _792315, _792313 = _792311, _792309 = _792307], (662 ^ _782464) ^ [_792576, _792578] : [-(c_List_Onat__list(_792576)), _792578 = _792576, c_List_Onat__list(_792578)], (672 ^ _782464) ^ [_792701, _792703, _792705, _792707, _792709, _792711, _792713, _792715, _792717, _792719] : [-(c_List_Olist__all2(_792717, _792713, _792709, _792705, _792701)), c_List_Olist__all2(_792719, _792715, _792711, _792707, _792703), _792719 = _792717, _792715 = _792713, _792711 = _792709, _792707 = _792705, _792703 = _792701], (698 ^ _782464) ^ [_793146, _793148, _793150, _793152] : [-(c_List_Olinorder__class_Osorted(_793150, _793146)), c_List_Olinorder__class_Osorted(_793152, _793148), _793152 = _793150, _793148 = _793146], (712 ^ _782464) ^ [_793339, _793341, _793343, _793345] : [-(c_FunDef_Ois__measure(_793343, _793339)), c_FunDef_Ois__measure(_793345, _793341), _793345 = _793343, _793341 = _793339], (726 ^ _782464) ^ [_793532, _793534, _793536, _793538, _793540, _793542, _793544, _793546] : [-(c_Nat__Transfer_Otransfer__morphism(_793544, _793540, _793536, _793532)), c_Nat__Transfer_Otransfer__morphism(_793546, _793542, _793538, _793534), _793546 = _793544, _793542 = _793540, _793538 = _793536, _793534 = _793532], (748 ^ _782464) ^ [_793885, _793887, _793889, _793891, _793893, _793895, _793897, _793899, _793901, _793903] : [-(c_Fun_Obij__betw(_793901, _793897, _793893, _793889, _793885)), c_Fun_Obij__betw(_793903, _793899, _793895, _793891, _793887), _793903 = _793901, _793899 = _793897, _793895 = _793893, _793891 = _793889, _793887 = _793885], (774 ^ _782464) ^ [_794330, _794332, _794334, _794336, _794338, _794340, _794342, _794344] : [-(c_Fun_Oinj__on(_794342, _794338, _794334, _794330)), c_Fun_Oinj__on(_794344, _794340, _794336, _794332), _794344 = _794342, _794340 = _794338, _794336 = _794334, _794332 = _794330], (796 ^ _782464) ^ [_794683, _794685] : [-(class_Fields_Olinordered__field(_794683)), _794685 = _794683, class_Fields_Olinordered__field(_794685)], (806 ^ _782464) ^ [_794808, _794810, _794812, _794814, _794816, _794818] : [-(c_List_Olist__ex1(_794816, _794812, _794808)), c_List_Olist__ex1(_794818, _794814, _794810), _794818 = _794816, _794814 = _794812, _794810 = _794808], (824 ^ _782464) ^ [_795077, _795079, _795081, _795083, _795085, _795087] : [-(c_List_Oall__interval__int(_795085, _795081, _795077)), c_List_Oall__interval__int(_795087, _795083, _795079), _795087 = _795085, _795083 = _795081, _795079 = _795077], (842 ^ _782464) ^ [_795346, _795348, _795350, _795352] : [-(c_Predicate_Oreflp(_795350, _795346)), c_Predicate_Oreflp(_795352, _795348), _795352 = _795350, _795348 = _795346], (856 ^ _782464) ^ [_795539, _795541, _795543, _795545, _795547, _795549, _795551, _795553] : [-(c_Wellfounded_Omax__extp(_795551, _795547, _795543, _795539)), c_Wellfounded_Omax__extp(_795553, _795549, _795545, _795541), _795553 = _795551, _795549 = _795547, _795545 = _795543, _795541 = _795539], (878 ^ _782464) ^ [_795892, _795894, _795896, _795898] : [-(c_Wellfounded_Oacyclic(_795896, _795892)), c_Wellfounded_Oacyclic(_795898, _795894), _795898 = _795896, _795894 = _795892], (892 ^ _782464) ^ [_796085, _796087, _796089, _796091] : [-(c_Relation_Oantisym(_796089, _796085)), c_Relation_Oantisym(_796091, _796087), _796091 = _796089, _796087 = _796085], (906 ^ _782464) ^ [_796278, _796280, _796282, _796284, _796286, _796288] : [-(c_Equiv__Relations_Oequiv(_796286, _796282, _796278)), c_Equiv__Relations_Oequiv(_796288, _796284, _796280), _796288 = _796286, _796284 = _796282, _796280 = _796278], (924 ^ _782464) ^ [_796547, _796549, _796551, _796553] : [-(c_Relation_Otrans(_796551, _796547)), c_Relation_Otrans(_796553, _796549), _796553 = _796551, _796549 = _796547], (938 ^ _782464) ^ [_796740, _796742, _796744, _796746] : [-(c_Relation_Osym(_796744, _796740)), c_Relation_Osym(_796746, _796742), _796746 = _796744, _796742 = _796740], (952 ^ _782464) ^ [_796933, _796935, _796937, _796939] : [-(c_Predicate_Osymp(_796937, _796933)), c_Predicate_Osymp(_796939, _796935), _796939 = _796937, _796935 = _796933], (966 ^ _782464) ^ [_797126, _797128, _797130, _797132] : [-(c_Predicate_Otransp(_797130, _797126)), c_Predicate_Otransp(_797132, _797128), _797132 = _797130, _797128 = _797126], (980 ^ _782464) ^ [_797319, _797321, _797323, _797325] : [-(c_Equiv__Relations_Opart__equivp(_797323, _797319)), c_Equiv__Relations_Opart__equivp(_797325, _797321), _797325 = _797323, _797321 = _797319], (994 ^ _782464) ^ [_797512, _797514, _797516, _797518, _797520, _797522] : [-(c_Relation_Orefl__on(_797520, _797516, _797512)), c_Relation_Orefl__on(_797522, _797518, _797514), _797522 = _797520, _797518 = _797516, _797514 = _797512], (1012 ^ _782464) ^ [_797781, _797783, _797785, _797787] : [-(c_Wellfounded_Owf(_797785, _797781)), c_Wellfounded_Owf(_797787, _797783), _797787 = _797785, _797783 = _797781], (1026 ^ _782464) ^ [_797974, _797976, _797978, _797980] : [-(c_Equiv__Relations_Oequivp(_797978, _797974)), c_Equiv__Relations_Oequivp(_797980, _797976), _797980 = _797978, _797976 = _797974], (1040 ^ _782464) ^ [_798167, _798169, _798171, _798173, _798175, _798177, _798179, _798181, _798183, _798185, _798187, _798189] : [-(c_Equiv__Relations_Ocongruent2(_798187, _798183, _798179, _798175, _798171, _798167)), c_Equiv__Relations_Ocongruent2(_798189, _798185, _798181, _798177, _798173, _798169), _798189 = _798187, _798185 = _798183, _798181 = _798179, _798177 = _798175, _798173 = _798171, _798169 = _798167], (1070 ^ _782464) ^ [_798712, _798714, _798716, _798718, _798720, _798722, _798724, _798726] : [-(c_Equiv__Relations_Ocongruent(_798724, _798720, _798716, _798712)), c_Equiv__Relations_Ocongruent(_798726, _798722, _798718, _798714), _798726 = _798724, _798722 = _798720, _798718 = _798716, _798714 = _798712], (1092 ^ _782464) ^ [_799065, _799067, _799069, _799071, _799073, _799075] : [-(c_List_Olist__all(_799073, _799069, _799065)), c_List_Olist__all(_799075, _799071, _799067), _799075 = _799073, _799071 = _799069, _799067 = _799065], (1110 ^ _782464) ^ [_799334, _799336, _799338, _799340, _799342, _799344] : [-(c_List_Olist__ex(_799342, _799338, _799334)), c_List_Olist__ex(_799344, _799340, _799336), _799344 = _799342, _799340 = _799338, _799336 = _799334], (1128 ^ _782464) ^ [_799603, _799605, _799607, _799609, _799611, _799613] : [-(c_List_Oall__interval__nat(_799611, _799607, _799603)), c_List_Oall__interval__nat(_799613, _799609, _799605), _799613 = _799611, _799609 = _799607, _799605 = _799603], (1146 ^ _782464) ^ [_799872, _799874, _799876, _799878, _799880, _799882, _799884, _799886, _799888, _799890] : [-(c_Finite__Set_Ofolding__image(_799888, _799884, _799880, _799876, _799872)), c_Finite__Set_Ofolding__image(_799890, _799886, _799882, _799878, _799874), _799890 = _799888, _799886 = _799884, _799882 = _799880, _799878 = _799876, _799874 = _799872], (1172 ^ _782464) ^ [_800317, _800319] : [-(class_Lattices_Obounded__lattice(_800317)), _800319 = _800317, class_Lattices_Obounded__lattice(_800319)], (1182 ^ _782464) ^ [_800442, _800444] : [-(class_Rings_Olinordered__semiring__1__strict(_800442)), _800444 = _800442, class_Rings_Olinordered__semiring__1__strict(_800444)], (1192 ^ _782464) ^ [_800567, _800569] : [-(class_Groups_Oordered__ab__group__add__abs(_800567)), _800569 = _800567, class_Groups_Oordered__ab__group__add__abs(_800569)], (1202 ^ _782464) ^ [_800692, _800694] : [-(class_Groups_Olinordered__ab__group__add(_800692)), _800694 = _800692, class_Groups_Olinordered__ab__group__add(_800694)], (1212 ^ _782464) ^ [_800817, _800819] : [-(class_Rings_Oring__1__no__zero__divisors(_800817)), _800819 = _800817, class_Rings_Oring__1__no__zero__divisors(_800819)], (1222 ^ _782464) ^ [_800942, _800944] : [-(class_Rings_Olinordered__ring__strict(_800942)), _800944 = _800942, class_Rings_Olinordered__ring__strict(_800944)], (1232 ^ _782464) ^ [_801067, _801069] : [-(class_Rings_Oring__no__zero__divisors(_801067)), _801069 = _801067, class_Rings_Oring__no__zero__divisors(_801069)], (1242 ^ _782464) ^ [_801192, _801194] : [-(class_Rings_Olinordered__semiring__1(_801192)), _801194 = _801192, class_Rings_Olinordered__semiring__1(_801194)], (1252 ^ _782464) ^ [_801317, _801319] : [-(class_Groups_Oordered__ab__group__add(_801317)), _801319 = _801317, class_Groups_Oordered__ab__group__add(_801319)], (1262 ^ _782464) ^ [_801442, _801444] : [-(class_Rings_Oordered__ring__abs(_801442)), _801444 = _801442, class_Rings_Oordered__ring__abs(_801444)], (1272 ^ _782464) ^ [_801567, _801569] : [-(class_Rings_Olinordered__ring(_801567)), _801569 = _801567, class_Rings_Olinordered__ring(_801569)], (1282 ^ _782464) ^ [_801692, _801694] : [-(class_Rings_Olinordered__idom(_801692)), _801694 = _801692, class_Rings_Olinordered__idom(_801694)], (1292 ^ _782464) ^ [_801817, _801819] : [-(class_Groups_Oab__group__add(_801817)), _801819 = _801817, class_Groups_Oab__group__add(_801819)], (1302 ^ _782464) ^ [_801942, _801944] : [-(class_Rings_Oordered__ring(_801942)), _801944 = _801942, class_Rings_Oordered__ring(_801944)], (1312 ^ _782464) ^ [_802067, _802069] : [-(class_Rings_Ocomm__ring__1(_802067)), _802069 = _802067, class_Rings_Ocomm__ring__1(_802069)], (1322 ^ _782464) ^ [_802192, _802194] : [-(class_Groups_Ogroup__add(_802192)), _802194 = _802192, class_Groups_Ogroup__add(_802194)], (1332 ^ _782464) ^ [_802317, _802319] : [-(class_Divides_Oring__div(_802317)), _802319 = _802317, class_Divides_Oring__div(_802319)], (1342 ^ _782464) ^ [_802442, _802444] : [-(class_Rings_Ocomm__ring(_802442)), _802444 = _802442, class_Rings_Ocomm__ring(_802444)], (1352 ^ _782464) ^ [_802567, _802569] : [-(class_Int_Oring__char__0(_802567)), _802569 = _802567, class_Int_Oring__char__0(_802569)], (1362 ^ _782464) ^ [_802692, _802694] : [-(class_Int_Onumber__ring(_802692)), _802694 = _802692, class_Int_Onumber__ring(_802694)], (1372 ^ _782464) ^ [_802817, _802819] : [-(class_Groups_Osgn__if(_802817)), _802819 = _802817, class_Groups_Osgn__if(_802819)], (1382 ^ _782464) ^ [_802942, _802944] : [-(class_Groups_Oabs__if(_802942)), _802944 = _802942, class_Groups_Oabs__if(_802944)], (1392 ^ _782464) ^ [_803067, _803069] : [-(class_Rings_Oring__1(_803067)), _803069 = _803067, class_Rings_Oring__1(_803069)], (1402 ^ _782464) ^ [_803192, _803194] : [-(class_Rings_Oring(_803192)), _803194 = _803192, class_Rings_Oring(_803194)], (1412 ^ _782464) ^ [_803317, _803319] : [-(class_Rings_Oidom(_803317)), _803319 = _803317, class_Rings_Oidom(_803319)], (1422 ^ _782464) ^ [_803442, _803444] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803442)), _803444 = _803442, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803444)], (1432 ^ _782464) ^ [_803567, _803569] : [-(class_Orderings_Owellorder(_803567)), _803569 = _803567, class_Orderings_Owellorder(_803569)], (1442 ^ _782464) ^ [_803692, _803694] : [-(class_Complete__Lattice_Ocomplete__lattice(_803692)), _803694 = _803692, class_Complete__Lattice_Ocomplete__lattice(_803694)], (1452 ^ _782464) ^ [_803817, _803819] : [-(class_Lattices_Obounded__lattice__top(_803817)), _803819 = _803817, class_Lattices_Obounded__lattice__top(_803819)], (1462 ^ _782464) ^ [_803942, _803944] : [-(class_Lattices_Obounded__lattice__bot(_803942)), _803944 = _803942, class_Lattices_Obounded__lattice__bot(_803944)], (1472 ^ _782464) ^ [_804067, _804069] : [-(class_Lattices_Osemilattice__sup(_804067)), _804069 = _804067, class_Lattices_Osemilattice__sup(_804069)], (1482 ^ _782464) ^ [_804192, _804194] : [-(class_Lattices_Osemilattice__inf(_804192)), _804194 = _804192, class_Lattices_Osemilattice__inf(_804194)], (1492 ^ _782464) ^ [_804317, _804319] : [-(class_Lattices_Odistrib__lattice(_804317)), _804319 = _804317, class_Lattices_Odistrib__lattice(_804319)], (1502 ^ _782464) ^ [_804442, _804444] : [-(class_Lattices_Oboolean__algebra(_804442)), _804444 = _804442, class_Lattices_Oboolean__algebra(_804444)], (1512 ^ _782464) ^ [_804567, _804569] : [-(class_Lattices_Olattice(_804567)), _804569 = _804567, class_Lattices_Olattice(_804569)], (1522 ^ _782464) ^ [_804692, _804694] : [-(class_Orderings_Otop(_804692)), _804694 = _804692, class_Orderings_Otop(_804694)], (1532 ^ _782464) ^ [_804817, _804819] : [-(class_Orderings_Obot(_804817)), _804819 = _804817, class_Orderings_Obot(_804819)], (1542 ^ _782464) ^ [_804942, _804944] : [-(class_Groups_Ouminus(_804942)), _804944 = _804942, class_Groups_Ouminus(_804944)], (1552 ^ _782464) ^ [_805067, _805069] : [-(class_Lazy__Sequence_Osmall__lazy(_805067)), _805069 = _805067, class_Lazy__Sequence_Osmall__lazy(_805069)], (1562 ^ _782464) ^ [_805192, _805194] : [-(class_Finite__Set_Ofinite(_805192)), _805194 = _805192, class_Finite__Set_Ofinite(_805194)], (1572 ^ _782464) ^ [_805317, _805319] : [-(class_Enum_Oenum(_805317)), _805319 = _805317, class_Enum_Oenum(_805319)], (1582 ^ _782464) ^ [_805442, _805444] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_805442)), _805444 = _805442, class_Groups_Oordered__cancel__ab__semigroup__add(_805444)], (1592 ^ _782464) ^ [_805567, _805569] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_805567)), _805569 = _805567, class_Groups_Oordered__ab__semigroup__add__imp__le(_805569)], (1602 ^ _782464) ^ [_805692, _805694] : [-(class_Rings_Olinordered__comm__semiring__strict(_805692)), _805694 = _805692, class_Rings_Olinordered__comm__semiring__strict(_805694)], (1612 ^ _782464) ^ [_805817, _805819] : [-(class_Groups_Olinordered__ab__semigroup__add(_805817)), _805819 = _805817, class_Groups_Olinordered__ab__semigroup__add(_805819)], (1622 ^ _782464) ^ [_805942, _805944] : [-(class_Rings_Olinordered__semiring__strict(_805942)), _805944 = _805942, class_Rings_Olinordered__semiring__strict(_805944)], (1632 ^ _782464) ^ [_806067, _806069] : [-(class_Groups_Oordered__ab__semigroup__add(_806067)), _806069 = _806067, class_Groups_Oordered__ab__semigroup__add(_806069)], (1642 ^ _782464) ^ [_806192, _806194] : [-(class_Groups_Oordered__comm__monoid__add(_806192)), _806194 = _806192, class_Groups_Oordered__comm__monoid__add(_806194)], (1652 ^ _782464) ^ [_806317, _806319] : [-(class_Groups_Ocancel__ab__semigroup__add(_806317)), _806319 = _806317, class_Groups_Ocancel__ab__semigroup__add(_806319)], (1662 ^ _782464) ^ [_806442, _806444] : [-(class_Rings_Oordered__cancel__semiring(_806442)), _806444 = _806442, class_Rings_Oordered__cancel__semiring(_806444)], (1672 ^ _782464) ^ [_806567, _806569] : [-(class_Rings_Oordered__comm__semiring(_806567)), _806569 = _806567, class_Rings_Oordered__comm__semiring(_806569)], (1682 ^ _782464) ^ [_806692, _806694] : [-(class_Groups_Ocancel__semigroup__add(_806692)), _806694 = _806692, class_Groups_Ocancel__semigroup__add(_806694)], (1692 ^ _782464) ^ [_806817, _806819] : [-(class_Rings_Olinordered__semiring(_806817)), _806819 = _806817, class_Rings_Olinordered__semiring(_806819)], (1702 ^ _782464) ^ [_806942, _806944] : [-(class_Rings_Olinordered__semidom(_806942)), _806944 = _806942, class_Rings_Olinordered__semidom(_806944)], (1712 ^ _782464) ^ [_807067, _807069] : [-(class_Groups_Oab__semigroup__mult(_807067)), _807069 = _807067, class_Groups_Oab__semigroup__mult(_807069)], (1722 ^ _782464) ^ [_807192, _807194] : [-(class_Groups_Ocomm__monoid__mult(_807192)), _807194 = _807192, class_Groups_Ocomm__monoid__mult(_807194)], (1732 ^ _782464) ^ [_807317, _807319] : [-(class_Groups_Oab__semigroup__add(_807317)), _807319 = _807317, class_Groups_Oab__semigroup__add(_807319)], (1742 ^ _782464) ^ [_807442, _807444] : [-(class_Rings_Oordered__semiring(_807442)), _807444 = _807442, class_Rings_Oordered__semiring(_807444)], (1752 ^ _782464) ^ [_807567, _807569] : [-(class_Rings_Ono__zero__divisors(_807567)), _807569 = _807567, class_Rings_Ono__zero__divisors(_807569)], (1762 ^ _782464) ^ [_807692, _807694] : [-(class_Groups_Ocomm__monoid__add(_807692)), _807694 = _807692, class_Groups_Ocomm__monoid__add(_807694)], (1772 ^ _782464) ^ [_807817, _807819] : [-(class_Rings_Ocomm__semiring__1(_807817)), _807819 = _807817, class_Rings_Ocomm__semiring__1(_807819)], (1782 ^ _782464) ^ [_807942, _807944] : [-(class_Groups_Osemigroup__add(_807942)), _807944 = _807942, class_Groups_Osemigroup__add(_807944)], (1792 ^ _782464) ^ [_808067, _808069] : [-(class_Divides_Osemiring__div(_808067)), _808069 = _808067, class_Divides_Osemiring__div(_808069)], (1802 ^ _782464) ^ [_808192, _808194] : [-(class_Rings_Ocomm__semiring(_808192)), _808194 = _808192, class_Rings_Ocomm__semiring(_808194)], (1812 ^ _782464) ^ [_808317, _808319] : [-(class_Nat_Osemiring__char__0(_808317)), _808319 = _808317, class_Nat_Osemiring__char__0(_808319)], (1822 ^ _782464) ^ [_808442, _808444] : [-(class_Rings_Ozero__neq__one(_808442)), _808444 = _808442, class_Rings_Ozero__neq__one(_808444)], (1832 ^ _782464) ^ [_808567, _808569] : [-(class_Orderings_Opreorder(_808567)), _808569 = _808567, class_Orderings_Opreorder(_808569)], (1842 ^ _782464) ^ [_808692, _808694] : [-(class_Orderings_Olinorder(_808692)), _808694 = _808692, class_Orderings_Olinorder(_808694)], (1852 ^ _782464) ^ [_808817, _808819] : [-(class_Groups_Omonoid__mult(_808817)), _808819 = _808817, class_Groups_Omonoid__mult(_808819)], (1862 ^ _782464) ^ [_808942, _808944] : [-(class_Groups_Omonoid__add(_808942)), _808944 = _808942, class_Groups_Omonoid__add(_808944)], (1872 ^ _782464) ^ [_809067, _809069] : [-(class_Rings_Osemiring__1(_809067)), _809069 = _809067, class_Rings_Osemiring__1(_809069)], (1882 ^ _782464) ^ [_809192, _809194] : [-(class_Rings_Osemiring__0(_809192)), _809194 = _809192, class_Rings_Osemiring__0(_809194)], (1892 ^ _782464) ^ [_809317, _809319] : [-(class_Rings_Omult__zero(_809317)), _809319 = _809317, class_Rings_Omult__zero(_809319)], (1902 ^ _782464) ^ [_809442, _809444] : [-(class_Orderings_Oorder(_809442)), _809444 = _809442, class_Orderings_Oorder(_809444)], (1912 ^ _782464) ^ [_809567, _809569] : [-(class_Rings_Osemiring(_809567)), _809569 = _809567, class_Rings_Osemiring(_809569)], (1922 ^ _782464) ^ [_809692, _809694] : [-(class_Orderings_Oord(_809692)), _809694 = _809692, class_Orderings_Oord(_809694)], (1932 ^ _782464) ^ [_809817, _809819] : [-(class_Groups_Ominus(_809817)), _809819 = _809817, class_Groups_Ominus(_809819)], (1942 ^ _782464) ^ [_809942, _809944] : [-(class_Power_Opower(_809942)), _809944 = _809942, class_Power_Opower(_809944)], (1952 ^ _782464) ^ [_810067, _810069] : [-(class_Groups_Ozero(_810067)), _810069 = _810067, class_Groups_Ozero(_810069)], (1962 ^ _782464) ^ [_810192, _810194] : [-(class_Int_Onumber(_810192)), _810194 = _810192, class_Int_Onumber(_810194)], (1972 ^ _782464) ^ [_810317, _810319] : [-(class_Groups_Oone(_810317)), _810319 = _810317, class_Groups_Oone(_810319)], (1982 ^ _782464) ^ [_810442, _810444] : [-(class_Rings_Odvd(_810442)), _810444 = _810442, class_Rings_Odvd(_810444)], (1992 ^ _782464) ^ [_810567, _810569] : [-(class_Nat_Osize(_810567)), _810569 = _810567, class_Nat_Osize(_810569)], (2002 ^ _782464) ^ [_810692, _810694] : [-(hBOOL(_810692)), _810694 = _810692, hBOOL(_810694)], (2012 ^ _782464) ^ [_810813, _810815, _810817, _810819, _810821, _810823] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_810821, _810817, _810813)), c_Hoare__Mirabelle_Ohoare__derivs(_810823, _810819, _810815), _810823 = _810821, _810819 = _810817, _810815 = _810813], (2030 ^ _782464) ^ [_811896, _811898, _811900, _811902, _811904, _811906] : [-(c_SetInterval_Oord_OgreaterThan(_811906, _811902, _811898) = c_SetInterval_Oord_OgreaterThan(_811904, _811900, _811896)), _811906 = _811904, _811902 = _811900, _811898 = _811896], (2044 ^ _782464) ^ [_812117, _812119, _812121, _812123, _812125, _812127] : [-(c_SetInterval_Oord_OlessThan(_812127, _812123, _812119) = c_SetInterval_Oord_OlessThan(_812125, _812121, _812117)), _812127 = _812125, _812123 = _812121, _812119 = _812117], (2058 ^ _782464) ^ [_812338, _812340, _812342, _812344, _812346, _812348] : [-(c_SetInterval_Oord_OatLeast(_812348, _812344, _812340) = c_SetInterval_Oord_OatLeast(_812346, _812342, _812338)), _812348 = _812346, _812344 = _812342, _812340 = _812338], (2072 ^ _782464) ^ [_812559, _812561, _812563, _812565, _812567, _812569] : [-(c_SetInterval_Oord_OatMost(_812569, _812565, _812561) = c_SetInterval_Oord_OatMost(_812567, _812563, _812559)), _812569 = _812567, _812565 = _812563, _812561 = _812559], (2086 ^ _782464) ^ [_812780, _812782, _812784, _812786] : [-(c_Enum_Oenum__the(_812786, _812782) = c_Enum_Oenum__the(_812784, _812780)), _812786 = _812784, _812782 = _812780], (2096 ^ _782464) ^ [_812929, _812931, _812933, _812935, _812937, _812939] : [-(c_Partial__Function_Oflat__lub(_812939, _812935, _812931) = c_Partial__Function_Oflat__lub(_812937, _812933, _812929)), _812939 = _812937, _812935 = _812933, _812931 = _812929], (2110 ^ _782464) ^ [_813150, _813152, _813154, _813156, _813158, _813160, _813162, _813164] : [-(c_Fun_Othe__inv__into(_813164, _813160, _813156, _813152) = c_Fun_Othe__inv__into(_813162, _813158, _813154, _813150)), _813164 = _813162, _813160 = _813158, _813156 = _813154, _813152 = _813150], (2128 ^ _782464) ^ [_813451, _813453, _813455, _813457, _813459, _813461, _813463, _813465, _813467, _813469] : [-(c_Fun_Ooverride__on(_813469, _813465, _813461, _813457, _813453) = c_Fun_Ooverride__on(_813467, _813463, _813459, _813455, _813451)), _813469 = _813467, _813465 = _813463, _813461 = _813459, _813457 = _813455, _813453 = _813451], (2150 ^ _782464) ^ [_813840, _813842, _813844, _813846, _813848, _813850, _813852, _813854] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_813854, _813850, _813846, _813842) = c_Nat_Osemiring__1__class_Oof__nat__aux(_813852, _813848, _813844, _813840)), _813854 = _813852, _813850 = _813848, _813846 = _813844, _813842 = _813840], (2168 ^ _782464) ^ [_814141, _814143] : [_814143 = _814141, -(c_SetInterval_Oord__class_OgreaterThan(_814143) = c_SetInterval_Oord__class_OgreaterThan(_814141))], (2174 ^ _782464) ^ [_814226, _814228, _814230, _814232] : [-(c_Int_Onat__aux(_814232, _814228) = c_Int_Onat__aux(_814230, _814226)), _814232 = _814230, _814228 = _814226], (2184 ^ _782464) ^ [_814375, _814377, _814379, _814381, _814383, _814385, _814387, _814389] : [-(c_Sum__Type_OPlus(_814389, _814385, _814381, _814377) = c_Sum__Type_OPlus(_814387, _814383, _814379, _814375)), _814389 = _814387, _814385 = _814383, _814381 = _814379, _814377 = _814375], (2202 ^ _782464) ^ [_814676, _814678, _814680, _814682] : [-(c_Nat__Transfer_Otsub(_814682, _814678) = c_Nat__Transfer_Otsub(_814680, _814676)), _814682 = _814680, _814678 = _814676], (2212 ^ _782464) ^ [_814825, _814827, _814829, _814831] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_814831, _814827) = c_Inductive_Ocomplete__lattice__class_Ogfp(_814829, _814825)), _814831 = _814829, _814827 = _814825], (2222 ^ _782464) ^ [_814974, _814976] : [_814976 = _814974, -(c_SetInterval_Oord__class_OatLeast(_814976) = c_SetInterval_Oord__class_OatLeast(_814974))], (2228 ^ _782464) ^ [_815059, _815061, _815063, _815065] : [-(c_Orderings_Oord_Omax(_815065, _815061) = c_Orderings_Oord_Omax(_815063, _815059)), _815065 = _815063, _815061 = _815059], (2238 ^ _782464) ^ [_815208, _815210, _815212, _815214] : [-(c_Orderings_Oord_Omin(_815214, _815210) = c_Orderings_Oord_Omin(_815212, _815208)), _815214 = _815212, _815210 = _815208], (2248 ^ _782464) ^ [_815357, _815359, _815361, _815363, _815365, _815367] : [-(c_Power_Opower_Opower(_815367, _815363, _815359) = c_Power_Opower_Opower(_815365, _815361, _815357)), _815367 = _815365, _815363 = _815361, _815359 = _815357], (2262 ^ _782464) ^ [_815578, _815580, _815582, _815584] : [-(c_SMT_Oz3div(_815584, _815580) = c_SMT_Oz3div(_815582, _815578)), _815584 = _815582, _815580 = _815578], (2272 ^ _782464) ^ [_815727, _815729, _815731, _815733] : [-(c_Nitpick_Onat__lcm(_815733, _815729) = c_Nitpick_Onat__lcm(_815731, _815727)), _815733 = _815731, _815729 = _815727], (2282 ^ _782464) ^ [_815876, _815878, _815880, _815882] : [-(c_SMT_Oz3mod(_815882, _815878) = c_SMT_Oz3mod(_815880, _815876)), _815882 = _815880, _815878 = _815876], (2292 ^ _782464) ^ [_816025, _816027] : [_816027 = _816025, -(c_Int_Oring__1__class_OInts(_816027) = c_Int_Oring__1__class_OInts(_816025))], (2298 ^ _782464) ^ [_816110, _816112, _816114, _816116, _816118, _816120] : [-(c_Nat_Onat_Onat__rec(_816120, _816116, _816112) = c_Nat_Onat_Onat__rec(_816118, _816114, _816110)), _816120 = _816118, _816116 = _816114, _816112 = _816110], (2312 ^ _782464) ^ [_816331, _816333] : [_816333 = _816331, -(c_Int_Opred(_816333) = c_Int_Opred(_816331))], (2318 ^ _782464) ^ [_816416, _816418] : [_816418 = _816416, -(c_Int_Osucc(_816418) = c_Int_Osucc(_816416))], (2324 ^ _782464) ^ [_816501, _816503, _816505, _816507, _816509, _816511, _816513, _816515] : [-(c_Nitpick_Oprod(_816515, _816511, _816507, _816503) = c_Nitpick_Oprod(_816513, _816509, _816505, _816501)), _816515 = _816513, _816511 = _816509, _816507 = _816505, _816503 = _816501], (2342 ^ _782464) ^ [_816802, _816804] : [_816804 = _816802, -(c_Enum_Oenum__class_Oenum__ex(_816804) = c_Enum_Oenum__class_Oenum__ex(_816802))], (2348 ^ _782464) ^ [_816887, _816889] : [_816889 = _816887, -(c_Enum_Oenum__class_Oenum__all(_816889) = c_Enum_Oenum__class_Oenum__all(_816887))], (2354 ^ _782464) ^ [_816972, _816974] : [_816974 = _816972, -(c_Nat_Osemiring__1__class_ONats(_816974) = c_Nat_Osemiring__1__class_ONats(_816972))], (2360 ^ _782464) ^ [_817057, _817059, _817061, _817063] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_817063, _817059) = c_Code__Numeral_Odiv__mod__code__numeral(_817061, _817057)), _817063 = _817061, _817059 = _817057], (2370 ^ _782464) ^ [_817206, _817208, _817210, _817212] : [-(c_Divides_Odivmod__int__rel(_817212, _817208) = c_Divides_Odivmod__int__rel(_817210, _817206)), _817212 = _817210, _817208 = _817206], (2380 ^ _782464) ^ [_817355, _817357, _817359, _817361] : [-(c_Groups_Osgn__class_Osgn(_817361, _817357) = c_Groups_Osgn__class_Osgn(_817359, _817355)), _817361 = _817359, _817357 = _817355], (2390 ^ _782464) ^ [_817504, _817506, _817508, _817510] : [-(c_Divides_Opdivmod(_817510, _817506) = c_Divides_Opdivmod(_817508, _817504)), _817510 = _817508, _817506 = _817504], (2400 ^ _782464) ^ [_817653, _817655] : [_817655 = _817653, -(c_Divides_Oadjust(_817655) = c_Divides_Oadjust(_817653))], (2406 ^ _782464) ^ [_817738, _817740] : [_817740 = _817738, -(c_Int_OBit0(_817740) = c_Int_OBit0(_817738))], (2412 ^ _782464) ^ [_817823, _817825, _817827, _817829] : [-(c_Nitpick_Onat__gcd(_817829, _817825) = c_Nitpick_Onat__gcd(_817827, _817823)), _817829 = _817827, _817825 = _817823], (2422 ^ _782464) ^ [_817972, _817974] : [_817974 = _817972, -(c_Nat_Onat_Onat__size(_817974) = c_Nat_Onat_Onat__size(_817972))], (2428 ^ _782464) ^ [_818057, _818059, _818061, _818063] : [-(c_Divides_Odivmod__int(_818063, _818059) = c_Divides_Odivmod__int(_818061, _818057)), _818063 = _818061, _818059 = _818057], (2438 ^ _782464) ^ [_818206, _818208, _818210, _818212] : [-(c_Divides_OnegDivAlg(_818212, _818208) = c_Divides_OnegDivAlg(_818210, _818206)), _818212 = _818210, _818208 = _818206], (2448 ^ _782464) ^ [_818355, _818357, _818359, _818361] : [-(c_Divides_OposDivAlg(_818361, _818357) = c_Divides_OposDivAlg(_818359, _818355)), _818361 = _818359, _818357 = _818355], (2458 ^ _782464) ^ [_818504, _818506, _818508, _818510, _818512, _818514, _818516, _818518, _818520, _818522] : [-(c_Product__Type_Oprod_Oprod__size(_818522, _818518, _818514, _818510, _818506) = c_Product__Type_Oprod_Oprod__size(_818520, _818516, _818512, _818508, _818504)), _818522 = _818520, _818518 = _818516, _818514 = _818512, _818510 = _818508, _818506 = _818504], (2480 ^ _782464) ^ [_818893, _818895, _818897, _818899] : [-(c_Divides_Odivmod__nat(_818899, _818895) = c_Divides_Odivmod__nat(_818897, _818893)), _818899 = _818897, _818895 = _818893], (2490 ^ _782464) ^ [_819042, _819044, _819046, _819048] : [-(c_Divides_Odivmod__nat__rel(_819048, _819044) = c_Divides_Odivmod__nat__rel(_819046, _819042)), _819048 = _819046, _819044 = _819042], (2500 ^ _782464) ^ [_819191, _819193, _819195, _819197] : [-(c_Set_Othe__elem(_819197, _819193) = c_Set_Othe__elem(_819195, _819191)), _819197 = _819195, _819193 = _819191], (2510 ^ _782464) ^ [_819340, _819342] : [_819342 = _819340, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819342) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819340))], (2516 ^ _782464) ^ [_819425, _819427, _819429, _819431, _819433, _819435, _819437, _819439, _819441, _819443] : [-(c_Product__Type_Oprod_Oprod__rec(_819443, _819439, _819435, _819431, _819427) = c_Product__Type_Oprod_Oprod__rec(_819441, _819437, _819433, _819429, _819425)), _819443 = _819441, _819439 = _819437, _819435 = _819433, _819431 = _819429, _819427 = _819425], (2538 ^ _782464) ^ [_819814, _819816, _819818, _819820] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_819820, _819816) = c_Inductive_Ocomplete__lattice__class_Olfp(_819818, _819814)), _819820 = _819818, _819816 = _819814], (2548 ^ _782464) ^ [_819963, _819965, _819967, _819969] : [-(c_FunDef_Orp__inv__image(_819969, _819965) = c_FunDef_Orp__inv__image(_819967, _819963)), _819969 = _819967, _819965 = _819963], (2558 ^ _782464) ^ [_820112, _820114, _820116, _820118, _820120, _820122, _820124, _820126] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820126, _820122, _820118, _820114) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820124, _820120, _820116, _820112)), _820126 = _820124, _820122 = _820120, _820118 = _820116, _820114 = _820112], (2576 ^ _782464) ^ [_820413, _820415] : [_820415 = _820413, -(c_Wellfounded_Omeasure(_820415) = c_Wellfounded_Omeasure(_820413))], (2582 ^ _782464) ^ [_820498, _820500, _820502, _820504] : [-(c_Wellfounded_Omin__ext(_820504, _820500) = c_Wellfounded_Omin__ext(_820502, _820498)), _820504 = _820502, _820500 = _820498], (2592 ^ _782464) ^ [_820647, _820649, _820651, _820653, _820655, _820657] : [-(c_Wellfounded_Omlex__prod(_820657, _820653, _820649) = c_Wellfounded_Omlex__prod(_820655, _820651, _820647)), _820657 = _820655, _820653 = _820651, _820649 = _820647], (2606 ^ _782464) ^ [_820868, _820870] : [_820870 = _820868, -(c_Int_Oint__ge__less__than(_820870) = c_Int_Oint__ge__less__than(_820868))], (2612 ^ _782464) ^ [_820953, _820955] : [_820955 = _820953, -(c_Int_Oint__ge__less__than2(_820955) = c_Int_Oint__ge__less__than2(_820953))], (2618 ^ _782464) ^ [_821038, _821040, _821042, _821044, _821046, _821048, _821050, _821052] : [-(c_Recdef_Osame__fst(_821052, _821048, _821044, _821040) = c_Recdef_Osame__fst(_821050, _821046, _821042, _821038)), _821052 = _821050, _821048 = _821046, _821044 = _821042, _821040 = _821038], (2636 ^ _782464) ^ [_821339, _821341] : [_821341 = _821339, -(c_Nitpick_Ozero__frac(_821341) = c_Nitpick_Ozero__frac(_821339))], (2642 ^ _782464) ^ [_821424, _821426] : [_821426 = _821424, -(c_Nitpick_Oone__frac(_821426) = c_Nitpick_Oone__frac(_821424))], (2648 ^ _782464) ^ [_821509, _821511, _821513, _821515] : [-(c_Nitpick_Onumber__of__frac(_821515, _821511) = c_Nitpick_Onumber__of__frac(_821513, _821509)), _821515 = _821513, _821511 = _821509], (2658 ^ _782464) ^ [_821658, _821660, _821662, _821664] : [-(c_Nitpick_Onorm__frac(_821664, _821660) = c_Nitpick_Onorm__frac(_821662, _821658)), _821664 = _821662, _821660 = _821658], (2668 ^ _782464) ^ [_821807, _821809] : [_821809 = _821807, -(c_Equiv__Relations_Oquotient(_821809) = c_Equiv__Relations_Oquotient(_821807))], (2674 ^ _782464) ^ [_821892, _821894, _821896, _821898, _821900, _821902, _821904, _821906] : [-(c_Product__Type_Oapsnd(_821906, _821902, _821898, _821894) = c_Product__Type_Oapsnd(_821904, _821900, _821896, _821892)), _821906 = _821904, _821902 = _821900, _821898 = _821896, _821894 = _821892], (2692 ^ _782464) ^ [_822193, _822195, _822197, _822199, _822201, _822203, _822205, _822207] : [-(c_Product__Type_Oapfst(_822207, _822203, _822199, _822195) = c_Product__Type_Oapfst(_822205, _822201, _822197, _822193)), _822207 = _822205, _822203 = _822201, _822199 = _822197, _822195 = _822193], (2710 ^ _782464) ^ [_822494, _822496, _822498, _822500, _822502, _822504] : [-(c_FunDef_Oin__rel(_822504, _822500, _822496) = c_FunDef_Oin__rel(_822502, _822498, _822494)), _822504 = _822502, _822500 = _822498, _822496 = _822494], (2724 ^ _782464) ^ [_822715, _822717, _822719, _822721] : [-(c_Predicate_OPowp(_822721, _822717) = c_Predicate_OPowp(_822719, _822715)), _822721 = _822719, _822717 = _822715], (2734 ^ _782464) ^ [_822864, _822866] : [_822866 = _822864, -(c_Set_OBall(_822866) = c_Set_OBall(_822864))], (2740 ^ _782464) ^ [_822949, _822951, _822953, _822955, _822957, _822959] : [-(c_Predicate_ODomainP(_822959, _822955, _822951) = c_Predicate_ODomainP(_822957, _822953, _822949)), _822959 = _822957, _822955 = _822953, _822951 = _822949], (2754 ^ _782464) ^ [_823170, _823172, _823174, _823176, _823178, _823180] : [-(c_Predicate_ORangeP(_823180, _823176, _823172) = c_Predicate_ORangeP(_823178, _823174, _823170)), _823180 = _823178, _823176 = _823174, _823172 = _823170], (2768 ^ _782464) ^ [_823391, _823393] : [_823393 = _823391, -(c_HOL_OAll(_823393) = c_HOL_OAll(_823391))], (2774 ^ _782464) ^ [_823476, _823478, _823480, _823482] : [-(c_Wellfounded_Omax__ext(_823482, _823478) = c_Wellfounded_Omax__ext(_823480, _823476)), _823482 = _823480, _823478 = _823476], (2784 ^ _782464) ^ [_823625, _823627, _823629, _823631, _823633, _823635, _823637, _823639] : [-(c_Random_Oiterate(_823639, _823635, _823631, _823627) = c_Random_Oiterate(_823637, _823633, _823629, _823625)), _823639 = _823637, _823635 = _823633, _823631 = _823629, _823627 = _823625], (2802 ^ _782464) ^ [_823926, _823928, _823930, _823932] : [-(c_Random_Olog(_823932, _823928) = c_Random_Olog(_823930, _823926)), _823932 = _823930, _823928 = _823926], (2812 ^ _782464) ^ [_824075, _824077, _824079, _824081, _824083, _824085] : [-(c_Random_Ominus__shift(_824085, _824081, _824077) = c_Random_Ominus__shift(_824083, _824079, _824075)), _824085 = _824083, _824081 = _824079, _824077 = _824075], (2826 ^ _782464) ^ [_824296, _824298, _824300, _824302] : [-(c_Random_Oinc__shift(_824302, _824298) = c_Random_Oinc__shift(_824300, _824296)), _824302 = _824300, _824298 = _824296], (2836 ^ _782464) ^ [_824445, _824447] : [_824447 = _824445, -(c_Relation_OField(_824447) = c_Relation_OField(_824445))], (2842 ^ _782464) ^ [_824530, _824532, _824534, _824536] : [-(c_Relation_ORange(_824536, _824532) = c_Relation_ORange(_824534, _824530)), _824536 = _824534, _824532 = _824530], (2852 ^ _782464) ^ [_824679, _824681, _824683, _824685] : [-(c_Relation_ODomain(_824685, _824681) = c_Relation_ODomain(_824683, _824679)), _824685 = _824683, _824681 = _824679], (2862 ^ _782464) ^ [_824828, _824830] : [_824830 = _824828, -(c_Nat_Ofunpow(_824830) = c_Nat_Ofunpow(_824828))], (2868 ^ _782464) ^ [_824913, _824915, _824917, _824919, _824921, _824923, _824925, _824927, _824929, _824931] : [-(c_Finite__Set_Ofold__graph(_824931, _824927, _824923, _824919, _824915) = c_Finite__Set_Ofold__graph(_824929, _824925, _824921, _824917, _824913)), _824931 = _824929, _824927 = _824925, _824923 = _824921, _824919 = _824917, _824915 = _824913], (2890 ^ _782464) ^ [_825302, _825304, _825306, _825308] : [-(c_Nitpick_Oint__lcm(_825308, _825304) = c_Nitpick_Oint__lcm(_825306, _825302)), _825308 = _825306, _825304 = _825302], (2900 ^ _782464) ^ [_825451, _825453, _825455, _825457, _825459, _825461] : [-(c_Nitpick_Otimes__frac(_825461, _825457, _825453) = c_Nitpick_Otimes__frac(_825459, _825455, _825451)), _825461 = _825459, _825457 = _825455, _825453 = _825451], (2914 ^ _782464) ^ [_825672, _825674, _825676, _825678, _825680, _825682] : [-(c_Nitpick_Oof__frac(_825682, _825678, _825674) = c_Nitpick_Oof__frac(_825680, _825676, _825672)), _825682 = _825680, _825678 = _825676, _825674 = _825672], (2928 ^ _782464) ^ [_825893, _825895] : [_825895 = _825893, -(c_Rings_Oinverse__class_Odivide(_825895) = c_Rings_Oinverse__class_Odivide(_825893))], (2934 ^ _782464) ^ [_825978, _825980] : [_825980 = _825978, -(c_Int_Oring__1__class_Oof__int(_825980) = c_Int_Oring__1__class_Oof__int(_825978))], (2940 ^ _782464) ^ [_826063, _826065, _826067, _826069] : [-(c_Nitpick_Oinverse__frac(_826069, _826065) = c_Nitpick_Oinverse__frac(_826067, _826063)), _826069 = _826067, _826065 = _826063], (2950 ^ _782464) ^ [_826212, _826214] : [_826214 = _826212, -(c_Nitpick_Ofrac(_826214) = c_Nitpick_Ofrac(_826212))], (2956 ^ _782464) ^ [_826297, _826299, _826301, _826303] : [-(c_Nitpick_OAbs__Frac(_826303, _826299) = c_Nitpick_OAbs__Frac(_826301, _826297)), _826303 = _826301, _826299 = _826297], (2966 ^ _782464) ^ [_826446, _826448, _826450, _826452, _826454, _826456] : [-(c_Nitpick_Oplus__frac(_826456, _826452, _826448) = c_Nitpick_Oplus__frac(_826454, _826450, _826446)), _826456 = _826454, _826452 = _826450, _826448 = _826446], (2980 ^ _782464) ^ [_826667, _826669, _826671, _826673] : [-(c_Nitpick_Ouminus__frac(_826673, _826669) = c_Nitpick_Ouminus__frac(_826671, _826667)), _826673 = _826671, _826669 = _826667], (2990 ^ _782464) ^ [_826816, _826818] : [_826818 = _826816, -(c_Nitpick_Onum(_826818) = c_Nitpick_Onum(_826816))], (2996 ^ _782464) ^ [_826901, _826903] : [_826903 = _826901, -(c_Nitpick_Odenom(_826903) = c_Nitpick_Odenom(_826901))], (3002 ^ _782464) ^ [_826986, _826988] : [_826988 = _826986, -(c_Nitpick_ORep__Frac(_826988) = c_Nitpick_ORep__Frac(_826986))], (3008 ^ _782464) ^ [_827071, _827073, _827075, _827077, _827079, _827081] : [-(c_Product__Type_Ointernal__split(_827081, _827077, _827073) = c_Product__Type_Ointernal__split(_827079, _827075, _827071)), _827081 = _827079, _827077 = _827075, _827073 = _827071], (3022 ^ _782464) ^ [_827292, _827294, _827296, _827298] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_827298, _827294) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_827296, _827292)), _827298 = _827296, _827294 = _827292], (3032 ^ _782464) ^ [_827441, _827443] : [_827443 = _827441, -(c_HOL_Obool_Obool__size(_827443) = c_HOL_Obool_Obool__size(_827441))], (3038 ^ _782464) ^ [_827526, _827528, _827530, _827532] : [-(c_List_Olenlex(_827532, _827528) = c_List_Olenlex(_827530, _827526)), _827532 = _827530, _827528 = _827526], (3048 ^ _782464) ^ [_827675, _827677, _827679, _827681, _827683, _827685, _827687, _827689, _827691, _827693, _827695, _827697] : [-(c_Product__Type_Omap__pair(_827697, _827693, _827689, _827685, _827681, _827677) = c_Product__Type_Omap__pair(_827695, _827691, _827687, _827683, _827679, _827675)), _827697 = _827695, _827693 = _827691, _827689 = _827687, _827685 = _827683, _827681 = _827679, _827677 = _827675], (3074 ^ _782464) ^ [_828160, _828162, _828164, _828166] : [-(c_List_Olexn(_828166, _828162) = c_List_Olexn(_828164, _828160)), _828166 = _828164, _828162 = _828160], (3084 ^ _782464) ^ [_828309, _828311, _828313, _828315] : [-(c_Wellfounded_Oacc(_828315, _828311) = c_Wellfounded_Oacc(_828313, _828309)), _828315 = _828313, _828311 = _828309], (3094 ^ _782464) ^ [_828458, _828460] : [_828460 = _828458, -(c_Set_OPow(_828460) = c_Set_OPow(_828458))], (3100 ^ _782464) ^ [_828543, _828545, _828547, _828549] : [-(c_Product__Type_OSigma(_828549, _828545) = c_Product__Type_OSigma(_828547, _828543)), _828549 = _828547, _828545 = _828543], (3110 ^ _782464) ^ [_828692, _828694, _828696, _828698] : [-(c_Nitpick_Ocard_H(_828698, _828694) = c_Nitpick_Ocard_H(_828696, _828692)), _828698 = _828696, _828694 = _828692], (3120 ^ _782464) ^ [_828841, _828843, _828845, _828847, _828849, _828851] : [-(c_List_Oset__Cons(_828851, _828847, _828843) = c_List_Oset__Cons(_828849, _828845, _828841)), _828851 = _828849, _828847 = _828845, _828843 = _828841], (3134 ^ _782464) ^ [_829062, _829064, _829066, _829068] : [-(c_List_Olistset(_829068, _829064) = c_List_Olistset(_829066, _829062)), _829068 = _829066, _829064 = _829062], (3144 ^ _782464) ^ [_829211, _829213, _829215, _829217] : [-(c_List_Olistrel1(_829217, _829213) = c_List_Olistrel1(_829215, _829211)), _829217 = _829215, _829213 = _829211], (3154 ^ _782464) ^ [_829360, _829362, _829364, _829366, _829368, _829370, _829372, _829374] : [-(c_Nat_Onat_Onat__case(_829374, _829370, _829366, _829362) = c_Nat_Onat_Onat__case(_829372, _829368, _829364, _829360)), _829374 = _829372, _829370 = _829368, _829366 = _829364, _829362 = _829360], (3172 ^ _782464) ^ [_829661, _829663, _829665, _829667] : [-(c_Nat_Ocompow(_829667, _829663) = c_Nat_Ocompow(_829665, _829661)), _829667 = _829665, _829663 = _829661], (3182 ^ _782464) ^ [_829810, _829812] : [_829812 = _829810, -(c_List_Orotate1(_829812) = c_List_Orotate1(_829810))], (3188 ^ _782464) ^ [_829895, _829897, _829899, _829901] : [-(c_Finite__Set_Ofold1(_829901, _829897) = c_Finite__Set_Ofold1(_829899, _829895)), _829901 = _829899, _829897 = _829895], (3198 ^ _782464) ^ [_830044, _830046, _830048, _830050] : [-(c_Big__Operators_Olattice__class_OSup__fin(_830050, _830046) = c_Big__Operators_Olattice__class_OSup__fin(_830048, _830044)), _830050 = _830048, _830046 = _830044], (3208 ^ _782464) ^ [_830193, _830195, _830197, _830199] : [-(c_Big__Operators_Olattice__class_OInf__fin(_830199, _830195) = c_Big__Operators_Olattice__class_OInf__fin(_830197, _830193)), _830199 = _830197, _830195 = _830193], (3218 ^ _782464) ^ [_830342, _830344, _830346, _830348] : [-(c_Big__Operators_Olinorder__class_OMin(_830348, _830344) = c_Big__Operators_Olinorder__class_OMin(_830346, _830342)), _830348 = _830346, _830344 = _830342], (3228 ^ _782464) ^ [_830491, _830493, _830495, _830497] : [-(c_Big__Operators_Olinorder__class_OMax(_830497, _830493) = c_Big__Operators_Olinorder__class_OMax(_830495, _830491)), _830497 = _830495, _830493 = _830491], (3238 ^ _782464) ^ [_830640, _830642, _830644, _830646, _830648, _830650] : [-(c_Big__Operators_Olattice_OInf__fin(_830650, _830646, _830642) = c_Big__Operators_Olattice_OInf__fin(_830648, _830644, _830640)), _830650 = _830648, _830646 = _830644, _830642 = _830640], (3252 ^ _782464) ^ [_830861, _830863, _830865, _830867, _830869, _830871] : [-(c_Big__Operators_Olattice_OSup__fin(_830871, _830867, _830863) = c_Big__Operators_Olattice_OSup__fin(_830869, _830865, _830861)), _830871 = _830869, _830867 = _830865, _830863 = _830861], (3266 ^ _782464) ^ [_831082, _831084, _831086, _831088, _831090, _831092, _831094, _831096, _831098, _831100] : [-(c_Fun_Ofun__upd(_831100, _831096, _831092, _831088, _831084) = c_Fun_Ofun__upd(_831098, _831094, _831090, _831086, _831082)), _831100 = _831098, _831096 = _831094, _831092 = _831090, _831088 = _831086, _831084 = _831082], (3288 ^ _782464) ^ [_831471, _831473, _831475, _831477, _831479, _831481, _831483, _831485] : [-(c_Enum_Oproduct(_831485, _831481, _831477, _831473) = c_Enum_Oproduct(_831483, _831479, _831475, _831471)), _831485 = _831483, _831481 = _831479, _831477 = _831475, _831473 = _831471], (3306 ^ _782464) ^ [_831772, _831774, _831776, _831778, _831780, _831782, _831784, _831786] : [-(c_Nitpick_Osetsum_H(_831786, _831782, _831778, _831774) = c_Nitpick_Osetsum_H(_831784, _831780, _831776, _831772)), _831786 = _831784, _831782 = _831780, _831778 = _831776, _831774 = _831772], (3324 ^ _782464) ^ [_832073, _832075, _832077, _832079] : [-(c_HOL_OLet(_832079, _832075) = c_HOL_OLet(_832077, _832073)), _832079 = _832077, _832075 = _832073], (3334 ^ _782464) ^ [_832222, _832224, _832226, _832228] : [-(c_Enum_Osublists(_832228, _832224) = c_Enum_Osublists(_832226, _832222)), _832228 = _832226, _832224 = _832222], (3344 ^ _782464) ^ [_832371, _832373, _832375, _832377, _832379, _832381] : [-(c_List_Olist_Olist__size(_832381, _832377, _832373) = c_List_Olist_Olist__size(_832379, _832375, _832371)), _832381 = _832379, _832377 = _832375, _832373 = _832371], (3358 ^ _782464) ^ [_832592, _832594, _832596, _832598] : [-(c_Random_Oselect(_832598, _832594) = c_Random_Oselect(_832596, _832592)), _832598 = _832596, _832594 = _832592], (3368 ^ _782464) ^ [_832741, _832743] : [_832743 = _832741, -(c_Random_Orange(_832743) = c_Random_Orange(_832741))], (3374 ^ _782464) ^ [_832826, _832828, _832830, _832832] : [-(c_Code__Numeral_Onat__of__aux(_832832, _832828) = c_Code__Numeral_Onat__of__aux(_832830, _832826)), _832832 = _832830, _832828 = _832826], (3384 ^ _782464) ^ [_832975, _832977] : [_832977 = _832975, -(c_Lazy__Sequence_Ohb__not__seq(_832977) = c_Lazy__Sequence_Ohb__not__seq(_832975))], (3390 ^ _782464) ^ [_833060, _833062] : [_833062 = _833060, -(c_Int_OBit1(_833062) = c_Int_OBit1(_833060))], (3396 ^ _782464) ^ [_833145, _833147, _833149, _833151] : [-(c_List_Olistsp(_833151, _833147) = c_List_Olistsp(_833149, _833145)), _833151 = _833149, _833147 = _833145], (3406 ^ _782464) ^ [_833294, _833296, _833298, _833300] : [-(c_List_Olists(_833300, _833296) = c_List_Olists(_833298, _833294)), _833300 = _833298, _833296 = _833294], (3416 ^ _782464) ^ [_833443, _833445, _833447, _833449, _833451, _833453] : [-(c_Finite__Set_Ofold(_833453, _833449, _833445) = c_Finite__Set_Ofold(_833451, _833447, _833443)), _833453 = _833451, _833449 = _833447, _833445 = _833443], (3430 ^ _782464) ^ [_833664, _833666, _833668, _833670, _833672, _833674] : [-(c_Enum_On__lists(_833674, _833670, _833666) = c_Enum_On__lists(_833672, _833668, _833664)), _833674 = _833672, _833670 = _833668, _833666 = _833664], (3444 ^ _782464) ^ [_833885, _833887, _833889, _833891, _833893, _833895] : [-(c_List_Opartition(_833895, _833891, _833887) = c_List_Opartition(_833893, _833889, _833885)), _833895 = _833893, _833891 = _833889, _833887 = _833885], (3458 ^ _782464) ^ [_834106, _834108] : [_834108 = _834106, -(c_Finite__Set_Ocard(_834108) = c_Finite__Set_Ocard(_834106))], (3464 ^ _782464) ^ [_834191, _834193, _834195, _834197, _834199, _834201, _834203, _834205] : [-(c_List_Olist_Olist__case(_834205, _834201, _834197, _834193) = c_List_Olist_Olist__case(_834203, _834199, _834195, _834191)), _834205 = _834203, _834201 = _834199, _834197 = _834195, _834193 = _834191], (3482 ^ _782464) ^ [_834492, _834494, _834496, _834498] : [-(c_Random_Oselect__weight(_834498, _834494) = c_Random_Oselect__weight(_834496, _834492)), _834498 = _834496, _834494 = _834492], (3492 ^ _782464) ^ [_834641, _834643, _834645, _834647] : [-(c_Random_Opick(_834647, _834643) = c_Random_Opick(_834645, _834641)), _834647 = _834645, _834643 = _834641], (3502 ^ _782464) ^ [_834790, _834792] : [_834792 = _834790, -(c_List_Otranspose__rel(_834792) = c_List_Otranspose__rel(_834790))], (3508 ^ _782464) ^ [_834875, _834877, _834879, _834881, _834883, _834885] : [-(c_List_Osublist(_834885, _834881, _834877) = c_List_Osublist(_834883, _834879, _834875)), _834885 = _834883, _834881 = _834879, _834877 = _834875], (3522 ^ _782464) ^ [_835096, _835098] : [_835098 = _835096, -(c_Int_Onumber__class_Onumber__of(_835098) = c_Int_Onumber__class_Onumber__of(_835096))], (3528 ^ _782464) ^ [_835181, _835183] : [_835183 = _835181, -(c_SetInterval_Oord__class_OlessThan(_835183) = c_SetInterval_Oord__class_OlessThan(_835181))], (3534 ^ _782464) ^ [_835266, _835268, _835270, _835272, _835274, _835276] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_835276, _835272, _835268) = c_SetInterval_Oord__class_OgreaterThanAtMost(_835274, _835270, _835266)), _835276 = _835274, _835272 = _835270, _835268 = _835266], (3548 ^ _782464) ^ [_835487, _835489, _835491, _835493, _835495, _835497] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_835497, _835493, _835489) = c_SetInterval_Oord__class_OgreaterThanLessThan(_835495, _835491, _835487)), _835497 = _835495, _835493 = _835491, _835489 = _835487], (3562 ^ _782464) ^ [_835708, _835710] : [_835710 = _835708, -(c_SetInterval_Oord__class_OatMost(_835710) = c_SetInterval_Oord__class_OatMost(_835708))], (3568 ^ _782464) ^ [_835793, _835795, _835797, _835799, _835801, _835803, _835805, _835807] : [-(c_List_Olinorder__class_Osort__key(_835807, _835803, _835799, _835795) = c_List_Olinorder__class_Osort__key(_835805, _835801, _835797, _835793)), _835807 = _835805, _835803 = _835801, _835799 = _835797, _835795 = _835793], (3586 ^ _782464) ^ [_836094, _836096, _836098, _836100, _836102, _836104, _836106, _836108, _836110, _836112] : [-(c_List_Olinorder__class_Oinsort__insert__key(_836112, _836108, _836104, _836100, _836096) = c_List_Olinorder__class_Oinsort__insert__key(_836110, _836106, _836102, _836098, _836094)), _836112 = _836110, _836108 = _836106, _836104 = _836102, _836100 = _836098, _836096 = _836094], (3608 ^ _782464) ^ [_836483, _836485, _836487, _836489] : [-(c_List_Olinorder__class_Osorted__list__of__set(_836489, _836485) = c_List_Olinorder__class_Osorted__list__of__set(_836487, _836483)), _836489 = _836487, _836485 = _836483], (3618 ^ _782464) ^ [_836632, _836634, _836636, _836638] : [-(c_List_Orotate(_836638, _836634) = c_List_Orotate(_836636, _836632)), _836638 = _836636, _836634 = _836632], (3628 ^ _782464) ^ [_836781, _836783, _836785, _836787, _836789, _836791] : [-(c_Divides_Odiv__class_Omod(_836791, _836787, _836783) = c_Divides_Odiv__class_Omod(_836789, _836785, _836781)), _836791 = _836789, _836787 = _836785, _836783 = _836781], (3642 ^ _782464) ^ [_837002, _837004, _837006, _837008] : [-(c_List_Olist__update(_837008, _837004) = c_List_Olist__update(_837006, _837002)), _837008 = _837006, _837004 = _837002], (3652 ^ _782464) ^ [_837151, _837153, _837155, _837157, _837159, _837161, _837163, _837165, _837167, _837169] : [-(c_List_Ofoldr(_837169, _837165, _837161, _837157, _837153) = c_List_Ofoldr(_837167, _837163, _837159, _837155, _837151)), _837169 = _837167, _837165 = _837163, _837161 = _837159, _837157 = _837155, _837153 = _837151], (3674 ^ _782464) ^ [_837540, _837542] : [_837542 = _837540, -(c_Orderings_Oord__class_Omax(_837542) = c_Orderings_Oord__class_Omax(_837540))], (3680 ^ _782464) ^ [_837625, _837627, _837629, _837631] : [-(c_List_Otranspose(_837631, _837627) = c_List_Otranspose(_837629, _837625)), _837631 = _837629, _837627 = _837625], (3690 ^ _782464) ^ [_837774, _837776, _837778, _837780] : [-(c_List_Obutlast(_837780, _837776) = c_List_Obutlast(_837778, _837774)), _837780 = _837778, _837776 = _837774], (3700 ^ _782464) ^ [_837923, _837925] : [_837925 = _837923, -(c_List_Oreturn__list(_837925) = c_List_Oreturn__list(_837923))], (3706 ^ _782464) ^ [_838008, _838010] : [_838010 = _838008, -(c_List_Oembed__list(_838010) = c_List_Oembed__list(_838008))], (3712 ^ _782464) ^ [_838093, _838095] : [_838095 = _838093, -(c_List_Omonoid__add__class_Olistsum(_838095) = c_List_Omonoid__add__class_Olistsum(_838093))], (3718 ^ _782464) ^ [_838178, _838180, _838182, _838184] : [-(c_List_Oremdups(_838184, _838180) = c_List_Oremdups(_838182, _838178)), _838184 = _838182, _838180 = _838178], (3728 ^ _782464) ^ [_838327, _838329, _838331, _838333, _838335, _838337] : [-(c_List_Oremove1(_838337, _838333, _838329) = c_List_Oremove1(_838335, _838331, _838327)), _838337 = _838335, _838333 = _838331, _838329 = _838327], (3742 ^ _782464) ^ [_838548, _838550, _838552, _838554] : [-(c_List_OremoveAll(_838554, _838550) = c_List_OremoveAll(_838552, _838548)), _838554 = _838552, _838550 = _838548], (3752 ^ _782464) ^ [_838697, _838699, _838701, _838703, _838705, _838707] : [-(c_List_Oinsert(_838707, _838703, _838699) = c_List_Oinsert(_838705, _838701, _838697)), _838707 = _838705, _838703 = _838701, _838699 = _838697], (3766 ^ _782464) ^ [_838918, _838920, _838922, _838924, _838926, _838928, _838930, _838932] : [-(c_List_Omaps(_838932, _838928, _838924, _838920) = c_List_Omaps(_838930, _838926, _838922, _838918)), _838932 = _838930, _838928 = _838926, _838924 = _838922, _838920 = _838918], (3784 ^ _782464) ^ [_839219, _839221, _839223, _839225] : [-(c_List_Olex(_839225, _839221) = c_List_Olex(_839223, _839219)), _839225 = _839223, _839221 = _839219], (3794 ^ _782464) ^ [_839368, _839370, _839372, _839374] : [-(c_List_Omeasures(_839374, _839370) = c_List_Omeasures(_839372, _839368)), _839374 = _839372, _839370 = _839368], (3804 ^ _782464) ^ [_839517, _839519, _839521, _839523, _839525, _839527, _839529, _839531] : [-(c_List_Ofoldl(_839531, _839527, _839523, _839519) = c_List_Ofoldl(_839529, _839525, _839521, _839517)), _839531 = _839529, _839527 = _839525, _839523 = _839521, _839519 = _839517], (3822 ^ _782464) ^ [_839818, _839820, _839822, _839824, _839826, _839828, _839830, _839832] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_839832, _839828, _839824, _839820) = c_New__Random__Sequence_Opos__not__random__dseq(_839830, _839826, _839822, _839818)), _839832 = _839830, _839828 = _839826, _839824 = _839822, _839820 = _839818], (3840 ^ _782464) ^ [_840119, _840121] : [_840121 = _840119, -(c_New__DSequence_Opos__not__seq(_840121) = c_New__DSequence_Opos__not__seq(_840119))], (3846 ^ _782464) ^ [_840204, _840206, _840208, _840210, _840212, _840214] : [-(c_List_OdropWhile(_840214, _840210, _840206) = c_List_OdropWhile(_840212, _840208, _840204)), _840214 = _840212, _840210 = _840208, _840206 = _840204], (3860 ^ _782464) ^ [_840425, _840427] : [_840427 = _840425, -(c_List_Odistinct(_840427) = c_List_Odistinct(_840425))], (3866 ^ _782464) ^ [_840510, _840512, _840514, _840516, _840518, _840520] : [-(c_List_OtakeWhile(_840520, _840516, _840512) = c_List_OtakeWhile(_840518, _840514, _840510)), _840520 = _840518, _840516 = _840514, _840512 = _840510], (3880 ^ _782464) ^ [_840731, _840733, _840735, _840737, _840739, _840741] : [-(c_List_Olinorder__class_Oinsort__key(_840741, _840737, _840733) = c_List_Olinorder__class_Oinsort__key(_840739, _840735, _840731)), _840741 = _840739, _840737 = _840735, _840733 = _840731], (3894 ^ _782464) ^ [_840952, _840954] : [_840954 = _840952, -(c_Groups_Oabs__class_Oabs(_840954) = c_Groups_Oabs__class_Oabs(_840952))], (3900 ^ _782464) ^ [_841037, _841039] : [_841039 = _841037, -(c_Nat_Osemiring__1__class_Oof__nat(_841039) = c_Nat_Osemiring__1__class_Oof__nat(_841037))], (3906 ^ _782464) ^ [_841122, _841124] : [_841124 = _841122, -(c_Lazy__Sequence_Ohit__bound(_841124) = c_Lazy__Sequence_Ohit__bound(_841122))], (3912 ^ _782464) ^ [_841207, _841209, _841211, _841213, _841215, _841217, _841219, _841221, _841223, _841225, _841227, _841229, _841231, _841233] : [-(c_New__Random__Sequence_Oneg__decr__bind(_841233, _841229, _841225, _841221, _841217, _841213, _841209) = c_New__Random__Sequence_Oneg__decr__bind(_841231, _841227, _841223, _841219, _841215, _841211, _841207)), _841233 = _841231, _841229 = _841227, _841225 = _841223, _841221 = _841219, _841217 = _841215, _841213 = _841211, _841209 = _841207], (3942 ^ _782464) ^ [_841796, _841798, _841800, _841802, _841804, _841806, _841808, _841810] : [-(c_New__DSequence_Oneg__decr__bind(_841810, _841806, _841802, _841798) = c_New__DSequence_Oneg__decr__bind(_841808, _841804, _841800, _841796)), _841810 = _841808, _841806 = _841804, _841802 = _841800, _841798 = _841796], (3960 ^ _782464) ^ [_842097, _842099, _842101, _842103, _842105, _842107, _842109, _842111] : [-(c_Lazy__Sequence_Ohb__bind(_842111, _842107, _842103, _842099) = c_Lazy__Sequence_Ohb__bind(_842109, _842105, _842101, _842097)), _842111 = _842109, _842107 = _842105, _842103 = _842101, _842099 = _842097], (3978 ^ _782464) ^ [_842398, _842400, _842402, _842404, _842406, _842408, _842410, _842412] : [-(c_New__DSequence_Oneg__bind(_842412, _842408, _842404, _842400) = c_New__DSequence_Oneg__bind(_842410, _842406, _842402, _842398)), _842412 = _842410, _842408 = _842406, _842404 = _842402, _842400 = _842398], (3996 ^ _782464) ^ [_842699, _842701, _842703, _842705, _842707, _842709, _842711, _842713, _842715, _842717, _842719, _842721, _842723, _842725] : [-(c_New__Random__Sequence_Opos__decr__bind(_842725, _842721, _842717, _842713, _842709, _842705, _842701) = c_New__Random__Sequence_Opos__decr__bind(_842723, _842719, _842715, _842711, _842707, _842703, _842699)), _842725 = _842723, _842721 = _842719, _842717 = _842715, _842713 = _842711, _842709 = _842707, _842705 = _842703, _842701 = _842699], (4026 ^ _782464) ^ [_843288, _843290, _843292, _843294, _843296, _843298, _843300, _843302] : [-(c_New__DSequence_Opos__decr__bind(_843302, _843298, _843294, _843290) = c_New__DSequence_Opos__decr__bind(_843300, _843296, _843292, _843288)), _843302 = _843300, _843298 = _843296, _843294 = _843292, _843290 = _843288], (4044 ^ _782464) ^ [_843589, _843591, _843593, _843595, _843597, _843599, _843601, _843603] : [-(c_New__Random__Sequence_Opos__empty(_843603, _843599, _843595, _843591) = c_New__Random__Sequence_Opos__empty(_843601, _843597, _843593, _843589)), _843603 = _843601, _843599 = _843597, _843595 = _843593, _843591 = _843589], (4062 ^ _782464) ^ [_843890, _843892] : [_843892 = _843890, -(c_New__DSequence_Opos__empty(_843892) = c_New__DSequence_Opos__empty(_843890))], (4068 ^ _782464) ^ [_843975, _843977, _843979, _843981, _843983, _843985, _843987, _843989] : [-(c_New__DSequence_Opos__bind(_843989, _843985, _843981, _843977) = c_New__DSequence_Opos__bind(_843987, _843983, _843979, _843975)), _843989 = _843987, _843985 = _843983, _843981 = _843979, _843977 = _843975], (4086 ^ _782464) ^ [_844276, _844278, _844280, _844282, _844284, _844286, _844288, _844290] : [-(c_New__Random__Sequence_Oneg__map(_844290, _844286, _844282, _844278) = c_New__Random__Sequence_Oneg__map(_844288, _844284, _844280, _844276)), _844290 = _844288, _844286 = _844284, _844282 = _844280, _844278 = _844276], (4104 ^ _782464) ^ [_844577, _844579, _844581, _844583, _844585, _844587, _844589, _844591] : [-(c_New__Random__Sequence_Oneg__bind(_844591, _844587, _844583, _844579) = c_New__Random__Sequence_Oneg__bind(_844589, _844585, _844581, _844577)), _844591 = _844589, _844587 = _844585, _844583 = _844581, _844579 = _844577], (4122 ^ _782464) ^ [_844878, _844880] : [_844880 = _844878, -(c_New__Random__Sequence_Oneg__single(_844880) = c_New__Random__Sequence_Oneg__single(_844878))], (4128 ^ _782464) ^ [_844963, _844965, _844967, _844969, _844971, _844973, _844975, _844977] : [-(c_New__Random__Sequence_Opos__map(_844977, _844973, _844969, _844965) = c_New__Random__Sequence_Opos__map(_844975, _844971, _844967, _844963)), _844977 = _844975, _844973 = _844971, _844969 = _844967, _844965 = _844963], (4146 ^ _782464) ^ [_845264, _845266, _845268, _845270, _845272, _845274, _845276, _845278] : [-(c_New__Random__Sequence_Opos__bind(_845278, _845274, _845270, _845266) = c_New__Random__Sequence_Opos__bind(_845276, _845272, _845268, _845264)), _845278 = _845276, _845274 = _845272, _845270 = _845268, _845266 = _845264], (4164 ^ _782464) ^ [_845565, _845567, _845569, _845571] : [-(c_New__DSequence_Oneg__single(_845571, _845567) = c_New__DSequence_Oneg__single(_845569, _845565)), _845571 = _845569, _845567 = _845565], (4174 ^ _782464) ^ [_845714, _845716, _845718, _845720] : [-(c_Lazy__Sequence_Ohb__single(_845720, _845716) = c_Lazy__Sequence_Ohb__single(_845718, _845714)), _845720 = _845718, _845716 = _845714], (4184 ^ _782464) ^ [_845863, _845865] : [_845865 = _845863, -(c_New__Random__Sequence_Opos__single(_845865) = c_New__Random__Sequence_Opos__single(_845863))], (4190 ^ _782464) ^ [_845948, _845950, _845952, _845954] : [-(c_New__DSequence_Opos__single(_845954, _845950) = c_New__DSequence_Opos__single(_845952, _845948)), _845954 = _845952, _845950 = _845948], (4200 ^ _782464) ^ [_846097, _846099, _846101, _846103, _846105, _846107] : [-(c_List_Osplice(_846107, _846103, _846099) = c_List_Osplice(_846105, _846101, _846097)), _846107 = _846105, _846103 = _846101, _846099 = _846097], (4214 ^ _782464) ^ [_846318, _846320, _846322, _846324] : [-(c_Hilbert__Choice_OEps(_846324, _846320) = c_Hilbert__Choice_OEps(_846322, _846318)), _846324 = _846322, _846320 = _846318], (4224 ^ _782464) ^ [_846467, _846469] : [_846469 = _846467, -(c_Fun_Oid(_846469) = c_Fun_Oid(_846467))], (4230 ^ _782464) ^ [_846552, _846554, _846556, _846558, _846560, _846562] : [-(c_Set_Ovimage(_846562, _846558, _846554) = c_Set_Ovimage(_846560, _846556, _846552)), _846562 = _846560, _846558 = _846556, _846554 = _846552], (4244 ^ _782464) ^ [_846773, _846775, _846777, _846779, _846781, _846783] : [-(c_Set_Oimage(_846783, _846779, _846775) = c_Set_Oimage(_846781, _846777, _846773)), _846783 = _846781, _846779 = _846777, _846775 = _846773], (4258 ^ _782464) ^ [_846994, _846996, _846998, _847000, _847002, _847004, _847006, _847008] : [-(c_Hilbert__Choice_Oinv__into(_847008, _847004, _847000, _846996) = c_Hilbert__Choice_Oinv__into(_847006, _847002, _846998, _846994)), _847008 = _847006, _847004 = _847002, _847000 = _846998, _846996 = _846994], (4276 ^ _782464) ^ [_847295, _847297] : [_847297 = _847295, -(c_If(_847297) = c_If(_847295))], (4282 ^ _782464) ^ [_847380, _847382, _847384, _847386, _847388, _847390, _847392, _847394] : [-(c_Lazy__Sequence_Oproduct(_847394, _847390, _847386, _847382) = c_Lazy__Sequence_Oproduct(_847392, _847388, _847384, _847380)), _847394 = _847392, _847390 = _847388, _847386 = _847384, _847382 = _847380], (4300 ^ _782464) ^ [_847681, _847683, _847685, _847687, _847689, _847691] : [-(c_Predicate_Oconversep(_847691, _847687, _847683) = c_Predicate_Oconversep(_847689, _847685, _847681)), _847691 = _847689, _847687 = _847685, _847683 = _847681], (4314 ^ _782464) ^ [_847902, _847904, _847906, _847908, _847910, _847912, _847914, _847916, _847918, _847920, _847922, _847924] : [-(c_New__Random__Sequence_Opos__union(_847924, _847920, _847916, _847912, _847908, _847904) = c_New__Random__Sequence_Opos__union(_847922, _847918, _847914, _847910, _847906, _847902)), _847924 = _847922, _847920 = _847918, _847916 = _847914, _847912 = _847910, _847908 = _847906, _847904 = _847902], (4340 ^ _782464) ^ [_848387, _848389, _848391, _848393, _848395, _848397] : [-(c_New__DSequence_Opos__union(_848397, _848393, _848389) = c_New__DSequence_Opos__union(_848395, _848391, _848387)), _848397 = _848395, _848393 = _848391, _848389 = _848387], (4354 ^ _782464) ^ [_848608, _848610, _848612, _848614] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848614, _848610) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848612, _848608)), _848614 = _848612, _848610 = _848608], (4364 ^ _782464) ^ [_848757, _848759] : [_848759 = _848757, -(c_Groups_Ouminus__class_Ouminus(_848759) = c_Groups_Ouminus__class_Ouminus(_848757))], (4370 ^ _782464) ^ [_848842, _848844] : [_848844 = _848842, -(c_Lazy__Sequence_Oempty(_848844) = c_Lazy__Sequence_Oempty(_848842))], (4376 ^ _782464) ^ [_848927, _848929] : [_848929 = _848927, -(c_Lazy__Sequence_Osingle(_848929) = c_Lazy__Sequence_Osingle(_848927))], (4382 ^ _782464) ^ [_849012, _849014, _849016, _849018] : [-(c_Lazy__Sequence_Osmall__lazy_H(_849018, _849014) = c_Lazy__Sequence_Osmall__lazy_H(_849016, _849012)), _849018 = _849016, _849014 = _849012], (4392 ^ _782464) ^ [_849161, _849163] : [_849163 = _849161, -(c_List_Otl(_849163) = c_List_Otl(_849161))], (4398 ^ _782464) ^ [_849246, _849248, _849250, _849252] : [-(c_List_Oconcat(_849252, _849248) = c_List_Oconcat(_849250, _849246)), _849252 = _849250, _849248 = _849246], (4408 ^ _782464) ^ [_849395, _849397] : [_849397 = _849395, -(c_List_Onth(_849397) = c_List_Onth(_849395))], (4414 ^ _782464) ^ [_849480, _849482, _849484, _849486] : [-(c_List_Ozip(_849486, _849482) = c_List_Ozip(_849484, _849480)), _849486 = _849484, _849482 = _849480], (4424 ^ _782464) ^ [_849629, _849631] : [_849631 = _849629, -(c_List_Odrop(_849631) = c_List_Odrop(_849629))], (4430 ^ _782464) ^ [_849714, _849716] : [_849716 = _849714, -(c_List_Ohd(_849716) = c_List_Ohd(_849714))], (4436 ^ _782464) ^ [_849799, _849801] : [_849801 = _849799, -(c_List_Otake(_849801) = c_List_Otake(_849799))], (4442 ^ _782464) ^ [_849884, _849886] : [_849886 = _849884, -(c_Orderings_Oord__class_Omin(_849886) = c_Orderings_Oord__class_Omin(_849884))], (4448 ^ _782464) ^ [_849969, _849971, _849973, _849975] : [-(c_List_Olast(_849975, _849971) = c_List_Olast(_849973, _849969)), _849975 = _849973, _849971 = _849969], (4458 ^ _782464) ^ [_850118, _850120] : [_850120 = _850118, -(c_List_Orev(_850120) = c_List_Orev(_850118))], (4464 ^ _782464) ^ [_850203, _850205, _850207, _850209] : [-(c_List_Ofilter(_850209, _850205) = c_List_Ofilter(_850207, _850203)), _850209 = _850207, _850205 = _850203], (4474 ^ _782464) ^ [_850352, _850354] : [_850354 = _850352, -(c_List_Oappend(_850354) = c_List_Oappend(_850352))], (4480 ^ _782464) ^ [_850437, _850439, _850441, _850443] : [-(c_List_Omap(_850443, _850439) = c_List_Omap(_850441, _850437)), _850443 = _850441, _850439 = _850437], (4490 ^ _782464) ^ [_850586, _850588, _850590, _850592, _850594, _850596] : [-(c_List_Oreplicate(_850596, _850592, _850588) = c_List_Oreplicate(_850594, _850590, _850586)), _850596 = _850594, _850592 = _850590, _850588 = _850586], (4504 ^ _782464) ^ [_850807, _850809, _850811, _850813] : [-(c_Wellfounded_Oaccp(_850813, _850809) = c_Wellfounded_Oaccp(_850811, _850807)), _850813 = _850811, _850809 = _850807], (4514 ^ _782464) ^ [_850956, _850958, _850960, _850962, _850964, _850966, _850968, _850970, _850972, _850974] : [-(c_Predicate_Opred__comp(_850974, _850970, _850966, _850962, _850958) = c_Predicate_Opred__comp(_850972, _850968, _850964, _850960, _850956)), _850974 = _850972, _850970 = _850968, _850966 = _850964, _850962 = _850960, _850958 = _850956], (4536 ^ _782464) ^ [_851345, _851347, _851349, _851351, _851353, _851355, _851357, _851359, _851361, _851363] : [-(c_Option_Ooption_Ooption__case(_851363, _851359, _851355, _851351, _851347) = c_Option_Ooption_Ooption__case(_851361, _851357, _851353, _851349, _851345)), _851363 = _851361, _851359 = _851357, _851355 = _851353, _851351 = _851349, _851347 = _851345], (4558 ^ _782464) ^ [_851734, _851736] : [_851736 = _851734, -(c_Lazy__Sequence_Oyieldn(_851736) = c_Lazy__Sequence_Oyieldn(_851734))], (4564 ^ _782464) ^ [_851819, _851821, _851823, _851825, _851827, _851829] : [-(c_Lazy__Sequence_Oanamorph(_851829, _851825, _851821) = c_Lazy__Sequence_Oanamorph(_851827, _851823, _851819)), _851829 = _851827, _851825 = _851823, _851821 = _851819], (4578 ^ _782464) ^ [_852040, _852042] : [_852042 = _852040, -(c_Lazy__Sequence_Oyield(_852042) = c_Lazy__Sequence_Oyield(_852040))], (4584 ^ _782464) ^ [_852125, _852127] : [_852127 = _852125, -(c_List_Olist_OCons(_852127) = c_List_Olist_OCons(_852125))], (4590 ^ _782464) ^ [_852210, _852212] : [_852212 = _852210, -(c_List_Olist_ONil(_852212) = c_List_Olist_ONil(_852210))], (4596 ^ _782464) ^ [_852295, _852297] : [_852297 = _852295, -(c_List_Omember(_852297) = c_List_Omember(_852295))], (4602 ^ _782464) ^ [_852380, _852382, _852384, _852386, _852388, _852390, _852392, _852394, _852396, _852398] : [-(c_Nitpick_Opair__box_Opair__box__size(_852398, _852394, _852390, _852386, _852382) = c_Nitpick_Opair__box_Opair__box__size(_852396, _852392, _852388, _852384, _852380)), _852398 = _852396, _852394 = _852392, _852390 = _852388, _852386 = _852384, _852382 = _852380], (4624 ^ _782464) ^ [_852769, _852771, _852773, _852775, _852777, _852779, _852781, _852783, _852785, _852787] : [-(c_Nitpick_Opair__box_Opair__box__rec(_852787, _852783, _852779, _852775, _852771) = c_Nitpick_Opair__box_Opair__box__rec(_852785, _852781, _852777, _852773, _852769)), _852787 = _852785, _852783 = _852781, _852779 = _852777, _852775 = _852773, _852771 = _852769], (4646 ^ _782464) ^ [_853158, _853160, _853162, _853164, _853166, _853168, _853170, _853172, _853174, _853176] : [-(c_Nitpick_Opair__box_Opair__box__case(_853176, _853172, _853168, _853164, _853160) = c_Nitpick_Opair__box_Opair__box__case(_853174, _853170, _853166, _853162, _853158)), _853176 = _853174, _853172 = _853170, _853168 = _853166, _853164 = _853162, _853160 = _853158], (4668 ^ _782464) ^ [_853547, _853549, _853551, _853553, _853555, _853557, _853559, _853561] : [-(c_Nitpick_Opair__box_OPairBox(_853561, _853557, _853553, _853549) = c_Nitpick_Opair__box_OPairBox(_853559, _853555, _853551, _853547)), _853561 = _853559, _853557 = _853555, _853553 = _853551, _853549 = _853547], (4686 ^ _782464) ^ [_853848, _853850, _853852, _853854] : [-(c_HOL_OThe(_853854, _853850) = c_HOL_OThe(_853852, _853848)), _853854 = _853852, _853850 = _853848], (4696 ^ _782464) ^ [_853997, _853999, _854001, _854003, _854005, _854007] : [-(c_FunDef_OTHE__default(_854007, _854003, _853999) = c_FunDef_OTHE__default(_854005, _854001, _853997)), _854007 = _854005, _854003 = _854001, _853999 = _853997], (4710 ^ _782464) ^ [_854218, _854220, _854222, _854224] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854224, _854220) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854222, _854218)), _854224 = _854222, _854220 = _854218], (4720 ^ _782464) ^ [_854367, _854369] : [_854369 = _854367, -(c_Nat_Osize__class_Osize(_854369) = c_Nat_Osize__class_Osize(_854367))], (4726 ^ _782464) ^ [_854452, _854454, _854456, _854458, _854460, _854462, _854464, _854466, _854468, _854470] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854470, _854466, _854462, _854458, _854454) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854468, _854464, _854460, _854456, _854452)), _854470 = _854468, _854466 = _854464, _854462 = _854460, _854458 = _854456, _854454 = _854452], (4748 ^ _782464) ^ [_854841, _854843, _854845, _854847] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854847, _854843) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854845, _854841)), _854847 = _854845, _854843 = _854841], (4758 ^ _782464) ^ [_854990, _854992, _854994, _854996] : [-(c_List_Oupto(_854996, _854992) = c_List_Oupto(_854994, _854990)), _854996 = _854994, _854992 = _854990], (4768 ^ _782464) ^ [_855139, _855141, _855143, _855145, _855147, _855149] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855149, _855145, _855141) = c_SetInterval_Oord__class_OatLeastAtMost(_855147, _855143, _855139)), _855149 = _855147, _855145 = _855143, _855141 = _855139], (4782 ^ _782464) ^ [_855360, _855362] : [_855362 = _855360, -(c_Code__Numeral_OSuc__code__numeral(_855362) = c_Code__Numeral_OSuc__code__numeral(_855360))], (4788 ^ _782464) ^ [_855445, _855447, _855449, _855451, _855453, _855455, _855457, _855459] : [-(c_Product__Type_Oscomp(_855459, _855455, _855451, _855447) = c_Product__Type_Oscomp(_855457, _855453, _855449, _855445)), _855459 = _855457, _855455 = _855453, _855451 = _855449, _855447 = _855445], (4806 ^ _782464) ^ [_855746, _855748, _855750, _855752, _855754, _855756, _855758, _855760] : [-(c_Random__Sequence_ORandom(_855760, _855756, _855752, _855748) = c_Random__Sequence_ORandom(_855758, _855754, _855750, _855746)), _855760 = _855758, _855756 = _855754, _855752 = _855750, _855748 = _855746], (4824 ^ _782464) ^ [_856047, _856049] : [_856049 = _856047, -(c_DSequence_Ounion(_856049) = c_DSequence_Ounion(_856047))], (4830 ^ _782464) ^ [_856132, _856134, _856136, _856138, _856140, _856142, _856144, _856146] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_856146, _856142, _856138, _856134) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_856144, _856140, _856136, _856132)), _856146 = _856144, _856142 = _856140, _856138 = _856136, _856134 = _856132], (4848 ^ _782464) ^ [_856433, _856435, _856437, _856439, _856441, _856443] : [-(c_Random__Sequence_Oempty(_856443, _856439, _856435) = c_Random__Sequence_Oempty(_856441, _856437, _856433)), _856443 = _856441, _856439 = _856437, _856435 = _856433], (4862 ^ _782464) ^ [_856654, _856656] : [_856656 = _856654, -(c_DSequence_Oempty(_856656) = c_DSequence_Oempty(_856654))], (4868 ^ _782464) ^ [_856739, _856741] : [_856741 = _856739, -(c_DSequence_Osingle(_856741) = c_DSequence_Osingle(_856739))], (4874 ^ _782464) ^ [_856824, _856826, _856828, _856830, _856832, _856834, _856836, _856838] : [-(c_Random__Sequence_Omap(_856838, _856834, _856830, _856826) = c_Random__Sequence_Omap(_856836, _856832, _856828, _856824)), _856838 = _856836, _856834 = _856832, _856830 = _856828, _856826 = _856824], (4892 ^ _782464) ^ [_857125, _857127, _857129, _857131, _857133, _857135, _857137, _857139] : [-(c_Random__Sequence_Obind(_857139, _857135, _857131, _857127) = c_Random__Sequence_Obind(_857137, _857133, _857129, _857125)), _857139 = _857137, _857135 = _857133, _857131 = _857129, _857127 = _857125], (4910 ^ _782464) ^ [_857426, _857428] : [_857428 = _857426, -(c_Random__Sequence_Osingle(_857428) = c_Random__Sequence_Osingle(_857426))], (4916 ^ _782464) ^ [_857511, _857513, _857515, _857517] : [-(c_Product__Type_Osnd(_857517, _857513) = c_Product__Type_Osnd(_857515, _857511)), _857517 = _857515, _857513 = _857511], (4926 ^ _782464) ^ [_857660, _857662, _857664, _857666] : [-(c_Product__Type_Ofst(_857666, _857662) = c_Product__Type_Ofst(_857664, _857660)), _857666 = _857664, _857662 = _857660], (4936 ^ _782464) ^ [_857809, _857811, _857813, _857815, _857817, _857819] : [-(c_Relation_OImage(_857819, _857815, _857811) = c_Relation_OImage(_857817, _857813, _857809)), _857819 = _857817, _857815 = _857813, _857811 = _857809], (4950 ^ _782464) ^ [_858030, _858032, _858034, _858036, _858038, _858040, _858042, _858044] : [-(c_Wellfounded_Olex__prod(_858044, _858040, _858036, _858032) = c_Wellfounded_Olex__prod(_858042, _858038, _858034, _858030)), _858044 = _858042, _858040 = _858038, _858036 = _858034, _858032 = _858030], (4968 ^ _782464) ^ [_858331, _858333] : [_858333 = _858331, -(c_Set_OBex(_858333) = c_Set_OBex(_858331))], (4974 ^ _782464) ^ [_858416, _858418, _858420, _858422] : [-(c_List_Olexord(_858422, _858418) = c_List_Olexord(_858420, _858416)), _858422 = _858420, _858418 = _858416], (4984 ^ _782464) ^ [_858565, _858567] : [_858567 = _858565, -(c_Wellfounded_Ofinite__psubset(_858567) = c_Wellfounded_Ofinite__psubset(_858565))], (4990 ^ _782464) ^ [_858650, _858652] : [_858652 = _858650, -(c_List_Oset(_858652) = c_List_Oset(_858650))], (4996 ^ _782464) ^ [_858735, _858737, _858739, _858741] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858741, _858737) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858739, _858735)), _858741 = _858739, _858737 = _858735], (5006 ^ _782464) ^ [_858884, _858886, _858888, _858890] : [-(c_Complete__Lattice_OSup__class_OSup(_858890, _858886) = c_Complete__Lattice_OSup__class_OSup(_858888, _858884)), _858890 = _858888, _858886 = _858884], (5016 ^ _782464) ^ [_859033, _859035, _859037, _859039] : [-(c_Complete__Lattice_OInf__class_OInf(_859039, _859035) = c_Complete__Lattice_OInf__class_OInf(_859037, _859033)), _859039 = _859037, _859035 = _859033], (5026 ^ _782464) ^ [_859182, _859184, _859186, _859188, _859190, _859192, _859194, _859196, _859198, _859200, _859202, _859204] : [-(c_Partial__Function_Ofun__lub(_859204, _859200, _859196, _859192, _859188, _859184) = c_Partial__Function_Ofun__lub(_859202, _859198, _859194, _859190, _859186, _859182)), _859204 = _859202, _859200 = _859198, _859196 = _859194, _859192 = _859190, _859188 = _859186, _859184 = _859182], (5052 ^ _782464) ^ [_859667, _859669, _859671, _859673, _859675, _859677] : [-(c_Relation_Orel__comp(_859677, _859673, _859669) = c_Relation_Orel__comp(_859675, _859671, _859667)), _859677 = _859675, _859673 = _859671, _859669 = _859667], (5066 ^ _782464) ^ [_859888, _859890, _859892, _859894] : [-(c_Relation_Oinv__image(_859894, _859890) = c_Relation_Oinv__image(_859892, _859888)), _859894 = _859892, _859890 = _859888], (5076 ^ _782464) ^ [_860037, _860039, _860041, _860043] : [-(c_Relation_OId__on(_860043, _860039) = c_Relation_OId__on(_860041, _860037)), _860043 = _860041, _860039 = _860037], (5086 ^ _782464) ^ [_860186, _860188] : [_860188 = _860186, -(c_Relation_OId(_860188) = c_Relation_OId(_860186))], (5092 ^ _782464) ^ [_860271, _860273, _860275, _860277] : [-(c_List_Olistrel(_860277, _860273) = c_List_Olistrel(_860275, _860271)), _860277 = _860275, _860273 = _860271], (5102 ^ _782464) ^ [_860420, _860422] : [_860422 = _860420, -(c_Lattices_Osemilattice__sup__class_Osup(_860422) = c_Lattices_Osemilattice__sup__class_Osup(_860420))], (5108 ^ _782464) ^ [_860505, _860507, _860509, _860511] : [-(c_Relation_Oconverse(_860511, _860507) = c_Relation_Oconverse(_860509, _860505)), _860511 = _860509, _860507 = _860505], (5118 ^ _782464) ^ [_860654, _860656] : [_860656 = _860654, -(c_Set_OCollect(_860656) = c_Set_OCollect(_860654))], (5124 ^ _782464) ^ [_860739, _860741] : [_860741 = _860739, -(c_HOL_OEx(_860741) = c_HOL_OEx(_860739))], (5130 ^ _782464) ^ [_860824, _860826] : [_860826 = _860824, -(c_Lattices_Osemilattice__inf__class_Oinf(_860826) = c_Lattices_Osemilattice__inf__class_Oinf(_860824))], (5136 ^ _782464) ^ [_860909, _860911, _860913, _860915, _860917, _860919] : [-(c_Finite__Set_Ofold__image(_860919, _860915, _860911) = c_Finite__Set_Ofold__image(_860917, _860913, _860909)), _860919 = _860917, _860915 = _860913, _860911 = _860909], (5150 ^ _782464) ^ [_861130, _861132] : [_861132 = _861130, -(c_Orderings_Otop__class_Otop(_861132) = c_Orderings_Otop__class_Otop(_861130))], (5156 ^ _782464) ^ [_861215, _861217, _861219, _861221, _861223, _861225, _861227, _861229, _861231, _861233] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_861233, _861229, _861225, _861221, _861217) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_861231, _861227, _861223, _861219, _861215)), _861233 = _861231, _861229 = _861227, _861225 = _861223, _861221 = _861219, _861217 = _861215], (5178 ^ _782464) ^ [_861604, _861606, _861608, _861610] : [-(c_Orderings_Oord__class_OLeast(_861610, _861606) = c_Orderings_Oord__class_OLeast(_861608, _861604)), _861610 = _861608, _861606 = _861604], (5188 ^ _782464) ^ [_861753, _861755, _861757, _861759] : [-(c_Quickcheck_Obeyond(_861759, _861755) = c_Quickcheck_Obeyond(_861757, _861753)), _861759 = _861757, _861755 = _861753], (5198 ^ _782464) ^ [_861902, _861904, _861906, _861908] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861908, _861904) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861906, _861902)), _861908 = _861906, _861904 = _861902], (5208 ^ _782464) ^ [_862051, _862053, _862055, _862057, _862059, _862061] : [-(c_Product__Type_Oprod_Oprod__case(_862061, _862057, _862053) = c_Product__Type_Oprod_Oprod__case(_862059, _862055, _862051)), _862061 = _862059, _862057 = _862055, _862053 = _862051], (5222 ^ _782464) ^ [_862272, _862274, _862276, _862278, _862280, _862282, _862284, _862286] : [-(c_Product__Type_Ocurry(_862286, _862282, _862278, _862274) = c_Product__Type_Ocurry(_862284, _862280, _862276, _862272)), _862286 = _862284, _862282 = _862280, _862278 = _862276, _862274 = _862272], (5240 ^ _782464) ^ [_862573, _862575, _862577, _862579] : [-(c_Transitive__Closure_Otrancl(_862579, _862575) = c_Transitive__Closure_Otrancl(_862577, _862573)), _862579 = _862577, _862575 = _862573], (5250 ^ _782464) ^ [_862722, _862724, _862726, _862728] : [-(c_Quotient_ORespects(_862728, _862724) = c_Quotient_ORespects(_862726, _862722)), _862728 = _862726, _862724 = _862722], (5260 ^ _782464) ^ [_862871, _862873, _862875, _862877, _862879, _862881, _862883, _862885] : [-(c_Quotient_OBabs(_862885, _862881, _862877, _862873) = c_Quotient_OBabs(_862883, _862879, _862875, _862871)), _862885 = _862883, _862881 = _862879, _862877 = _862875, _862873 = _862871], (5278 ^ _782464) ^ [_863172, _863174, _863176, _863178] : [-(c_Transitive__Closure_Ortrancl(_863178, _863174) = c_Transitive__Closure_Ortrancl(_863176, _863172)), _863178 = _863176, _863174 = _863172], (5288 ^ _782464) ^ [_863321, _863323, _863325, _863327] : [-(c_Product__Type_OPair(_863327, _863323) = c_Product__Type_OPair(_863325, _863321)), _863327 = _863325, _863323 = _863321], (5298 ^ _782464) ^ [_863470, _863472, _863474, _863476, _863478, _863480] : [-(c_Lazy__Sequence_Oappend(_863480, _863476, _863472) = c_Lazy__Sequence_Oappend(_863478, _863474, _863470)), _863480 = _863478, _863476 = _863474, _863472 = _863470], (5312 ^ _782464) ^ [_863691, _863693, _863695, _863697, _863699, _863701] : [-(c_Lazy__Sequence_Obind(_863701, _863697, _863693) = c_Lazy__Sequence_Obind(_863699, _863695, _863691)), _863701 = _863699, _863697 = _863695, _863693 = _863691], (5326 ^ _782464) ^ [_863912, _863914, _863916, _863918] : [-(c_Lazy__Sequence_Oflat(_863918, _863914) = c_Lazy__Sequence_Oflat(_863916, _863912)), _863918 = _863916, _863914 = _863912], (5336 ^ _782464) ^ [_864061, _864063, _864065, _864067] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_864067, _864063) = c_SetInterval_Oord__class_OatLeastLessThan(_864065, _864061)), _864067 = _864065, _864063 = _864061], (5346 ^ _782464) ^ [_864210, _864212, _864214, _864216, _864218, _864220] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_864220, _864216, _864212) = c_Lazy__Sequence_Olazy__sequence_OInsert(_864218, _864214, _864210)), _864220 = _864218, _864216 = _864214, _864212 = _864210], (5360 ^ _782464) ^ [_864431, _864433] : [_864433 = _864431, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_864433) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_864431))], (5366 ^ _782464) ^ [_864516, _864518, _864520, _864522] : [-(c_List_Oupt(_864522, _864518) = c_List_Oupt(_864520, _864516)), _864522 = _864520, _864518 = _864516], (5376 ^ _782464) ^ [_864665, _864667, _864669, _864671, _864673, _864675, _864677, _864679] : [-(c_Fun_Ocomp(_864679, _864675, _864671, _864667) = c_Fun_Ocomp(_864677, _864673, _864669, _864665)), _864679 = _864677, _864675 = _864673, _864671 = _864669, _864667 = _864665], (5394 ^ _782464) ^ [_864966, _864968, _864970, _864972, _864974, _864976, _864978, _864980, _864982, _864984] : [-(c_New__DSequence_Opos__map(_864984, _864980, _864976, _864972, _864968) = c_New__DSequence_Opos__map(_864982, _864978, _864974, _864970, _864966)), _864984 = _864982, _864980 = _864978, _864976 = _864974, _864972 = _864970, _864968 = _864966], (5416 ^ _782464) ^ [_865355, _865357, _865359, _865361, _865363, _865365, _865367, _865369] : [-(c_Lazy__Sequence_Omap(_865369, _865365, _865361, _865357) = c_Lazy__Sequence_Omap(_865367, _865363, _865359, _865355)), _865369 = _865367, _865365 = _865363, _865361 = _865359, _865357 = _865355], (5434 ^ _782464) ^ [_865656, _865658] : [_865658 = _865656, -(c_member(_865658) = c_member(_865656))], (5440 ^ _782464) ^ [_865741, _865743] : [_865743 = _865741, -(c_Power_Opower__class_Opower(_865743) = c_Power_Opower__class_Opower(_865741))], (5446 ^ _782464) ^ [_865826, _865828] : [_865828 = _865826, -(c_Orderings_Oord__class_Oless(_865828) = c_Orderings_Oord__class_Oless(_865826))], (5452 ^ _782464) ^ [_865911, _865913] : [_865913 = _865911, -(c_Groups_Oone__class_Oone(_865913) = c_Groups_Oone__class_Oone(_865911))], (5458 ^ _782464) ^ [_865996, _865998] : [_865998 = _865996, -(c_Finite__Set_Ofinite(_865998) = c_Finite__Set_Ofinite(_865996))], (5464 ^ _782464) ^ [_866081, _866083, _866085, _866087, _866089, _866091] : [-(c_Finite__Set_Ofold1Set(_866091, _866087, _866083) = c_Finite__Set_Ofold1Set(_866089, _866085, _866081)), _866091 = _866089, _866087 = _866085, _866083 = _866081], (5478 ^ _782464) ^ [_866302, _866304] : [_866304 = _866302, -(c_Groups_Oplus__class_Oplus(_866304) = c_Groups_Oplus__class_Oplus(_866302))], (5484 ^ _782464) ^ [_866387, _866389] : [_866389 = _866387, -(c_Groups_Ominus__class_Ominus(_866389) = c_Groups_Ominus__class_Ominus(_866387))], (5490 ^ _782464) ^ [_866472, _866474] : [_866474 = _866472, -(c_Groups_Ozero__class_Ozero(_866474) = c_Groups_Ozero__class_Ozero(_866472))], (5496 ^ _782464) ^ [_866557, _866559] : [_866559 = _866557, -(c_Divides_Odiv__class_Odiv(_866559) = c_Divides_Odiv__class_Odiv(_866557))], (5502 ^ _782464) ^ [_866642, _866644] : [_866644 = _866642, -(c_Groups_Otimes__class_Otimes(_866644) = c_Groups_Otimes__class_Otimes(_866642))], (5508 ^ _782464) ^ [_866727, _866729, _866731, _866733, _866735, _866737, _866739, _866741] : [-(c_SetInterval_Oord_OatLeastAtMost(_866741, _866737, _866733, _866729) = c_SetInterval_Oord_OatLeastAtMost(_866739, _866735, _866731, _866727)), _866741 = _866739, _866737 = _866735, _866733 = _866731, _866729 = _866727], (5526 ^ _782464) ^ [_867028, _867030] : [_867030 = _867028, -(c_Set_Oinsert(_867030) = c_Set_Oinsert(_867028))], (5532 ^ _782464) ^ [_867113, _867115, _867117, _867119, _867121, _867123, _867125, _867127] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_867127, _867123, _867119, _867115) = c_SetInterval_Oord_OgreaterThanLessThan(_867125, _867121, _867117, _867113)), _867127 = _867125, _867123 = _867121, _867119 = _867117, _867115 = _867113], (5550 ^ _782464) ^ [_867414, _867416, _867418, _867420, _867422, _867424, _867426, _867428, _867430, _867432] : [-(c_SetInterval_Oord_OatLeastLessThan(_867432, _867428, _867424, _867420, _867416) = c_SetInterval_Oord_OatLeastLessThan(_867430, _867426, _867422, _867418, _867414)), _867432 = _867430, _867428 = _867426, _867424 = _867422, _867420 = _867418, _867416 = _867414], (5572 ^ _782464) ^ [_867803, _867805] : [_867805 = _867803, -(c_Orderings_Obot__class_Obot(_867805) = c_Orderings_Obot__class_Obot(_867803))], (5578 ^ _782464) ^ [_867888, _867890, _867892, _867894, _867896, _867898, _867900, _867902, _867904, _867906] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_867906, _867902, _867898, _867894, _867890) = c_SetInterval_Oord_OgreaterThanAtMost(_867904, _867900, _867896, _867892, _867888)), _867906 = _867904, _867902 = _867900, _867898 = _867896, _867894 = _867892, _867890 = _867888], (5600 ^ _782464) ^ [_868277, _868279] : [_868279 = _868277, -(c_Rings_Odvd__class_Odvd(_868279) = c_Rings_Odvd__class_Odvd(_868277))], (5606 ^ _782464) ^ [_868362, _868364] : [_868364 = _868362, -(tc_List_Olist(_868364) = tc_List_Olist(_868362))], (5612 ^ _782464) ^ [_868447, _868449, _868451, _868453] : [-(tc_sum(_868453, _868449) = tc_sum(_868451, _868447)), _868453 = _868451, _868449 = _868447], (5622 ^ _782464) ^ [_868596, _868598] : [_868598 = _868596, -(tc_Option_Ooption(_868598) = tc_Option_Ooption(_868596))], (5628 ^ _782464) ^ [_868681, _868683, _868685, _868687] : [-(tc_Nitpick_Opair__box(_868687, _868683) = tc_Nitpick_Opair__box(_868685, _868681)), _868687 = _868685, _868683 = _868681], (5638 ^ _782464) ^ [_868830, _868832, _868834, _868836] : [-(tc_prod(_868836, _868832) = tc_prod(_868834, _868830)), _868836 = _868834, _868832 = _868830], (5648 ^ _782464) ^ [_868979, _868981] : [_868981 = _868979, -(tc_Lazy__Sequence_Olazy__sequence(_868981) = tc_Lazy__Sequence_Olazy__sequence(_868979))], (5654 ^ _782464) ^ [_869064, _869066] : [_869066 = _869064, -(c_COMBI(_869066) = c_COMBI(_869064))], (5660 ^ _782464) ^ [_869149, _869151, _869153, _869155] : [-(c_COMBK(_869155, _869151) = c_COMBK(_869153, _869149)), _869155 = _869153, _869151 = _869149], (5670 ^ _782464) ^ [_869298, _869300, _869302, _869304, _869306, _869308] : [-(c_COMBB(_869308, _869304, _869300) = c_COMBB(_869306, _869302, _869298)), _869308 = _869306, _869304 = _869302, _869300 = _869298], (5684 ^ _782464) ^ [_869519, _869521, _869523, _869525, _869527, _869529] : [-(c_COMBC(_869529, _869525, _869521) = c_COMBC(_869527, _869523, _869519)), _869529 = _869527, _869525 = _869523, _869521 = _869519], (5698 ^ _782464) ^ [_869740, _869742, _869744, _869746, _869748, _869750] : [-(c_COMBS(_869750, _869746, _869742) = c_COMBS(_869748, _869744, _869740)), _869750 = _869748, _869746 = _869744, _869742 = _869740], (5712 ^ _782464) ^ [_869961, _869963, _869965, _869967] : [-(hAPP(_869967, _869963) = hAPP(_869965, _869961)), _869967 = _869965, _869963 = _869961], (5722 ^ _782464) ^ [_870110, _870112] : [_870112 = _870110, -(c_Orderings_Oord__class_Oless__eq(_870112) = c_Orderings_Oord__class_Oless__eq(_870110))], (5738 ^ _782464) ^ [_870340, _870342] : [_870342 = _870340, -(tc_Hoare__Mirabelle_Otriple(_870342) = tc_Hoare__Mirabelle_Otriple(_870340))], (5728 ^ _782464) ^ [_870195, _870197, _870199, _870201] : [-(tc_fun(_870201, _870197) = tc_fun(_870199, _870195)), _870201 = _870199, _870197 = _870195], (5744 ^ _782464) ^ [_873240, _873242] : [hAPP(_873240, 5745 ^ [_873240, _873242]) = hAPP(_873242, 5745 ^ [_873240, _873242]), -(_873240 = _873242)], (5751 ^ _782464) ^ [_873366, _873368, _873370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_873366), tc_HOL_Obool)), _873368), _873370)), -(c_Hoare__Mirabelle_Ohoare__derivs(_873366, _873370, _873368))], (5757 ^ _782464) ^ [_873471, _873473, _873475, _873477] : [c_Hoare__Mirabelle_Ohoare__derivs(_873471, _873473, _873475), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_873471), tc_HOL_Obool)), _873477), _873475)), -(c_Hoare__Mirabelle_Ohoare__derivs(_873471, _873473, _873477))], (5767 ^ _782464) ^ [_873636, _873638, _873640, _873642] : [c_Hoare__Mirabelle_Ohoare__derivs(_873636, _873638, _873640), c_Hoare__Mirabelle_Ohoare__derivs(_873636, _873642, _873638), -(c_Hoare__Mirabelle_Ohoare__derivs(_873636, _873642, _873640))], (5777 ^ _782464) ^ [_873779, _873781, _873783] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873779, tc_HOL_Obool)), _873781), _873783)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873779, tc_HOL_Obool)), _873783), _873781)), -(_873781 = _873783)], (5787 ^ _782464) ^ [_873952, _873954] : [class_Orderings_Opreorder(_873952), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873952), _873954), _873954)))], (5793 ^ _782464) ^ [_874041, _874043, _874045, _874047] : [class_Orderings_Oord(_874041), 5796 ^ _782464 : [(5797 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874043, _874041)), _874045), _874047)), 5800 ^ _782464 : [(5801 ^ _782464) ^ [_874198] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874041), hAPP(_874045, _874198)), hAPP(_874047, _874198))))]]], (5803 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874041), hAPP(_874045, 5804 ^ [_874041, _874043, _874045, _874047])), hAPP(_874047, 5804 ^ [_874041, _874043, _874045, _874047]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874043, _874041)), _874045), _874047)))]]], (5810 ^ _782464) ^ [_874387, _874389, _874391, _874393, _874395] : [class_Orderings_Oord(_874387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874389, _874387)), _874391), _874393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874387), hAPP(_874391, _874395)), hAPP(_874393, _874395))))], (5820 ^ _782464) ^ [_874572, _874574, _874576, _874578, _874580] : [class_Orderings_Oord(_874572), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874574, _874572)), _874576), _874578)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874572), hAPP(_874576, _874580)), hAPP(_874578, _874580))))], (5830 ^ _782464) ^ [_874757, _874759] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874757, tc_HOL_Obool)), _874759), _874759)))], (5832 ^ _782464) ^ [_874810, _874812, _874814] : [_874810 = _874812, 5835 ^ _782464 : [(5836 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874814, tc_HOL_Obool)), _874810), _874812)))], (5838 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874814, tc_HOL_Obool)), _874812), _874810)))]]], (5840 ^ _782464) ^ [_874951, _874953, _874955] : [-(_874951 = _874953), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874955, tc_HOL_Obool)), _874951), _874953)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874955, tc_HOL_Obool)), _874953), _874951))], (5850 ^ _782464) ^ [_875126, _875128, _875130, _875132] : [hBOOL(hAPP(_875126, _875128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875130, tc_HOL_Obool)), _875126), _875132)), -(hBOOL(hAPP(_875132, _875128)))], (5860 ^ _782464) ^ [_875291, _875293, _875295] : [_875291 = _875293, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875295, tc_HOL_Obool)), _875291), _875293)))], (5866 ^ _782464) ^ [_875390, _875392, _875394] : [_875390 = _875392, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875394, tc_HOL_Obool)), _875392), _875390)))], (5872 ^ _782464) ^ [_875489, _875491, _875493, _875495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875489, tc_HOL_Obool)), _875491), _875493)), hBOOL(hAPP(_875491, _875495)), -(hBOOL(hAPP(_875493, _875495)))], (5882 ^ _782464) ^ [_875654, _875656, _875658, _875660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875654, tc_HOL_Obool)), _875656), _875658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875654, tc_HOL_Obool)), _875658), _875660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875654, tc_HOL_Obool)), _875656), _875660)))], (5892 ^ _782464) ^ [_875851, _875853, _875855] : [class_Orderings_Olinorder(_875851), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875851), _875853), _875855))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875851), _875855), _875853)))], (5902 ^ _782464) ^ [_875971, _875973, _875975, _875977] : [class_Orderings_Oorder(_875971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875971), _875973), _875975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875971), _875977), _875973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875971), _875977), _875975)))], (5916 ^ _782464) ^ [_876204, _876206, _876208] : [class_Orderings_Oorder(_876204), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876204), _876206), _876208)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876204), _876208), _876206)), -(_876208 = _876206)], (5930 ^ _782464) ^ [_876417, _876419, _876421, _876423] : [class_Orderings_Opreorder(_876417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876417), _876419), _876421)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876417), _876421), _876423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876417), _876419), _876423)))], (5944 ^ _782464) ^ [_876650, _876652, _876654] : [class_Orderings_Oorder(_876650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876650), _876652), _876654)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876650), _876654), _876652)), -(_876652 = _876654)], (5958 ^ _782464) ^ [_876863, _876865, _876867, _876869] : [class_Orderings_Oorder(_876863), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876863), _876865), _876867)), _876865 = _876869, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876863), _876869), _876867)))], (5972 ^ _782464) ^ [_877082, _877084, _877086, _877088] : [class_Orderings_Oord(_877082), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877082), _877084), _877086)), _877086 = _877088, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877082), _877084), _877088)))], (5986 ^ _782464) ^ [_877301, _877303, _877305, _877307] : [class_Orderings_Oorder(_877301), _877303 = _877305, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877301), _877307), _877305)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877301), _877307), _877303)))], (6000 ^ _782464) ^ [_877520, _877522, _877524, _877526] : [class_Orderings_Oord(_877520), _877522 = _877524, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877520), _877524), _877526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877520), _877522), _877526)))], (6014 ^ _782464) ^ [_877739, _877741, _877743] : [class_Orderings_Oorder(_877739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877739), _877741), _877743)), 6021 ^ _782464 : [(6022 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877739), _877743), _877741)), -(_877743 = _877741)], (6028 ^ _782464) ^ [] : [_877743 = _877741, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877739), _877743), _877741)))]]], (6034 ^ _782464) ^ [_878039, _878041, _878043] : [class_Orderings_Opreorder(_878039), _878041 = _878043, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878039), _878041), _878043)))], (6044 ^ _782464) ^ [_878184, _878186, _878188] : [class_Orderings_Oorder(_878184), 6047 ^ _782464 : [(6048 ^ _782464) ^ [] : [_878186 = _878188, 6051 ^ _782464 : [(6052 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878184), _878186), _878188)))], (6054 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878184), _878188), _878186)))]]], (6056 ^ _782464) ^ [] : [-(_878186 = _878188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878184), _878186), _878188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878184), _878188), _878186))]]], (6066 ^ _782464) ^ [_878511, _878513, _878515] : [class_Orderings_Olinorder(_878511), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878511), _878513), _878515))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878511), _878515), _878513)))], (6076 ^ _782464) ^ [_878629, _878631, _878633] : [_878629 = _878631, 6079 ^ _782464 : [(6080 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878633, tc_HOL_Obool)), _878629), _878631)))], (6082 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878633, tc_HOL_Obool)), _878631), _878629)))]]], (6084 ^ _782464) ^ [_878778, _878780, _878782] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878778, tc_HOL_Obool)), _878780), _878782)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878778, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_878778, _878780)), c_Predicate_OPowp(_878778, _878782))))], (6090 ^ _782464) ^ [_878915, _878917, _878919, _878921] : [class_Orderings_Oorder(_878915), class_Enum_Oenum(_878917), 6097 ^ _782464 : [(6098 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878917, _878915)), _878919), _878921)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878917), hAPP(hAPP(c_COMBS(_878917, _878915, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878915, tc_fun(_878915, tc_HOL_Obool), _878917), c_Orderings_Oord__class_Oless__eq(_878915)), _878919)), _878921))))], (6104 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878917), hAPP(hAPP(c_COMBS(_878917, _878915, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878915, tc_fun(_878915, tc_HOL_Obool), _878917), c_Orderings_Oord__class_Oless__eq(_878915)), _878919)), _878921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878917, _878915)), _878919), _878921)))]]], (6110 ^ _782464) ^ [_879305, _879307, _879309] : [class_Orderings_Owellorder(_879305), hBOOL(hAPP(_879307, _879309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879305), c_Orderings_Oord__class_OLeast(_879305, _879307)), _879309)))], (6120 ^ _782464) ^ [_879460, _879462, _879464, _879466] : [class_Orderings_Oord(_879460), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879460), hAPP(_879462, 6125 ^ [_879460, _879462, _879464, _879466])), hAPP(_879464, 6125 ^ [_879460, _879462, _879464, _879466]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879466, _879460)), _879462), _879464)))], (6131 ^ _782464) ^ [_879724, _879726, _879728, _879730, _879732, _879734] : [c_Predicate_Oinv__imagep(_879724, _879726, _879728, _879730, _879732, _879734), -(hBOOL(hAPP(hAPP(_879728, hAPP(_879730, _879732)), hAPP(_879730, _879734))))], (6137 ^ _782464) ^ [_879835, _879837, _879839, _879841, _879843, _879845] : [hBOOL(hAPP(hAPP(_879839, hAPP(_879841, _879843)), hAPP(_879841, _879845))), -(c_Predicate_Oinv__imagep(_879835, _879837, _879839, _879841, _879843, _879845))], (6143 ^ _782464) ^ [_879952, _879954, _879956, _879958, _879960] : [class_Orderings_Oorder(_879952), class_Orderings_Olinorder(_879954), c_Orderings_Oorder__class_Ostrict__mono(_879954, _879952, _879956), 6154 ^ _782464 : [(6155 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879952), hAPP(_879956, _879958)), hAPP(_879956, _879960))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879954), _879958), _879960)))], (6161 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879954), _879958), _879960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879952), hAPP(_879956, _879958)), hAPP(_879956, _879960))))]]], (6167 ^ _782464) ^ [_880353, _880355, _880357] : [class_Orderings_Olinorder(_880353), 6170 ^ _782464 : [(6171 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880353, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880353), _880355)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880353), _880357))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880353), _880357), _880355)))], (6177 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880353), _880357), _880355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880353, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880353), _880355)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880353), _880357))))]]], (6183 ^ _782464) ^ [_880645, _880647, _880649] : [class_Orderings_Olinorder(_880645), 6186 ^ _782464 : [(6187 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880645, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_880645), _880647)), hAPP(c_SetInterval_Oord__class_OlessThan(_880645), _880649))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880645), _880647), _880649)))], (6193 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880645), _880647), _880649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880645, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_880645), _880647)), hAPP(c_SetInterval_Oord__class_OlessThan(_880645), _880649))))]]], (6199 ^ _782464) ^ [_880937, _880939, _880941] : [class_Orderings_Oorder(_880937), 6202 ^ _782464 : [(6203 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880937, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_880937), _880939)), hAPP(c_SetInterval_Oord__class_OatLeast(_880937), _880941))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880937), _880941), _880939)))], (6209 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880937), _880941), _880939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880937, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_880937), _880939)), hAPP(c_SetInterval_Oord__class_OatLeast(_880937), _880941))))]]], (6215 ^ _782464) ^ [_881229, _881231, _881233] : [class_Orderings_Oorder(_881229), 6218 ^ _782464 : [(6219 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881229, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_881229), _881231)), hAPP(c_SetInterval_Oord__class_OatMost(_881229), _881233))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881229), _881231), _881233)))], (6225 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881229), _881231), _881233)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881229, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_881229), _881231)), hAPP(c_SetInterval_Oord__class_OatMost(_881229), _881233))))]]], (6231 ^ _782464) ^ [_881521, _881523, _881525, _881527, _881529] : [class_Complete__Lattice_Ocomplete__lattice(_881521), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881523, tc_HOL_Obool)), _881525), _881527)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881521), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881523, _881521), _881525), _881529)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881523, _881521), _881527), _881529))))], (6241 ^ _782464) ^ [_881730, _881732, _881734, _881736, _881738] : [class_Complete__Lattice_Ocomplete__lattice(_881730), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881732, tc_HOL_Obool)), _881734), _881736)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881730), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_881732, _881730), _881736), _881738)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_881732, _881730), _881734), _881738))))], (6251 ^ _782464) ^ [_881939, _881941, _881943, _881945, _881947, _881949] : [class_Complete__Lattice_Ocomplete__lattice(_881939), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881941, tc_fun(_881943, _881939)), _881945), _881947), _881949) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881941, _881939), _881945), hAPP(hAPP(c_COMBC(_881941, _881943, _881939), _881947), _881949)))], (6257 ^ _782464) ^ [_882090, _882092, _882094, _882096, _882098, _882100] : [class_Complete__Lattice_Ocomplete__lattice(_882090), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_882092, tc_fun(_882094, _882090)), _882096), _882098), _882100) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_882092, _882090), _882096), hAPP(hAPP(c_COMBC(_882092, _882094, _882090), _882098), _882100)))], (6263 ^ _782464) ^ [_882241, _882243, _882245] : [class_Orderings_Olinorder(_882241), 6266 ^ _782464 : [(6267 ^ _782464) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_882241), _882243) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_882241), _882245), -(_882243 = _882245)], (6273 ^ _782464) ^ [] : [_882243 = _882245, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_882241), _882243) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_882241), _882245))]]], (6279 ^ _782464) ^ [_882482, _882484, _882486] : [class_Orderings_Olinorder(_882482), 6282 ^ _782464 : [(6283 ^ _782464) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_882482), _882484) = hAPP(c_SetInterval_Oord__class_OlessThan(_882482), _882486), -(_882484 = _882486)], (6289 ^ _782464) ^ [] : [_882484 = _882486, -(hAPP(c_SetInterval_Oord__class_OlessThan(_882482), _882484) = hAPP(c_SetInterval_Oord__class_OlessThan(_882482), _882486))]]], (6295 ^ _782464) ^ [_882723, _882725, _882727] : [class_Orderings_Olinorder(_882723), 6298 ^ _782464 : [(6299 ^ _782464) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_882723), _882725) = hAPP(c_SetInterval_Oord__class_OatLeast(_882723), _882727), -(_882725 = _882727)], (6305 ^ _782464) ^ [] : [_882725 = _882727, -(hAPP(c_SetInterval_Oord__class_OatLeast(_882723), _882725) = hAPP(c_SetInterval_Oord__class_OatLeast(_882723), _882727))]]], (6311 ^ _782464) ^ [_882964, _882966, _882968] : [class_Orderings_Olinorder(_882964), 6314 ^ _782464 : [(6315 ^ _782464) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_882964), _882966) = hAPP(c_SetInterval_Oord__class_OatMost(_882964), _882968), -(_882966 = _882968)], (6321 ^ _782464) ^ [] : [_882966 = _882968, -(hAPP(c_SetInterval_Oord__class_OatMost(_882964), _882966) = hAPP(c_SetInterval_Oord__class_OatMost(_882964), _882968))]]], (6327 ^ _782464) ^ [_883205, _883207, _883209, _883211, _883213, _883215] : [class_Complete__Lattice_Ocomplete__lattice(_883205), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883207, _883205), _883209), hAPP(hAPP(c_COMBB(tc_fun(_883211, _883205), _883205, _883207), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883211, _883205), _883213)), _883215)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883211, _883205), _883213), hAPP(hAPP(c_COMBB(tc_fun(_883207, _883205), _883205, _883211), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883207, _883205), _883209)), hAPP(c_COMBC(_883207, _883211, _883205), _883215))))], (6333 ^ _782464) ^ [_883414, _883416, _883418, _883420, _883422, _883424] : [class_Complete__Lattice_Ocomplete__lattice(_883414), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883416, _883414), _883418), hAPP(hAPP(c_COMBB(tc_fun(_883420, _883414), _883414, _883416), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883420, _883414), _883422)), _883424)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883420, _883414), _883422), hAPP(hAPP(c_COMBB(tc_fun(_883416, _883414), _883414, _883420), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883416, _883414), _883418)), hAPP(c_COMBC(_883416, _883420, _883414), _883424))))], (6339 ^ _782464) ^ [_883623, _883625] : [class_Enum_Oenum(_883623), 6342 ^ _782464 : [(6343 ^ _782464) ^ [] : [hBOOL(hAPP(_883625, 6344 ^ [_883623, _883625])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883623), _883625)))], (6350 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883623), _883625)), 6353 ^ _782464 : [(6354 ^ _782464) ^ [_883841] : [-(hBOOL(hAPP(_883625, _883841)))]]]]], (6356 ^ _782464) ^ [_883876, _883878] : [class_Enum_Oenum(_883876), 6359 ^ _782464 : [(6360 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883876), _883878)), 6363 ^ _782464 : [(6364 ^ _782464) ^ [_884002] : [-(hBOOL(hAPP(_883878, _884002)))]]], (6366 ^ _782464) ^ [] : [hBOOL(hAPP(_883878, 6367 ^ [_883876, _883878])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883876), _883878)))]]], (6373 ^ _782464) ^ [_884129, _884131] : [class_Orderings_Owellorder(_884129), 6378 ^ _782464 : [(6379 ^ _782464) ^ [_884223] : [hBOOL(hAPP(_884131, _884223))]], -(hBOOL(hAPP(_884131, c_Orderings_Oord__class_OLeast(_884129, _884131))))], (6383 ^ _782464) ^ [_884283, _884285, _884287, _884289, _884291] : [class_Orderings_Oorder(_884283), class_Orderings_Olinorder(_884285), c_Orderings_Oorder__class_Ostrict__mono(_884285, _884283, _884287), 6394 ^ _782464 : [(6395 ^ _782464) ^ [] : [hAPP(_884287, _884289) = hAPP(_884287, _884291), -(_884289 = _884291)], (6401 ^ _782464) ^ [] : [_884289 = _884291, -(hAPP(_884287, _884289) = hAPP(_884287, _884291))]]], (6417 ^ _782464) ^ [_884924, _884926, _884928, _884930, _884932] : [6419 ^ _782464 : [(6420 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_884928), 6418 ^ [_884924, _884926, _884928, _884930, _884932]), _884930)))], (6422 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884924, tc_HOL_Obool)), _884926), hAPP(_884932, 6418 ^ [_884924, _884926, _884928, _884930, _884932])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884924, tc_HOL_Obool)), _884926), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884928, tc_fun(_884924, tc_HOL_Obool)), _884930), _884932))))], (6407 ^ _782464) ^ [_884666, _884668, _884670, _884672, _884674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884666, tc_HOL_Obool)), _884668), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884670, tc_fun(_884666, tc_HOL_Obool)), _884672), _884674))), 6410 ^ _782464 : [(6411 ^ _782464) ^ [_884799] : [hBOOL(hAPP(hAPP(c_member(_884670), _884799), _884672)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884666, tc_HOL_Obool)), _884668), hAPP(_884674, _884799))))]]], (6436 ^ _782464) ^ [_885469, _885471, _885473, _885475, _885477] : [6438 ^ _782464 : [(6439 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885471), 6437 ^ [_885469, _885471, _885473, _885475, _885477]), _885473)))], (6441 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885469, tc_HOL_Obool)), hAPP(_885475, 6437 ^ [_885469, _885471, _885473, _885475, _885477])), _885477))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885469, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_885471, tc_fun(_885469, tc_HOL_Obool)), _885473), _885475)), _885477)))], (6426 ^ _782464) ^ [_885211, _885213, _885215, _885217, _885219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885211, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_885213, tc_fun(_885211, tc_HOL_Obool)), _885215), _885217)), _885219)), 6429 ^ _782464 : [(6430 ^ _782464) ^ [_885344] : [hBOOL(hAPP(hAPP(c_member(_885213), _885344), _885215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885211, tc_HOL_Obool)), hAPP(_885217, _885344)), _885219)))]]], (6445 ^ _782464) ^ [_885732, _885734, _885736] : [class_Orderings_Owellorder(_885732), hBOOL(hAPP(_885734, _885736)), -(hBOOL(hAPP(_885734, c_Orderings_Oord__class_OLeast(_885732, _885734))))], (6455 ^ _782464) ^ [_885877, _885879, _885881, _885883, _885885] : [class_Complete__Lattice_Ocomplete__lattice(_885877), 6458 ^ _782464 : [(6469 ^ _782464) ^ [] : [6471 ^ _782464 : [(6472 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885881), 6470 ^ [_885877, _885879, _885881, _885883, _885885]), _885883)))], (6474 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885877), _885879), hAPP(_885885, 6470 ^ [_885877, _885879, _885881, _885883, _885885])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885877), _885879), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_885881, _885877), _885883), _885885))))], (6459 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885877), _885879), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_885881, _885877), _885883), _885885))), 6462 ^ _782464 : [(6463 ^ _782464) ^ [_886058] : [hBOOL(hAPP(hAPP(c_member(_885881), _886058), _885883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885877), _885879), hAPP(_885885, _886058))))]]]]], (6478 ^ _782464) ^ [_886371, _886373, _886375, _886377, _886379] : [class_Complete__Lattice_Ocomplete__lattice(_886371), 6481 ^ _782464 : [(6492 ^ _782464) ^ [] : [6494 ^ _782464 : [(6495 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886373), 6493 ^ [_886371, _886373, _886375, _886377, _886379]), _886375)))], (6497 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886371), hAPP(_886377, 6493 ^ [_886371, _886373, _886375, _886377, _886379])), _886379))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886371), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_886373, _886371), _886375), _886377)), _886379)))], (6482 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886371), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_886373, _886371), _886375), _886377)), _886379)), 6485 ^ _782464 : [(6486 ^ _782464) ^ [_886552] : [hBOOL(hAPP(hAPP(c_member(_886373), _886552), _886375)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886371), hAPP(_886377, _886552)), _886379)))]]]]], (6501 ^ _782464) ^ [_886892, _886894, _886896, _886898, _886900, _886902] : [c_Predicate_Oinv__imagep(_886892, _886894, _886896, _886898, _886900, _886902), -(hBOOL(hAPP(hAPP(_886896, hAPP(_886898, _886900)), hAPP(_886898, _886902))))], (6507 ^ _782464) ^ [_887003, _887005, _887007, _887009, _887011, _887013] : [hBOOL(hAPP(hAPP(_887007, hAPP(_887009, _887011)), hAPP(_887009, _887013))), -(c_Predicate_Oinv__imagep(_887003, _887005, _887007, _887009, _887011, _887013))], (6513 ^ _782464) ^ [_887120, _887122, _887124] : [class_Orderings_Oorder(_887120), hBOOL(hAPP(_887122, _887124)), 6523 ^ _782464 : [(6524 ^ _782464) ^ [] : [-(hBOOL(hAPP(_887122, 6522 ^ [_887120, _887122, _887124])))], (6526 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887120), _887124), 6522 ^ [_887120, _887122, _887124]))]], -(c_Orderings_Oord__class_OLeast(_887120, _887122) = _887124)], (6530 ^ _782464) ^ [_887409, _887411, _887413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887409, tc_HOL_Obool)), _887411), _887413)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887409, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_887409), _887411)), hAPP(c_Set_OPow(_887409), _887413))))], (6536 ^ _782464) ^ [_887554, _887556, _887558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887554, tc_HOL_Obool), tc_HOL_Obool)), _887556), _887558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887554, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_887554, tc_HOL_Obool), _887558)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_887554, tc_HOL_Obool), _887556))))], (6542 ^ _782464) ^ [_887703, _887705, _887707, _887709, _887711] : [class_Complete__Lattice_Ocomplete__lattice(_887703), hBOOL(hAPP(hAPP(c_member(_887705), _887707), _887709)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887703), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_887705, _887703), _887709), _887711)), hAPP(_887711, _887707))))], (6552 ^ _782464) ^ [_887894, _887896, _887898, _887900, _887902] : [class_Complete__Lattice_Ocomplete__lattice(_887894), hBOOL(hAPP(hAPP(c_member(_887896), _887898), _887900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887894), hAPP(_887902, _887898)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_887896, _887894), _887900), _887902))))], (6562 ^ _782464) ^ [_888085, _888087, _888089, _888091, _888093] : [class_Orderings_Olinorder(_888085), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888085, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_888085, _888087), _888089)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_888085, _888091), _888093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888085), _888089), _888087))), 6573 ^ _782464 : [(6574 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888085), _888091), _888087)))], (6576 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888085), _888089), _888093)))]]], (6578 ^ _782464) ^ [_888366, _888368] : [class_Orderings_Olinorder(_888366), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888366, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_888366), _888368)) = hAPP(c_SetInterval_Oord__class_OatMost(_888366), _888368))], (6584 ^ _782464) ^ [_888477, _888479] : [class_Orderings_Olinorder(_888477), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888477, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888477), _888479)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888477), _888479))], (6590 ^ _782464) ^ [_888588, _888590, _888592, _888594, _888596] : [class_Orderings_Oorder(_888588), 6593 ^ _782464 : [(6594 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888588, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_888588, _888590, _888592)), c_SetInterval_Oord__class_OatLeastAtMost(_888588, _888594, _888596))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888588), _888590), _888592)), 6601 ^ _782464 : [(6602 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888588), _888594), _888590)))], (6604 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888588), _888592), _888596)))]]], (6606 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888588, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_888588, _888590, _888592)), c_SetInterval_Oord__class_OatLeastAtMost(_888588, _888594, _888596)))), 6607 ^ _782464 : [(6608 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888588), _888590), _888592)))], (6610 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888588), _888594), _888590)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888588), _888592), _888596))]]]]], (6618 ^ _782464) ^ [_889091, _889093] : [class_Orderings_Olinorder(_889091), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_889091, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_889091), _889093)) = hAPP(c_SetInterval_Oord__class_OatLeast(_889091), _889093))], (6624 ^ _782464) ^ [_889202, _889204] : [class_Orderings_Olinorder(_889202), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_889202, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_889202), _889204)) = hAPP(c_SetInterval_Oord__class_OlessThan(_889202), _889204))], (6630 ^ _782464) ^ [_889313, _889315, _889317] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_889313, tc_HOL_Obool), tc_HOL_Obool)), _889315), _889317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889313, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_889313, tc_HOL_Obool), _889315)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_889313, tc_HOL_Obool), _889317))))], (6636 ^ _782464) ^ [_889462, _889464, _889466, _889468] : [_889462 = _889464, 6641 ^ _782464 : [(6642 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889466), _889468), _889462)))], (6644 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889466), _889468), _889464)))]], 6645 ^ _782464 : [(6646 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889466), _889468), _889462))], (6648 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889466), _889468), _889464))]]], (6650 ^ _782464) ^ [_889725, _889727, _889729, _889731, _889733, _889735, _889737, _889739] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_889725, tc_fun(_889727, tc_fun(_889729, tc_HOL_Obool))), _889731), _889733), _889735), _889737)), -(hBOOL(hAPP(hAPP(hAPP(_889733, _889739), _889735), _889737))), hBOOL(hAPP(hAPP(c_member(_889725), _889739), _889731))], (6660 ^ _782464) ^ [_889952, _889954, _889956, _889958, _889960, _889962, _889964, _889966] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_889952, tc_fun(_889954, tc_fun(_889956, tc_HOL_Obool))), _889958), _889960), _889962), _889964)), hBOOL(hAPP(hAPP(c_member(_889952), _889966), _889958)), -(hBOOL(hAPP(hAPP(hAPP(_889960, _889966), _889962), _889964)))], (6670 ^ _782464) ^ [_890175, _890177, _890179, _890181, _890183, _890185, _890187, _890189] : [hBOOL(hAPP(hAPP(c_member(_890175), _890177), _890179)), hBOOL(hAPP(hAPP(hAPP(_890181, _890177), _890183), _890185)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_890175, tc_fun(_890187, tc_fun(_890189, tc_HOL_Obool))), _890179), _890181), _890183), _890185)))], (6680 ^ _782464) ^ [_890398, _890400, _890402, _890404] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890398, tc_HOL_Obool)), _890400), _890402)), hBOOL(hAPP(hAPP(c_member(_890398), _890404), _890400)), -(hBOOL(hAPP(hAPP(c_member(_890398), _890404), _890402)))], (6690 ^ _782464) ^ [_890579, _890581, _890583] : [-(hBOOL(hAPP(hAPP(c_member(_890579), _890581), _890583))), -(hBOOL(hAPP(hAPP(c_member(_890579), _890581), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_890579, tc_HOL_Obool)), _890583))))], (6696 ^ _782464) ^ [_890639, _890641, _890643, _890645] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_890639, tc_HOL_Obool)), _890641), _890643)), hBOOL(hAPP(hAPP(c_member(_890639), _890645), _890641)), -(hBOOL(hAPP(hAPP(c_member(_890639), _890645), c_Complete__Lattice_OSup__class_OSup(tc_fun(_890639, tc_HOL_Obool), _890643))))], (6706 ^ _782464) ^ [_890836, _890838, _890840, _890842] : [hBOOL(hAPP(hAPP(c_member(_890836), _890838), c_Complete__Lattice_OInf__class_OInf(tc_fun(_890836, tc_HOL_Obool), _890840))), hBOOL(hAPP(hAPP(c_member(tc_fun(_890836, tc_HOL_Obool)), _890842), _890840)), -(hBOOL(hAPP(hAPP(c_member(_890836), _890838), _890842)))], (6716 ^ _782464) ^ [_891033, _891035, _891037, _891039] : [hBOOL(hAPP(hAPP(c_member(_891033), _891035), c_Complete__Lattice_OInf__class_OInf(tc_fun(_891033, tc_HOL_Obool), _891037))), hBOOL(hAPP(hAPP(c_member(tc_fun(_891033, tc_HOL_Obool)), _891039), _891037)), -(hBOOL(hAPP(hAPP(c_member(_891033), _891035), _891039)))], (6726 ^ _782464) ^ [_891230, _891232, _891234] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891230, tc_HOL_Obool)), _891232), _891234)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_891230, tc_HOL_Obool)), _891232), hAPP(c_Set_OPow(_891230), _891234))))], (6732 ^ _782464) ^ [_891359, _891361, _891363, _891365, _891367, _891369] : [hBOOL(hAPP(hAPP(c_member(_891359), _891361), _891363)), hBOOL(hAPP(hAPP(c_member(_891365), _891367), hAPP(_891369, _891361))), -(hBOOL(hAPP(hAPP(c_member(_891365), _891367), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891359, tc_fun(_891365, tc_HOL_Obool)), _891363), _891369))))], (6742 ^ _782464) ^ [_891576, _891578, _891580, _891582, _891584, _891586] : [hBOOL(hAPP(hAPP(c_member(_891576), _891578), _891580)), hBOOL(hAPP(hAPP(_891582, _891578), _891584)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891576, tc_fun(_891586, tc_HOL_Obool)), _891580), _891582), _891584)))], (6752 ^ _782464) ^ [_891773, _891775, _891777, _891779, _891781, _891783] : [hBOOL(hAPP(hAPP(c_member(_891773), _891775), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891777, tc_fun(_891773, tc_HOL_Obool)), _891779), _891781))), hBOOL(hAPP(hAPP(c_member(_891777), _891783), _891779)), -(hBOOL(hAPP(hAPP(c_member(_891773), _891775), hAPP(_891781, _891783))))], (6762 ^ _782464) ^ [_891990, _891992, _891994, _891996, _891998, _892000] : [hBOOL(hAPP(hAPP(c_member(_891990), _891992), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891994, tc_fun(_891990, tc_HOL_Obool)), _891996), _891998))), -(hBOOL(hAPP(hAPP(c_member(_891990), _891992), hAPP(_891998, _892000)))), hBOOL(hAPP(hAPP(c_member(_891994), _892000), _891996))], (6772 ^ _782464) ^ [_892211, _892213, _892215, _892217, _892219, _892221] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892211, tc_fun(_892213, tc_HOL_Obool)), _892215), _892217), _892219)), -(hBOOL(hAPP(hAPP(_892217, _892221), _892219))), hBOOL(hAPP(hAPP(c_member(_892211), _892221), _892215))], (6782 ^ _782464) ^ [_892412, _892414, _892416, _892418, _892420, _892422] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892412, tc_fun(_892414, tc_HOL_Obool)), _892416), _892418), _892420)), hBOOL(hAPP(hAPP(c_member(_892412), _892422), _892416)), -(hBOOL(hAPP(hAPP(_892418, _892422), _892420)))], (6792 ^ _782464) ^ [_892609, _892611, _892613, _892615, _892617, _892619] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892609, tc_fun(_892611, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892613, tc_fun(_892609, tc_HOL_Obool)), _892615), _892617)), _892619) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892613, tc_fun(_892611, tc_HOL_Obool)), _892615), hAPP(hAPP(c_COMBC(_892613, tc_fun(_892609, tc_fun(_892611, tc_HOL_Obool)), tc_fun(_892611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892609, tc_HOL_Obool), tc_fun(tc_fun(_892609, tc_fun(_892611, tc_HOL_Obool)), tc_fun(_892611, tc_HOL_Obool)), _892613), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892609, tc_fun(_892611, tc_HOL_Obool))), _892617)), _892619)))], (6794 ^ _782464) ^ [_892728, _892730, _892732, _892734, _892736, _892738] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892728, tc_fun(_892730, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892732, tc_fun(_892728, tc_HOL_Obool)), _892734), _892736)), _892738) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892732, tc_fun(_892730, tc_HOL_Obool)), _892734), hAPP(hAPP(c_COMBC(_892732, tc_fun(_892728, tc_fun(_892730, tc_HOL_Obool)), tc_fun(_892730, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892728, tc_HOL_Obool), tc_fun(tc_fun(_892728, tc_fun(_892730, tc_HOL_Obool)), tc_fun(_892730, tc_HOL_Obool)), _892732), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892728, tc_fun(_892730, tc_HOL_Obool))), _892736)), _892738)))], (6796 ^ _782464) ^ [_892847, _892849, _892851, _892853, _892855, _892857] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892847, tc_fun(_892849, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892851, tc_fun(_892847, tc_HOL_Obool)), _892853), _892855)), _892857) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892851, tc_fun(_892849, tc_HOL_Obool)), _892853), hAPP(hAPP(c_COMBC(_892851, tc_fun(_892847, tc_fun(_892849, tc_HOL_Obool)), tc_fun(_892849, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892847, tc_HOL_Obool), tc_fun(tc_fun(_892847, tc_fun(_892849, tc_HOL_Obool)), tc_fun(_892849, tc_HOL_Obool)), _892851), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892847, tc_fun(_892849, tc_HOL_Obool))), _892855)), _892857)))], (6815 ^ _782464) ^ [_893426, _893428, _893430, _893432, _893434] : [6817 ^ _782464 : [(6818 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893428), 6816 ^ [_893426, _893428, _893430, _893432, _893434]), _893430)))], (6821 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893426), 6819 ^ [_893426, _893428, _893430, _893432, _893434]), hAPP(_893432, 6816 ^ [_893426, _893428, _893430, _893432, _893434]))))], (6823 ^ _782464) ^ [] : [hBOOL(hAPP(_893434, 6819 ^ [_893426, _893428, _893430, _893432, _893434]))]], 6824 ^ _782464 : [(6825 ^ _782464) ^ [_893736] : [hBOOL(hAPP(hAPP(c_member(_893426), _893736), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893428, tc_fun(_893426, tc_HOL_Obool)), _893430), _893432))), -(hBOOL(hAPP(_893434, _893736)))]]], (6798 ^ _782464) ^ [_892990, _892992, _892994, _892996, _892998] : [6800 ^ _782464 : [(6801 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_892990), 6799 ^ [_892990, _892992, _892994, _892996, _892998]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892992, tc_fun(_892990, tc_HOL_Obool)), _892994), _892996))))], (6803 ^ _782464) ^ [] : [hBOOL(hAPP(_892998, 6799 ^ [_892990, _892992, _892994, _892996, _892998]))]], 6804 ^ _782464 : [(6805 ^ _782464) ^ [_893212] : [hBOOL(hAPP(hAPP(c_member(_892992), _893212), _892994)), 6808 ^ _782464 : [(6809 ^ _782464) ^ [_893309] : [hBOOL(hAPP(hAPP(c_member(_892990), _893309), hAPP(_892996, _893212))), -(hBOOL(hAPP(_892998, _893309)))]]]]], (6831 ^ _782464) ^ [_893871, _893873, _893875, _893877, _893879, _893881] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893871, tc_fun(_893873, tc_HOL_Obool)), _893875), hAPP(hAPP(c_COMBC(_893871, tc_fun(_893877, tc_fun(_893873, tc_HOL_Obool)), tc_fun(_893873, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_893877, tc_HOL_Obool), tc_fun(tc_fun(_893877, tc_fun(_893873, tc_HOL_Obool)), tc_fun(_893873, tc_HOL_Obool)), _893871), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893877, tc_fun(_893873, tc_HOL_Obool))), _893879)), _893881)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893877, tc_fun(_893873, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893871, tc_fun(_893877, tc_HOL_Obool)), _893875), _893879)), _893881))], (6833 ^ _782464) ^ [_893990, _893992, _893994, _893996, _893998, _894000] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893990, tc_fun(_893992, tc_HOL_Obool)), _893994), hAPP(hAPP(c_COMBC(_893990, tc_fun(_893996, tc_fun(_893992, tc_HOL_Obool)), tc_fun(_893992, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_893996, tc_HOL_Obool), tc_fun(tc_fun(_893996, tc_fun(_893992, tc_HOL_Obool)), tc_fun(_893992, tc_HOL_Obool)), _893990), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893996, tc_fun(_893992, tc_HOL_Obool))), _893998)), _894000)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893996, tc_fun(_893992, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893990, tc_fun(_893996, tc_HOL_Obool)), _893994), _893998)), _894000))], (6835 ^ _782464) ^ [_894109, _894111] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_894109, tc_HOL_Obool), hAPP(c_Set_OPow(_894109), _894111)) = _894111)], (6847 ^ _782464) ^ [_894387, _894389, _894391, _894393, _894395] : [6849 ^ _782464 : [(6850 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894387), 6848 ^ [_894387, _894389, _894391, _894393, _894395]), _894391)))], (6852 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_894393, 6848 ^ [_894387, _894389, _894391, _894393, _894395]), _894395))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894387, tc_fun(_894389, tc_HOL_Obool)), _894391), _894393), _894395)))], (6837 ^ _782464) ^ [_894169, _894171, _894173, _894175, _894177] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894169, tc_fun(_894171, tc_HOL_Obool)), _894173), _894175), _894177)), 6840 ^ _782464 : [(6841 ^ _782464) ^ [_894278] : [hBOOL(hAPP(hAPP(c_member(_894169), _894278), _894173)), -(hBOOL(hAPP(hAPP(_894175, _894278), _894177)))]]], (6856 ^ _782464) ^ [_894634, _894636, _894638, _894640, _894642] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_894634, tc_fun(_894636, tc_HOL_Obool)), _894638), _894640), _894642)), 6860 ^ _782464 : [(6861 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894634), 6859 ^ [_894634, _894636, _894638, _894640, _894642]), _894638)))], (6863 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_894640, 6859 ^ [_894634, _894636, _894638, _894640, _894642]), _894642)))]]], (6865 ^ _782464) ^ [_894822, _894824, _894826, _894828, _894830] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_894822, tc_fun(_894824, tc_HOL_Obool)), _894826), _894828), _894830))), 6866 ^ _782464 : [(6867 ^ _782464) ^ [_894894] : [hBOOL(hAPP(hAPP(c_member(_894822), _894894), _894826)), hBOOL(hAPP(hAPP(_894828, _894894), _894830))]]], (6875 ^ _782464) ^ [_895046, _895048, _895050] : [hBOOL(hAPP(hAPP(c_member(_895046), _895048), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895046, tc_HOL_Obool)), _895050))), hBOOL(hAPP(hAPP(c_member(_895046), _895048), _895050))], (6881 ^ _782464) ^ [_895170, _895172, _895174] : [hBOOL(hAPP(hAPP(c_member(_895170), _895172), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895170, tc_HOL_Obool)), _895174))), hBOOL(hAPP(hAPP(c_member(_895170), _895172), _895174))], (6887 ^ _782464) ^ [_895294, _895296, _895298, _895300] : [_895294 = _895296, hBOOL(hAPP(hAPP(c_member(_895298), _895296), _895300)), -(hBOOL(hAPP(hAPP(c_member(_895298), _895294), _895300)))], (6897 ^ _782464) ^ [_895459, _895461, _895463, _895465] : [_895459 = _895461, 6900 ^ _782464 : [(6901 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895463), _895459), _895465)), -(hBOOL(hAPP(hAPP(c_member(_895463), _895461), _895465)))], (6907 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895463), _895461), _895465)), -(hBOOL(hAPP(hAPP(c_member(_895463), _895459), _895465)))]]], (6913 ^ _782464) ^ [_895720, _895722, _895724, _895726] : [_895720 = _895722, 6916 ^ _782464 : [(6917 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895724), _895726), _895720)), -(hBOOL(hAPP(hAPP(c_member(_895724), _895726), _895722)))], (6923 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895724), _895726), _895722)), -(hBOOL(hAPP(hAPP(c_member(_895724), _895726), _895720)))]]], (6929 ^ _782464) ^ [_895999, _896001, _896003] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895999, tc_HOL_Obool)), _896001) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895999, tc_HOL_Obool)), _896003), -(_896001 = _896003)], (6935 ^ _782464) ^ [_896106, _896108, _896110] : [_896108 = _896110, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896106, tc_HOL_Obool)), _896108) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896106, tc_HOL_Obool)), _896110))], (6941 ^ _782464) ^ [_896237, _896239, _896241] : [hBOOL(hAPP(hAPP(c_member(_896237), _896239), hAPP(c_fequal, _896241))), -(_896239 = _896241)], (6947 ^ _782464) ^ [_896332, _896334, _896336] : [_896334 = _896336, -(hBOOL(hAPP(hAPP(c_member(_896332), _896334), hAPP(c_fequal, _896336))))], (6953 ^ _782464) ^ [_896451, _896453, _896455] : [hBOOL(hAPP(hAPP(c_member(_896451), _896453), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896451, tc_HOL_Obool)), _896455))), hBOOL(hAPP(hAPP(c_member(_896451), _896453), _896455))], (6959 ^ _782464) ^ [_896569, _896571, _896573] : [-(hBOOL(hAPP(hAPP(c_member(_896569), _896571), _896573))), -(hBOOL(hAPP(hAPP(c_member(_896569), _896571), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896569, tc_HOL_Obool)), _896573))))], (6965 ^ _782464) ^ [_896649, _896651, _896653] : [hBOOL(hAPP(hAPP(c_member(_896649), _896651), _896653)), -(hBOOL(hAPP(_896653, _896651)))], (6971 ^ _782464) ^ [_896742, _896744, _896746] : [hBOOL(hAPP(_896746, _896744)), -(hBOOL(hAPP(hAPP(c_member(_896742), _896744), _896746)))], (6977 ^ _782464) ^ [_896841, _896843] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896841, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896841, tc_HOL_Obool)), _896843)) = _896843)], (6979 ^ _782464) ^ [_896882, _896884] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_896882, tc_HOL_Obool)), _896884), hAPP(c_Set_OPow(_896882), _896884))))], (6981 ^ _782464) ^ [_896922, _896924, _896926] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_896922, tc_HOL_Obool)), _896924), _896926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896922, tc_HOL_Obool)), _896924), c_Complete__Lattice_OSup__class_OSup(tc_fun(_896922, tc_HOL_Obool), _896926))))], (6987 ^ _782464) ^ [_897053, _897055, _897057] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_897053, tc_HOL_Obool)), _897055), _897057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897053, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_897053, tc_HOL_Obool), _897057)), _897055)))], (6993 ^ _782464) ^ [_897184, _897186, _897188, _897190] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_897184, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897186, tc_fun(_897184, tc_HOL_Obool)), _897188), _897190)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897186, tc_fun(_897184, tc_HOL_Obool)), _897188), hAPP(hAPP(c_COMBB(tc_fun(_897184, tc_HOL_Obool), tc_fun(_897184, tc_HOL_Obool), _897186), c_Groups_Ouminus__class_Ouminus(tc_fun(_897184, tc_HOL_Obool))), _897190)))], (6995 ^ _782464) ^ [_897266, _897268, _897270, _897272] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_897266, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897268, tc_fun(_897266, tc_HOL_Obool)), _897270), _897272)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897268, tc_fun(_897266, tc_HOL_Obool)), _897270), hAPP(hAPP(c_COMBB(tc_fun(_897266, tc_HOL_Obool), tc_fun(_897266, tc_HOL_Obool), _897268), c_Groups_Ouminus__class_Ouminus(tc_fun(_897266, tc_HOL_Obool))), _897272)))], (6997 ^ _782464) ^ [_897348, _897350] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_897348, tc_HOL_Obool), _897350) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897348, tc_HOL_Obool), tc_fun(_897348, tc_HOL_Obool)), _897350), c_COMBI(tc_fun(_897348, tc_HOL_Obool))))], (6999 ^ _782464) ^ [_897399, _897401, _897403, _897405] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_897399, tc_HOL_Obool), tc_fun(_897401, tc_HOL_Obool)), _897403), hAPP(hAPP(c_COMBC(tc_fun(_897399, tc_HOL_Obool), tc_fun(_897399, tc_fun(_897401, tc_HOL_Obool)), tc_fun(_897401, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897399, tc_fun(_897401, tc_HOL_Obool))), _897405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897399, tc_fun(_897401, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897399, tc_HOL_Obool), _897403)), _897405))], (7001 ^ _782464) ^ [_897489, _897491, _897493, _897495] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897489, tc_HOL_Obool), tc_fun(_897491, tc_HOL_Obool)), _897493), hAPP(hAPP(c_COMBC(tc_fun(_897489, tc_HOL_Obool), tc_fun(_897489, tc_fun(_897491, tc_HOL_Obool)), tc_fun(_897491, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897489, tc_fun(_897491, tc_HOL_Obool))), _897495)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897489, tc_fun(_897491, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897489, tc_HOL_Obool), _897493)), _897495))], (7003 ^ _782464) ^ [_897579, _897581, _897583, _897585] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897579, tc_fun(_897581, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897579, tc_HOL_Obool), _897583)), _897585) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_897579, tc_HOL_Obool), tc_fun(_897581, tc_HOL_Obool)), _897583), hAPP(hAPP(c_COMBC(tc_fun(_897579, tc_HOL_Obool), tc_fun(_897579, tc_fun(_897581, tc_HOL_Obool)), tc_fun(_897581, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897579, tc_fun(_897581, tc_HOL_Obool))), _897585)))], (7005 ^ _782464) ^ [_897669, _897671, _897673, _897675] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897669, tc_fun(_897671, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897669, tc_HOL_Obool), _897673)), _897675) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897669, tc_HOL_Obool), tc_fun(_897671, tc_HOL_Obool)), _897673), hAPP(hAPP(c_COMBC(tc_fun(_897669, tc_HOL_Obool), tc_fun(_897669, tc_fun(_897671, tc_HOL_Obool)), tc_fun(_897671, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897669, tc_fun(_897671, tc_HOL_Obool))), _897675)))], (7007 ^ _782464) ^ [_897777, _897779, _897781] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_897777, tc_HOL_Obool)), _897779), hAPP(c_Set_OPow(_897777), _897781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897777, tc_HOL_Obool)), _897779), _897781)))], (7013 ^ _782464) ^ [_897902, _897904, _897906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897902, tc_HOL_Obool)), _897904), _897906)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_897902, tc_HOL_Obool)), _897904), hAPP(c_Set_OPow(_897902), _897906))))], (7019 ^ _782464) ^ [_898033, _898035, _898037] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_898033, tc_HOL_Obool)), _898035), hAPP(c_Set_OPow(_898033), _898037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898033, tc_HOL_Obool)), _898035), _898037)))], (7025 ^ _782464) ^ [_898180, _898182, _898184] : [hAPP(hAPP(c_COMBC(_898180, tc_fun(_898180, tc_HOL_Obool), tc_HOL_Obool), c_member(_898180)), _898182) = hAPP(hAPP(c_COMBC(_898180, tc_fun(_898180, tc_HOL_Obool), tc_HOL_Obool), c_member(_898180)), _898184), -(_898182 = _898184)], (7031 ^ _782464) ^ [_898315, _898317, _898319] : [_898317 = _898319, -(hAPP(hAPP(c_COMBC(_898315, tc_fun(_898315, tc_HOL_Obool), tc_HOL_Obool), c_member(_898315)), _898317) = hAPP(hAPP(c_COMBC(_898315, tc_fun(_898315, tc_HOL_Obool), tc_HOL_Obool), c_member(_898315)), _898319))], (7047 ^ _782464) ^ [_898723, _898725, _898727, _898729, _898731] : [7049 ^ _782464 : [(7050 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898727), 7048 ^ [_898723, _898725, _898727, _898729, _898731]), _898729)))], (7052 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898723), _898725), hAPP(_898731, 7048 ^ [_898723, _898725, _898727, _898729, _898731])))]], -(hBOOL(hAPP(hAPP(c_member(_898723), _898725), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_898727, tc_fun(_898723, tc_HOL_Obool)), _898729), _898731))))], (7037 ^ _782464) ^ [_898480, _898482, _898484, _898486, _898488] : [hBOOL(hAPP(hAPP(c_member(_898480), _898482), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_898484, tc_fun(_898480, tc_HOL_Obool)), _898486), _898488))), 7040 ^ _782464 : [(7041 ^ _782464) ^ [_898604] : [hBOOL(hAPP(hAPP(c_member(_898484), _898604), _898486)), -(hBOOL(hAPP(hAPP(c_member(_898480), _898482), hAPP(_898488, _898604))))]]], (7056 ^ _782464) ^ [_898995, _898997, _898999, _899001, _899003] : [hBOOL(hAPP(hAPP(c_member(_898995), _898997), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_898999, tc_fun(_898995, tc_HOL_Obool)), _899001), _899003))), 7060 ^ _782464 : [(7061 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898999), 7059 ^ [_898995, _898997, _898999, _899001, _899003]), _899001)))], (7063 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898995), _898997), hAPP(_899003, 7059 ^ [_898995, _898997, _898999, _899001, _899003]))))]]], (7065 ^ _782464) ^ [_899203, _899205, _899207, _899209, _899211] : [-(hBOOL(hAPP(hAPP(c_member(_899203), _899205), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_899207, tc_fun(_899203, tc_HOL_Obool)), _899209), _899211)))), 7066 ^ _782464 : [(7067 ^ _782464) ^ [_899285] : [hBOOL(hAPP(hAPP(c_member(_899207), _899285), _899209)), hBOOL(hAPP(hAPP(c_member(_899203), _899205), hAPP(_899211, _899285)))]]], (7075 ^ _782464) ^ [_899452, _899454, _899456] : [class_Complete__Lattice_Ocomplete__lattice(_899452), hBOOL(hAPP(hAPP(c_member(_899452), _899454), _899456)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899452), _899454), c_Complete__Lattice_OSup__class_OSup(_899452, _899456))))], (7085 ^ _782464) ^ [_899617, _899619, _899621] : [class_Complete__Lattice_Ocomplete__lattice(_899617), hBOOL(hAPP(hAPP(c_member(_899617), _899619), _899621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899617), c_Complete__Lattice_OInf__class_OInf(_899617, _899621)), _899619)))], (7095 ^ _782464) ^ [_899782, _899784] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_899782, tc_HOL_Obool), _899784) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_899782, tc_HOL_Obool), tc_fun(_899782, tc_HOL_Obool)), _899784), c_COMBI(tc_fun(_899782, tc_HOL_Obool))))], (7097 ^ _782464) ^ [_899851, _899853, _899855] : [hBOOL(hAPP(c_Predicate_OPowp(_899851, hAPP(hAPP(c_COMBC(_899851, tc_fun(_899851, tc_HOL_Obool), tc_HOL_Obool), c_member(_899851)), _899853)), _899855)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_899851, tc_HOL_Obool)), _899855), hAPP(c_Set_OPow(_899851), _899853))))], (7103 ^ _782464) ^ [_899996, _899998, _900000] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_899996, tc_HOL_Obool)), _900000), hAPP(c_Set_OPow(_899996), _899998))), -(hBOOL(hAPP(c_Predicate_OPowp(_899996, hAPP(hAPP(c_COMBC(_899996, tc_fun(_899996, tc_HOL_Obool), tc_HOL_Obool), c_member(_899996)), _899998)), _900000)))], (7109 ^ _782464) ^ [_900147, _900149, _900151, _900153] : [-(hAPP(c_Set_OPow(_900147), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_900149, tc_fun(_900147, tc_HOL_Obool)), _900151), _900153)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_900149, tc_fun(tc_fun(_900147, tc_HOL_Obool), tc_HOL_Obool)), _900151), hAPP(hAPP(c_COMBB(tc_fun(_900147, tc_HOL_Obool), tc_fun(tc_fun(_900147, tc_HOL_Obool), tc_HOL_Obool), _900149), c_Set_OPow(_900147)), _900153)))], (7111 ^ _782464) ^ [_900229, _900231] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_900229, tc_HOL_Obool), tc_HOL_Obool)), _900231), hAPP(c_Set_OPow(_900229), c_Complete__Lattice_OSup__class_OSup(tc_fun(_900229, tc_HOL_Obool), _900231)))))], (7113 ^ _782464) ^ [_900278, _900280, _900282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900278, tc_HOL_Obool)), _900280), _900282)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900278, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900278, tc_HOL_Obool)), _900282)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900278, tc_HOL_Obool)), _900280))))], (7119 ^ _782464) ^ [_900447, _900449, _900451] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900447, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900447, tc_HOL_Obool)), _900449)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900447, tc_HOL_Obool)), _900451))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900447, tc_HOL_Obool)), _900451), _900449)))], (7125 ^ _782464) ^ [_900594, _900596, _900598] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900594, tc_HOL_Obool)), _900598), _900596)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900594, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900594, tc_HOL_Obool)), _900596)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900594, tc_HOL_Obool)), _900598))))], (7131 ^ _782464) ^ [_900747, _900749, _900751, _900753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900747, tc_HOL_Obool)), _900749), _900751)), hBOOL(hAPP(hAPP(c_member(_900747), _900753), _900749)), -(hBOOL(hAPP(hAPP(c_member(_900747), _900753), _900751)))], (7141 ^ _782464) ^ [_900932, _900934, _900936, _900938] : [hBOOL(hAPP(hAPP(c_member(_900932), _900934), _900936)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900932, tc_HOL_Obool)), _900936), _900938)), -(hBOOL(hAPP(hAPP(c_member(_900932), _900934), _900938)))], (7151 ^ _782464) ^ [_901117, _901119, _901121, _901123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901117, tc_HOL_Obool)), _901119), _901121)), hBOOL(hAPP(hAPP(c_member(_901117), _901123), _901119)), -(hBOOL(hAPP(hAPP(c_member(_901117), _901123), _901121)))], (7161 ^ _782464) ^ [_901320, _901322, _901324] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901320, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_901320, tc_fun(_901320, tc_HOL_Obool), tc_HOL_Obool), c_member(_901320)), _901322)), hAPP(hAPP(c_COMBC(_901320, tc_fun(_901320, tc_HOL_Obool), tc_HOL_Obool), c_member(_901320)), _901324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901320, tc_HOL_Obool)), _901322), _901324)))], (7167 ^ _782464) ^ [_901495, _901497, _901499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901495, tc_HOL_Obool)), _901497), _901499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901495, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_901495, tc_fun(_901495, tc_HOL_Obool), tc_HOL_Obool), c_member(_901495)), _901497)), hAPP(hAPP(c_COMBC(_901495, tc_fun(_901495, tc_HOL_Obool), tc_HOL_Obool), c_member(_901495)), _901499))))], (7173 ^ _782464) ^ [_901676, _901678, _901680, _901682, _901684] : [hBOOL(hAPP(hAPP(c_member(_901676), _901678), _901680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901682, tc_HOL_Obool)), hAPP(_901684, _901678)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_901676, tc_fun(_901682, tc_HOL_Obool)), _901680), _901684))))], (7179 ^ _782464) ^ [_901823, _901825, _901827, _901829, _901831] : [hBOOL(hAPP(hAPP(c_member(_901823), _901825), _901827)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901829, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_901823, tc_fun(_901829, tc_HOL_Obool)), _901827), _901831)), hAPP(_901831, _901825))))], (7185 ^ _782464) ^ [_901970, _901972, _901974] : [class_Complete__Lattice_Ocomplete__lattice(_901970), 7188 ^ _782464 : [(7199 ^ _782464) ^ [] : [7201 ^ _782464 : [(7202 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901970), 7200 ^ [_901970, _901972, _901974]), _901972)))], (7204 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901970), 7200 ^ [_901970, _901972, _901974]), _901974))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901970), c_Complete__Lattice_OSup__class_OSup(_901970, _901972)), _901974)))], (7189 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901970), c_Complete__Lattice_OSup__class_OSup(_901970, _901972)), _901974)), 7192 ^ _782464 : [(7193 ^ _782464) ^ [_902128] : [hBOOL(hAPP(hAPP(c_member(_901970), _902128), _901972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901970), _902128), _901974)))]]]]], (7208 ^ _782464) ^ [_902404, _902406, _902408] : [class_Complete__Lattice_Ocomplete__lattice(_902404), 7211 ^ _782464 : [(7222 ^ _782464) ^ [] : [7224 ^ _782464 : [(7225 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902404), 7223 ^ [_902404, _902406, _902408]), _902408)))], (7227 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902404), _902406), 7223 ^ [_902404, _902406, _902408]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902404), _902406), c_Complete__Lattice_OInf__class_OInf(_902404, _902408))))], (7212 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902404), _902406), c_Complete__Lattice_OInf__class_OInf(_902404, _902408))), 7215 ^ _782464 : [(7216 ^ _782464) ^ [_902562] : [hBOOL(hAPP(hAPP(c_member(_902404), _902562), _902408)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902404), _902406), _902562)))]]]]], (7231 ^ _782464) ^ [_902838, _902840, _902842, _902844] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_902838, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_902840, tc_fun(tc_fun(_902838, tc_HOL_Obool), tc_HOL_Obool)), _902842), hAPP(hAPP(c_COMBB(tc_fun(_902838, tc_HOL_Obool), tc_fun(tc_fun(_902838, tc_HOL_Obool), tc_HOL_Obool), _902840), c_Set_OPow(_902838)), _902844))), hAPP(c_Set_OPow(_902838), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_902840, tc_fun(_902838, tc_HOL_Obool)), _902842), _902844)))))], (7233 ^ _782464) ^ [_902933, _902935, _902937] : [class_Orderings_Oord(_902933), 7236 ^ _782464 : [(7237 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902933), _902935), hAPP(c_SetInterval_Oord__class_OatMost(_902933), _902937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902933), _902935), _902937)))], (7243 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902933), _902935), _902937)), -(hBOOL(hAPP(hAPP(c_member(_902933), _902935), hAPP(c_SetInterval_Oord__class_OatMost(_902933), _902937))))]]], (7249 ^ _782464) ^ [_903201, _903203, _903205] : [class_Orderings_Oord(_903201), 7252 ^ _782464 : [(7253 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903201), _903203), hAPP(c_SetInterval_Oord__class_OatLeast(_903201), _903205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903201), _903205), _903203)))], (7259 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903201), _903205), _903203)), -(hBOOL(hAPP(hAPP(c_member(_903201), _903203), hAPP(c_SetInterval_Oord__class_OatLeast(_903201), _903205))))]]], (7265 ^ _782464) ^ [_903469, _903471, _903473, _903475] : [class_Groups_Ouminus(_903469), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_903471, _903469)), _903473), _903475) = hAPP(c_Groups_Ouminus__class_Ouminus(_903469), hAPP(_903473, _903475)))], (7271 ^ _782464) ^ [_903586, _903588, _903590, _903592] : [class_Groups_Ouminus(_903586), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_903588, _903586)), _903590), _903592) = hAPP(c_Groups_Ouminus__class_Ouminus(_903586), hAPP(_903590, _903592)))], (7277 ^ _782464) ^ [_903730, _903732, _903734, _903736, _903738, _903740] : [hBOOL(hAPP(hAPP(c_member(_903730), _903732), c_SetInterval_Oord_OgreaterThanAtMost(_903730, _903734, _903736, _903738, _903740))), 7280 ^ _782464 : [(7281 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_903736, _903738), _903732)))], (7283 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_903734, _903732), _903740)))]]], (7285 ^ _782464) ^ [_903883, _903885, _903887, _903889, _903891, _903893] : [-(hBOOL(hAPP(hAPP(c_member(_903883), _903885), c_SetInterval_Oord_OgreaterThanAtMost(_903883, _903887, _903889, _903891, _903893)))), hBOOL(hAPP(hAPP(_903889, _903891), _903885)), hBOOL(hAPP(hAPP(_903887, _903885), _903893))], (7295 ^ _782464) ^ [_904103, _904105, _904107, _904109, _904111, _904113] : [hBOOL(hAPP(hAPP(c_member(_904103), _904105), c_SetInterval_Oord_OatLeastLessThan(_904103, _904107, _904109, _904111, _904113))), 7298 ^ _782464 : [(7299 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_904107, _904111), _904105)))], (7301 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_904109, _904105), _904113)))]]], (7303 ^ _782464) ^ [_904256, _904258, _904260, _904262, _904264, _904266] : [-(hBOOL(hAPP(hAPP(c_member(_904256), _904258), c_SetInterval_Oord_OatLeastLessThan(_904256, _904260, _904262, _904264, _904266)))), hBOOL(hAPP(hAPP(_904260, _904264), _904258)), hBOOL(hAPP(hAPP(_904262, _904258), _904266))], (7313 ^ _782464) ^ [_904473, _904475, _904477, _904479, _904481] : [hBOOL(hAPP(hAPP(c_member(_904473), _904475), c_SetInterval_Oord_OgreaterThanLessThan(_904473, _904477, _904479, _904481))), 7316 ^ _782464 : [(7317 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_904477, _904479), _904475)))], (7319 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_904477, _904475), _904481)))]]], (7321 ^ _782464) ^ [_904622, _904624, _904626, _904628, _904630] : [-(hBOOL(hAPP(hAPP(c_member(_904622), _904624), c_SetInterval_Oord_OgreaterThanLessThan(_904622, _904626, _904628, _904630)))), hBOOL(hAPP(hAPP(_904626, _904628), _904624)), hBOOL(hAPP(hAPP(_904626, _904624), _904630))], (7331 ^ _782464) ^ [_904833, _904835, _904837, _904839, _904841] : [hBOOL(hAPP(hAPP(c_member(_904833), _904835), c_SetInterval_Oord_OatLeastAtMost(_904833, _904837, _904839, _904841))), 7334 ^ _782464 : [(7335 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_904837, _904839), _904835)))], (7337 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_904837, _904835), _904841)))]]], (7339 ^ _782464) ^ [_904982, _904984, _904986, _904988, _904990] : [-(hBOOL(hAPP(hAPP(c_member(_904982), _904984), c_SetInterval_Oord_OatLeastAtMost(_904982, _904986, _904988, _904990)))), hBOOL(hAPP(hAPP(_904986, _904988), _904984)), hBOOL(hAPP(hAPP(_904986, _904984), _904990))], (7349 ^ _782464) ^ [_905190, _905192, _905194, _905196] : [hBOOL(hAPP(hAPP(c_member(_905190), _905192), c_SetInterval_Oord_OgreaterThan(_905190, _905194, _905196))), -(hBOOL(hAPP(hAPP(_905194, _905196), _905192)))], (7355 ^ _782464) ^ [_905299, _905301, _905303, _905305] : [hBOOL(hAPP(hAPP(_905303, _905305), _905301)), -(hBOOL(hAPP(hAPP(c_member(_905299), _905301), c_SetInterval_Oord_OgreaterThan(_905299, _905303, _905305))))], (7361 ^ _782464) ^ [_905435, _905437, _905439, _905441] : [hBOOL(hAPP(hAPP(c_member(_905435), _905437), c_SetInterval_Oord_OlessThan(_905435, _905439, _905441))), -(hBOOL(hAPP(hAPP(_905439, _905437), _905441)))], (7367 ^ _782464) ^ [_905544, _905546, _905548, _905550] : [hBOOL(hAPP(hAPP(_905548, _905546), _905550)), -(hBOOL(hAPP(hAPP(c_member(_905544), _905546), c_SetInterval_Oord_OlessThan(_905544, _905548, _905550))))], (7373 ^ _782464) ^ [_905680, _905682, _905684, _905686] : [hBOOL(hAPP(hAPP(c_member(_905680), _905682), c_SetInterval_Oord_OatLeast(_905680, _905684, _905686))), -(hBOOL(hAPP(hAPP(_905684, _905686), _905682)))], (7379 ^ _782464) ^ [_905789, _905791, _905793, _905795] : [hBOOL(hAPP(hAPP(_905793, _905795), _905791)), -(hBOOL(hAPP(hAPP(c_member(_905789), _905791), c_SetInterval_Oord_OatLeast(_905789, _905793, _905795))))], (7385 ^ _782464) ^ [_905925, _905927, _905929, _905931] : [hBOOL(hAPP(hAPP(c_member(_905925), _905927), c_SetInterval_Oord_OatMost(_905925, _905929, _905931))), -(hBOOL(hAPP(hAPP(_905929, _905927), _905931)))], (7391 ^ _782464) ^ [_906034, _906036, _906038, _906040] : [hBOOL(hAPP(hAPP(_906038, _906036), _906040)), -(hBOOL(hAPP(hAPP(c_member(_906034), _906036), c_SetInterval_Oord_OatMost(_906034, _906038, _906040))))], (7397 ^ _782464) ^ [_906149, _906151, _906153] : [class_Lattices_Oboolean__algebra(_906149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906149), _906151), _906153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906149), hAPP(c_Groups_Ouminus__class_Ouminus(_906149), _906153)), hAPP(c_Groups_Ouminus__class_Ouminus(_906149), _906151))))], (7407 ^ _782464) ^ [_906328, _906330, _906332] : [class_Groups_Oordered__ab__group__add(_906328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906328), _906330), _906332)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906328), hAPP(c_Groups_Ouminus__class_Ouminus(_906328), _906332)), hAPP(c_Groups_Ouminus__class_Ouminus(_906328), _906330))))], (7417 ^ _782464) ^ [_906537, _906539, _906541, _906543, _906545, _906547, _906549] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_906537, tc_fun(_906539, tc_fun(_906541, tc_HOL_Obool))), _906543), _906545), _906547), _906549)), 7421 ^ _782464 : [(7422 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906537), 7420 ^ [_906537, _906539, _906541, _906543, _906545, _906547, _906549]), _906543)))], (7424 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_906545, 7420 ^ [_906537, _906539, _906541, _906543, _906545, _906547, _906549]), _906547), _906549)))]]], (7426 ^ _782464) ^ [_906755, _906757, _906759, _906761, _906763, _906765, _906767] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_906755, tc_fun(_906757, tc_fun(_906759, tc_HOL_Obool))), _906761), _906763), _906765), _906767))), 7427 ^ _782464 : [(7428 ^ _782464) ^ [_906840] : [hBOOL(hAPP(hAPP(c_member(_906755), _906840), _906761)), hBOOL(hAPP(hAPP(hAPP(_906763, _906840), _906765), _906767))]]], (7446 ^ _782464) ^ [_907285, _907287, _907289, _907291, _907293, _907295, _907297] : [7448 ^ _782464 : [(7449 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907285), 7447 ^ [_907285, _907287, _907289, _907291, _907293, _907295, _907297]), _907291)))], (7451 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_907293, 7447 ^ [_907285, _907287, _907289, _907291, _907293, _907295, _907297]), _907295), _907297))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_907285, tc_fun(_907287, tc_fun(_907289, tc_HOL_Obool))), _907291), _907293), _907295), _907297)))], (7436 ^ _782464) ^ [_907038, _907040, _907042, _907044, _907046, _907048, _907050] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_907038, tc_fun(_907040, tc_fun(_907042, tc_HOL_Obool))), _907044), _907046), _907048), _907050)), 7439 ^ _782464 : [(7440 ^ _782464) ^ [_907166] : [hBOOL(hAPP(hAPP(c_member(_907038), _907166), _907044)), -(hBOOL(hAPP(hAPP(hAPP(_907046, _907166), _907048), _907050)))]]], (7455 ^ _782464) ^ [_907545, _907547, _907549] : [class_Lattices_Oboolean__algebra(_907545), 7458 ^ _782464 : [(7459 ^ _782464) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907545), _907547) = hAPP(c_Groups_Ouminus__class_Ouminus(_907545), _907549), -(_907547 = _907549)], (7465 ^ _782464) ^ [] : [_907547 = _907549, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907545), _907547) = hAPP(c_Groups_Ouminus__class_Ouminus(_907545), _907549))]]], (7471 ^ _782464) ^ [_907786, _907788, _907790] : [class_Groups_Ogroup__add(_907786), 7474 ^ _782464 : [(7475 ^ _782464) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907786), _907788) = hAPP(c_Groups_Ouminus__class_Ouminus(_907786), _907790), -(_907788 = _907790)], (7481 ^ _782464) ^ [] : [_907788 = _907790, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907786), _907788) = hAPP(c_Groups_Ouminus__class_Ouminus(_907786), _907790))]]], (7487 ^ _782464) ^ [_908027, _908029, _908031] : [class_Groups_Ogroup__add(_908027), 7490 ^ _782464 : [(7491 ^ _782464) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_908027), _908029) = _908031, -(hAPP(c_Groups_Ouminus__class_Ouminus(_908027), _908031) = _908029)], (7497 ^ _782464) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_908027), _908031) = _908029, -(hAPP(c_Groups_Ouminus__class_Ouminus(_908027), _908029) = _908031)]]], (7503 ^ _782464) ^ [_908268, _908270, _908272] : [class_Groups_Ogroup__add(_908268), 7506 ^ _782464 : [(7507 ^ _782464) ^ [] : [_908270 = hAPP(c_Groups_Ouminus__class_Ouminus(_908268), _908272), -(_908272 = hAPP(c_Groups_Ouminus__class_Ouminus(_908268), _908270))], (7513 ^ _782464) ^ [] : [_908272 = hAPP(c_Groups_Ouminus__class_Ouminus(_908268), _908270), -(_908270 = hAPP(c_Groups_Ouminus__class_Ouminus(_908268), _908272))]]], (7519 ^ _782464) ^ [_908509, _908511] : [class_Lattices_Oboolean__algebra(_908509), -(hAPP(c_Groups_Ouminus__class_Ouminus(_908509), hAPP(c_Groups_Ouminus__class_Ouminus(_908509), _908511)) = _908511)], (7525 ^ _782464) ^ [_908604, _908606] : [class_Groups_Ogroup__add(_908604), -(hAPP(c_Groups_Ouminus__class_Ouminus(_908604), hAPP(c_Groups_Ouminus__class_Ouminus(_908604), _908606)) = _908606)], (7531 ^ _782464) ^ [_908699, _908701, _908703] : [class_Groups_Oordered__ab__group__add(_908699), 7534 ^ _782464 : [(7535 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908699), _908701), hAPP(c_Groups_Ouminus__class_Ouminus(_908699), _908703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908699), _908703), hAPP(c_Groups_Ouminus__class_Ouminus(_908699), _908701))))], (7541 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908699), _908703), hAPP(c_Groups_Ouminus__class_Ouminus(_908699), _908701))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908699), _908701), hAPP(c_Groups_Ouminus__class_Ouminus(_908699), _908703))))]]], (7547 ^ _782464) ^ [_908982, _908984, _908986] : [class_Groups_Oordered__ab__group__add(_908982), 7550 ^ _782464 : [(7551 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908982), hAPP(c_Groups_Ouminus__class_Ouminus(_908982), _908984)), _908986)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908982), hAPP(c_Groups_Ouminus__class_Ouminus(_908982), _908986)), _908984)))], (7557 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908982), hAPP(c_Groups_Ouminus__class_Ouminus(_908982), _908986)), _908984)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908982), hAPP(c_Groups_Ouminus__class_Ouminus(_908982), _908984)), _908986)))]]], (7563 ^ _782464) ^ [_909265, _909267, _909269] : [class_Groups_Oordered__ab__group__add(_909265), 7566 ^ _782464 : [(7567 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909265), hAPP(c_Groups_Ouminus__class_Ouminus(_909265), _909267)), hAPP(c_Groups_Ouminus__class_Ouminus(_909265), _909269))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909265), _909269), _909267)))], (7573 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909265), _909269), _909267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909265), hAPP(c_Groups_Ouminus__class_Ouminus(_909265), _909267)), hAPP(c_Groups_Ouminus__class_Ouminus(_909265), _909269))))]]], (7579 ^ _782464) ^ [_909548, _909550, _909552] : [class_Lattices_Oboolean__algebra(_909548), 7582 ^ _782464 : [(7583 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909548), hAPP(c_Groups_Ouminus__class_Ouminus(_909548), _909550)), hAPP(c_Groups_Ouminus__class_Ouminus(_909548), _909552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909548), _909552), _909550)))], (7589 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909548), _909552), _909550)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909548), hAPP(c_Groups_Ouminus__class_Ouminus(_909548), _909550)), hAPP(c_Groups_Ouminus__class_Ouminus(_909548), _909552))))]]], (7595 ^ _782464) ^ [_909831, _909833, _909835] : [7597 ^ _782464 : [(7598 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_909831, tc_HOL_Obool)), 7596 ^ [_909831, _909833, _909835]), _909833)))], (7600 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_909831), _909835), 7596 ^ [_909831, _909833, _909835]))]], -(hBOOL(hAPP(hAPP(c_member(_909831), _909835), c_Complete__Lattice_OInf__class_OInf(tc_fun(_909831, tc_HOL_Obool), _909833))))], (7604 ^ _782464) ^ [_910047, _910049, _910051] : [hBOOL(hAPP(hAPP(c_member(_910047), _910049), c_Complete__Lattice_OSup__class_OSup(tc_fun(_910047, tc_HOL_Obool), _910051))), 7608 ^ _782464 : [(7609 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910047), _910049), 7607 ^ [_910047, _910049, _910051])))], (7611 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_910047, tc_HOL_Obool)), 7607 ^ [_910047, _910049, _910051]), _910051)))]]], (7613 ^ _782464) ^ [_910239, _910241, _910243, _910245, _910247, _910249, _910251] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_910239, tc_fun(_910241, tc_fun(_910243, tc_HOL_Obool))), _910245), _910247), _910249), _910251)), 7617 ^ _782464 : [(7618 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910239), 7616 ^ [_910239, _910241, _910243, _910245, _910247, _910249, _910251]), _910245)))], (7620 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_910247, 7616 ^ [_910239, _910241, _910243, _910245, _910247, _910249, _910251]), _910249), _910251)))]]], (7622 ^ _782464) ^ [_910465, _910467, _910469, _910471, _910473, _910475, _910477] : [7624 ^ _782464 : [(7625 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910465), 7623 ^ [_910465, _910467, _910469, _910471, _910473, _910475, _910477]), _910467)))], (7627 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_910469, 7623 ^ [_910465, _910467, _910469, _910471, _910473, _910475, _910477]), _910471), _910473))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_910465, tc_fun(_910475, tc_fun(_910477, tc_HOL_Obool))), _910467), _910469), _910471), _910473)))], (7631 ^ _782464) ^ [_910723, _910725, _910727] : [class_Orderings_Olinorder(_910723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910723), _910725), _910727)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910723, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_910723, _910725, _910727)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_910723), _910727)) = hAPP(c_SetInterval_Oord__class_OatLeast(_910723), _910725))], (7641 ^ _782464) ^ [_910918, _910920, _910922] : [class_Orderings_Olinorder(_910918), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910918), _910920), _910922)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910918, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_910918), _910920)), c_SetInterval_Oord__class_OatLeastAtMost(_910918, _910920, _910922)) = hAPP(c_SetInterval_Oord__class_OatMost(_910918), _910922))], (7651 ^ _782464) ^ [_911113, _911115, _911117, _911119, _911121] : [7653 ^ _782464 : [(7654 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911113), 7652 ^ [_911113, _911115, _911117, _911119, _911121]), _911115)))], (7656 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911117, tc_HOL_Obool)), _911119), hAPP(_911121, 7652 ^ [_911113, _911115, _911117, _911119, _911121])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911117, tc_HOL_Obool)), _911119), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911113, tc_fun(_911117, tc_HOL_Obool)), _911115), _911121))))], (7660 ^ _782464) ^ [_911374, _911376, _911378, _911380, _911382, _911384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911374, tc_HOL_Obool)), _911376), _911378)), 7666 ^ _782464 : [(7667 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911374), 7665 ^ [_911374, _911376, _911378, _911380, _911382, _911384]), _911378)))], (7669 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911380, tc_HOL_Obool)), hAPP(_911382, 7665 ^ [_911374, _911376, _911378, _911380, _911382, _911384])), hAPP(_911384, 7665 ^ [_911374, _911376, _911378, _911380, _911382, _911384])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911380, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911374, tc_fun(_911380, tc_HOL_Obool)), _911378), _911382)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911374, tc_fun(_911380, tc_HOL_Obool)), _911378), _911384))))], (7673 ^ _782464) ^ [_911771, _911773, _911775, _911777, _911779] : [7675 ^ _782464 : [(7676 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911771), 7674 ^ [_911771, _911773, _911775, _911777, _911779]), _911773)))], (7678 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911775, tc_HOL_Obool)), hAPP(_911777, 7674 ^ [_911771, _911773, _911775, _911777, _911779])), _911779))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911775, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_911771, tc_fun(_911775, tc_HOL_Obool)), _911773), _911777)), _911779)))], (7682 ^ _782464) ^ [_912032, _912034, _912036, _912038, _912040, _912042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912032, tc_HOL_Obool)), _912034), _912036)), 7688 ^ _782464 : [(7689 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912032), 7687 ^ [_912032, _912034, _912036, _912038, _912040, _912042]), _912034)))], (7691 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912038, tc_HOL_Obool)), hAPP(_912040, 7687 ^ [_912032, _912034, _912036, _912038, _912040, _912042])), hAPP(_912042, 7687 ^ [_912032, _912034, _912036, _912038, _912040, _912042])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912038, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_912032, tc_fun(_912038, tc_HOL_Obool)), _912034), _912040)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_912032, tc_fun(_912038, tc_HOL_Obool)), _912036), _912042))))], (7695 ^ _782464) ^ [_912429, _912431, _912433, _912435, _912437] : [class_Complete__Lattice_Ocomplete__lattice(_912429), 7701 ^ _782464 : [(7702 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912431), 7700 ^ [_912429, _912431, _912433, _912435, _912437]), _912433)))], (7704 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912429), _912435), hAPP(_912437, 7700 ^ [_912429, _912431, _912433, _912435, _912437])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912429), _912435), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_912431, _912429), _912433), _912437))))], (7708 ^ _782464) ^ [_912725, _912727, _912729, _912731] : [7709 ^ _782464 : [(7710 ^ _782464) ^ [] : [hBOOL(hAPP(_912725, _912727))], (7712 ^ _782464) ^ [] : [hBOOL(hAPP(_912729, _912727))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912731, tc_HOL_Obool)), _912729), _912725), _912727)))], (7716 ^ _782464) ^ [_912880, _912882, _912884, _912886] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912880, tc_HOL_Obool)), _912882), _912884), _912886)), -(hBOOL(hAPP(_912882, _912886))), -(hBOOL(hAPP(_912884, _912886)))], (7726 ^ _782464) ^ [_913010, _913012, _913014, _913016] : [7727 ^ _782464 : [(7728 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913010), _913012), _913014))], (7730 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_913010), _913012), _913016))]], -(hBOOL(hAPP(hAPP(c_member(_913010), _913012), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913010, tc_HOL_Obool)), _913016), _913014))))], (7734 ^ _782464) ^ [_913195, _913197, _913199, _913201] : [hBOOL(hAPP(hAPP(c_member(_913195), _913197), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913195, tc_HOL_Obool)), _913199), _913201))), -(hBOOL(hAPP(hAPP(c_member(_913195), _913197), _913199))), -(hBOOL(hAPP(hAPP(c_member(_913195), _913197), _913201)))], (7744 ^ _782464) ^ [_913355, _913357, _913359, _913361, _913363] : [class_Lattices_Olattice(_913355), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913357, _913355)), _913359), _913361), _913363) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913355), hAPP(_913359, _913363)), hAPP(_913361, _913363)))], (7750 ^ _782464) ^ [_913492, _913494, _913496, _913498] : [class_Lattices_Osemilattice__sup(_913492), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913492), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913492), _913494), _913496)), _913498) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913492), _913494), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913492), _913496), _913498)))], (7756 ^ _782464) ^ [_913635, _913637, _913639, _913641] : [class_Lattices_Olattice(_913635), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913635), _913637), _913639)), _913641) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913635), _913637), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913635), _913639), _913641)))], (7762 ^ _782464) ^ [_913778, _913780, _913782, _913784] : [class_Lattices_Osemilattice__sup(_913778), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913778), _913780), _913782)), _913784) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913778), _913780), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913778), _913782), _913784)))], (7768 ^ _782464) ^ [_913921, _913923, _913925, _913927] : [class_Lattices_Osemilattice__sup(_913921), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913921), _913923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913921), _913925), _913927)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913921), _913925), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913921), _913923), _913927)))], (7774 ^ _782464) ^ [_914064, _914066, _914068, _914070] : [class_Lattices_Olattice(_914064), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914064), _914066), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914064), _914068), _914070)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914064), _914068), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914064), _914066), _914070)))], (7780 ^ _782464) ^ [_914207, _914209, _914211, _914213] : [class_Lattices_Osemilattice__sup(_914207), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914207), _914209), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914207), _914211), _914213)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914207), _914211), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914207), _914209), _914213)))], (7786 ^ _782464) ^ [_914350, _914352, _914354] : [class_Lattices_Osemilattice__sup(_914350), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914350), _914352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914350), _914352), _914354)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914350), _914352), _914354))], (7792 ^ _782464) ^ [_914475, _914477, _914479] : [class_Lattices_Olattice(_914475), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914475), _914477), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914475), _914477), _914479)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914475), _914477), _914479))], (7798 ^ _782464) ^ [_914600, _914602, _914604] : [class_Lattices_Osemilattice__sup(_914600), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914600), _914602), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914600), _914602), _914604)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914600), _914602), _914604))], (7804 ^ _782464) ^ [_914725, _914727, _914729] : [class_Lattices_Osemilattice__sup(_914725), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914725), _914727), _914729) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914725), _914729), _914727))], (7810 ^ _782464) ^ [_914834, _914836, _914838] : [class_Lattices_Olattice(_914834), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914834), _914836), _914838) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914834), _914838), _914836))], (7816 ^ _782464) ^ [_914943, _914945, _914947] : [class_Lattices_Osemilattice__sup(_914943), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914943), _914945), _914947) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914943), _914947), _914945))], (7822 ^ _782464) ^ [_915052, _915054, _915056, _915058, _915060] : [class_Lattices_Olattice(_915052), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915054, _915052)), _915056), _915058), _915060) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915052), hAPP(_915056, _915060)), hAPP(_915058, _915060)))], (7828 ^ _782464) ^ [_915189, _915191] : [class_Lattices_Osemilattice__sup(_915189), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915189), _915191), _915191) = _915191)], (7834 ^ _782464) ^ [_915280, _915282] : [class_Lattices_Osemilattice__sup(_915280), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915280), _915282), _915282) = _915282)], (7840 ^ _782464) ^ [_915371, _915373, _915375, _915377] : [hBOOL(hAPP(_915371, _915373)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915375, tc_HOL_Obool)), _915377), _915371), _915373)))], (7846 ^ _782464) ^ [_915482, _915484, _915486, _915488] : [hBOOL(hAPP(_915482, _915484)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915486, tc_HOL_Obool)), _915482), _915488), _915484)))], (7871 ^ _782464) ^ [_916036, _916038, _916040, _916042] : [7875 ^ _782464 : [(7876 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916036), 7874 ^ [_916036, _916038, _916040, _916042]), _916038)))], (7878 ^ _782464) ^ [] : [hBOOL(hAPP(_916042, 7874 ^ [_916036, _916038, _916040, _916042]))]], 7880 ^ _782464 : [(7881 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916036), 7879 ^ [_916036, _916038, _916040, _916042]), _916040)))], (7883 ^ _782464) ^ [] : [hBOOL(hAPP(_916042, 7879 ^ [_916036, _916038, _916040, _916042]))]], 7884 ^ _782464 : [(7885 ^ _782464) ^ [_916369] : [hBOOL(hAPP(hAPP(c_member(_916036), _916369), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916036, tc_HOL_Obool)), _916038), _916040))), -(hBOOL(hAPP(_916042, _916369)))]]], (7852 ^ _782464) ^ [_915614, _915616, _915618, _915620] : [7854 ^ _782464 : [(7855 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915614), 7853 ^ [_915614, _915616, _915618, _915620]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915614, tc_HOL_Obool)), _915616), _915618))))], (7857 ^ _782464) ^ [] : [hBOOL(hAPP(_915620, 7853 ^ [_915614, _915616, _915618, _915620]))]], 7858 ^ _782464 : [(7859 ^ _782464) ^ [_915834] : [hBOOL(hAPP(hAPP(c_member(_915614), _915834), _915616)), -(hBOOL(hAPP(_915620, _915834)))], (7865 ^ _782464) ^ [_915931] : [hBOOL(hAPP(hAPP(c_member(_915614), _915931), _915618)), -(hBOOL(hAPP(_915620, _915931)))]]], (7891 ^ _782464) ^ [_916521, _916523, _916525, _916527] : [7892 ^ _782464 : [(7893 ^ _782464) ^ [_916631] : [hBOOL(hAPP(hAPP(c_member(_916521), _916631), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916521, tc_HOL_Obool)), _916523), _916525))), hBOOL(hAPP(_916527, _916631))]], 7901 ^ _782464 : [(7902 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916521), 7900 ^ [_916521, _916523, _916525, _916527]), _916523)))], (7904 ^ _782464) ^ [] : [-(hBOOL(hAPP(_916527, 7900 ^ [_916521, _916523, _916525, _916527])))]], 7906 ^ _782464 : [(7907 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916521), 7905 ^ [_916521, _916523, _916525, _916527]), _916525)))], (7909 ^ _782464) ^ [] : [-(hBOOL(hAPP(_916527, 7905 ^ [_916521, _916523, _916525, _916527])))]]], (7911 ^ _782464) ^ [_916920, _916922, _916924, _916926] : [7925 ^ _782464 : [(7926 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916920), 7924 ^ [_916920, _916922, _916924, _916926]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916920, tc_HOL_Obool)), _916922), _916924))))], (7928 ^ _782464) ^ [] : [-(hBOOL(hAPP(_916926, 7924 ^ [_916920, _916922, _916924, _916926])))]], 7912 ^ _782464 : [(7913 ^ _782464) ^ [_917033] : [hBOOL(hAPP(hAPP(c_member(_916920), _917033), _916922)), hBOOL(hAPP(_916926, _917033))], (7919 ^ _782464) ^ [_917129] : [hBOOL(hAPP(hAPP(c_member(_916920), _917129), _916924)), hBOOL(hAPP(_916926, _917129))]]], (7930 ^ _782464) ^ [_917323, _917325, _917327, _917329] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917323, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917323, tc_HOL_Obool)), _917325), _917327)), _917329) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917323, tc_HOL_Obool)), _917325), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917323, tc_HOL_Obool)), _917327), _917329)))], (7932 ^ _782464) ^ [_917396, _917398, _917400, _917402] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917396, tc_HOL_Obool)), _917398), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917396, tc_HOL_Obool)), _917400), _917402)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917396, tc_HOL_Obool)), _917400), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917396, tc_HOL_Obool)), _917398), _917402)))], (7934 ^ _782464) ^ [_917469, _917471, _917473] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917469, tc_HOL_Obool)), _917471), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917469, tc_HOL_Obool)), _917471), _917473)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917469, tc_HOL_Obool)), _917471), _917473))], (7936 ^ _782464) ^ [_917529, _917531, _917533] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917529, tc_HOL_Obool)), _917531), _917533) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917529, tc_HOL_Obool)), _917533), _917531))], (7938 ^ _782464) ^ [_917578, _917580] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917578, tc_HOL_Obool)), _917580), _917580) = _917580)], (7940 ^ _782464) ^ [_917614, _917616, _917618] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_917614, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_917614, tc_HOL_Obool), tc_HOL_Obool)), _917616), _917618)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917614, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917614, tc_HOL_Obool), _917616)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917614, tc_HOL_Obool), _917618)))], (7942 ^ _782464) ^ [_917684, _917686, _917688, _917690] : [class_Lattices_Osemilattice__sup(_917684), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917684), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917684), _917686), _917688)), _917690)), 7949 ^ _782464 : [(7950 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917684), _917686), _917690)))], (7952 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917684), _917688), _917690)))]]], (7954 ^ _782464) ^ [_917907, _917909, _917911, _917913, _917915] : [class_Lattices_Osemilattice__sup(_917907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917907), _917909), _917911)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917907), _917913), _917915)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917907), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917907), _917909), _917913)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917907), _917911), _917915))))], (7968 ^ _782464) ^ [_918178, _918180, _918182, _918184] : [class_Lattices_Osemilattice__sup(_918178), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918178), _918180), _918182)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918178), _918184), _918182)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918178), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918178), _918180), _918184)), _918182)))], (7982 ^ _782464) ^ [_918427, _918429, _918431, _918433] : [class_Lattices_Osemilattice__sup(_918427), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918427), _918429), _918431)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918427), _918433), _918431)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918427), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918427), _918429), _918433)), _918431)))], (7996 ^ _782464) ^ [_918676, _918678, _918680] : [class_Lattices_Osemilattice__sup(_918676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918676), _918678), _918680)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918676), _918680), _918678) = _918680)], (8006 ^ _782464) ^ [_918837, _918839, _918841] : [class_Lattices_Osemilattice__sup(_918837), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918837), _918839), _918841)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918837), _918839), _918841) = _918841)], (8016 ^ _782464) ^ [_918998, _919000, _919002, _919004] : [class_Lattices_Osemilattice__sup(_918998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918998), _919000), _919002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918998), _919000), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918998), _919004), _919002))))], (8026 ^ _782464) ^ [_919177, _919179, _919181, _919183] : [class_Lattices_Osemilattice__sup(_919177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919177), _919179), _919181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919177), _919179), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919177), _919181), _919183))))], (8036 ^ _782464) ^ [_919356, _919358, _919360, _919362] : [class_Lattices_Osemilattice__sup(_919356), 8039 ^ _782464 : [(8040 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919356), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919356), _919358), _919360)), _919362)), 8043 ^ _782464 : [(8044 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919356), _919358), _919362)))], (8046 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919356), _919360), _919362)))]]], (8048 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919356), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919356), _919358), _919360)), _919362))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919356), _919358), _919362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919356), _919360), _919362))]]], (8058 ^ _782464) ^ [_919736, _919738, _919740] : [class_Lattices_Osemilattice__sup(_919736), 8061 ^ _782464 : [(8062 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919736), _919738), _919740)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919736), _919738), _919740) = _919740)], (8068 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919736), _919738), _919740) = _919740, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919736), _919738), _919740)))]]], (8074 ^ _782464) ^ [_919992, _919994, _919996] : [class_Lattices_Osemilattice__sup(_919992), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919992), _919994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919992), _919996), _919994))))], (8080 ^ _782464) ^ [_920099, _920101, _920103] : [class_Lattices_Olattice(_920099), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920099), _920101), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920099), _920103), _920101))))], (8086 ^ _782464) ^ [_920206, _920208, _920210] : [class_Lattices_Osemilattice__sup(_920206), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920206), _920208), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920206), _920208), _920210))))], (8092 ^ _782464) ^ [_920313, _920315, _920317] : [class_Lattices_Olattice(_920313), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920313), _920315), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920313), _920315), _920317))))], (8098 ^ _782464) ^ [_920420, _920422, _920424, _920426] : [hBOOL(hAPP(hAPP(c_member(_920420), _920422), _920424)), -(hBOOL(hAPP(hAPP(c_member(_920420), _920422), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920420, tc_HOL_Obool)), _920426), _920424))))], (8104 ^ _782464) ^ [_920551, _920553, _920555, _920557] : [hBOOL(hAPP(hAPP(c_member(_920551), _920553), _920555)), -(hBOOL(hAPP(hAPP(c_member(_920551), _920553), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920551, tc_HOL_Obool)), _920555), _920557))))], (8120 ^ _782464) ^ [_920857, _920859, _920861, _920863] : [8121 ^ _782464 : [(8122 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920857), _920859), _920861))], (8124 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920857), _920859), _920863))]], -(hBOOL(hAPP(hAPP(c_member(_920857), _920859), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920857, tc_HOL_Obool)), _920861), _920863))))], (8110 ^ _782464) ^ [_920703, _920705, _920707, _920709] : [hBOOL(hAPP(hAPP(c_member(_920703), _920705), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920703, tc_HOL_Obool)), _920707), _920709))), -(hBOOL(hAPP(hAPP(c_member(_920703), _920705), _920707))), -(hBOOL(hAPP(hAPP(c_member(_920703), _920705), _920709)))], (8128 ^ _782464) ^ [_921042, _921044, _921046, _921048, _921050] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921042, tc_HOL_Obool)), _921044), _921046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921042, tc_HOL_Obool)), _921048), _921050)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921042, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921042, tc_HOL_Obool)), _921044), _921048)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921042, tc_HOL_Obool)), _921046), _921050))))], (8138 ^ _782464) ^ [_921287, _921289, _921291, _921293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921287, tc_HOL_Obool)), _921289), _921291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921287, tc_HOL_Obool)), _921293), _921291)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921287, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921287, tc_HOL_Obool)), _921289), _921293)), _921291)))], (8148 ^ _782464) ^ [_921506, _921508, _921510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921506, tc_HOL_Obool)), _921508), _921510)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921506, tc_HOL_Obool)), _921510), _921508) = _921510)], (8154 ^ _782464) ^ [_921627, _921629, _921631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921627, tc_HOL_Obool)), _921629), _921631)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921627, tc_HOL_Obool)), _921629), _921631) = _921631)], (8160 ^ _782464) ^ [_921766, _921768, _921770] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921766, tc_HOL_Obool)), _921768), _921770)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921766, tc_HOL_Obool)), _921768), _921770) = _921770)], (8166 ^ _782464) ^ [_921883, _921885, _921887] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921883, tc_HOL_Obool)), _921885), _921887) = _921887, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921883, tc_HOL_Obool)), _921885), _921887)))], (8172 ^ _782464) ^ [_922006, _922008, _922010] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922006, tc_HOL_Obool)), _922008), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922006, tc_HOL_Obool)), _922010), _922008))))], (8174 ^ _782464) ^ [_922054, _922056, _922058] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922054, tc_HOL_Obool)), _922056), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922054, tc_HOL_Obool)), _922056), _922058))))], (8176 ^ _782464) ^ [_922102, _922104, _922106] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_922102, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_922102, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_922102), _922104)), hAPP(c_Set_OPow(_922102), _922106))), hAPP(c_Set_OPow(_922102), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922102, tc_HOL_Obool)), _922104), _922106)))))], (8178 ^ _782464) ^ [_922203, _922205, _922207, _922209] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922203, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922203, tc_fun(_922203, tc_HOL_Obool), tc_HOL_Obool), c_member(_922203)), _922205)), hAPP(hAPP(c_COMBC(_922203, tc_fun(_922203, tc_HOL_Obool), tc_HOL_Obool), c_member(_922203)), _922207)), _922209)), -(hBOOL(hAPP(hAPP(c_member(_922203), _922209), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922203, tc_HOL_Obool)), _922205), _922207))))], (8184 ^ _782464) ^ [_922402, _922404, _922406, _922408] : [hBOOL(hAPP(hAPP(c_member(_922402), _922408), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922402, tc_HOL_Obool)), _922404), _922406))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922402, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922402, tc_fun(_922402, tc_HOL_Obool), tc_HOL_Obool), c_member(_922402)), _922404)), hAPP(hAPP(c_COMBC(_922402, tc_fun(_922402, tc_HOL_Obool), tc_HOL_Obool), c_member(_922402)), _922406)), _922408)))], (8190 ^ _782464) ^ [_922607, _922609, _922611, _922613, _922615] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922607, tc_fun(_922609, tc_HOL_Obool)), _922611), hAPP(hAPP(c_COMBS(_922607, tc_fun(_922609, tc_HOL_Obool), tc_fun(_922609, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_922609, tc_HOL_Obool), tc_fun(tc_fun(_922609, tc_HOL_Obool), tc_fun(_922609, tc_HOL_Obool)), _922607), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922609, tc_HOL_Obool))), _922613)), _922615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922609, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922607, tc_fun(_922609, tc_HOL_Obool)), _922611), _922613)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922607, tc_fun(_922609, tc_HOL_Obool)), _922611), _922615)))], (8192 ^ _782464) ^ [_922728, _922730, _922732, _922734, _922736] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922728, tc_fun(_922730, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922728, tc_HOL_Obool)), _922732), _922734)), _922736) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922730, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922728, tc_fun(_922730, tc_HOL_Obool)), _922732), _922736)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922728, tc_fun(_922730, tc_HOL_Obool)), _922734), _922736)))], (8194 ^ _782464) ^ [_922817, _922819, _922821, _922823, _922825] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922817, tc_fun(_922819, tc_HOL_Obool)), _922821), hAPP(hAPP(c_COMBB(tc_fun(_922819, tc_HOL_Obool), tc_fun(_922819, tc_HOL_Obool), _922817), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922819, tc_HOL_Obool)), _922823)), _922825)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922819, tc_HOL_Obool)), _922823), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922817, tc_fun(_922819, tc_HOL_Obool)), _922821), _922825)))], (8196 ^ _782464) ^ [_922907, _922909, _922911, _922913, _922915] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922907, tc_fun(_922909, tc_HOL_Obool)), _922911), hAPP(hAPP(c_COMBC(_922907, tc_fun(_922909, tc_HOL_Obool), tc_fun(_922909, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_922909, tc_HOL_Obool), tc_fun(tc_fun(_922909, tc_HOL_Obool), tc_fun(_922909, tc_HOL_Obool)), _922907), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922909, tc_HOL_Obool))), _922913)), _922915)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922909, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922907, tc_fun(_922909, tc_HOL_Obool)), _922911), _922913)), _922915))], (8198 ^ _782464) ^ [_923016, _923018, _923020, _923022, _923024] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923016, tc_HOL_Obool)), _923018), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923020, tc_fun(_923016, tc_HOL_Obool)), _923022), _923024)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923020, tc_fun(_923016, tc_HOL_Obool)), _923022), hAPP(hAPP(c_COMBB(tc_fun(_923016, tc_HOL_Obool), tc_fun(_923016, tc_HOL_Obool), _923020), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923016, tc_HOL_Obool)), _923018)), _923024)))], (8200 ^ _782464) ^ [_923106, _923108, _923110, _923112, _923114] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923106, tc_HOL_Obool)), _923108), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923110, tc_fun(_923106, tc_HOL_Obool)), _923112), _923114)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923110, tc_fun(_923106, tc_HOL_Obool)), _923112), hAPP(hAPP(c_COMBB(tc_fun(_923106, tc_HOL_Obool), tc_fun(_923106, tc_HOL_Obool), _923110), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923106, tc_HOL_Obool)), _923108)), _923114)))], (8202 ^ _782464) ^ [_923196, _923198, _923200, _923202, _923204] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923196, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923198, tc_fun(_923196, tc_HOL_Obool)), _923200), _923202)), _923204) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923198, tc_fun(_923196, tc_HOL_Obool)), _923200), hAPP(hAPP(c_COMBC(_923198, tc_fun(_923196, tc_HOL_Obool), tc_fun(_923196, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_923196, tc_HOL_Obool), tc_fun(tc_fun(_923196, tc_HOL_Obool), tc_fun(_923196, tc_HOL_Obool)), _923198), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923196, tc_HOL_Obool))), _923202)), _923204)))], (8204 ^ _782464) ^ [_923305, _923307, _923309, _923311, _923313, _923315, _923317] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923305, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923307, tc_fun(_923305, tc_HOL_Obool)), _923309), _923311)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923313, tc_fun(_923305, tc_HOL_Obool)), _923315), _923317)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923307, tc_fun(_923305, tc_HOL_Obool)), _923309), hAPP(hAPP(c_COMBB(tc_fun(_923313, tc_fun(_923305, tc_HOL_Obool)), tc_fun(_923305, tc_HOL_Obool), _923307), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923313, tc_fun(_923305, tc_HOL_Obool)), _923315)), hAPP(hAPP(c_COMBC(_923307, tc_fun(_923313, tc_fun(_923305, tc_HOL_Obool)), tc_fun(_923313, tc_fun(_923305, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_923305, tc_HOL_Obool), tc_fun(_923305, tc_HOL_Obool)), tc_fun(tc_fun(_923313, tc_fun(_923305, tc_HOL_Obool)), tc_fun(_923313, tc_fun(_923305, tc_HOL_Obool))), _923307), c_COMBB(tc_fun(_923305, tc_HOL_Obool), tc_fun(_923305, tc_HOL_Obool), _923313)), hAPP(hAPP(c_COMBB(tc_fun(_923305, tc_HOL_Obool), tc_fun(tc_fun(_923305, tc_HOL_Obool), tc_fun(_923305, tc_HOL_Obool)), _923307), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923305, tc_HOL_Obool))), _923311))), _923317))))], (8206 ^ _782464) ^ [_923508, _923510, _923512, _923514] : [class_Orderings_Olinorder(_923508), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923508), _923510), _923512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923508), _923512), _923514)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923508, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923508, _923510), _923512)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923508, _923512), _923514)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923508, _923510), _923514))], (8220 ^ _782464) ^ [_923785, _923787, _923789, _923791, _923793] : [hBOOL(hAPP(hAPP(c_member(_923785), _923787), _923789)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923791, tc_HOL_Obool)), hAPP(_923793, _923787)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_923785, tc_fun(_923791, tc_HOL_Obool)), _923789), _923793)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_923785, tc_fun(_923791, tc_HOL_Obool)), _923789), _923793))], (8226 ^ _782464) ^ [_923958, _923960, _923962, _923964] : [class_Orderings_Olinorder(_923958), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923958), _923960), _923962)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923958), _923962), _923964)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923958, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923958, _923960), _923962)), c_SetInterval_Oord__class_OatLeastAtMost(_923958, _923962, _923964)) = c_SetInterval_Oord__class_OatLeastAtMost(_923958, _923960, _923964))], (8240 ^ _782464) ^ [_924227, _924229, _924231] : [class_Orderings_Olinorder(_924227), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924227), _924229), _924231)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924227, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_924227), _924229)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_924227, _924229), _924231)) = hAPP(c_SetInterval_Oord__class_OlessThan(_924227), _924231))], (8250 ^ _782464) ^ [_924426, _924428, _924430] : [class_Orderings_Olinorder(_924426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924426), _924428), _924430)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924426, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_924426, _924428), _924430)), hAPP(c_SetInterval_Oord__class_OatLeast(_924426), _924430)) = hAPP(c_SetInterval_Oord__class_OatLeast(_924426), _924428))], (8260 ^ _782464) ^ [_924625, _924627, _924629] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924625, tc_HOL_Obool)), _924627), c_Complete__Lattice_OInf__class_OInf(tc_fun(_924625, tc_HOL_Obool), _924629)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_924625, tc_HOL_Obool), tc_fun(_924625, tc_HOL_Obool)), _924629), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924625, tc_HOL_Obool)), _924627)))], (8262 ^ _782464) ^ [_924692, _924694, _924696] : [class_Orderings_Olinorder(_924692), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924692), _924694), _924696)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924692, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_924692, _924694, _924696)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_924692), _924696)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_924692), _924694))], (8272 ^ _782464) ^ [_924887, _924889, _924891] : [class_Orderings_Olinorder(_924887), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924887), _924889), _924891)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924887, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_924887), _924889)), c_SetInterval_Oord__class_OgreaterThanAtMost(_924887, _924889, _924891)) = hAPP(c_SetInterval_Oord__class_OatMost(_924887), _924891))], (8282 ^ _782464) ^ [_925082, _925084, _925086, _925088, _925090] : [class_Complete__Lattice_Ocomplete__lattice(_925082), 8288 ^ _782464 : [(8289 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925084), 8287 ^ [_925082, _925084, _925086, _925088, _925090]), _925086)))], (8291 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925082), hAPP(_925088, 8287 ^ [_925082, _925084, _925086, _925088, _925090])), _925090))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925082), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_925084, _925082), _925086), _925088)), _925090)))], (8295 ^ _782464) ^ [_925378, _925380, _925382, _925384] : [class_Orderings_Olinorder(_925378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925378), _925380), _925382)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925378), _925382), _925384)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_925378, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_925378, _925380, _925382)), c_SetInterval_Oord__class_OgreaterThanAtMost(_925378, _925382, _925384)) = c_SetInterval_Oord__class_OatLeastAtMost(_925378, _925380, _925384))], (8309 ^ _782464) ^ [_925643, _925645, _925647] : [8311 ^ _782464 : [(8312 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_925643, tc_HOL_Obool)), 8310 ^ [_925643, _925645, _925647]), _925645)))], (8314 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925643, tc_HOL_Obool)), _925647), 8310 ^ [_925643, _925645, _925647]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925643, tc_HOL_Obool)), _925647), c_Complete__Lattice_OInf__class_OInf(tc_fun(_925643, tc_HOL_Obool), _925645))))], (8318 ^ _782464) ^ [_925874, _925876, _925878] : [8320 ^ _782464 : [(8321 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_925874, tc_HOL_Obool)), 8319 ^ [_925874, _925876, _925878]), _925876)))], (8323 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925874, tc_HOL_Obool)), 8319 ^ [_925874, _925876, _925878]), _925878))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925874, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_925874, tc_HOL_Obool), _925876)), _925878)))], (8327 ^ _782464) ^ [_926105, _926107, _926109, _926111, _926113] : [8329 ^ _782464 : [(8330 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926105), 8328 ^ [_926105, _926107, _926109, _926111, _926113]), _926107)))], (8332 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_926109, 8328 ^ [_926105, _926107, _926109, _926111, _926113]), _926111))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_926105, tc_fun(_926113, tc_HOL_Obool)), _926107), _926109), _926111)))], (8336 ^ _782464) ^ [_926326, _926328, _926330, _926332, _926334] : [8338 ^ _782464 : [(8339 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926326), 8337 ^ [_926326, _926328, _926330, _926332, _926334]), _926328)))], (8341 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926330), _926332), hAPP(_926334, 8337 ^ [_926326, _926328, _926330, _926332, _926334])))]], -(hBOOL(hAPP(hAPP(c_member(_926330), _926332), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_926326, tc_fun(_926330, tc_HOL_Obool)), _926328), _926334))))], (8345 ^ _782464) ^ [_926572, _926574, _926576, _926578, _926580] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_926572, tc_fun(_926574, tc_HOL_Obool)), _926576), _926578), _926580)), 8349 ^ _782464 : [(8350 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926572), 8348 ^ [_926572, _926574, _926576, _926578, _926580]), _926576)))], (8352 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_926578, 8348 ^ [_926572, _926574, _926576, _926578, _926580]), _926580)))]]], (8354 ^ _782464) ^ [_926768, _926770, _926772, _926774, _926776] : [hBOOL(hAPP(hAPP(c_member(_926768), _926770), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_926772, tc_fun(_926768, tc_HOL_Obool)), _926774), _926776))), 8358 ^ _782464 : [(8359 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926772), 8357 ^ [_926768, _926770, _926772, _926774, _926776]), _926774)))], (8361 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926768), _926770), hAPP(_926776, 8357 ^ [_926768, _926770, _926772, _926774, _926776]))))]]], (8363 ^ _782464) ^ [_926984, _926986, _926988] : [class_Complete__Lattice_Ocomplete__lattice(_926984), 8369 ^ _782464 : [(8370 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926984), 8368 ^ [_926984, _926986, _926988]), _926986)))], (8372 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926984), _926988), 8368 ^ [_926984, _926986, _926988]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926984), _926988), c_Complete__Lattice_OInf__class_OInf(_926984, _926986))))], (8376 ^ _782464) ^ [_927240, _927242, _927244, _927246] : [class_Orderings_Olinorder(_927240), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927240), _927242), _927244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927240), _927244), _927246)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927240, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_927240, _927242, _927244)), c_SetInterval_Oord__class_OgreaterThanAtMost(_927240, _927244, _927246)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_927240, _927242, _927246))], (8390 ^ _782464) ^ [_927505, _927507, _927509] : [class_Complete__Lattice_Ocomplete__lattice(_927505), 8396 ^ _782464 : [(8397 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927505), 8395 ^ [_927505, _927507, _927509]), _927507)))], (8399 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927505), 8395 ^ [_927505, _927507, _927509]), _927509))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927505), c_Complete__Lattice_OSup__class_OSup(_927505, _927507)), _927509)))], (8403 ^ _782464) ^ [_927761, _927763] : [class_Lattices_Olattice(_927761), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927761), _927763), _927763) = _927763)], (8409 ^ _782464) ^ [_927852, _927854, _927856, _927858, _927860] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_927852, tc_fun(_927854, tc_HOL_Obool)), _927856), hAPP(hAPP(c_COMBS(_927852, tc_fun(_927854, tc_HOL_Obool), tc_fun(_927854, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_927854, tc_HOL_Obool), tc_fun(tc_fun(_927854, tc_HOL_Obool), tc_fun(_927854, tc_HOL_Obool)), _927852), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927854, tc_HOL_Obool))), _927858)), _927860)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927854, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_927854, tc_HOL_Obool), hAPP(c_Set_Oimage(_927852, tc_fun(_927854, tc_HOL_Obool), _927858), _927856))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_927854, tc_HOL_Obool), hAPP(c_Set_Oimage(_927852, tc_fun(_927854, tc_HOL_Obool), _927860), _927856))))], (8411 ^ _782464) ^ [_927981, _927983, _927985] : [8413 ^ _782464 : [(8414 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927981), 8412 ^ [_927981, _927983, _927985]), _927983)))], (8416 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_927981), 8412 ^ [_927981, _927983, _927985]), _927985))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927981, tc_HOL_Obool)), _927983), _927985)))], (8420 ^ _782464) ^ [_928185, _928187, _928189] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928185, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928185, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928185, tc_HOL_Obool), _928187)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928185, tc_HOL_Obool), _928189))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928185, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_928185, tc_HOL_Obool), tc_HOL_Obool)), _928187), _928189)))))], (8422 ^ _782464) ^ [_928265, _928267] : [class_Groups_Oordered__ab__group__add(_928265), -(hAPP(c_Set_Oimage(_928265, _928265, c_Groups_Ouminus__class_Ouminus(_928265)), hAPP(c_SetInterval_Oord__class_OatLeast(_928265), _928267)) = hAPP(c_SetInterval_Oord__class_OatMost(_928265), hAPP(c_Groups_Ouminus__class_Ouminus(_928265), _928267)))], (8428 ^ _782464) ^ [_928388, _928390] : [class_Groups_Oordered__ab__group__add(_928388), -(hAPP(c_Set_Oimage(_928388, _928388, c_Groups_Ouminus__class_Ouminus(_928388)), hAPP(c_SetInterval_Oord__class_OatMost(_928388), _928390)) = hAPP(c_SetInterval_Oord__class_OatLeast(_928388), hAPP(c_Groups_Ouminus__class_Ouminus(_928388), _928390)))], (8434 ^ _782464) ^ [_928511, _928513] : [class_Groups_Oordered__ab__group__add(_928511), -(hAPP(c_Set_Oimage(_928511, _928511, c_Groups_Ouminus__class_Ouminus(_928511)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_928511), _928513)) = hAPP(c_SetInterval_Oord__class_OlessThan(_928511), hAPP(c_Groups_Ouminus__class_Ouminus(_928511), _928513)))], (8440 ^ _782464) ^ [_928634, _928636] : [class_Groups_Oordered__ab__group__add(_928634), -(hAPP(c_Set_Oimage(_928634, _928634, c_Groups_Ouminus__class_Ouminus(_928634)), hAPP(c_SetInterval_Oord__class_OlessThan(_928634), _928636)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_928634), hAPP(c_Groups_Ouminus__class_Ouminus(_928634), _928636)))], (8446 ^ _782464) ^ [_928757, _928759, _928761, _928763, _928765, _928767] : [_928757 = _928759, 8452 ^ _782464 : [(8453 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928761), 8451 ^ [_928757, _928759, _928761, _928763, _928765, _928767]), _928759)))], (8455 ^ _782464) ^ [] : [hAPP(_928763, 8451 ^ [_928757, _928759, _928761, _928763, _928765, _928767]) = hAPP(_928765, 8451 ^ [_928757, _928759, _928761, _928763, _928765, _928767])]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_928761, tc_fun(_928767, tc_HOL_Obool)), _928757), _928763) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_928761, tc_fun(_928767, tc_HOL_Obool)), _928759), _928765))], (8459 ^ _782464) ^ [_929084, _929086] : [class_Lattices_Oboolean__algebra(_929084), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_929084), _929086), hAPP(c_Groups_Ouminus__class_Ouminus(_929084), _929086)) = c_Orderings_Otop__class_Otop(_929084))], (8465 ^ _782464) ^ [_929189, _929191] : [-(hBOOL(hAPP(hAPP(c_member(_929189), _929191), c_Orderings_Otop__class_Otop(tc_fun(_929189, tc_HOL_Obool)))))], (8467 ^ _782464) ^ [_929226, _929228, _929230, _929232] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929226, tc_HOL_Obool)), _929228), _929230), _929232)), 8470 ^ _782464 : [(8471 ^ _782464) ^ [] : [-(hBOOL(hAPP(_929228, _929232)))], (8473 ^ _782464) ^ [] : [-(hBOOL(hAPP(_929230, _929232)))]]], (8475 ^ _782464) ^ [_929371, _929373, _929375, _929377] : [hBOOL(hAPP(_929371, _929373)), hBOOL(hAPP(_929375, _929373)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929377, tc_HOL_Obool)), _929371), _929375), _929373)))], (8485 ^ _782464) ^ [_929542, _929544, _929546, _929548, _929550, _929552] : [_929542 = hAPP(_929544, _929546), hBOOL(hAPP(hAPP(c_member(_929548), _929546), _929550)), -(hBOOL(hAPP(hAPP(c_member(_929552), _929542), hAPP(c_Set_Oimage(_929548, _929552, _929544), _929550))))], (8495 ^ _782464) ^ [_929735, _929737, _929739, _929741] : [hBOOL(hAPP(hAPP(c_member(_929735), _929737), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929735, tc_HOL_Obool)), _929739), _929741))), 8498 ^ _782464 : [(8499 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929735), _929737), _929739)))], (8501 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929735), _929737), _929741)))]]], (8503 ^ _782464) ^ [_929910, _929912, _929914, _929916] : [hBOOL(hAPP(hAPP(c_member(_929910), _929912), _929914)), hBOOL(hAPP(hAPP(c_member(_929910), _929912), _929916)), -(hBOOL(hAPP(hAPP(c_member(_929910), _929912), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929910, tc_HOL_Obool)), _929914), _929916))))], (8513 ^ _782464) ^ [_930111, _930113, _930115, _930117] : [-(hBOOL(hAPP(hAPP(c_member(_930111), hAPP(_930113, _930115)), hAPP(c_Set_Oimage(_930117, _930111, _930113), c_Orderings_Otop__class_Otop(tc_fun(_930117, tc_HOL_Obool))))))], (8515 ^ _782464) ^ [_930162, _930164, _930166, _930168, _930170] : [_930162 = hAPP(_930164, _930166), -(hBOOL(hAPP(hAPP(c_member(_930168), _930162), hAPP(c_Set_Oimage(_930170, _930168, _930164), c_Orderings_Otop__class_Otop(tc_fun(_930170, tc_HOL_Obool))))))], (8521 ^ _782464) ^ [_930289, _930291, _930293, _930295, _930297] : [class_Lattices_Olattice(_930289), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930291, _930289)), _930293), _930295), _930297) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930289), hAPP(_930293, _930297)), hAPP(_930295, _930297)))], (8527 ^ _782464) ^ [_930426, _930428, _930430, _930432] : [class_Lattices_Osemilattice__inf(_930426), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930426), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930426), _930428), _930430)), _930432) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930426), _930428), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930426), _930430), _930432)))], (8533 ^ _782464) ^ [_930569, _930571, _930573, _930575] : [class_Lattices_Olattice(_930569), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930569), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930569), _930571), _930573)), _930575) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930569), _930571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930569), _930573), _930575)))], (8539 ^ _782464) ^ [_930712, _930714, _930716, _930718] : [class_Lattices_Osemilattice__inf(_930712), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930712), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930712), _930714), _930716)), _930718) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930712), _930714), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930712), _930716), _930718)))], (8545 ^ _782464) ^ [_930855, _930857, _930859] : [class_Lattices_Obounded__lattice__top(_930855), 8548 ^ _782464 : [(8549 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930855), _930857), _930859) = c_Orderings_Otop__class_Otop(_930855), 8552 ^ _782464 : [(8553 ^ _782464) ^ [] : [-(_930857 = c_Orderings_Otop__class_Otop(_930855))], (8555 ^ _782464) ^ [] : [-(_930859 = c_Orderings_Otop__class_Otop(_930855))]]], (8557 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930855), _930857), _930859) = c_Orderings_Otop__class_Otop(_930855)), _930857 = c_Orderings_Otop__class_Otop(_930855), _930859 = c_Orderings_Otop__class_Otop(_930855)]]], (8567 ^ _782464) ^ [_931182, _931184, _931186, _931188] : [class_Lattices_Osemilattice__inf(_931182), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931182), _931184), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931182), _931186), _931188)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931182), _931186), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931182), _931184), _931188)))], (8573 ^ _782464) ^ [_931325, _931327, _931329, _931331] : [class_Lattices_Olattice(_931325), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931325), _931327), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931325), _931329), _931331)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931325), _931329), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931325), _931327), _931331)))], (8579 ^ _782464) ^ [_931468, _931470, _931472, _931474] : [class_Lattices_Osemilattice__inf(_931468), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931468), _931470), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931468), _931472), _931474)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931468), _931472), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931468), _931470), _931474)))], (8585 ^ _782464) ^ [_931611, _931613, _931615] : [class_Lattices_Osemilattice__inf(_931611), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931611), _931613), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931611), _931613), _931615)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931611), _931613), _931615))], (8591 ^ _782464) ^ [_931736, _931738, _931740] : [class_Lattices_Olattice(_931736), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931736), _931738), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931736), _931738), _931740)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931736), _931738), _931740))], (8597 ^ _782464) ^ [_931861, _931863, _931865] : [class_Lattices_Osemilattice__inf(_931861), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931861), _931863), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931861), _931863), _931865)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931861), _931863), _931865))], (8603 ^ _782464) ^ [_931986, _931988, _931990] : [class_Lattices_Osemilattice__inf(_931986), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931986), _931988), _931990) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931986), _931990), _931988))], (8609 ^ _782464) ^ [_932095, _932097, _932099] : [class_Lattices_Olattice(_932095), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932095), _932097), _932099) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932095), _932099), _932097))], (8615 ^ _782464) ^ [_932204, _932206, _932208] : [class_Lattices_Osemilattice__inf(_932204), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932204), _932206), _932208) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932204), _932208), _932206))], (8621 ^ _782464) ^ [_932313, _932315, _932317, _932319, _932321] : [class_Lattices_Olattice(_932313), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932315, _932313)), _932317), _932319), _932321) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932313), hAPP(_932317, _932321)), hAPP(_932319, _932321)))], (8627 ^ _782464) ^ [_932450, _932452] : [class_Lattices_Osemilattice__inf(_932450), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932450), _932452), _932452) = _932452)], (8633 ^ _782464) ^ [_932541, _932543] : [class_Lattices_Osemilattice__inf(_932541), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932541), _932543), _932543) = _932543)], (8639 ^ _782464) ^ [_932632, _932634] : [class_Lattices_Obounded__lattice__top(_932632), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932632), _932634), c_Orderings_Otop__class_Otop(_932632)) = _932634)], (8645 ^ _782464) ^ [_932727, _932729] : [class_Lattices_Obounded__lattice__top(_932727), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932727), c_Orderings_Otop__class_Otop(_932727)), _932729) = _932729)], (8651 ^ _782464) ^ [_932822, _932824] : [class_Lattices_Olattice(_932822), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932822), _932824), _932824) = _932824)], (8657 ^ _782464) ^ [_932913, _932915, _932917, _932919] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932913, tc_HOL_Obool)), _932915), _932917), _932919)), -(hBOOL(hAPP(_932917, _932919)))], (8663 ^ _782464) ^ [_933024, _933026, _933028, _933030] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933024, tc_HOL_Obool)), _933026), _933028), _933030)), -(hBOOL(hAPP(_933026, _933030)))], (8669 ^ _782464) ^ [_933135, _933137, _933139, _933141] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933135, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933135, tc_HOL_Obool)), _933137), _933139)), _933141) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933135, tc_HOL_Obool)), _933137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933135, tc_HOL_Obool)), _933139), _933141)))], (8671 ^ _782464) ^ [_933208, _933210, _933212, _933214, _933216] : [-(hAPP(c_Set_Oimage(_933208, _933210, hAPP(hAPP(c_COMBB(_933212, _933210, _933208), _933214), _933216)), c_Orderings_Otop__class_Otop(tc_fun(_933208, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_933212, _933210, _933214), hAPP(c_Set_Oimage(_933208, _933212, _933216), c_Orderings_Otop__class_Otop(tc_fun(_933208, tc_HOL_Obool)))))], (8673 ^ _782464) ^ [_933280, _933282, _933284, _933286] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933280, tc_HOL_Obool)), _933282), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933280, tc_HOL_Obool)), _933284), _933286)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933280, tc_HOL_Obool)), _933284), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933280, tc_HOL_Obool)), _933282), _933286)))], (8675 ^ _782464) ^ [_933353, _933355, _933357] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933353, tc_HOL_Obool)), _933355), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933353, tc_HOL_Obool)), _933355), _933357)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933353, tc_HOL_Obool)), _933355), _933357))], (8677 ^ _782464) ^ [_933413, _933415, _933417] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933413, tc_HOL_Obool)), _933415), _933417) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933413, tc_HOL_Obool)), _933417), _933415))], (8679 ^ _782464) ^ [_933462, _933464] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933462, tc_HOL_Obool)), _933464), _933464) = _933464)], (8681 ^ _782464) ^ [_933498, _933500] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933498, tc_HOL_Obool)), _933500), c_Orderings_Otop__class_Otop(tc_fun(_933498, tc_HOL_Obool))) = _933500)], (8683 ^ _782464) ^ [_933539, _933541] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933539, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_933539, tc_HOL_Obool))), _933541) = _933541)], (8685 ^ _782464) ^ [_933580, _933582, _933584] : [class_Orderings_Otop(_933580), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_933582, _933580)), _933584) = c_Orderings_Otop__class_Otop(_933580))], (8691 ^ _782464) ^ [_933677, _933679, _933681, _933683, _933685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933677, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933679, _933677, _933681), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933679, tc_HOL_Obool)), _933683), _933685))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933677, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933679, _933677, _933681), _933683)), hAPP(c_Set_Oimage(_933679, _933677, _933681), _933685)))))], (8693 ^ _782464) ^ [_933761, _933763, _933765, _933767, _933769, _933771] : [-(hAPP(c_Set_Oimage(_933761, _933763, _933765), hAPP(c_Set_Oimage(_933767, _933761, _933769), _933771)) = hAPP(c_Set_Oimage(_933767, _933763, hAPP(hAPP(c_COMBB(_933761, _933763, _933767), _933765), _933769)), _933771))], (8695 ^ _782464) ^ [_933825, _933827, _933829, _933831, _933833] : [hAPP(c_Set_Oimage(_933825, _933827, _933829), _933831) = _933833, -(hAPP(c_Set_Oimage(tc_fun(_933825, tc_HOL_Obool), tc_fun(_933827, tc_HOL_Obool), c_Set_Oimage(_933825, _933827, _933829)), hAPP(c_Set_OPow(_933825), _933831)) = hAPP(c_Set_OPow(_933827), _933833))], (8701 ^ _782464) ^ [_933976, _933978, _933980] : [-(hAPP(c_Set_OPow(_933976), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933976, tc_HOL_Obool)), _933978), _933980)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_933976, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_933976), _933978)), hAPP(c_Set_OPow(_933976), _933980)))], (8703 ^ _782464) ^ [_934043] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_934043, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_934043, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_934043, tc_HOL_Obool)))], (8705 ^ _782464) ^ [_934085] : [-(hAPP(c_Set_OPow(_934085), c_Orderings_Otop__class_Otop(tc_fun(_934085, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_934085, tc_HOL_Obool), tc_HOL_Obool)))], (8707 ^ _782464) ^ [_934126] : [class_Complete__Lattice_Ocomplete__lattice(_934126), -(c_Complete__Lattice_OSup__class_OSup(_934126, c_Orderings_Otop__class_Otop(tc_fun(_934126, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_934126))], (8713 ^ _782464) ^ [_934219, _934221, _934223, _934225, _934227, _934229] : [hBOOL(hAPP(hAPP(c_member(_934219), _934221), _934223)), _934225 = hAPP(_934227, _934221), -(hBOOL(hAPP(hAPP(c_member(_934229), _934225), hAPP(c_Set_Oimage(_934219, _934229, _934227), _934223))))], (8723 ^ _782464) ^ [_934412, _934414, _934416, _934418, _934420] : [hBOOL(hAPP(hAPP(c_member(_934412), _934414), _934416)), -(hBOOL(hAPP(hAPP(c_member(_934418), hAPP(_934420, _934414)), hAPP(c_Set_Oimage(_934412, _934418, _934420), _934416))))], (8729 ^ _782464) ^ [_934567, _934569, _934571, _934573, _934575] : [hBOOL(hAPP(hAPP(c_member(_934567), _934569), hAPP(c_Set_Oimage(_934571, _934567, _934573), _934575))), 8733 ^ _782464 : [(8734 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_934571), 8732 ^ [_934567, _934569, _934571, _934573, _934575]), _934575)))], (8736 ^ _782464) ^ [] : [-(_934569 = hAPP(_934573, 8732 ^ [_934567, _934569, _934571, _934573, _934575]))]]], (8738 ^ _782464) ^ [_934751, _934753, _934755, _934757, _934759] : [-(hBOOL(hAPP(hAPP(c_member(_934751), _934753), hAPP(c_Set_Oimage(_934755, _934751, _934757), _934759)))), 8739 ^ _782464 : [(8740 ^ _782464) ^ [_934821] : [hBOOL(hAPP(hAPP(c_member(_934755), _934821), _934759)), _934753 = hAPP(_934757, _934821)]]], (8748 ^ _782464) ^ [_934969, _934971, _934973] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934969, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934969, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_934969, tc_HOL_Obool), tc_HOL_Obool)), _934971), _934973))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934969, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934969, tc_HOL_Obool), _934971)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934969, tc_HOL_Obool), _934973)))))], (8750 ^ _782464) ^ [_935049, _935051, _935053, _935055] : [class_Lattices_Osemilattice__inf(_935049), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935049), _935051), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935049), _935053), _935055))), 8757 ^ _782464 : [(8758 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935049), _935051), _935053)))], (8760 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935049), _935051), _935055)))]]], (8762 ^ _782464) ^ [_935272, _935274, _935276, _935278, _935280] : [class_Lattices_Osemilattice__inf(_935272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935272), _935274), _935276)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935272), _935278), _935280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935272), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935272), _935274), _935278)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935272), _935276), _935280))))], (8776 ^ _782464) ^ [_935543, _935545, _935547, _935549] : [class_Lattices_Osemilattice__inf(_935543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935543), _935545), _935547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935543), _935545), _935549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935543), _935545), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935543), _935547), _935549))))], (8790 ^ _782464) ^ [_935792, _935794, _935796, _935798] : [class_Lattices_Osemilattice__inf(_935792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935792), _935794), _935796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935792), _935794), _935798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935792), _935794), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935792), _935796), _935798))))], (8804 ^ _782464) ^ [_936041, _936043, _936045] : [class_Lattices_Osemilattice__inf(_936041), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936041), _936043), _936045)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936041), _936045), _936043) = _936043)], (8814 ^ _782464) ^ [_936202, _936204, _936206] : [class_Lattices_Osemilattice__inf(_936202), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936202), _936204), _936206)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936202), _936204), _936206) = _936204)], (8824 ^ _782464) ^ [_936363, _936365, _936367, _936369] : [class_Lattices_Osemilattice__inf(_936363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936363), _936365), _936367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936363), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936363), _936369), _936365)), _936367)))], (8834 ^ _782464) ^ [_936542, _936544, _936546, _936548] : [class_Lattices_Osemilattice__inf(_936542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936542), _936544), _936546)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936542), _936544), _936548)), _936546)))], (8844 ^ _782464) ^ [_936721, _936723, _936725, _936727] : [class_Lattices_Osemilattice__inf(_936721), 8847 ^ _782464 : [(8848 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936721), _936723), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936721), _936725), _936727))), 8851 ^ _782464 : [(8852 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936721), _936723), _936725)))], (8854 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936721), _936723), _936727)))]]], (8856 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936721), _936723), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936721), _936725), _936727)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936721), _936723), _936725)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936721), _936723), _936727))]]], (8866 ^ _782464) ^ [_937101, _937103, _937105] : [class_Lattices_Osemilattice__inf(_937101), 8869 ^ _782464 : [(8870 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937101), _937103), _937105)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937101), _937103), _937105) = _937103)], (8876 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937101), _937103), _937105) = _937103, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937101), _937103), _937105)))]]], (8882 ^ _782464) ^ [_937357, _937359, _937361] : [class_Lattices_Osemilattice__inf(_937357), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937357), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937357), _937359), _937361)), _937361)))], (8888 ^ _782464) ^ [_937464, _937466, _937468] : [class_Lattices_Olattice(_937464), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937464), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937464), _937466), _937468)), _937468)))], (8894 ^ _782464) ^ [_937571, _937573, _937575] : [class_Lattices_Osemilattice__inf(_937571), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937571), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937571), _937573), _937575)), _937573)))], (8900 ^ _782464) ^ [_937678, _937680, _937682] : [class_Lattices_Olattice(_937678), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937678), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937678), _937680), _937682)), _937680)))], (8906 ^ _782464) ^ [_937785, _937787, _937789, _937791, _937793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937785, tc_HOL_Obool)), _937787), _937789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937791, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937785, _937791, _937793), _937787)), hAPP(c_Set_Oimage(_937785, _937791, _937793), _937789))))], (8912 ^ _782464) ^ [_937960, _937962, _937964, _937966, _937968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937960, tc_HOL_Obool)), _937962), hAPP(c_Set_Oimage(_937964, _937960, _937966), _937968))), 8916 ^ _782464 : [(8917 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937964, tc_HOL_Obool)), 8915 ^ [_937960, _937962, _937964, _937966, _937968]), _937968)))], (8919 ^ _782464) ^ [] : [-(_937962 = hAPP(c_Set_Oimage(_937964, _937960, _937966), 8915 ^ [_937960, _937962, _937964, _937966, _937968]))]]], (8921 ^ _782464) ^ [_938164, _938166, _938168, _938170, _938172] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938164, tc_HOL_Obool)), _938166), hAPP(c_Set_Oimage(_938168, _938164, _938170), _938172)))), 8922 ^ _782464 : [(8923 ^ _782464) ^ [_938244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938168, tc_HOL_Obool)), _938244), _938172)), _938166 = hAPP(c_Set_Oimage(_938168, _938164, _938170), _938244)]]], (8931 ^ _782464) ^ [_938409, _938411, _938413, _938415, _938417] : [-(hAPP(c_Set_Oimage(_938409, _938411, _938413), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938409, tc_HOL_Obool)), _938415), _938417)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938411, tc_HOL_Obool)), hAPP(c_Set_Oimage(_938409, _938411, _938413), _938415)), hAPP(c_Set_Oimage(_938409, _938411, _938413), _938417)))], (8933 ^ _782464) ^ [_938483, _938485, _938487, _938489] : [class_Lattices_Odistrib__lattice(_938483), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938483), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938483), _938485), _938487)), _938489) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938483), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938483), _938485), _938489)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938483), _938487), _938489)))], (8939 ^ _782464) ^ [_938642, _938644, _938646, _938648] : [class_Lattices_Odistrib__lattice(_938642), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938642), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938642), _938644), _938646)), _938648) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938642), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938642), _938644), _938648)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938642), _938646), _938648)))], (8945 ^ _782464) ^ [_938801, _938803, _938805, _938807] : [class_Lattices_Odistrib__lattice(_938801), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938801), _938803), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938801), _938805), _938807)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938801), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938801), _938803), _938805)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938801), _938803), _938807)))], (8951 ^ _782464) ^ [_938960, _938962, _938964, _938966] : [class_Lattices_Odistrib__lattice(_938960), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938960), _938962), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938960), _938964), _938966)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938960), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938960), _938962), _938964)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938960), _938962), _938966)))], (8957 ^ _782464) ^ [_939119, _939121, _939123] : [class_Lattices_Olattice(_939119), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939119), _939121), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939119), _939121), _939123)) = _939121)], (8963 ^ _782464) ^ [_939228, _939230, _939232] : [class_Lattices_Olattice(_939228), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939228), _939230), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939228), _939230), _939232)) = _939230)], (8969 ^ _782464) ^ [_939337, _939339, _939341, _939343] : [hBOOL(hAPP(hAPP(c_member(_939337), _939339), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939337, tc_HOL_Obool)), _939341), _939343))), -(hBOOL(hAPP(hAPP(c_member(_939337), _939339), _939343)))], (8975 ^ _782464) ^ [_939468, _939470, _939472, _939474] : [hBOOL(hAPP(hAPP(c_member(_939468), _939470), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939468, tc_HOL_Obool)), _939472), _939474))), -(hBOOL(hAPP(hAPP(c_member(_939468), _939470), _939472)))], (8981 ^ _782464) ^ [_939620, _939622, _939624, _939626] : [hBOOL(hAPP(hAPP(c_member(_939620), _939622), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939620, tc_HOL_Obool)), _939624), _939626))), 8984 ^ _782464 : [(8985 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939620), _939622), _939624)))], (8987 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939620), _939622), _939626)))]]], (8989 ^ _782464) ^ [_939787, _939789, _939791, _939793] : [-(hBOOL(hAPP(hAPP(c_member(_939787), _939789), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939787, tc_HOL_Obool)), _939791), _939793)))), hBOOL(hAPP(hAPP(c_member(_939787), _939789), _939791)), hBOOL(hAPP(hAPP(c_member(_939787), _939789), _939793))], (8999 ^ _782464) ^ [_939990, _939992, _939994, _939996, _939998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939990, tc_HOL_Obool)), _939992), _939994)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939990, tc_HOL_Obool)), _939996), _939998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939990, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939990, tc_HOL_Obool)), _939992), _939996)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939990, tc_HOL_Obool)), _939994), _939998))))], (9009 ^ _782464) ^ [_940235, _940237, _940239, _940241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940235, tc_HOL_Obool)), _940237), _940239)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940235, tc_HOL_Obool)), _940237), _940241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940235, tc_HOL_Obool)), _940237), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940235, tc_HOL_Obool)), _940239), _940241))))], (9019 ^ _782464) ^ [_940454, _940456, _940458] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940454, tc_HOL_Obool)), _940456), _940458)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940454, tc_HOL_Obool)), _940458), _940456) = _940456)], (9025 ^ _782464) ^ [_940575, _940577, _940579] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940575, tc_HOL_Obool)), _940577), _940579)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940575, tc_HOL_Obool)), _940577), _940579) = _940577)], (9031 ^ _782464) ^ [_940696, _940698, _940700] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940696, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940696, tc_HOL_Obool)), _940698), _940700)), _940700)))], (9033 ^ _782464) ^ [_940744, _940746, _940748] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940744, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940744, tc_HOL_Obool)), _940746), _940748)), _940746)))], (9035 ^ _782464) ^ [_940792, _940794, _940796, _940798] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940792, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940792, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940792, tc_HOL_Obool)), _940794), _940796)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940792, tc_HOL_Obool)), _940796), _940798))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940792, tc_HOL_Obool)), _940798), _940794)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940792, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940792, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940792, tc_HOL_Obool)), _940794), _940796)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940792, tc_HOL_Obool)), _940796), _940798))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940792, tc_HOL_Obool)), _940798), _940794)))], (9037 ^ _782464) ^ [_940931, _940933, _940935, _940937] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940931, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940931, tc_HOL_Obool)), _940933), _940935)), _940937) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940931, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940931, tc_HOL_Obool)), _940933), _940937)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940931, tc_HOL_Obool)), _940935), _940937)))], (9039 ^ _782464) ^ [_941015, _941017, _941019, _941021] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941015, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941015, tc_HOL_Obool)), _941017), _941019)), _941021) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941015, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941015, tc_HOL_Obool)), _941017), _941021)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941015, tc_HOL_Obool)), _941019), _941021)))], (9041 ^ _782464) ^ [_941099, _941101, _941103, _941105] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941099, tc_HOL_Obool)), _941101), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941099, tc_HOL_Obool)), _941103), _941105)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941099, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941099, tc_HOL_Obool)), _941101), _941103)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941099, tc_HOL_Obool)), _941101), _941105)))], (9043 ^ _782464) ^ [_941183, _941185, _941187, _941189] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941183, tc_HOL_Obool)), _941185), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941183, tc_HOL_Obool)), _941187), _941189)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941183, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941183, tc_HOL_Obool)), _941185), _941187)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941183, tc_HOL_Obool)), _941185), _941189)))], (9045 ^ _782464) ^ [_941267, _941269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941267, tc_HOL_Obool)), _941269), c_Orderings_Otop__class_Otop(tc_fun(_941267, tc_HOL_Obool)))))], (9047 ^ _782464) ^ [_941307, _941309] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941307, tc_HOL_Obool)), _941309), c_Orderings_Otop__class_Otop(tc_fun(_941307, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_941307, tc_HOL_Obool)))], (9049 ^ _782464) ^ [_941353, _941355] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941353, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_941353, tc_HOL_Obool))), _941355) = c_Orderings_Otop__class_Otop(tc_fun(_941353, tc_HOL_Obool)))], (9051 ^ _782464) ^ [_941399, _941401, _941403, _941405, _941407] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941399, tc_fun(_941401, tc_HOL_Obool)), _941403), hAPP(hAPP(c_COMBS(_941399, tc_fun(_941401, tc_HOL_Obool), tc_fun(_941401, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_941401, tc_HOL_Obool), tc_fun(tc_fun(_941401, tc_HOL_Obool), tc_fun(_941401, tc_HOL_Obool)), _941399), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941401, tc_HOL_Obool))), _941405)), _941407)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941401, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_941401, tc_HOL_Obool), hAPP(c_Set_Oimage(_941399, tc_fun(_941401, tc_HOL_Obool), _941405), _941403))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_941401, tc_HOL_Obool), hAPP(c_Set_Oimage(_941399, tc_fun(_941401, tc_HOL_Obool), _941407), _941403))))], (9053 ^ _782464) ^ [_941528, _941530, _941532, _941534, _941536, _941538] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941528, tc_fun(_941530, tc_HOL_Obool)), _941532), hAPP(hAPP(c_COMBB(_941534, tc_fun(_941530, tc_HOL_Obool), _941528), _941536), _941538)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941534, tc_fun(_941530, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941528, _941534, _941538), _941532)), _941536))], (9055 ^ _782464) ^ [_941605, _941607, _941609, _941611, _941613, _941615] : [-(hAPP(c_Set_Oimage(_941605, _941607, _941609), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941611, tc_fun(_941605, tc_HOL_Obool)), _941613), _941615)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941611, tc_fun(_941607, tc_HOL_Obool)), _941613), hAPP(hAPP(c_COMBB(tc_fun(_941605, tc_HOL_Obool), tc_fun(_941607, tc_HOL_Obool), _941611), c_Set_Oimage(_941605, _941607, _941609)), _941615)))], (9057 ^ _782464) ^ [_941689, _941691, _941693, _941695, _941697, _941699] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941689, tc_fun(_941691, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941693, _941689, _941695), _941697)), _941699) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941693, tc_fun(_941691, tc_HOL_Obool)), _941697), hAPP(hAPP(c_COMBB(_941689, tc_fun(_941691, tc_HOL_Obool), _941693), _941699), _941695)))], (9059 ^ _782464) ^ [_941766, _941768, _941770, _941772, _941774, _941776] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941766, tc_fun(_941768, tc_HOL_Obool)), _941770), hAPP(hAPP(c_COMBB(_941772, tc_fun(_941768, tc_HOL_Obool), _941766), _941774), _941776)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941772, tc_fun(_941768, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941766, _941772, _941776), _941770)), _941774))], (9061 ^ _782464) ^ [_941843, _941845, _941847, _941849, _941851, _941853] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941843, tc_fun(_941845, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941847, _941843, _941849), _941851)), _941853) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941847, tc_fun(_941845, tc_HOL_Obool)), _941851), hAPP(hAPP(c_COMBB(_941843, tc_fun(_941845, tc_HOL_Obool), _941847), _941853), _941849)))], (9063 ^ _782464) ^ [_941941, _941943, _941945, _941947] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941941, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_941941, tc_fun(_941941, tc_HOL_Obool), tc_HOL_Obool), c_member(_941941)), _941943)), hAPP(hAPP(c_COMBC(_941941, tc_fun(_941941, tc_HOL_Obool), tc_HOL_Obool), c_member(_941941)), _941945)), _941947)), -(hBOOL(hAPP(hAPP(c_member(_941941), _941947), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941941, tc_HOL_Obool)), _941943), _941945))))], (9069 ^ _782464) ^ [_942140, _942142, _942144, _942146] : [hBOOL(hAPP(hAPP(c_member(_942140), _942146), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942140, tc_HOL_Obool)), _942142), _942144))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942140, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_942140, tc_fun(_942140, tc_HOL_Obool), tc_HOL_Obool), c_member(_942140)), _942142)), hAPP(hAPP(c_COMBC(_942140, tc_fun(_942140, tc_HOL_Obool), tc_HOL_Obool), c_member(_942140)), _942144)), _942146)))], (9075 ^ _782464) ^ [_942345, _942347, _942349, _942351, _942353] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942345, tc_fun(_942347, tc_HOL_Obool)), _942349), hAPP(hAPP(c_COMBB(tc_fun(_942347, tc_HOL_Obool), tc_fun(_942347, tc_HOL_Obool), _942345), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942347, tc_HOL_Obool)), _942351)), _942353)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942347, tc_HOL_Obool)), _942351), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942345, tc_fun(_942347, tc_HOL_Obool)), _942349), _942353)))], (9077 ^ _782464) ^ [_942435, _942437, _942439, _942441, _942443] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942435, tc_fun(_942437, tc_HOL_Obool)), _942439), hAPP(hAPP(c_COMBC(_942435, tc_fun(_942437, tc_HOL_Obool), tc_fun(_942437, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_942437, tc_HOL_Obool), tc_fun(tc_fun(_942437, tc_HOL_Obool), tc_fun(_942437, tc_HOL_Obool)), _942435), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942437, tc_HOL_Obool))), _942441)), _942443)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942437, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942435, tc_fun(_942437, tc_HOL_Obool)), _942439), _942441)), _942443))], (9079 ^ _782464) ^ [_942544, _942546, _942548, _942550, _942552] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942544, tc_HOL_Obool)), _942546), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942548, tc_fun(_942544, tc_HOL_Obool)), _942550), _942552)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942548, tc_fun(_942544, tc_HOL_Obool)), _942550), hAPP(hAPP(c_COMBB(tc_fun(_942544, tc_HOL_Obool), tc_fun(_942544, tc_HOL_Obool), _942548), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942544, tc_HOL_Obool)), _942546)), _942552)))], (9081 ^ _782464) ^ [_942634, _942636, _942638, _942640, _942642] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942634, tc_HOL_Obool)), _942636), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942638, tc_fun(_942634, tc_HOL_Obool)), _942640), _942642)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942638, tc_fun(_942634, tc_HOL_Obool)), _942640), hAPP(hAPP(c_COMBB(tc_fun(_942634, tc_HOL_Obool), tc_fun(_942634, tc_HOL_Obool), _942638), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942634, tc_HOL_Obool)), _942636)), _942642)))], (9083 ^ _782464) ^ [_942724, _942726, _942728, _942730, _942732] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942724, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942726, tc_fun(_942724, tc_HOL_Obool)), _942728), _942730)), _942732) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942726, tc_fun(_942724, tc_HOL_Obool)), _942728), hAPP(hAPP(c_COMBC(_942726, tc_fun(_942724, tc_HOL_Obool), tc_fun(_942724, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_942724, tc_HOL_Obool), tc_fun(tc_fun(_942724, tc_HOL_Obool), tc_fun(_942724, tc_HOL_Obool)), _942726), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942724, tc_HOL_Obool))), _942730)), _942732)))], (9085 ^ _782464) ^ [_942833, _942835, _942837, _942839, _942841, _942843, _942845] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942833, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942835, tc_fun(_942833, tc_HOL_Obool)), _942837), _942839)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942841, tc_fun(_942833, tc_HOL_Obool)), _942843), _942845)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942835, tc_fun(_942833, tc_HOL_Obool)), _942837), hAPP(hAPP(c_COMBB(tc_fun(_942841, tc_fun(_942833, tc_HOL_Obool)), tc_fun(_942833, tc_HOL_Obool), _942835), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942841, tc_fun(_942833, tc_HOL_Obool)), _942843)), hAPP(hAPP(c_COMBC(_942835, tc_fun(_942841, tc_fun(_942833, tc_HOL_Obool)), tc_fun(_942841, tc_fun(_942833, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_942833, tc_HOL_Obool), tc_fun(_942833, tc_HOL_Obool)), tc_fun(tc_fun(_942841, tc_fun(_942833, tc_HOL_Obool)), tc_fun(_942841, tc_fun(_942833, tc_HOL_Obool))), _942835), c_COMBB(tc_fun(_942833, tc_HOL_Obool), tc_fun(_942833, tc_HOL_Obool), _942841)), hAPP(hAPP(c_COMBB(tc_fun(_942833, tc_HOL_Obool), tc_fun(tc_fun(_942833, tc_HOL_Obool), tc_fun(_942833, tc_HOL_Obool)), _942835), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942833, tc_HOL_Obool))), _942839))), _942845))))], (9087 ^ _782464) ^ [_943036, _943038, _943040, _943042, _943044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943036, tc_HOL_Obool)), hAPP(c_Set_Oimage(_943038, _943036, _943040), _943042)), _943044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_943036, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_943038, tc_HOL_Obool), tc_fun(_943036, tc_HOL_Obool), c_Set_Oimage(_943038, _943036, _943040)), hAPP(c_Set_OPow(_943038), _943042))), hAPP(c_Set_OPow(_943036), _943044))))], (9093 ^ _782464) ^ [_943233, _943235, _943237, _943239, _943241] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943233, tc_fun(_943235, tc_HOL_Obool)), _943237), hAPP(hAPP(c_COMBS(_943233, tc_fun(_943235, tc_HOL_Obool), tc_fun(_943235, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_943235, tc_HOL_Obool), tc_fun(tc_fun(_943235, tc_HOL_Obool), tc_fun(_943235, tc_HOL_Obool)), _943233), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943235, tc_HOL_Obool))), _943239)), _943241)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943235, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943233, tc_fun(_943235, tc_HOL_Obool)), _943237), _943239)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943233, tc_fun(_943235, tc_HOL_Obool)), _943237), _943241)))], (9105 ^ _782464) ^ [_943604, _943606, _943608, _943610] : [9107 ^ _782464 : [(9108 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_943606), 9106 ^ [_943604, _943606, _943608, _943610]), _943608)))], (9110 ^ _782464) ^ [] : [hAPP(_943610, 9106 ^ [_943604, _943606, _943608, _943610]) = c_Orderings_Otop__class_Otop(tc_fun(_943604, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_943604, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943606, tc_fun(_943604, tc_HOL_Obool)), _943608), _943610))], (9095 ^ _782464) ^ [_943375, _943377, _943379, _943381] : [c_Orderings_Otop__class_Otop(tc_fun(_943375, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943377, tc_fun(_943375, tc_HOL_Obool)), _943379), _943381), 9098 ^ _782464 : [(9099 ^ _782464) ^ [_943491] : [hBOOL(hAPP(hAPP(c_member(_943377), _943491), _943379)), -(hAPP(_943381, _943491) = c_Orderings_Otop__class_Otop(tc_fun(_943375, tc_HOL_Obool)))]]], (9124 ^ _782464) ^ [_944084, _944086, _944088, _944090] : [9126 ^ _782464 : [(9127 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944084), 9125 ^ [_944084, _944086, _944088, _944090]), _944088)))], (9129 ^ _782464) ^ [] : [hAPP(_944090, 9125 ^ [_944084, _944086, _944088, _944090]) = c_Orderings_Otop__class_Otop(tc_fun(_944086, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_944084, tc_fun(_944086, tc_HOL_Obool)), _944088), _944090) = c_Orderings_Otop__class_Otop(tc_fun(_944086, tc_HOL_Obool)))], (9114 ^ _782464) ^ [_943855, _943857, _943859, _943861] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943855, tc_fun(_943857, tc_HOL_Obool)), _943859), _943861) = c_Orderings_Otop__class_Otop(tc_fun(_943857, tc_HOL_Obool)), 9117 ^ _782464 : [(9118 ^ _782464) ^ [_943971] : [hBOOL(hAPP(hAPP(c_member(_943855), _943971), _943859)), -(hAPP(_943861, _943971) = c_Orderings_Otop__class_Otop(tc_fun(_943857, tc_HOL_Obool)))]]], (9133 ^ _782464) ^ [_944314, _944316] : [class_Orderings_Otop(_944314), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944314), _944316), c_Orderings_Otop__class_Otop(_944314))))], (9139 ^ _782464) ^ [_944407, _944409] : [class_Lattices_Obounded__lattice__top(_944407), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944407), _944409), c_Orderings_Otop__class_Otop(_944407)) = c_Orderings_Otop__class_Otop(_944407))], (9145 ^ _782464) ^ [_944506, _944508] : [class_Lattices_Obounded__lattice__top(_944506), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944506), c_Orderings_Otop__class_Otop(_944506)), _944508) = c_Orderings_Otop__class_Otop(_944506))], (9151 ^ _782464) ^ [_944605, _944607, _944609, _944611] : [class_Lattices_Olattice(_944605), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944605), _944607), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944605), _944609), _944611))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944605), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944605), _944607), _944609)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944605), _944607), _944611)))))], (9157 ^ _782464) ^ [_944778, _944780, _944782, _944784] : [class_Lattices_Olattice(_944778), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944778), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944778), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944778), _944780), _944782)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944778), _944780), _944784))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944778), _944780), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944778), _944782), _944784)))))], (9163 ^ _782464) ^ [_944951, _944953, _944955] : [class_Lattices_Oboolean__algebra(_944951), -(hAPP(c_Groups_Ouminus__class_Ouminus(_944951), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944951), _944953), _944955)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944951), hAPP(c_Groups_Ouminus__class_Ouminus(_944951), _944953)), hAPP(c_Groups_Ouminus__class_Ouminus(_944951), _944955)))], (9169 ^ _782464) ^ [_945090, _945092, _945094] : [class_Lattices_Oboolean__algebra(_945090), -(hAPP(c_Groups_Ouminus__class_Ouminus(_945090), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945090), _945092), _945094)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_945090), hAPP(c_Groups_Ouminus__class_Ouminus(_945090), _945092)), hAPP(c_Groups_Ouminus__class_Ouminus(_945090), _945094)))], (9175 ^ _782464) ^ [_945229, _945231, _945233] : [class_Groups_Oordered__ab__group__add(_945229), -(hAPP(c_Set_Oimage(_945229, _945229, c_Groups_Ouminus__class_Ouminus(_945229)), c_SetInterval_Oord__class_OatLeastAtMost(_945229, _945231, _945233)) = c_SetInterval_Oord__class_OatLeastAtMost(_945229, hAPP(c_Groups_Ouminus__class_Ouminus(_945229), _945233), hAPP(c_Groups_Ouminus__class_Ouminus(_945229), _945231)))], (9181 ^ _782464) ^ [_945381, _945383, _945385, _945387] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945381, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945381, tc_HOL_Obool)), _945383), _945385)), _945387) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945381, tc_HOL_Obool)), _945383), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945381, tc_HOL_Obool)), _945385), _945387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945381, tc_HOL_Obool)), _945387), _945383)))], (9187 ^ _782464) ^ [_945566, _945568, _945570, _945572] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945566, tc_HOL_Obool)), _945572), _945568)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945566, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945566, tc_HOL_Obool)), _945568), _945570)), _945572) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945566, tc_HOL_Obool)), _945568), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945566, tc_HOL_Obool)), _945570), _945572)))], (9193 ^ _782464) ^ [_945757, _945759, _945761] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945757, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945757, tc_HOL_Obool)), _945759), _945761)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945757, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945757, tc_HOL_Obool)), _945759)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945757, tc_HOL_Obool)), _945761)))], (9195 ^ _782464) ^ [_945830, _945832, _945834] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945830, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945830, tc_HOL_Obool)), _945832), _945834)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945830, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945830, tc_HOL_Obool)), _945832)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945830, tc_HOL_Obool)), _945834)))], (9197 ^ _782464) ^ [_945903, _945905] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945903, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945903, tc_HOL_Obool)), _945905)), _945905) = c_Orderings_Otop__class_Otop(tc_fun(_945903, tc_HOL_Obool)))], (9199 ^ _782464) ^ [_945952, _945954] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945952, tc_HOL_Obool)), _945954), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945952, tc_HOL_Obool)), _945954)) = c_Orderings_Otop__class_Otop(tc_fun(_945952, tc_HOL_Obool)))], (9201 ^ _782464) ^ [_946001, _946003, _946005, _946007] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946001, tc_fun(_946003, tc_HOL_Obool)), _946005), _946007) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_946003, tc_HOL_Obool), hAPP(c_Set_Oimage(_946001, tc_fun(_946003, tc_HOL_Obool), _946007), _946005)))], (9203 ^ _782464) ^ [_946058, _946060, _946062, _946064] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_946058, tc_HOL_Obool), hAPP(c_Set_Oimage(_946060, tc_fun(_946058, tc_HOL_Obool), _946062), _946064)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946060, tc_fun(_946058, tc_HOL_Obool)), _946064), _946062))], (9205 ^ _782464) ^ [_946115, _946117, _946119, _946121, _946123] : [hBOOL(hAPP(hAPP(c_member(_946115), _946117), _946119)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946121, tc_HOL_Obool)), hAPP(_946123, _946117)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946115, tc_fun(_946121, tc_HOL_Obool)), _946119), _946123)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946115, tc_fun(_946121, tc_HOL_Obool)), _946119), _946123))], (9211 ^ _782464) ^ [_946288, _946290, _946292, _946294] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946288, tc_fun(_946290, tc_HOL_Obool)), _946292), _946294) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_946290, tc_HOL_Obool), hAPP(c_Set_Oimage(_946288, tc_fun(_946290, tc_HOL_Obool), _946294), _946292)))], (9213 ^ _782464) ^ [_946345, _946347, _946349, _946351] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_946345, tc_HOL_Obool), hAPP(c_Set_Oimage(_946347, tc_fun(_946345, tc_HOL_Obool), _946349), _946351)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946347, tc_fun(_946345, tc_HOL_Obool)), _946351), _946349))], (9215 ^ _782464) ^ [_946402, _946404, _946406, _946408, _946410] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946402, tc_fun(_946404, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946402, tc_HOL_Obool)), _946406), _946408)), _946410) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946404, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946402, tc_fun(_946404, tc_HOL_Obool)), _946406), _946410)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946402, tc_fun(_946404, tc_HOL_Obool)), _946408), _946410)))], (9217 ^ _782464) ^ [_946512, _946514, _946516, _946518] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946512, tc_fun(_946514, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946512, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946514, tc_HOL_Obool), tc_fun(_946514, tc_HOL_Obool), _946512), hAPP(c_COMBC(_946514, tc_fun(_946514, tc_HOL_Obool), tc_HOL_Obool), c_member(_946514))), _946516)), _946518)), -(hBOOL(hAPP(hAPP(c_member(_946514), _946518), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946512, tc_fun(_946514, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946512, tc_HOL_Obool))), _946516))))], (9223 ^ _782464) ^ [_946731, _946733, _946735, _946737] : [hBOOL(hAPP(hAPP(c_member(_946733), _946737), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946731, tc_fun(_946733, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946731, tc_HOL_Obool))), _946735))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946731, tc_fun(_946733, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946731, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946733, tc_HOL_Obool), tc_fun(_946733, tc_HOL_Obool), _946731), hAPP(c_COMBC(_946733, tc_fun(_946733, tc_HOL_Obool), tc_HOL_Obool), c_member(_946733))), _946735)), _946737)))], (9229 ^ _782464) ^ [_946977, _946979, _946981, _946983] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946977, tc_fun(_946979, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946977, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946979, tc_HOL_Obool), tc_fun(_946979, tc_HOL_Obool), _946977), hAPP(c_COMBC(_946979, tc_fun(_946979, tc_HOL_Obool), tc_HOL_Obool), c_member(_946979))), _946981)), _946983)), -(hBOOL(hAPP(hAPP(c_member(_946979), _946983), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946977, tc_fun(_946979, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946977, tc_HOL_Obool))), _946981))))], (9235 ^ _782464) ^ [_947196, _947198, _947200, _947202] : [hBOOL(hAPP(hAPP(c_member(_947198), _947202), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_947196, tc_fun(_947198, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_947196, tc_HOL_Obool))), _947200))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_947196, tc_fun(_947198, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_947196, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_947198, tc_HOL_Obool), tc_fun(_947198, tc_HOL_Obool), _947196), hAPP(c_COMBC(_947198, tc_fun(_947198, tc_HOL_Obool), tc_HOL_Obool), c_member(_947198))), _947200)), _947202)))], (9241 ^ _782464) ^ [_947421, _947423, _947425, _947427] : [-(hAPP(c_Set_Oimage(_947421, _947423, _947425), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947421, tc_HOL_Obool), _947427)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947421, tc_HOL_Obool), tc_fun(_947423, tc_HOL_Obool)), _947427), c_Set_Oimage(_947421, _947423, _947425)))], (9243 ^ _782464) ^ [_947482, _947484, _947486] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_947482, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_947482, tc_HOL_Obool), tc_HOL_Obool)), _947484), _947486)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947482, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_947482, tc_HOL_Obool), _947484)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_947482, tc_HOL_Obool), _947486)))], (9245 ^ _782464) ^ [_947552, _947554, _947556] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947552, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947552, tc_HOL_Obool), _947554)), _947556) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947552, tc_HOL_Obool), tc_fun(_947552, tc_HOL_Obool)), _947554), hAPP(hAPP(c_COMBC(tc_fun(_947552, tc_HOL_Obool), tc_fun(_947552, tc_HOL_Obool), tc_fun(_947552, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947552, tc_HOL_Obool))), _947556)))], (9247 ^ _782464) ^ [_947635, _947637, _947639] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947635, tc_HOL_Obool)), _947637), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947635, tc_HOL_Obool), _947639)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947635, tc_HOL_Obool), tc_fun(_947635, tc_HOL_Obool)), _947639), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947635, tc_HOL_Obool)), _947637)))], (9249 ^ _782464) ^ [_947702, _947704, _947706] : [class_Groups_Oordered__ab__group__add(_947702), -(hAPP(c_Set_Oimage(_947702, _947702, c_Groups_Ouminus__class_Ouminus(_947702)), c_SetInterval_Oord__class_OgreaterThanAtMost(_947702, _947704, _947706)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_947702, hAPP(c_Groups_Ouminus__class_Ouminus(_947702), _947706)), hAPP(c_Groups_Ouminus__class_Ouminus(_947702), _947704)))], (9255 ^ _782464) ^ [_947837, _947839, _947841] : [class_Groups_Oordered__ab__group__add(_947837), -(hAPP(c_Set_Oimage(_947837, _947837, c_Groups_Ouminus__class_Ouminus(_947837)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_947837, _947839), _947841)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_947837, hAPP(c_Groups_Ouminus__class_Ouminus(_947837), _947841), hAPP(c_Groups_Ouminus__class_Ouminus(_947837), _947839)))], (9261 ^ _782464) ^ [_947972, _947974] : [class_Lattices_Oboolean__algebra(_947972), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947972), hAPP(c_Groups_Ouminus__class_Ouminus(_947972), _947974)), _947974) = c_Orderings_Otop__class_Otop(_947972))], (9267 ^ _782464) ^ [_948077, _948079, _948081, _948083] : [hAPP(c_Set_Oimage(_948077, _948079, _948081), c_Orderings_Otop__class_Otop(tc_fun(_948077, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_948079, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948079, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_948079, tc_HOL_Obool)), hAPP(c_Set_Oimage(_948077, _948079, _948081), _948083))), hAPP(c_Set_Oimage(_948077, _948079, _948081), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_948077, tc_HOL_Obool)), _948083)))))], (9273 ^ _782464) ^ [_948288, _948290, _948292] : [hAPP(c_Set_Oimage(_948290, tc_fun(_948290, tc_HOL_Obool), _948288), _948292) = hAPP(c_Set_OPow(_948290), _948292)], (9275 ^ _782464) ^ [_948330, _948332, _948334, _948336] : [class_Orderings_Oorder(_948330), class_Orderings_Oorder(_948332), c_Orderings_Oorder__class_Omono(_948332, _948330, _948334), -(c_Orderings_Oord__class_OLeast(_948330, hAPP(hAPP(c_COMBC(_948330, tc_fun(_948330, tc_HOL_Obool), tc_HOL_Obool), c_member(_948330)), hAPP(c_Set_Oimage(_948332, _948330, _948334), _948336))) = hAPP(_948334, c_Orderings_Oord__class_OLeast(_948332, hAPP(hAPP(c_COMBC(_948332, tc_fun(_948332, tc_HOL_Obool), tc_HOL_Obool), c_member(_948332)), _948336)))), 9288 ^ _782464 : [(9289 ^ _782464) ^ [_948614] : [hBOOL(hAPP(hAPP(c_member(_948332), _948614), _948336)), 9293 ^ _782464 : [(9294 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_948332), 9292 ^ [_948330, _948332, _948334, _948336, _948614]), _948336)))], (9296 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948332), _948614), 9292 ^ [_948330, _948332, _948334, _948336, _948614]))]]]]], (9300 ^ _782464) ^ [_948907, _948909, _948911] : [class_Lattices_Oboolean__algebra(_948907), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948907), _948909), _948911) = c_Orderings_Obot__class_Obot(_948907), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_948907), _948909), _948911) = c_Orderings_Otop__class_Otop(_948907), -(hAPP(c_Groups_Ouminus__class_Ouminus(_948907), _948909) = _948911)], (9314 ^ _782464) ^ [_949142, _949144] : [-(hAPP(c_Set_Oimage(_949142, _949142, c_COMBI(_949142)), _949144) = _949144)], (9316 ^ _782464) ^ [_949176, _949178, _949180, _949182, _949184] : [hBOOL(hAPP(hAPP(c_member(_949176), _949178), hAPP(c_Set_Oimage(_949180, _949176, _949182), _949184))), 9320 ^ _782464 : [(9321 ^ _782464) ^ [] : [-(_949178 = hAPP(_949182, 9319 ^ [_949176, _949178, _949180, _949182, _949184]))], (9323 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_949180), 9319 ^ [_949176, _949178, _949180, _949182, _949184]), _949184)))]]], (9325 ^ _782464) ^ [_949368, _949370, _949372, _949374, _949376] : [9327 ^ _782464 : [(9328 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_949368), 9326 ^ [_949368, _949370, _949372, _949374, _949376]), _949370)))], (9330 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_949372), hAPP(_949374, 9326 ^ [_949368, _949370, _949372, _949374, _949376])), _949376))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949372, tc_HOL_Obool)), hAPP(c_Set_Oimage(_949368, _949372, _949374), _949370)), _949376)))], (9334 ^ _782464) ^ [_949610, _949612, _949614] : [class_Orderings_Oorder(_949610), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949610, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949610, _949612, _949614)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949610), _949614)) = c_Orderings_Obot__class_Obot(tc_fun(_949610, tc_HOL_Obool)))], (9340 ^ _782464) ^ [_949737, _949739, _949741] : [class_Orderings_Oorder(_949737), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949737, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_949737), _949739)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949737, _949739, _949741)) = c_Orderings_Obot__class_Obot(tc_fun(_949737, tc_HOL_Obool)))], (9346 ^ _782464) ^ [_949864, _949866, _949868] : [class_Orderings_Oorder(_949864), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949864, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949864, _949866, _949868)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949864), _949868)) = c_Orderings_Obot__class_Obot(tc_fun(_949864, tc_HOL_Obool)))], (9352 ^ _782464) ^ [_949991, _949993, _949995] : [class_Orderings_Oorder(_949991), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949991, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_949991, _949993), _949995)), hAPP(c_SetInterval_Oord__class_OatLeast(_949991), _949995)) = c_Orderings_Obot__class_Obot(tc_fun(_949991, tc_HOL_Obool)))], (9358 ^ _782464) ^ [_950122, _950124] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_950122, tc_HOL_Obool)), _950124)))], (9360 ^ _782464) ^ [_950166, _950168] : [hBOOL(hAPP(hAPP(c_member(_950166), _950168), c_Orderings_Obot__class_Obot(tc_fun(_950166, tc_HOL_Obool))))], (9362 ^ _782464) ^ [_950203, _950205] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950203, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_950203, tc_HOL_Obool))), _950205)))], (9364 ^ _782464) ^ [_950252] : [c_Orderings_Otop__class_Otop(tc_fun(_950252, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_950252, tc_HOL_Obool))], (9366 ^ _782464) ^ [_950285, _950287, _950289] : [class_Orderings_Obot(_950285), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_950287, _950285)), _950289) = c_Orderings_Obot__class_Obot(_950285))], (9372 ^ _782464) ^ [_950382, _950384, _950386] : [class_Orderings_Obot(_950382), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_950384, _950382)), _950386) = c_Orderings_Obot__class_Obot(_950382))], (9378 ^ _782464) ^ [_950479] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_950479, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_950479, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_950479, tc_HOL_Obool)))], (9380 ^ _782464) ^ [_950521] : [class_Complete__Lattice_Ocomplete__lattice(_950521), -(c_Complete__Lattice_OSup__class_OSup(_950521, c_Orderings_Obot__class_Obot(tc_fun(_950521, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_950521))], (9386 ^ _782464) ^ [_950623, _950625] : [-(hBOOL(hAPP(hAPP(c_member(_950623), 9387 ^ [_950623, _950625]), _950625))), -(_950625 = c_Orderings_Obot__class_Obot(tc_fun(_950623, tc_HOL_Obool)))], (9393 ^ _782464) ^ [_950674, _950676] : [_950676 = c_Orderings_Obot__class_Obot(tc_fun(_950674, tc_HOL_Obool)), 9396 ^ _782464 : [(9397 ^ _782464) ^ [_950754] : [hBOOL(hAPP(hAPP(c_member(_950674), _950754), _950676))]]], (9399 ^ _782464) ^ [_950805, _950807] : [9400 ^ _782464 : [(9401 ^ _782464) ^ [_950858] : [hBOOL(hAPP(hAPP(c_member(_950805), _950858), _950807))]], _950807 = c_Orderings_Obot__class_Obot(tc_fun(_950805, tc_HOL_Obool))], (9405 ^ _782464) ^ [_950914, _950916] : [-(_950916 = c_Orderings_Obot__class_Obot(tc_fun(_950914, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_950914), 9408 ^ [_950914, _950916]), _950916)))], (9412 ^ _782464) ^ [_950983, _950985] : [hBOOL(hAPP(hAPP(c_member(_950983), _950985), c_Orderings_Obot__class_Obot(tc_fun(_950983, tc_HOL_Obool))))], (9414 ^ _782464) ^ [_951020, _951022, _951024] : [_951020 = c_Orderings_Obot__class_Obot(tc_fun(_951022, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_951022), _951024), _951020))], (9420 ^ _782464) ^ [_951139, _951141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951139, tc_HOL_Obool)), _951141), c_Orderings_Obot__class_Obot(tc_fun(_951139, tc_HOL_Obool)))), -(_951141 = c_Orderings_Obot__class_Obot(tc_fun(_951139, tc_HOL_Obool)))], (9426 ^ _782464) ^ [_951252, _951254] : [_951254 = c_Orderings_Obot__class_Obot(tc_fun(_951252, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951252, tc_HOL_Obool)), _951254), c_Orderings_Obot__class_Obot(tc_fun(_951252, tc_HOL_Obool)))))], (9432 ^ _782464) ^ [_951392, _951394, _951396, _951398] : [c_Orderings_Obot__class_Obot(tc_fun(_951392, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_951394, _951392, _951396), _951398), -(_951398 = c_Orderings_Obot__class_Obot(tc_fun(_951394, tc_HOL_Obool)))], (9438 ^ _782464) ^ [_951503, _951505, _951507, _951509] : [_951509 = c_Orderings_Obot__class_Obot(tc_fun(_951505, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_951503, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_951505, _951503, _951507), _951509))], (9444 ^ _782464) ^ [_951620, _951622, _951624] : [-(hAPP(c_Set_Oimage(_951620, _951622, _951624), c_Orderings_Obot__class_Obot(tc_fun(_951620, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_951622, tc_HOL_Obool)))], (9446 ^ _782464) ^ [_951685, _951687, _951689, _951691] : [hAPP(c_Set_Oimage(_951685, _951687, _951689), _951691) = c_Orderings_Obot__class_Obot(tc_fun(_951687, tc_HOL_Obool)), -(_951691 = c_Orderings_Obot__class_Obot(tc_fun(_951685, tc_HOL_Obool)))], (9452 ^ _782464) ^ [_951796, _951798, _951800, _951802] : [_951802 = c_Orderings_Obot__class_Obot(tc_fun(_951796, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_951796, _951798, _951800), _951802) = c_Orderings_Obot__class_Obot(tc_fun(_951798, tc_HOL_Obool)))], (9458 ^ _782464) ^ [_951913, _951915] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951913, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_951913, tc_HOL_Obool))), _951915) = _951915)], (9460 ^ _782464) ^ [_951954, _951956] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951954, tc_HOL_Obool)), _951956), c_Orderings_Obot__class_Obot(tc_fun(_951954, tc_HOL_Obool))) = _951956)], (9462 ^ _782464) ^ [_952013, _952015, _952017] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952013, tc_HOL_Obool)), _952015), _952017) = c_Orderings_Obot__class_Obot(tc_fun(_952013, tc_HOL_Obool)), 9465 ^ _782464 : [(9466 ^ _782464) ^ [] : [-(_952015 = c_Orderings_Obot__class_Obot(tc_fun(_952013, tc_HOL_Obool)))], (9468 ^ _782464) ^ [] : [-(_952017 = c_Orderings_Obot__class_Obot(tc_fun(_952013, tc_HOL_Obool)))]]], (9470 ^ _782464) ^ [_952166, _952168, _952170] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952166, tc_HOL_Obool)), _952168), _952170) = c_Orderings_Obot__class_Obot(tc_fun(_952166, tc_HOL_Obool))), _952168 = c_Orderings_Obot__class_Obot(tc_fun(_952166, tc_HOL_Obool)), _952170 = c_Orderings_Obot__class_Obot(tc_fun(_952166, tc_HOL_Obool))], (9480 ^ _782464) ^ [_952353, _952355] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952353, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_952353, tc_HOL_Obool))), _952355) = c_Orderings_Obot__class_Obot(tc_fun(_952353, tc_HOL_Obool)))], (9482 ^ _782464) ^ [_952399, _952401] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952399, tc_HOL_Obool)), _952401), c_Orderings_Obot__class_Obot(tc_fun(_952399, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_952399, tc_HOL_Obool)))], (9498 ^ _782464) ^ [_952777, _952779, _952781] : [9500 ^ _782464 : [(9501 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952777), 9499 ^ [_952777, _952779, _952781]), _952779)))], (9504 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952777), 9502 ^ [_952777, _952779, _952781]), _952781)))], (9506 ^ _782464) ^ [] : [-(9499 ^ [_952777, _952779, _952781] = 9502 ^ [_952777, _952779, _952781])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952777, tc_HOL_Obool)), _952779), _952781) = c_Orderings_Obot__class_Obot(tc_fun(_952777, tc_HOL_Obool)))], (9484 ^ _782464) ^ [_952463, _952465, _952467] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952463, tc_HOL_Obool)), _952465), _952467) = c_Orderings_Obot__class_Obot(tc_fun(_952463, tc_HOL_Obool)), 9487 ^ _782464 : [(9488 ^ _782464) ^ [_952587] : [hBOOL(hAPP(hAPP(c_member(_952463), _952587), _952465)), 9491 ^ _782464 : [(9492 ^ _782464) ^ [_952677] : [hBOOL(hAPP(hAPP(c_member(_952463), _952677), _952467)), _952587 = _952677]]]]], (9510 ^ _782464) ^ [_952938] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952938, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_952938, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_952938, tc_HOL_Obool)))], (9512 ^ _782464) ^ [_952979] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952979, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_952979, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_952979, tc_HOL_Obool)))], (9514 ^ _782464) ^ [_953020, _953022] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_953020, _953022, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_953020), tc_HOL_Obool))))], (9516 ^ _782464) ^ [_953053, _953055] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_953053, _953055, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_953053), tc_HOL_Obool))))], (9518 ^ _782464) ^ [_953098, _953100] : [hAPP(c_Set_OPow(_953098), _953100) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_953098, tc_HOL_Obool), tc_HOL_Obool))], (9520 ^ _782464) ^ [_953136] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_953136, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_953136, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_953136, tc_HOL_Obool)))], (9522 ^ _782464) ^ [_953178] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_953178, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_953178, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_953178, tc_HOL_Obool)))], (9524 ^ _782464) ^ [_953220, _953222, _953224, _953226, _953228] : [class_Orderings_Oorder(_953220), class_Orderings_Oorder(_953222), c_Orderings_Oorder__class_Omono(_953222, _953220, _953224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953222), _953226), _953228)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953220), hAPP(_953224, _953226)), hAPP(_953224, _953228))))], (9542 ^ _782464) ^ [_953532, _953534] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_953532, tc_HOL_Obool)), _953534)), -(hBOOL(hAPP(hAPP(c_member(_953532), _953534), c_Orderings_Obot__class_Obot(tc_fun(_953532, tc_HOL_Obool)))))], (9548 ^ _782464) ^ [_953643, _953645] : [hBOOL(hAPP(hAPP(c_member(_953643), _953645), c_Orderings_Obot__class_Obot(tc_fun(_953643, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_953643, tc_HOL_Obool)), _953645)))], (9554 ^ _782464) ^ [_953760, _953762] : [class_Orderings_Obot(_953760), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953760), c_Orderings_Obot__class_Obot(_953760)), _953762)))], (9560 ^ _782464) ^ [_953853, _953855, _953857, _953859] : [class_Complete__Lattice_Ocomplete__lattice(_953853), -(_953855 = c_Orderings_Obot__class_Obot(tc_fun(_953857, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_953857, _953853), _953855), hAPP(c_COMBK(_953853, _953857), _953859)) = _953859)], (9580 ^ _782464) ^ [_954237, _954239, _954241, _954243] : [9582 ^ _782464 : [(9583 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954237), 9581 ^ [_954237, _954239, _954241, _954243]), _954241)))], (9585 ^ _782464) ^ [] : [hAPP(_954243, 9581 ^ [_954237, _954239, _954241, _954243]) = c_Orderings_Obot__class_Obot(tc_fun(_954239, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954237, tc_fun(_954239, tc_HOL_Obool)), _954241), _954243) = c_Orderings_Obot__class_Obot(tc_fun(_954239, tc_HOL_Obool)))], (9570 ^ _782464) ^ [_954008, _954010, _954012, _954014] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954008, tc_fun(_954010, tc_HOL_Obool)), _954012), _954014) = c_Orderings_Obot__class_Obot(tc_fun(_954010, tc_HOL_Obool)), 9573 ^ _782464 : [(9574 ^ _782464) ^ [_954124] : [hBOOL(hAPP(hAPP(c_member(_954008), _954124), _954012)), -(hAPP(_954014, _954124) = c_Orderings_Obot__class_Obot(tc_fun(_954010, tc_HOL_Obool)))]]], (9589 ^ _782464) ^ [_954482, _954484, _954486, _954488] : [_954482 = c_Orderings_Obot__class_Obot(tc_fun(_954484, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954484, tc_fun(_954486, tc_HOL_Obool)), _954482), hAPP(c_COMBK(tc_fun(_954486, tc_HOL_Obool), _954484), _954488)) = c_Orderings_Obot__class_Obot(tc_fun(_954486, tc_HOL_Obool)))], (9595 ^ _782464) ^ [_954619, _954621, _954623, _954625] : [-(_954619 = c_Orderings_Obot__class_Obot(tc_fun(_954621, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954621, tc_fun(_954623, tc_HOL_Obool)), _954619), hAPP(c_COMBK(tc_fun(_954623, tc_HOL_Obool), _954621), _954625)) = _954625)], (9601 ^ _782464) ^ [_954687, _954689, _954691] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954687, tc_fun(_954689, tc_HOL_Obool)), _954691), hAPP(c_COMBK(tc_fun(_954689, tc_HOL_Obool), _954687), c_Orderings_Obot__class_Obot(tc_fun(_954689, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_954689, tc_HOL_Obool)))], (9613 ^ _782464) ^ [_954995, _954997, _954999, _955001] : [9615 ^ _782464 : [(9616 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954997), 9614 ^ [_954995, _954997, _954999, _955001]), _954999)))], (9618 ^ _782464) ^ [] : [hAPP(_955001, 9614 ^ [_954995, _954997, _954999, _955001]) = c_Orderings_Obot__class_Obot(tc_fun(_954995, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_954995, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954997, tc_fun(_954995, tc_HOL_Obool)), _954999), _955001))], (9603 ^ _782464) ^ [_954766, _954768, _954770, _954772] : [c_Orderings_Obot__class_Obot(tc_fun(_954766, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954768, tc_fun(_954766, tc_HOL_Obool)), _954770), _954772), 9606 ^ _782464 : [(9607 ^ _782464) ^ [_954882] : [hBOOL(hAPP(hAPP(c_member(_954768), _954882), _954770)), -(hAPP(_954772, _954882) = c_Orderings_Obot__class_Obot(tc_fun(_954766, tc_HOL_Obool)))]]], (9622 ^ _782464) ^ [_955225, _955227, _955229, _955231] : [class_Complete__Lattice_Ocomplete__lattice(_955225), -(_955227 = c_Orderings_Obot__class_Obot(tc_fun(_955229, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955229, _955225), _955227), hAPP(c_COMBK(_955225, _955229), _955231)) = _955231)], (9632 ^ _782464) ^ [_955359, _955361, _955363] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955359, tc_fun(_955361, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_955359, tc_HOL_Obool))), _955363) = c_Orderings_Otop__class_Otop(tc_fun(_955361, tc_HOL_Obool)))], (9634 ^ _782464) ^ [_955423, _955425, _955427, _955429] : [_955423 = c_Orderings_Obot__class_Obot(tc_fun(_955425, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955425, tc_fun(_955427, tc_HOL_Obool)), _955423), hAPP(c_COMBK(tc_fun(_955427, tc_HOL_Obool), _955425), _955429)) = c_Orderings_Otop__class_Otop(tc_fun(_955427, tc_HOL_Obool)))], (9640 ^ _782464) ^ [_955560, _955562, _955564, _955566] : [-(_955560 = c_Orderings_Obot__class_Obot(tc_fun(_955562, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955562, tc_fun(_955564, tc_HOL_Obool)), _955560), hAPP(c_COMBK(tc_fun(_955564, tc_HOL_Obool), _955562), _955566)) = _955566)], (9646 ^ _782464) ^ [_955628, _955630] : [class_Lattices_Obounded__lattice__bot(_955628), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955628), c_Orderings_Obot__class_Obot(_955628)), _955630) = _955630)], (9652 ^ _782464) ^ [_955723, _955725] : [class_Lattices_Obounded__lattice__bot(_955723), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955723), _955725), c_Orderings_Obot__class_Obot(_955723)) = _955725)], (9658 ^ _782464) ^ [_955818, _955820, _955822] : [class_Lattices_Obounded__lattice__bot(_955818), 9661 ^ _782464 : [(9662 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955818), _955820), _955822) = c_Orderings_Obot__class_Obot(_955818), 9665 ^ _782464 : [(9666 ^ _782464) ^ [] : [-(_955820 = c_Orderings_Obot__class_Obot(_955818))], (9668 ^ _782464) ^ [] : [-(_955822 = c_Orderings_Obot__class_Obot(_955818))]]], (9670 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955818), _955820), _955822) = c_Orderings_Obot__class_Obot(_955818)), _955820 = c_Orderings_Obot__class_Obot(_955818), _955822 = c_Orderings_Obot__class_Obot(_955818)]]], (9680 ^ _782464) ^ [_956145, _956147] : [class_Lattices_Obounded__lattice__bot(_956145), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956145), c_Orderings_Obot__class_Obot(_956145)), _956147) = c_Orderings_Obot__class_Obot(_956145))], (9686 ^ _782464) ^ [_956244, _956246] : [class_Lattices_Obounded__lattice__bot(_956244), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956244), _956246), c_Orderings_Obot__class_Obot(_956244)) = c_Orderings_Obot__class_Obot(_956244))], (9692 ^ _782464) ^ [_956343] : [class_Complete__Lattice_Ocomplete__lattice(_956343), -(c_Complete__Lattice_OInf__class_OInf(_956343, c_Orderings_Otop__class_Otop(tc_fun(_956343, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_956343))], (9698 ^ _782464) ^ [_956436, _956438, _956440] : [class_Orderings_Oorder(_956436), class_Orderings_Oorder(_956438), c_Orderings_Oorder__class_Ostrict__mono(_956438, _956436, _956440), -(c_Orderings_Oorder__class_Omono(_956438, _956436, _956440))], (9712 ^ _782464) ^ [_956625, _956627, _956629] : [class_Orderings_Oorder(_956625), 9715 ^ _782464 : [(9716 ^ _782464) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_956625, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_956625, _956627, _956629), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956625), _956627), _956629))], (9722 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956625), _956627), _956629))), -(c_Orderings_Obot__class_Obot(tc_fun(_956625, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_956625, _956627, _956629))]]], (9728 ^ _782464) ^ [_956844, _956846, _956848] : [class_Orderings_Oorder(_956844), 9731 ^ _782464 : [(9732 ^ _782464) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_956844, _956846, _956848) = c_Orderings_Obot__class_Obot(tc_fun(_956844, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956844), _956846), _956848))], (9738 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956844), _956846), _956848))), -(c_SetInterval_Oord__class_OatLeastAtMost(_956844, _956846, _956848) = c_Orderings_Obot__class_Obot(tc_fun(_956844, tc_HOL_Obool)))]]], (9744 ^ _782464) ^ [_957063, _957065, _957067] : [class_Orderings_Oorder(_957063), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957063), _957065), _957067)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957063, _957067), _957065) = c_Orderings_Obot__class_Obot(tc_fun(_957063, tc_HOL_Obool)))], (9754 ^ _782464) ^ [_957230, _957232, _957234, _957236] : [class_Orderings_Oorder(_957230), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957230, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957230, _957232), _957234)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957230, _957234), _957236)) = c_Orderings_Obot__class_Obot(tc_fun(_957230, tc_HOL_Obool)))], (9760 ^ _782464) ^ [_957380, _957382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957380, tc_HOL_Obool)), _957382), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957380, tc_HOL_Obool)), _957382))), -(_957382 = c_Orderings_Obot__class_Obot(tc_fun(_957380, tc_HOL_Obool)))], (9766 ^ _782464) ^ [_957499, _957501] : [_957501 = c_Orderings_Obot__class_Obot(tc_fun(_957499, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957499, tc_HOL_Obool)), _957501), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957499, tc_HOL_Obool)), _957501))))], (9772 ^ _782464) ^ [_957624, _957626] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957624, tc_HOL_Obool)), _957626), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957624, tc_HOL_Obool)), _957626)) = c_Orderings_Obot__class_Obot(tc_fun(_957624, tc_HOL_Obool)))], (9774 ^ _782464) ^ [_957673, _957675] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957673, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957673, tc_HOL_Obool)), _957675)), _957675) = c_Orderings_Obot__class_Obot(tc_fun(_957673, tc_HOL_Obool)))], (9776 ^ _782464) ^ [_957722, _957724, _957726] : [class_Orderings_Oorder(_957722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957722), _957724), _957726)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_957722, _957726, _957724) = c_Orderings_Obot__class_Obot(tc_fun(_957722, tc_HOL_Obool)))], (9786 ^ _782464) ^ [_957885] : [class_Complete__Lattice_Ocomplete__lattice(_957885), -(c_Complete__Lattice_OInf__class_OInf(_957885, c_Orderings_Obot__class_Obot(tc_fun(_957885, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_957885))], (9802 ^ _782464) ^ [_958264, _958266, _958268] : [9804 ^ _782464 : [(9805 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_958264, tc_HOL_Obool)), 9803 ^ [_958264, _958266, _958268]), _958266)))], (9807 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958264, tc_HOL_Obool)), 9803 ^ [_958264, _958266, _958268]), _958268) = c_Orderings_Obot__class_Obot(tc_fun(_958264, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958264, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_958264, tc_HOL_Obool), _958266)), _958268) = c_Orderings_Obot__class_Obot(tc_fun(_958264, tc_HOL_Obool)))], (9792 ^ _782464) ^ [_957996, _957998, _958000] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957996, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_957996, tc_HOL_Obool), _957998)), _958000) = c_Orderings_Obot__class_Obot(tc_fun(_957996, tc_HOL_Obool)), 9795 ^ _782464 : [(9796 ^ _782464) ^ [_958131] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_957996, tc_HOL_Obool)), _958131), _957998)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957996, tc_HOL_Obool)), _958131), _958000) = c_Orderings_Obot__class_Obot(tc_fun(_957996, tc_HOL_Obool)))]]], (9811 ^ _782464) ^ [_958527, _958529] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_958527, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_958527, tc_HOL_Obool))), hAPP(c_Set_OPow(_958527), _958529))))], (9813 ^ _782464) ^ [_958572, _958574, _958576, _958578] : [class_Orderings_Oorder(_958572), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958572, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_958572, _958574, _958576)), c_SetInterval_Oord__class_OgreaterThanAtMost(_958572, _958576, _958578)) = c_Orderings_Obot__class_Obot(tc_fun(_958572, tc_HOL_Obool)))], (9819 ^ _782464) ^ [_958699, _958701, _958703, _958705, _958707] : [c_Orderings_Oorder__class_Omono(tc_fun(_958699, tc_HOL_Obool), tc_fun(_958701, tc_HOL_Obool), _958703), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958701, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958701, tc_HOL_Obool)), hAPP(_958703, _958705)), hAPP(_958703, _958707))), hAPP(_958703, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958699, tc_HOL_Obool)), _958705), _958707)))))], (9825 ^ _782464) ^ [_958878, _958880, _958882, _958884, _958886] : [c_Orderings_Oorder__class_Omono(tc_fun(_958878, tc_HOL_Obool), tc_fun(_958880, tc_HOL_Obool), _958882), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958880, tc_HOL_Obool)), hAPP(_958882, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958878, tc_HOL_Obool)), _958884), _958886))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958880, tc_HOL_Obool)), hAPP(_958882, _958884)), hAPP(_958882, _958886)))))], (9831 ^ _782464) ^ [_959075, _959077, _959079, _959081, _959083] : [_959075 = c_Orderings_Obot__class_Obot(tc_fun(_959077, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959077, tc_fun(_959079, tc_HOL_Obool)), _959075), hAPP(hAPP(c_COMBB(tc_fun(_959079, tc_HOL_Obool), tc_fun(_959079, tc_HOL_Obool), _959077), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959079, tc_HOL_Obool)), _959081)), _959083)) = c_Orderings_Obot__class_Obot(tc_fun(_959079, tc_HOL_Obool)))], (9837 ^ _782464) ^ [_959244, _959246, _959248, _959250, _959252] : [-(_959244 = c_Orderings_Obot__class_Obot(tc_fun(_959246, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959246, tc_fun(_959248, tc_HOL_Obool)), _959244), hAPP(hAPP(c_COMBB(tc_fun(_959248, tc_HOL_Obool), tc_fun(_959248, tc_HOL_Obool), _959246), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959248, tc_HOL_Obool)), _959250)), _959252)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959248, tc_HOL_Obool)), _959250), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959246, tc_fun(_959248, tc_HOL_Obool)), _959244), _959252)))], (9843 ^ _782464) ^ [_959370, _959372, _959374, _959376, _959378] : [_959370 = c_Orderings_Obot__class_Obot(tc_fun(_959372, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959372, tc_fun(_959374, tc_HOL_Obool)), _959370), hAPP(hAPP(c_COMBC(_959372, tc_fun(_959374, tc_HOL_Obool), tc_fun(_959374, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_959374, tc_HOL_Obool), tc_fun(tc_fun(_959374, tc_HOL_Obool), tc_fun(_959374, tc_HOL_Obool)), _959372), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959374, tc_HOL_Obool))), _959376)), _959378)) = c_Orderings_Obot__class_Obot(tc_fun(_959374, tc_HOL_Obool)))], (9849 ^ _782464) ^ [_959577, _959579, _959581, _959583, _959585] : [-(_959577 = c_Orderings_Obot__class_Obot(tc_fun(_959579, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959579, tc_fun(_959581, tc_HOL_Obool)), _959577), hAPP(hAPP(c_COMBC(_959579, tc_fun(_959581, tc_HOL_Obool), tc_fun(_959581, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_959581, tc_HOL_Obool), tc_fun(tc_fun(_959581, tc_HOL_Obool), tc_fun(_959581, tc_HOL_Obool)), _959579), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959581, tc_HOL_Obool))), _959583)), _959585)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959581, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959579, tc_fun(_959581, tc_HOL_Obool)), _959577), _959583)), _959585))], (9855 ^ _782464) ^ [_959722, _959724, _959726, _959728, _959730] : [_959722 = c_Orderings_Obot__class_Obot(tc_fun(_959724, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959726, tc_HOL_Obool)), _959728), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959724, tc_fun(_959726, tc_HOL_Obool)), _959722), _959730)) = _959728)], (9861 ^ _782464) ^ [_959855, _959857, _959859, _959861, _959863] : [-(_959855 = c_Orderings_Obot__class_Obot(tc_fun(_959857, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959859, tc_HOL_Obool)), _959861), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959857, tc_fun(_959859, tc_HOL_Obool)), _959855), _959863)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959857, tc_fun(_959859, tc_HOL_Obool)), _959855), hAPP(hAPP(c_COMBB(tc_fun(_959859, tc_HOL_Obool), tc_fun(_959859, tc_HOL_Obool), _959857), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959859, tc_HOL_Obool)), _959861)), _959863)))], (9867 ^ _782464) ^ [_959981, _959983, _959985, _959987, _959989] : [_959981 = c_Orderings_Obot__class_Obot(tc_fun(_959983, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959985, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959983, tc_fun(_959985, tc_HOL_Obool)), _959981), _959987)), _959989) = _959989)], (9873 ^ _782464) ^ [_960114, _960116, _960118, _960120, _960122] : [-(_960114 = c_Orderings_Obot__class_Obot(tc_fun(_960116, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960118, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_960116, tc_fun(_960118, tc_HOL_Obool)), _960114), _960120)), _960122) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_960116, tc_fun(_960118, tc_HOL_Obool)), _960114), hAPP(hAPP(c_COMBC(_960116, tc_fun(_960118, tc_HOL_Obool), tc_fun(_960118, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960118, tc_HOL_Obool), tc_fun(tc_fun(_960118, tc_HOL_Obool), tc_fun(_960118, tc_HOL_Obool)), _960116), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960118, tc_HOL_Obool))), _960120)), _960122)))], (9879 ^ _782464) ^ [_960259, _960261, _960263, _960265, _960267] : [_960259 = c_Orderings_Obot__class_Obot(tc_fun(_960261, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960263, tc_HOL_Obool)), _960265), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960261, tc_fun(_960263, tc_HOL_Obool)), _960259), _960267)) = _960265)], (9885 ^ _782464) ^ [_960392, _960394, _960396, _960398, _960400] : [-(_960392 = c_Orderings_Obot__class_Obot(tc_fun(_960394, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960396, tc_HOL_Obool)), _960398), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960394, tc_fun(_960396, tc_HOL_Obool)), _960392), _960400)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960394, tc_fun(_960396, tc_HOL_Obool)), _960392), hAPP(hAPP(c_COMBB(tc_fun(_960396, tc_HOL_Obool), tc_fun(_960396, tc_HOL_Obool), _960394), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960396, tc_HOL_Obool)), _960398)), _960400)))], (9891 ^ _782464) ^ [_960518, _960520, _960522, _960524, _960526] : [_960518 = c_Orderings_Obot__class_Obot(tc_fun(_960520, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960522, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960520, tc_fun(_960522, tc_HOL_Obool)), _960518), _960524)), _960526) = _960526)], (9897 ^ _782464) ^ [_960651, _960653, _960655, _960657, _960659] : [-(_960651 = c_Orderings_Obot__class_Obot(tc_fun(_960653, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960655, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960653, tc_fun(_960655, tc_HOL_Obool)), _960651), _960657)), _960659) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960653, tc_fun(_960655, tc_HOL_Obool)), _960651), hAPP(hAPP(c_COMBC(_960653, tc_fun(_960655, tc_HOL_Obool), tc_fun(_960655, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960655, tc_HOL_Obool), tc_fun(tc_fun(_960655, tc_HOL_Obool), tc_fun(_960655, tc_HOL_Obool)), _960653), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960655, tc_HOL_Obool))), _960657)), _960659)))], (9903 ^ _782464) ^ [_960796, _960798, _960800, _960802, _960804] : [_960796 = c_Orderings_Obot__class_Obot(tc_fun(_960798, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960798, tc_fun(_960800, tc_HOL_Obool)), _960796), hAPP(hAPP(c_COMBC(_960798, tc_fun(_960800, tc_HOL_Obool), tc_fun(_960800, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960800, tc_HOL_Obool), tc_fun(tc_fun(_960800, tc_HOL_Obool), tc_fun(_960800, tc_HOL_Obool)), _960798), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960800, tc_HOL_Obool))), _960802)), _960804)) = c_Orderings_Otop__class_Otop(tc_fun(_960800, tc_HOL_Obool)))], (9909 ^ _782464) ^ [_961003, _961005, _961007, _961009, _961011] : [-(_961003 = c_Orderings_Obot__class_Obot(tc_fun(_961005, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961005, tc_fun(_961007, tc_HOL_Obool)), _961003), hAPP(hAPP(c_COMBC(_961005, tc_fun(_961007, tc_HOL_Obool), tc_fun(_961007, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_961007, tc_HOL_Obool), tc_fun(tc_fun(_961007, tc_HOL_Obool), tc_fun(_961007, tc_HOL_Obool)), _961005), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961007, tc_HOL_Obool))), _961009)), _961011)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961007, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961005, tc_fun(_961007, tc_HOL_Obool)), _961003), _961009)), _961011))], (9915 ^ _782464) ^ [_961148, _961150, _961152, _961154, _961156] : [_961148 = c_Orderings_Obot__class_Obot(tc_fun(_961150, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961150, tc_fun(_961152, tc_HOL_Obool)), _961148), hAPP(hAPP(c_COMBB(tc_fun(_961152, tc_HOL_Obool), tc_fun(_961152, tc_HOL_Obool), _961150), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961152, tc_HOL_Obool)), _961154)), _961156)) = c_Orderings_Otop__class_Otop(tc_fun(_961152, tc_HOL_Obool)))], (9921 ^ _782464) ^ [_961317, _961319, _961321, _961323, _961325] : [-(_961317 = c_Orderings_Obot__class_Obot(tc_fun(_961319, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961319, tc_fun(_961321, tc_HOL_Obool)), _961317), hAPP(hAPP(c_COMBB(tc_fun(_961321, tc_HOL_Obool), tc_fun(_961321, tc_HOL_Obool), _961319), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961321, tc_HOL_Obool)), _961323)), _961325)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961321, tc_HOL_Obool)), _961323), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961319, tc_fun(_961321, tc_HOL_Obool)), _961317), _961325)))], (9927 ^ _782464) ^ [_961425, _961427, _961429, _961431, _961433] : [class_Lattices_Osemilattice__sup(_961425), class_Lattices_Osemilattice__sup(_961427), c_Orderings_Oorder__class_Omono(_961427, _961425, _961429), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961425), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961425), hAPP(_961429, _961431)), hAPP(_961429, _961433))), hAPP(_961429, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961427), _961431), _961433)))))], (9941 ^ _782464) ^ [_961688, _961690, _961692, _961694, _961696] : [class_Lattices_Osemilattice__inf(_961688), class_Lattices_Osemilattice__inf(_961690), c_Orderings_Oorder__class_Omono(_961690, _961688, _961692), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961688), hAPP(_961692, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961690), _961694), _961696))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961688), hAPP(_961692, _961694)), hAPP(_961692, _961696)))))], (9955 ^ _782464) ^ [_961951, _961953] : [class_Lattices_Oboolean__algebra(_961951), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961951), _961953), hAPP(c_Groups_Ouminus__class_Ouminus(_961951), _961953)) = c_Orderings_Obot__class_Obot(_961951))], (9961 ^ _782464) ^ [_962056, _962058] : [class_Lattices_Oboolean__algebra(_962056), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_962056), hAPP(c_Groups_Ouminus__class_Ouminus(_962056), _962058)), _962058) = c_Orderings_Obot__class_Obot(_962056))], (9967 ^ _782464) ^ [_962161] : [class_Lattices_Oboolean__algebra(_962161), -(hAPP(c_Groups_Ouminus__class_Ouminus(_962161), c_Orderings_Otop__class_Otop(_962161)) = c_Orderings_Obot__class_Obot(_962161))], (9973 ^ _782464) ^ [_962252] : [class_Lattices_Oboolean__algebra(_962252), -(hAPP(c_Groups_Ouminus__class_Ouminus(_962252), c_Orderings_Obot__class_Obot(_962252)) = c_Orderings_Otop__class_Otop(_962252))], (9979 ^ _782464) ^ [_962361, _962363, _962365] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962361, tc_HOL_Obool)), _962363), _962365) = c_Orderings_Obot__class_Obot(tc_fun(_962361, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962361, tc_HOL_Obool)), _962363), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962361, tc_HOL_Obool)), _962365))))], (9985 ^ _782464) ^ [_962504, _962506, _962508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962504, tc_HOL_Obool)), _962506), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962504, tc_HOL_Obool)), _962508))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962504, tc_HOL_Obool)), _962506), _962508) = c_Orderings_Obot__class_Obot(tc_fun(_962504, tc_HOL_Obool)))], (9991 ^ _782464) ^ [_962653, _962655, _962657, _962659] : [class_Orderings_Oorder(_962653), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962653, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962653, _962655), _962657)), c_SetInterval_Oord__class_OatLeastAtMost(_962653, _962657, _962659)) = c_Orderings_Obot__class_Obot(tc_fun(_962653, tc_HOL_Obool)))], (9997 ^ _782464) ^ [_962784, _962786, _962788] : [class_Orderings_Oorder(_962784), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962784, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_962784), _962786)), c_SetInterval_Oord__class_OatLeastAtMost(_962784, _962786, _962788)) = c_Orderings_Obot__class_Obot(tc_fun(_962784, tc_HOL_Obool)))], (10003 ^ _782464) ^ [_962911, _962913, _962915] : [class_Orderings_Oorder(_962911), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962911, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_962911), _962913)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962911, _962913), _962915)) = c_Orderings_Obot__class_Obot(tc_fun(_962911, tc_HOL_Obool)))], (10009 ^ _782464) ^ [_963042, _963044, _963046, _963048] : [class_Orderings_Oorder(_963042), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963042, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_963042, _963044, _963046)), c_SetInterval_Oord__class_OgreaterThanAtMost(_963042, _963046, _963048)) = c_Orderings_Obot__class_Obot(tc_fun(_963042, tc_HOL_Obool)))], (10015 ^ _782464) ^ [_963169, _963171] : [-(hBOOL(hAPP(hAPP(c_member(_963169), _963171), c_Orderings_Otop__class_Otop(tc_fun(_963169, tc_HOL_Obool)))))], (10017 ^ _782464) ^ [_963206, _963208, _963210] : [class_Orderings_Olinorder(_963206), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963206), _963208), _963210)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963206, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_963206), _963208), c_Orderings_Obot__class_Obot(tc_fun(_963206, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_963206, _963208, _963210)) = c_SetInterval_Oord__class_OatLeastAtMost(_963206, _963208, _963210))], (10027 ^ _782464) ^ [_963415, _963417, _963419] : [class_Orderings_Olinorder(_963415), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963415), _963417), _963419)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963415, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963415, _963417), _963419)), hAPP(hAPP(c_Set_Oinsert(_963415), _963419), c_Orderings_Obot__class_Obot(tc_fun(_963415, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_963415, _963417, _963419))], (10037 ^ _782464) ^ [_963628, _963630, _963632, _963634, _963636] : [class_Orderings_Oorder(_963628), c_Orderings_Oorder__class_Omono(_963628, tc_fun(_963630, tc_HOL_Obool), _963632), -(c_Orderings_Oorder__class_Omono(_963628, tc_fun(_963630, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_963628, tc_fun(_963630, tc_HOL_Obool), tc_fun(_963630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_963630, tc_HOL_Obool), tc_fun(tc_fun(_963630, tc_HOL_Obool), tc_fun(_963630, tc_HOL_Obool)), _963628), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963630, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_963628, tc_fun(_963630, tc_HOL_Obool), tc_fun(_963630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_963630, tc_HOL_Obool), tc_fun(tc_fun(_963630, tc_HOL_Obool), tc_fun(_963630, tc_HOL_Obool)), _963628), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963630, tc_HOL_Obool))), _963632)), _963634))), _963636)))], (10047 ^ _782464) ^ [_963955, _963957, _963959] : [class_Orderings_Oorder(_963955), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963955, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_963955, _963957, _963959)), hAPP(c_SetInterval_Oord__class_OatLeast(_963955), _963959)) = c_Orderings_Obot__class_Obot(tc_fun(_963955, tc_HOL_Obool)))], (10053 ^ _782464) ^ [_964082, _964084, _964086] : [class_Orderings_Oorder(_964082), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964082, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_964082), _964084)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964082, _964084, _964086)) = c_Orderings_Obot__class_Obot(tc_fun(_964082, tc_HOL_Obool)))], (10059 ^ _782464) ^ [_964209, _964211, _964213, _964215] : [class_Orderings_Oorder(_964209), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964209, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_964209, _964211, _964213)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964209, _964213, _964215)) = c_Orderings_Obot__class_Obot(tc_fun(_964209, tc_HOL_Obool)))], (10065 ^ _782464) ^ [_964336, _964338] : [class_Orderings_Olinorder(_964336), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964336, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_964336), _964338), c_Orderings_Obot__class_Obot(tc_fun(_964336, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_964336), _964338)) = hAPP(c_SetInterval_Oord__class_OatLeast(_964336), _964338))], (10071 ^ _782464) ^ [_964497, _964499, _964501, _964503, _964505] : [_964497 = c_Orderings_Obot__class_Obot(tc_fun(_964499, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_964499, tc_fun(_964501, tc_HOL_Obool)), _964497), hAPP(hAPP(c_COMBB(tc_fun(_964501, tc_HOL_Obool), tc_fun(_964501, tc_HOL_Obool), _964499), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964501, tc_HOL_Obool)), _964503)), _964505)) = c_Orderings_Otop__class_Otop(tc_fun(_964501, tc_HOL_Obool)))], (10077 ^ _782464) ^ [_964666, _964668, _964670, _964672, _964674] : [-(_964666 = c_Orderings_Obot__class_Obot(tc_fun(_964668, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_964668, tc_fun(_964670, tc_HOL_Obool)), _964666), hAPP(hAPP(c_COMBB(tc_fun(_964670, tc_HOL_Obool), tc_fun(_964670, tc_HOL_Obool), _964668), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964670, tc_HOL_Obool)), _964672)), _964674)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964670, tc_HOL_Obool)), _964672), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_964668, tc_fun(_964670, tc_HOL_Obool)), _964666), _964674)))], (10083 ^ _782464) ^ [_964774, _964776] : [class_Orderings_Oorder(_964774), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964774, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_964774), _964776)), hAPP(c_SetInterval_Oord__class_OatLeast(_964774), _964776)) = hAPP(hAPP(c_Set_Oinsert(_964774), _964776), c_Orderings_Obot__class_Obot(tc_fun(_964774, tc_HOL_Obool))))], (10089 ^ _782464) ^ [_964917, _964919, _964921, _964923] : [10090 ^ _782464 : [(10091 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_964917), _964919), _964921))], (10093 ^ _782464) ^ [] : [_964919 = _964923]], -(hBOOL(hAPP(hAPP(c_member(_964917), _964919), hAPP(hAPP(c_Set_Oinsert(_964917), _964923), _964921))))], (10097 ^ _782464) ^ [_965082, _965084, _965086, _965088] : [hBOOL(hAPP(hAPP(c_member(_965082), _965084), hAPP(hAPP(c_Set_Oinsert(_965082), _965086), _965088))), -(_965084 = _965086), -(hBOOL(hAPP(hAPP(c_member(_965082), _965084), _965088)))], (10107 ^ _782464) ^ [_965222, _965224, _965226, _965228] : [hBOOL(hAPP(hAPP(c_member(_965222), _965224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965222, tc_HOL_Obool)), _965226), _965228))), 10110 ^ _782464 : [(10111 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_965222), _965224), _965226)))], (10113 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_965222), _965224), _965228))]]], (10115 ^ _782464) ^ [_965401, _965403, _965405, _965407] : [hBOOL(hAPP(hAPP(c_member(_965401), _965403), _965405)), -(hBOOL(hAPP(hAPP(c_member(_965401), _965403), _965407))), -(hBOOL(hAPP(hAPP(c_member(_965401), _965403), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965401, tc_HOL_Obool)), _965405), _965407))))], (10125 ^ _782464) ^ [_965561, _965563, _965565, _965567] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965561, tc_HOL_Obool)), _965563), hAPP(hAPP(c_Set_Oinsert(_965561), _965565), _965567)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965561, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965561, tc_HOL_Obool)), _965563), _965567)), hAPP(hAPP(c_Set_Oinsert(_965561), _965565), c_Orderings_Obot__class_Obot(tc_fun(_965561, tc_HOL_Obool)))))], (10127 ^ _782464) ^ [_965644, _965646, _965648, _965650] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965644, tc_HOL_Obool)), _965646), hAPP(hAPP(c_Set_Oinsert(_965644), _965648), _965650)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965644, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965644, tc_HOL_Obool)), _965646), hAPP(hAPP(c_Set_Oinsert(_965644), _965648), c_Orderings_Obot__class_Obot(tc_fun(_965644, tc_HOL_Obool))))), _965650))], (10129 ^ _782464) ^ [_965727, _965729, _965731] : [-(hAPP(hAPP(c_Set_Oinsert(_965727), _965729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965727, tc_HOL_Obool)), _965731), hAPP(hAPP(c_Set_Oinsert(_965727), _965729), c_Orderings_Obot__class_Obot(tc_fun(_965727, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_965727), _965729), _965731))], (10131 ^ _782464) ^ [_965809, _965811, _965813, _965815] : [hBOOL(hAPP(hAPP(c_member(_965809), _965811), _965813)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965809, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_965809), _965811), _965815)), _965813) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965809, tc_HOL_Obool)), _965815), _965813))], (10137 ^ _782464) ^ [_965958, _965960, _965962, _965964] : [-(hBOOL(hAPP(hAPP(c_member(_965958), _965960), _965962))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965958, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_965958), _965960), _965964)), _965962) = hAPP(hAPP(c_Set_Oinsert(_965958), _965960), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965958, tc_HOL_Obool)), _965964), _965962)))], (10143 ^ _782464) ^ [_966045, _966047, _966049, _966051] : [hBOOL(hAPP(hAPP(c_member(_966045), _966047), _966049)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966045, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_966045), _966047), _966051)), _966049) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966045, tc_HOL_Obool)), _966051), _966049))], (10149 ^ _782464) ^ [_966200, _966202, _966204, _966206, _966208] : [class_Groups_Oab__group__add(_966200), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966200), _966202), _966204) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966200), _966206), _966208), 10156 ^ _782464 : [(10157 ^ _782464) ^ [] : [_966202 = _966204, -(_966206 = _966208)], (10163 ^ _782464) ^ [] : [_966206 = _966208, -(_966202 = _966204)]]], (10169 ^ _782464) ^ [_966513, _966515, _966517, _966519, _966521] : [class_Groups_Ominus(_966513), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966515, _966513)), _966517), _966519), _966521) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966513), hAPP(_966517, _966521)), hAPP(_966519, _966521)))], (10175 ^ _782464) ^ [_966650, _966652, _966654, _966656, _966658] : [class_Groups_Ominus(_966650), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966652, _966650)), _966654), _966656), _966658) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966650), hAPP(_966654, _966658)), hAPP(_966656, _966658)))], (10191 ^ _782464) ^ [_966922, _966924, _966926, _966928] : [10192 ^ _782464 : [(10193 ^ _782464) ^ [] : [_966924 = _966928], (10195 ^ _782464) ^ [] : [hBOOL(hAPP(_966926, _966928))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_966922), _966924), _966926), _966928)))], (10181 ^ _782464) ^ [_966808, _966810, _966812, _966814] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_966808), _966810), _966812), _966814)), -(_966810 = _966814), -(hBOOL(hAPP(_966812, _966814)))], (10199 ^ _782464) ^ [_967067, _967069, _967071] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967067, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967067, tc_HOL_Obool)), _967069), _967071)), _967071) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967067, tc_HOL_Obool)), _967069), _967071))], (10201 ^ _782464) ^ [_967127, _967129, _967131, _967133] : [-(hAPP(hAPP(c_Set_Oinsert(_967127), _967129), hAPP(hAPP(c_Set_Oinsert(_967127), _967131), _967133)) = hAPP(hAPP(c_Set_Oinsert(_967127), _967131), hAPP(hAPP(c_Set_Oinsert(_967127), _967129), _967133)))], (10203 ^ _782464) ^ [_967188, _967190, _967192] : [-(hAPP(hAPP(c_Set_Oinsert(_967188), _967190), hAPP(hAPP(c_Set_Oinsert(_967188), _967190), _967192)) = hAPP(hAPP(c_Set_Oinsert(_967188), _967190), _967192))], (10205 ^ _782464) ^ [_967239, _967241, _967243] : [hBOOL(hAPP(hAPP(c_member(_967239), _967241), _967243)), -(hAPP(hAPP(c_Set_Oinsert(_967239), _967241), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967239, tc_HOL_Obool)), _967243), hAPP(hAPP(c_Set_Oinsert(_967239), _967241), c_Orderings_Obot__class_Obot(tc_fun(_967239, tc_HOL_Obool))))) = _967243)], (10211 ^ _782464) ^ [_967392, _967394, _967396] : [-(hBOOL(hAPP(hAPP(c_member(_967392), _967394), _967396))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967392, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_967392), _967394), _967396)), hAPP(hAPP(c_Set_Oinsert(_967392), _967394), c_Orderings_Obot__class_Obot(tc_fun(_967392, tc_HOL_Obool)))) = _967396)], (10217 ^ _782464) ^ [_967469, _967471, _967473, _967475, _967477] : [class_Groups_Oordered__ab__group__add(_967469), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967469), _967471), _967473) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967469), _967475), _967477), 10224 ^ _782464 : [(10225 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967469), _967471), _967473)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967469), _967475), _967477)))], (10231 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967469), _967475), _967477)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967469), _967471), _967473)))]]], (10237 ^ _782464) ^ [_967824, _967826] : [class_Orderings_Oorder(_967824), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967824, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_967824), _967826), c_Orderings_Obot__class_Obot(tc_fun(_967824, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_967824), _967826)) = hAPP(hAPP(c_Set_Oinsert(_967824), _967826), c_Orderings_Obot__class_Obot(tc_fun(_967824, tc_HOL_Obool))))], (10243 ^ _782464) ^ [_967983, _967985, _967987] : [class_Groups_Oab__group__add(_967983), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967983), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967983), _967985), _967987)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967983), _967987), _967985))], (10249 ^ _782464) ^ [_968102, _968104, _968106, _968108] : [hBOOL(hAPP(hAPP(c_member(_968102), _968104), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968102, tc_HOL_Obool)), _968106), _968108))), hBOOL(hAPP(hAPP(c_member(_968102), _968104), _968108))], (10255 ^ _782464) ^ [_968234, _968236, _968238, _968240] : [hBOOL(hAPP(hAPP(c_member(_968234), _968236), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968234, tc_HOL_Obool)), _968238), _968240))), -(hBOOL(hAPP(hAPP(c_member(_968234), _968236), _968238)))], (10261 ^ _782464) ^ [_968386, _968388, _968390, _968392] : [hBOOL(hAPP(hAPP(c_member(_968386), _968388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968386, tc_HOL_Obool)), _968390), _968392))), 10264 ^ _782464 : [(10265 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968386), _968388), _968390)))], (10267 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_968386), _968388), _968392))]]], (10269 ^ _782464) ^ [_968561, _968563, _968565, _968567] : [-(hBOOL(hAPP(hAPP(c_member(_968561), _968563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968561, tc_HOL_Obool)), _968565), _968567)))), hBOOL(hAPP(hAPP(c_member(_968561), _968563), _968565)), -(hBOOL(hAPP(hAPP(c_member(_968561), _968563), _968567)))], (10279 ^ _782464) ^ [_968767, _968769, _968771] : [hBOOL(hAPP(hAPP(c_member(_968767), _968769), _968771)), -(hAPP(hAPP(c_Set_Oinsert(_968767), _968769), _968771) = _968771)], (10285 ^ _782464) ^ [_968876, _968878, _968880, _968882] : [hBOOL(hAPP(hAPP(c_member(_968876), _968878), _968880)), -(hBOOL(hAPP(hAPP(c_member(_968876), _968878), hAPP(hAPP(c_Set_Oinsert(_968876), _968882), _968880))))], (10291 ^ _782464) ^ [_969000, _969002, _969004, _969006] : [-(hBOOL(hAPP(hAPP(c_member(_969000), _969002), _969004))), -(hBOOL(hAPP(hAPP(c_member(_969000), _969002), _969006))), 10298 ^ _782464 : [(10299 ^ _782464) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_969000), _969002), _969004) = hAPP(hAPP(c_Set_Oinsert(_969000), _969002), _969006), -(_969004 = _969006)], (10305 ^ _782464) ^ [] : [_969004 = _969006, -(hAPP(hAPP(c_Set_Oinsert(_969000), _969002), _969004) = hAPP(hAPP(c_Set_Oinsert(_969000), _969002), _969006))]]], (10321 ^ _782464) ^ [_969500, _969502, _969504, _969506] : [10322 ^ _782464 : [(10323 ^ _782464) ^ [] : [_969502 = _969504], (10325 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969500), _969502), _969506))]], -(hBOOL(hAPP(hAPP(c_member(_969500), _969502), hAPP(hAPP(c_Set_Oinsert(_969500), _969504), _969506))))], (10311 ^ _782464) ^ [_969366, _969368, _969370, _969372] : [hBOOL(hAPP(hAPP(c_member(_969366), _969368), hAPP(hAPP(c_Set_Oinsert(_969366), _969370), _969372))), -(_969368 = _969370), -(hBOOL(hAPP(hAPP(c_member(_969366), _969368), _969372)))], (10329 ^ _782464) ^ [_969665, _969667, _969669] : [-(hBOOL(hAPP(hAPP(c_member(_969665), _969667), hAPP(hAPP(c_Set_Oinsert(_969665), _969667), _969669))))], (10331 ^ _782464) ^ [_969707, _969709] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969707, tc_HOL_Obool)), _969709), _969709) = c_Orderings_Obot__class_Obot(tc_fun(_969707, tc_HOL_Obool)))], (10333 ^ _782464) ^ [_969748, _969750] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969748, tc_HOL_Obool)), _969750), c_Orderings_Obot__class_Obot(tc_fun(_969748, tc_HOL_Obool))) = _969750)], (10335 ^ _782464) ^ [_969789, _969791] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969789, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_969789, tc_HOL_Obool))), _969791) = c_Orderings_Obot__class_Obot(tc_fun(_969789, tc_HOL_Obool)))], (10337 ^ _782464) ^ [_969835, _969837, _969839] : [hAPP(hAPP(c_Set_Oinsert(_969835), _969837), c_Orderings_Obot__class_Obot(tc_fun(_969835, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_969835), _969839), c_Orderings_Obot__class_Obot(tc_fun(_969835, tc_HOL_Obool))), -(_969837 = _969839)], (10343 ^ _782464) ^ [_969990, _969992, _969994, _969996, _969998] : [hAPP(hAPP(c_Set_Oinsert(_969990), _969992), hAPP(hAPP(c_Set_Oinsert(_969990), _969994), c_Orderings_Obot__class_Obot(tc_fun(_969990, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_969990), _969996), hAPP(hAPP(c_Set_Oinsert(_969990), _969998), c_Orderings_Obot__class_Obot(tc_fun(_969990, tc_HOL_Obool)))), 10348 ^ _782464 : [(10349 ^ _782464) ^ [] : [-(_969992 = _969996)], (10351 ^ _782464) ^ [] : [-(_969994 = _969998)]], 10352 ^ _782464 : [(10353 ^ _782464) ^ [] : [-(_969992 = _969998)], (10355 ^ _782464) ^ [] : [-(_969994 = _969996)]]], (10357 ^ _782464) ^ [_970252, _970254, _970256, _970258, _970260] : [-(hAPP(hAPP(c_Set_Oinsert(_970252), _970254), hAPP(hAPP(c_Set_Oinsert(_970252), _970256), c_Orderings_Obot__class_Obot(tc_fun(_970252, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_970252), _970258), hAPP(hAPP(c_Set_Oinsert(_970252), _970260), c_Orderings_Obot__class_Obot(tc_fun(_970252, tc_HOL_Obool))))), 10358 ^ _782464 : [(10359 ^ _782464) ^ [] : [_970254 = _970258, _970256 = _970260], (10365 ^ _782464) ^ [] : [_970254 = _970260, _970256 = _970258]]], (10373 ^ _782464) ^ [_970583, _970585, _970587] : [hAPP(hAPP(c_Set_Oinsert(_970583), _970585), _970587) = c_Orderings_Obot__class_Obot(tc_fun(_970583, tc_HOL_Obool))], (10375 ^ _782464) ^ [_970638, _970640, _970642] : [c_Orderings_Obot__class_Obot(tc_fun(_970638, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_970638), _970640), _970642)], (10377 ^ _782464) ^ [_970678, _970680, _970682, _970684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970678, tc_HOL_Obool)), _970680), _970682)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970678, tc_HOL_Obool)), _970682), _970684)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970678, tc_HOL_Obool)), _970682), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970678, tc_HOL_Obool)), _970684), _970680)) = _970680)], (10387 ^ _782464) ^ [_970899, _970901, _970903, _970905, _970907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970899, tc_HOL_Obool)), _970901), _970903)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970899, tc_HOL_Obool)), _970905), _970907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970899, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970899, tc_HOL_Obool)), _970901), _970907)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970899, tc_HOL_Obool)), _970903), _970905))))], (10397 ^ _782464) ^ [_971144, _971146, _971148] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971144, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971144, tc_HOL_Obool)), _971146), _971148)), _971146)))], (10399 ^ _782464) ^ [_971192, _971194, _971196, _971198] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971192, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971192, tc_HOL_Obool)), _971194), _971196)), _971198) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971192, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971192, tc_HOL_Obool)), _971194), _971198)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971192, tc_HOL_Obool)), _971196), _971198)))], (10401 ^ _782464) ^ [_971276, _971278, _971280] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971276, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971276, tc_HOL_Obool)), _971278), _971280)), _971280) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971276, tc_HOL_Obool)), _971278), _971280))], (10403 ^ _782464) ^ [_971336, _971338, _971340] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971336, tc_HOL_Obool)), _971338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971336, tc_HOL_Obool)), _971340), _971338)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971336, tc_HOL_Obool)), _971338), _971340))], (10405 ^ _782464) ^ [_971396, _971398, _971400, _971402] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971396, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971396, tc_HOL_Obool)), _971398), _971400)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971396, tc_HOL_Obool)), _971402), _971400)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971396, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971396, tc_HOL_Obool)), _971398), _971400)), _971402))], (10407 ^ _782464) ^ [_971480, _971482, _971484, _971486] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971480, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971480, tc_HOL_Obool)), _971482), _971484)), _971486) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971480, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971480, tc_HOL_Obool)), _971482), _971486)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971480, tc_HOL_Obool)), _971484), _971486)))], (10409 ^ _782464) ^ [_971564, _971566, _971568, _971570] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971564, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971564, tc_HOL_Obool)), _971566), _971568)), _971570) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971564, tc_HOL_Obool)), _971566), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971564, tc_HOL_Obool)), _971568), _971570)))], (10411 ^ _782464) ^ [_971637, _971639, _971641, _971643] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971637, tc_HOL_Obool)), _971639), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971637, tc_HOL_Obool)), _971641), _971643)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971637, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971637, tc_HOL_Obool)), _971639), _971641)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971637, tc_HOL_Obool)), _971639), _971643)))], (10413 ^ _782464) ^ [_971721, _971723, _971725, _971727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971721, tc_HOL_Obool)), _971723), _971725)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971721, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_971721), _971727), _971723)), hAPP(hAPP(c_Set_Oinsert(_971721), _971727), _971725))))], (10419 ^ _782464) ^ [_971874, _971876, _971878, _971880] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971874, tc_HOL_Obool)), _971876), _971878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971874, tc_HOL_Obool)), _971876), hAPP(hAPP(c_Set_Oinsert(_971874), _971880), _971878))))], (10425 ^ _782464) ^ [_972011, _972013, _972015] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972011, tc_HOL_Obool)), _972013), hAPP(hAPP(c_Set_Oinsert(_972011), _972015), _972013))))], (10427 ^ _782464) ^ [_972056, _972058, _972060, _972062, _972064] : [-(hAPP(c_Set_Oimage(_972056, _972058, _972060), hAPP(hAPP(c_Set_Oinsert(_972056), _972062), _972064)) = hAPP(hAPP(c_Set_Oinsert(_972058), hAPP(_972060, _972062)), hAPP(c_Set_Oimage(_972056, _972058, _972060), _972064)))], (10429 ^ _782464) ^ [_972120, _972122, _972124, _972126] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972120, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_972120), _972122), _972124)), _972126) = hAPP(hAPP(c_Set_Oinsert(_972120), _972122), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972120, tc_HOL_Obool)), _972124), _972126)))], (10431 ^ _782464) ^ [_972187, _972189, _972191, _972193] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972187, tc_HOL_Obool)), _972189), hAPP(hAPP(c_Set_Oinsert(_972187), _972191), _972193)) = hAPP(hAPP(c_Set_Oinsert(_972187), _972191), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972187, tc_HOL_Obool)), _972189), _972193)))], (10433 ^ _782464) ^ [_972254, _972256, _972258, _972260] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972254, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_972254), _972256), _972258)), hAPP(hAPP(c_Set_Oinsert(_972254), _972256), _972260)) = hAPP(hAPP(c_Set_Oinsert(_972254), _972256), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972254, tc_HOL_Obool)), _972258), _972260)))], (10435 ^ _782464) ^ [_972329, _972331, _972333, _972335] : [c_Hoare__Mirabelle_Ohoare__derivs(_972329, _972331, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_972329)), _972333), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_972329), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_972329, _972331, _972335), -(c_Hoare__Mirabelle_Ohoare__derivs(_972329, _972331, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_972329)), _972333), _972335)))], (10461 ^ _782464) ^ [_972879, _972881, _972883, _972885] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972879, tc_HOL_Obool)), _972881), hAPP(hAPP(c_Set_Oinsert(_972879), _972883), _972885)))), 10464 ^ _782464 : [(10465 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972879), _972883), _972881)))], (10467 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972879, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972879, tc_HOL_Obool)), _972881), hAPP(hAPP(c_Set_Oinsert(_972879), _972883), c_Orderings_Obot__class_Obot(tc_fun(_972879, tc_HOL_Obool))))), _972885))]], 10468 ^ _782464 : [(10469 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972879), _972883), _972881))], (10471 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972879, tc_HOL_Obool)), _972881), _972885))]]], (10445 ^ _782464) ^ [_972547, _972549, _972551, _972553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972547, tc_HOL_Obool)), _972549), hAPP(hAPP(c_Set_Oinsert(_972547), _972551), _972553))), 10448 ^ _782464 : [(10449 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972547), _972551), _972549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972547, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972547, tc_HOL_Obool)), _972549), hAPP(hAPP(c_Set_Oinsert(_972547), _972551), c_Orderings_Obot__class_Obot(tc_fun(_972547, tc_HOL_Obool))))), _972553)))], (10455 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972547), _972551), _972549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972547, tc_HOL_Obool)), _972549), _972553)))]]], (10475 ^ _782464) ^ [_973243, _973245, _973247, _973249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973243, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973243, tc_HOL_Obool)), _973245), hAPP(hAPP(c_Set_Oinsert(_973243), _973247), c_Orderings_Obot__class_Obot(tc_fun(_973243, tc_HOL_Obool))))), _973249)), hBOOL(hAPP(hAPP(c_member(_973243), _973247), _973245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973243, tc_HOL_Obool)), _973245), hAPP(hAPP(c_Set_Oinsert(_973243), _973247), _973249))))], (10485 ^ _782464) ^ [_973498, _973500, _973502, _973504, _973506] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973498, tc_fun(_973500, tc_HOL_Obool)), _973502), hAPP(hAPP(c_COMBC(_973498, tc_fun(_973500, tc_HOL_Obool), tc_fun(_973500, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_973500, tc_HOL_Obool), tc_fun(tc_fun(_973500, tc_HOL_Obool), tc_fun(_973500, tc_HOL_Obool)), _973498), c_Groups_Ominus__class_Ominus(tc_fun(_973500, tc_HOL_Obool))), _973504)), _973506)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973500, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973498, tc_fun(_973500, tc_HOL_Obool)), _973502), _973504)), _973506))], (10487 ^ _782464) ^ [_973607, _973609, _973611, _973613, _973615] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973607, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973609, tc_fun(_973607, tc_HOL_Obool)), _973611), _973613)), _973615) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973609, tc_fun(_973607, tc_HOL_Obool)), _973611), hAPP(hAPP(c_COMBC(_973609, tc_fun(_973607, tc_HOL_Obool), tc_fun(_973607, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_973607, tc_HOL_Obool), tc_fun(tc_fun(_973607, tc_HOL_Obool), tc_fun(_973607, tc_HOL_Obool)), _973609), c_Groups_Ominus__class_Ominus(tc_fun(_973607, tc_HOL_Obool))), _973613)), _973615)))], (10489 ^ _782464) ^ [_973716, _973718, _973720, _973722, _973724] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973716, tc_fun(_973718, tc_HOL_Obool)), _973720), hAPP(hAPP(c_COMBB(tc_fun(_973718, tc_HOL_Obool), tc_fun(_973718, tc_HOL_Obool), _973716), hAPP(c_Set_Oinsert(_973718), _973722)), _973724)) = hAPP(hAPP(c_Set_Oinsert(_973718), _973722), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973716, tc_fun(_973718, tc_HOL_Obool)), _973720), _973724)))], (10491 ^ _782464) ^ [_973800, _973802, _973804, _973806, _973808] : [-(hAPP(hAPP(c_Set_Oinsert(_973800), _973802), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973804, tc_fun(_973800, tc_HOL_Obool)), _973806), _973808)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973804, tc_fun(_973800, tc_HOL_Obool)), _973806), hAPP(hAPP(c_COMBB(tc_fun(_973800, tc_HOL_Obool), tc_fun(_973800, tc_HOL_Obool), _973804), hAPP(c_Set_Oinsert(_973800), _973802)), _973808)))], (10493 ^ _782464) ^ [_973884, _973886, _973888] : [class_Lattices_Oboolean__algebra(_973884), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973884), _973886), _973888) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973884), _973886), hAPP(c_Groups_Ouminus__class_Ouminus(_973884), _973888)))], (10499 ^ _782464) ^ [_974003, _974005, _974007] : [hBOOL(hAPP(hAPP(c_member(_974003), _974005), hAPP(hAPP(c_Set_Oinsert(_974003), _974007), c_Orderings_Obot__class_Obot(tc_fun(_974003, tc_HOL_Obool))))), -(_974005 = _974007)], (10505 ^ _782464) ^ [_974140, _974142, _974144] : [hBOOL(hAPP(hAPP(c_member(_974140), _974142), hAPP(hAPP(c_Set_Oinsert(_974140), _974144), c_Orderings_Obot__class_Obot(tc_fun(_974140, tc_HOL_Obool))))), -(_974142 = _974144)], (10511 ^ _782464) ^ [_974255, _974257, _974259] : [_974257 = _974259, -(hBOOL(hAPP(hAPP(c_member(_974255), _974257), hAPP(hAPP(c_Set_Oinsert(_974255), _974259), c_Orderings_Obot__class_Obot(tc_fun(_974255, tc_HOL_Obool))))))], (10517 ^ _782464) ^ [_974397, _974399, _974401, _974403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974397, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_974397), _974399), _974401)), _974403)), 10520 ^ _782464 : [(10521 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_974397), _974399), _974403)))], (10523 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974397, tc_HOL_Obool)), _974401), _974403)))]]], (10525 ^ _782464) ^ [_974570, _974572, _974574, _974576] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974570, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_974570), _974572), _974574)), _974576))), hBOOL(hAPP(hAPP(c_member(_974570), _974572), _974576)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974570, tc_HOL_Obool)), _974574), _974576))], (10535 ^ _782464) ^ [_974778, _974780, _974782, _974784] : [-(hBOOL(hAPP(hAPP(c_member(_974778), _974780), _974782))), 10538 ^ _782464 : [(10539 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974778, tc_HOL_Obool)), _974782), hAPP(hAPP(c_Set_Oinsert(_974778), _974780), _974784))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974778, tc_HOL_Obool)), _974782), _974784)))], (10545 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974778, tc_HOL_Obool)), _974782), _974784)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974778, tc_HOL_Obool)), _974782), hAPP(hAPP(c_Set_Oinsert(_974778), _974780), _974784))))]]], (10551 ^ _782464) ^ [_975086, _975088, _975090, _975092, _975094] : [hBOOL(hAPP(hAPP(c_member(_975086), _975088), _975090)), -(hAPP(hAPP(c_Set_Oinsert(_975092), hAPP(_975094, _975088)), hAPP(c_Set_Oimage(_975086, _975092, _975094), _975090)) = hAPP(c_Set_Oimage(_975086, _975092, _975094), _975090))], (10557 ^ _782464) ^ [_975233, _975235] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975233, tc_HOL_Obool)), _975235), c_Orderings_Otop__class_Otop(tc_fun(_975233, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_975233, tc_HOL_Obool)))], (10559 ^ _782464) ^ [_975279, _975281, _975283, _975285] : [hBOOL(hAPP(hAPP(c_member(_975279), _975281), _975283)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975279, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975279), _975281), _975285)), _975283) = hAPP(hAPP(c_Set_Oinsert(_975279), _975281), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975279, tc_HOL_Obool)), _975285), _975283)))], (10565 ^ _782464) ^ [_975450, _975452, _975454, _975456] : [hBOOL(hAPP(hAPP(c_member(_975450), _975452), _975454)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975450, tc_HOL_Obool)), _975454), hAPP(hAPP(c_Set_Oinsert(_975450), _975452), _975456)) = hAPP(hAPP(c_Set_Oinsert(_975450), _975452), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975450, tc_HOL_Obool)), _975454), _975456)))], (10571 ^ _782464) ^ [_975617, _975619, _975621, _975623] : [-(hBOOL(hAPP(hAPP(c_member(_975617), _975619), _975621))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975617, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975617), _975619), _975623)), _975621) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975617, tc_HOL_Obool)), _975623), _975621))], (10577 ^ _782464) ^ [_975690, _975692, _975694, _975696] : [-(hBOOL(hAPP(hAPP(c_member(_975690), _975692), _975694))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975690, tc_HOL_Obool)), _975694), hAPP(hAPP(c_Set_Oinsert(_975690), _975692), _975696)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975690, tc_HOL_Obool)), _975694), _975696))], (10583 ^ _782464) ^ [_975782, _975784, _975786, _975788] : [hBOOL(hAPP(hAPP(c_member(_975782), _975784), _975786)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975782, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975782), _975784), _975788)), _975786) = hAPP(hAPP(c_Set_Oinsert(_975782), _975784), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975782, tc_HOL_Obool)), _975788), _975786)))], (10589 ^ _782464) ^ [_975947, _975949, _975951, _975953] : [-(hBOOL(hAPP(hAPP(c_member(_975947), _975949), _975951))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975947, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975947), _975949), _975953)), _975951) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975947, tc_HOL_Obool)), _975953), _975951))], (10595 ^ _782464) ^ [_976041, _976043, _976045, _976047] : [hBOOL(hAPP(hAPP(c_member(_976041), _976043), _976045)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976041, tc_HOL_Obool)), _976045), hAPP(hAPP(c_Set_Oinsert(_976041), _976043), _976047)) = hAPP(hAPP(c_Set_Oinsert(_976041), _976043), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976041, tc_HOL_Obool)), _976045), _976047)))], (10601 ^ _782464) ^ [_976206, _976208, _976210, _976212] : [-(hBOOL(hAPP(hAPP(c_member(_976206), _976208), _976210))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976206, tc_HOL_Obool)), _976210), hAPP(hAPP(c_Set_Oinsert(_976206), _976208), _976212)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976206, tc_HOL_Obool)), _976210), _976212))], (10607 ^ _782464) ^ [_976285, _976287, _976289] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976285, tc_HOL_Obool)), _976287), _976289) = c_Orderings_Obot__class_Obot(tc_fun(_976285, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976285, tc_HOL_Obool)), _976287), _976289) = _976287)], (10613 ^ _782464) ^ [_976418, _976420, _976422] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976418, tc_HOL_Obool)), _976420), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976418, tc_HOL_Obool)), _976422), _976420)) = c_Orderings_Obot__class_Obot(tc_fun(_976418, tc_HOL_Obool)))], (10615 ^ _782464) ^ [_976472, _976474, _976476, _976478, _976480] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976472, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976472, tc_HOL_Obool)), hAPP(c_Set_Oimage(_976474, _976472, _976476), _976478)), hAPP(c_Set_Oimage(_976474, _976472, _976476), _976480))), hAPP(c_Set_Oimage(_976474, _976472, _976476), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976474, tc_HOL_Obool)), _976478), _976480)))))], (10617 ^ _782464) ^ [_976556, _976558, _976560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976556, tc_HOL_Obool)), _976558), hAPP(hAPP(c_Set_Oinsert(_976556), _976560), c_Orderings_Obot__class_Obot(tc_fun(_976556, tc_HOL_Obool))))), -(_976558 = c_Orderings_Obot__class_Obot(tc_fun(_976556, tc_HOL_Obool))), -(_976558 = hAPP(hAPP(c_Set_Oinsert(_976556), _976560), c_Orderings_Obot__class_Obot(tc_fun(_976556, tc_HOL_Obool))))], (10627 ^ _782464) ^ [_976751, _976753, _976755, _976757] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976751, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976751, tc_HOL_Obool)), _976753), _976755)), _976757)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976751, tc_HOL_Obool)), _976753), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976751, tc_HOL_Obool)), _976755), _976757))))], (10633 ^ _782464) ^ [_976912, _976914, _976916, _976918] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976912, tc_HOL_Obool)), _976914), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976912, tc_HOL_Obool)), _976916), _976918))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976912, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976912, tc_HOL_Obool)), _976914), _976916)), _976918)))], (10639 ^ _782464) ^ [_977079, _977081, _977083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977079, tc_HOL_Obool)), _977081), _977083)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977079, tc_HOL_Obool)), _977081), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977079, tc_HOL_Obool)), _977083), _977081)) = _977083)], (10645 ^ _782464) ^ [_977222, _977224, _977226] : [-(hAPP(hAPP(c_Set_Oinsert(_977222), _977224), _977226) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977222, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977222), _977224), c_Orderings_Obot__class_Obot(tc_fun(_977222, tc_HOL_Obool)))), _977226))], (10647 ^ _782464) ^ [_977281, _977283, _977285] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977281, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977281, tc_HOL_Obool)), _977283), _977285)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977281, tc_HOL_Obool)), _977283), _977285)) = _977283)], (10649 ^ _782464) ^ [_977341, _977343, _977345, _977347] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977341, tc_HOL_Obool)), _977343), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977341, tc_HOL_Obool)), _977345), _977347)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977341, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977341, tc_HOL_Obool)), _977343), _977345)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977341, tc_HOL_Obool)), _977343), _977347)))], (10651 ^ _782464) ^ [_977425, _977427, _977429, _977431] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977425, tc_HOL_Obool)), _977427), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977425, tc_HOL_Obool)), _977429), _977431)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977425, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977425, tc_HOL_Obool)), _977427), _977429)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977425, tc_HOL_Obool)), _977427), _977431)))], (10653 ^ _782464) ^ [_977509, _977511, _977513, _977515] : [class_Orderings_Olinorder(_977509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977509), _977511), _977513)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977509, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977509, _977511), _977515)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977509, _977511), _977513)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977509, _977513), _977515))], (10663 ^ _782464) ^ [_977716, _977718, _977720] : [class_Orderings_Oorder(_977716), _977718 = _977720, -(c_SetInterval_Oord__class_OatLeastAtMost(_977716, _977718, _977720) = hAPP(hAPP(c_Set_Oinsert(_977716), _977718), c_Orderings_Obot__class_Obot(tc_fun(_977716, tc_HOL_Obool))))], (10673 ^ _782464) ^ [_977881, _977883, _977885, _977887] : [class_Orderings_Oorder(_977881), 10676 ^ _782464 : [(10677 ^ _782464) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_977881, _977883, _977885) = hAPP(hAPP(c_Set_Oinsert(_977881), _977887), c_Orderings_Obot__class_Obot(tc_fun(_977881, tc_HOL_Obool))), 10680 ^ _782464 : [(10681 ^ _782464) ^ [] : [-(_977883 = _977885)], (10683 ^ _782464) ^ [] : [-(_977885 = _977887)]]], (10685 ^ _782464) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_977881, _977883, _977885) = hAPP(hAPP(c_Set_Oinsert(_977881), _977887), c_Orderings_Obot__class_Obot(tc_fun(_977881, tc_HOL_Obool)))), _977883 = _977885, _977885 = _977887]]], (10695 ^ _782464) ^ [_978225, _978227] : [class_Orderings_Oorder(_978225), -(c_SetInterval_Oord__class_OatLeastAtMost(_978225, _978227, _978227) = hAPP(hAPP(c_Set_Oinsert(_978225), _978227), c_Orderings_Obot__class_Obot(tc_fun(_978225, tc_HOL_Obool))))], (10701 ^ _782464) ^ [_978334, _978336] : [class_Complete__Lattice_Ocomplete__lattice(_978334), -(c_Complete__Lattice_OSup__class_OSup(_978334, hAPP(hAPP(c_Set_Oinsert(_978334), _978336), c_Orderings_Obot__class_Obot(tc_fun(_978334, tc_HOL_Obool)))) = _978336)], (10707 ^ _782464) ^ [_978441, _978443, _978445] : [class_Complete__Lattice_Ocomplete__lattice(_978441), -(c_Complete__Lattice_OSup__class_OSup(_978441, hAPP(hAPP(c_Set_Oinsert(_978441), _978443), _978445)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_978441), _978443), c_Complete__Lattice_OSup__class_OSup(_978441, _978445)))], (10713 ^ _782464) ^ [_978562, _978564] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978562, tc_HOL_Obool)), _978564) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978562, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_978562, tc_HOL_Obool))), _978564))], (10715 ^ _782464) ^ [_978611, _978613, _978615] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978611, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978611, tc_HOL_Obool)), _978613), _978615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978611, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978611, tc_HOL_Obool)), _978613)), _978615))], (10717 ^ _782464) ^ [_978676, _978678, _978680] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978676, tc_HOL_Obool)), _978678), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978676, tc_HOL_Obool)), _978680)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978676, tc_HOL_Obool)), _978678), _978680))], (10719 ^ _782464) ^ [_978733, _978735, _978737] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978733, tc_HOL_Obool)), _978735), _978737) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978733, tc_HOL_Obool)), _978735), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978733, tc_HOL_Obool)), _978737)))], (10721 ^ _782464) ^ [_978790, _978792] : [class_Complete__Lattice_Ocomplete__lattice(_978790), -(c_Complete__Lattice_OInf__class_OInf(_978790, hAPP(hAPP(c_Set_Oinsert(_978790), _978792), c_Orderings_Obot__class_Obot(tc_fun(_978790, tc_HOL_Obool)))) = _978792)], (10727 ^ _782464) ^ [_978897, _978899, _978901] : [class_Complete__Lattice_Ocomplete__lattice(_978897), -(c_Complete__Lattice_OInf__class_OInf(_978897, hAPP(hAPP(c_Set_Oinsert(_978897), _978899), _978901)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978897), _978899), c_Complete__Lattice_OInf__class_OInf(_978897, _978901)))], (10733 ^ _782464) ^ [_979018, _979020, _979022] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_979018, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979018, tc_HOL_Obool)), _979020), _979022)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979018, tc_HOL_Obool)), _979020), c_Complete__Lattice_OSup__class_OSup(tc_fun(_979018, tc_HOL_Obool), _979022)))], (10735 ^ _782464) ^ [_979079, _979081, _979083] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979079, tc_HOL_Obool)), _979081), _979083) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_979079, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979079, tc_HOL_Obool)), _979081), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979079, tc_HOL_Obool)), _979083), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979079, tc_HOL_Obool), tc_HOL_Obool))))))], (10737 ^ _782464) ^ [_979153] : [-(hAPP(c_Set_OPow(_979153), c_Orderings_Obot__class_Obot(tc_fun(_979153, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_979153, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_979153, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979153, tc_HOL_Obool), tc_HOL_Obool))))], (10739 ^ _782464) ^ [_979210, _979212, _979214] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_979210, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979210, tc_HOL_Obool)), _979212), _979214)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979210, tc_HOL_Obool)), _979212), c_Complete__Lattice_OInf__class_OInf(tc_fun(_979210, tc_HOL_Obool), _979214)))], (10741 ^ _782464) ^ [_979271, _979273, _979275] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979271, tc_HOL_Obool)), _979273), _979275) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_979271, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979271, tc_HOL_Obool)), _979273), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979271, tc_HOL_Obool)), _979275), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979271, tc_HOL_Obool), tc_HOL_Obool))))))], (10743 ^ _782464) ^ [_979345, _979347, _979349, _979351, _979353, _979355] : [hBOOL(hAPP(hAPP(c_member(_979345), _979347), _979349)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979345, tc_fun(_979351, tc_HOL_Obool)), _979349), hAPP(hAPP(c_COMBB(tc_fun(_979351, tc_HOL_Obool), tc_fun(_979351, tc_HOL_Obool), _979345), hAPP(c_Set_Oinsert(_979351), _979353)), _979355)) = hAPP(hAPP(c_Set_Oinsert(_979351), _979353), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979345, tc_fun(_979351, tc_HOL_Obool)), _979349), _979355)))], (10749 ^ _782464) ^ [_979565, _979567, _979569, _979571] : [_979565 = c_Orderings_Obot__class_Obot(tc_fun(_979567, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_979567, _979569, hAPP(c_COMBK(_979569, _979567), _979571)), _979565) = c_Orderings_Obot__class_Obot(tc_fun(_979569, tc_HOL_Obool)))], (10755 ^ _782464) ^ [_979686, _979688, _979690, _979692] : [-(_979686 = c_Orderings_Obot__class_Obot(tc_fun(_979688, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_979688, _979690, hAPP(c_COMBK(_979690, _979688), _979692)), _979686) = hAPP(hAPP(c_Set_Oinsert(_979690), _979692), c_Orderings_Obot__class_Obot(tc_fun(_979690, tc_HOL_Obool))))], (10761 ^ _782464) ^ [_979777, _979779, _979781, _979783, _979785] : [_979777 = c_Orderings_Obot__class_Obot(tc_fun(_979779, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_979781), _979783), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979779, tc_fun(_979781, tc_HOL_Obool)), _979777), _979785)) = hAPP(hAPP(c_Set_Oinsert(_979781), _979783), c_Orderings_Obot__class_Obot(tc_fun(_979781, tc_HOL_Obool))))], (10767 ^ _782464) ^ [_979930, _979932, _979934, _979936, _979938] : [-(_979930 = c_Orderings_Obot__class_Obot(tc_fun(_979932, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_979934), _979936), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979932, tc_fun(_979934, tc_HOL_Obool)), _979930), _979938)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979932, tc_fun(_979934, tc_HOL_Obool)), _979930), hAPP(hAPP(c_COMBB(tc_fun(_979934, tc_HOL_Obool), tc_fun(_979934, tc_HOL_Obool), _979932), hAPP(c_Set_Oinsert(_979934), _979936)), _979938)))], (10773 ^ _782464) ^ [_980032, _980034] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980032, tc_fun(_980032, tc_HOL_Obool)), _980034), hAPP(hAPP(c_COMBC(_980032, tc_fun(_980032, tc_HOL_Obool), tc_fun(_980032, tc_HOL_Obool)), c_Set_Oinsert(_980032)), c_Orderings_Obot__class_Obot(tc_fun(_980032, tc_HOL_Obool)))) = _980034)], (10775 ^ _782464) ^ [_980110, _980112, _980114, _980116, _980118] : [_980110 = c_Orderings_Obot__class_Obot(tc_fun(_980112, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980112, tc_fun(_980114, tc_HOL_Obool)), _980110), hAPP(hAPP(c_COMBB(tc_fun(_980114, tc_HOL_Obool), tc_fun(_980114, tc_HOL_Obool), _980112), hAPP(c_Set_Oinsert(_980114), _980116)), _980118)) = c_Orderings_Obot__class_Obot(tc_fun(_980114, tc_HOL_Obool)))], (10781 ^ _782464) ^ [_980273, _980275, _980277, _980279, _980281] : [-(_980273 = c_Orderings_Obot__class_Obot(tc_fun(_980275, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980275, tc_fun(_980277, tc_HOL_Obool)), _980273), hAPP(hAPP(c_COMBB(tc_fun(_980277, tc_HOL_Obool), tc_fun(_980277, tc_HOL_Obool), _980275), hAPP(c_Set_Oinsert(_980277), _980279)), _980281)) = hAPP(hAPP(c_Set_Oinsert(_980277), _980279), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980275, tc_fun(_980277, tc_HOL_Obool)), _980273), _980281)))], (10787 ^ _782464) ^ [_980375, _980377, _980379, _980381, _980383, _980385] : [hBOOL(hAPP(hAPP(c_member(_980375), _980377), _980379)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980375, tc_fun(_980381, tc_HOL_Obool)), _980379), hAPP(hAPP(c_COMBB(tc_fun(_980381, tc_HOL_Obool), tc_fun(_980381, tc_HOL_Obool), _980375), hAPP(c_Set_Oinsert(_980381), _980383)), _980385)) = hAPP(hAPP(c_Set_Oinsert(_980381), _980383), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980375, tc_fun(_980381, tc_HOL_Obool)), _980379), _980385)))], (10793 ^ _782464) ^ [_980580, _980582, _980584, _980586, _980588] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980580, tc_fun(_980582, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980580), _980584), _980586)), _980588) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980582, tc_HOL_Obool)), hAPP(_980588, _980584)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980580, tc_fun(_980582, tc_HOL_Obool)), _980586), _980588)))], (10795 ^ _782464) ^ [_980657, _980659, _980661, _980663, _980665] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980657, tc_fun(_980659, tc_HOL_Obool)), _980661), hAPP(hAPP(c_COMBB(tc_fun(_980659, tc_HOL_Obool), tc_fun(_980659, tc_HOL_Obool), _980657), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980659, tc_HOL_Obool)), _980663)), _980665)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980659, tc_HOL_Obool)), _980663), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980657, tc_fun(_980659, tc_HOL_Obool)), _980661), _980665)))], (10797 ^ _782464) ^ [_980747, _980749, _980751, _980753, _980755] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980747, tc_HOL_Obool)), _980749), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980751, tc_fun(_980747, tc_HOL_Obool)), _980753), _980755)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980751, tc_fun(_980747, tc_HOL_Obool)), _980753), hAPP(hAPP(c_COMBB(tc_fun(_980747, tc_HOL_Obool), tc_fun(_980747, tc_HOL_Obool), _980751), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980747, tc_HOL_Obool)), _980749)), _980755)))], (10799 ^ _782464) ^ [_980837, _980839, _980841, _980843, _980845] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980837, tc_fun(_980839, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980837), _980841), _980843)), _980845) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980839, tc_HOL_Obool)), hAPP(_980845, _980841)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980837, tc_fun(_980839, tc_HOL_Obool)), _980843), _980845)))], (10801 ^ _782464) ^ [_980914, _980916, _980918] : [class_Orderings_Oorder(_980914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980914), _980916), _980918)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_980914, _980918, _980916) = c_Orderings_Obot__class_Obot(tc_fun(_980914, tc_HOL_Obool)))], (10811 ^ _782464) ^ [_981077, _981079, _981081] : [class_Groups_Oordered__ab__group__add(_981077), -(hAPP(c_Set_Oimage(_981077, _981077, c_Groups_Ouminus__class_Ouminus(_981077)), c_SetInterval_Oord__class_OgreaterThanLessThan(_981077, _981079, _981081)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_981077, hAPP(c_Groups_Ouminus__class_Ouminus(_981077), _981081), hAPP(c_Groups_Ouminus__class_Ouminus(_981077), _981079)))], (10817 ^ _782464) ^ [_981208, _981210, _981212] : [class_Complete__Lattice_Ocomplete__lattice(_981208), -(c_Complete__Lattice_OSup__class_OSup(_981208, hAPP(hAPP(c_Set_Oinsert(_981208), _981210), hAPP(hAPP(c_Set_Oinsert(_981208), _981212), c_Orderings_Obot__class_Obot(tc_fun(_981208, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_981208), _981210), _981212))], (10823 ^ _782464) ^ [_981349, _981351, _981353] : [class_Complete__Lattice_Ocomplete__lattice(_981349), -(c_Complete__Lattice_OInf__class_OInf(_981349, hAPP(hAPP(c_Set_Oinsert(_981349), _981351), hAPP(hAPP(c_Set_Oinsert(_981349), _981353), c_Orderings_Obot__class_Obot(tc_fun(_981349, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981349), _981351), _981353))], (10829 ^ _782464) ^ [_981490, _981492, _981494, _981496, _981498] : [hBOOL(hAPP(hAPP(c_member(_981490), _981492), _981494)), -(hAPP(c_Set_Oimage(_981490, _981496, hAPP(c_COMBK(_981496, _981490), _981498)), _981494) = hAPP(hAPP(c_Set_Oinsert(_981496), _981498), c_Orderings_Obot__class_Obot(tc_fun(_981496, tc_HOL_Obool))))], (10835 ^ _782464) ^ [_981657, _981659, _981661, _981663, _981665] : [_981657 = c_Orderings_Obot__class_Obot(tc_fun(_981659, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981659, tc_fun(_981661, tc_HOL_Obool)), _981657), hAPP(hAPP(c_COMBC(_981659, tc_fun(_981661, tc_HOL_Obool), tc_fun(_981661, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_981661, tc_HOL_Obool), tc_fun(tc_fun(_981661, tc_HOL_Obool), tc_fun(_981661, tc_HOL_Obool)), _981659), c_Groups_Ominus__class_Ominus(tc_fun(_981661, tc_HOL_Obool))), _981663)), _981665)) = c_Orderings_Otop__class_Otop(tc_fun(_981661, tc_HOL_Obool)))], (10841 ^ _782464) ^ [_981864, _981866, _981868, _981870, _981872] : [-(_981864 = c_Orderings_Obot__class_Obot(tc_fun(_981866, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981866, tc_fun(_981868, tc_HOL_Obool)), _981864), hAPP(hAPP(c_COMBC(_981866, tc_fun(_981868, tc_HOL_Obool), tc_fun(_981868, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_981868, tc_HOL_Obool), tc_fun(tc_fun(_981868, tc_HOL_Obool), tc_fun(_981868, tc_HOL_Obool)), _981866), c_Groups_Ominus__class_Ominus(tc_fun(_981868, tc_HOL_Obool))), _981870)), _981872)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981868, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981866, tc_fun(_981868, tc_HOL_Obool)), _981864), _981870)), _981872))], (10847 ^ _782464) ^ [_982009, _982011, _982013, _982015, _982017] : [_982009 = c_Orderings_Obot__class_Obot(tc_fun(_982011, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982013, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982011, tc_fun(_982013, tc_HOL_Obool)), _982009), _982015)), _982017) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982013, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_982013, tc_HOL_Obool))), _982017))], (10853 ^ _782464) ^ [_982174, _982176, _982178, _982180, _982182] : [-(_982174 = c_Orderings_Obot__class_Obot(tc_fun(_982176, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982178, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982176, tc_fun(_982178, tc_HOL_Obool)), _982174), _982180)), _982182) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982176, tc_fun(_982178, tc_HOL_Obool)), _982174), hAPP(hAPP(c_COMBC(_982176, tc_fun(_982178, tc_HOL_Obool), tc_fun(_982178, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_982178, tc_HOL_Obool), tc_fun(tc_fun(_982178, tc_HOL_Obool), tc_fun(_982178, tc_HOL_Obool)), _982176), c_Groups_Ominus__class_Ominus(tc_fun(_982178, tc_HOL_Obool))), _982180)), _982182)))], (10859 ^ _782464) ^ [_982301, _982303, _982305, _982307] : [-(hAPP(c_Set_Oimage(_982301, _982303, _982305), _982307) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982301, tc_fun(_982303, tc_HOL_Obool)), _982307), hAPP(hAPP(c_COMBC(_982301, tc_fun(_982303, tc_HOL_Obool), tc_fun(_982303, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_982303, tc_fun(tc_fun(_982303, tc_HOL_Obool), tc_fun(_982303, tc_HOL_Obool)), _982301), c_Set_Oinsert(_982303)), _982305)), c_Orderings_Obot__class_Obot(tc_fun(_982303, tc_HOL_Obool)))))], (10861 ^ _782464) ^ [_982409, _982411, _982413, _982415, _982417] : [_982409 = c_Orderings_Obot__class_Obot(tc_fun(_982411, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982413, tc_HOL_Obool)), _982415), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982411, tc_fun(_982413, tc_HOL_Obool)), _982409), _982417)) = _982415)], (10867 ^ _782464) ^ [_982542, _982544, _982546, _982548, _982550] : [-(_982542 = c_Orderings_Obot__class_Obot(tc_fun(_982544, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982546, tc_HOL_Obool)), _982548), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982544, tc_fun(_982546, tc_HOL_Obool)), _982542), _982550)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982544, tc_fun(_982546, tc_HOL_Obool)), _982542), hAPP(hAPP(c_COMBB(tc_fun(_982546, tc_HOL_Obool), tc_fun(_982546, tc_HOL_Obool), _982544), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982546, tc_HOL_Obool)), _982548)), _982550)))], (10873 ^ _782464) ^ [_982650, _982652, _982654] : [-(hAPP(c_Set_OPow(_982650), hAPP(hAPP(c_Set_Oinsert(_982650), _982652), _982654)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_982650, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_982650), _982654)), hAPP(c_Set_Oimage(tc_fun(_982650, tc_HOL_Obool), tc_fun(_982650, tc_HOL_Obool), hAPP(c_Set_Oinsert(_982650), _982652)), hAPP(c_Set_OPow(_982650), _982654))))], (10875 ^ _782464) ^ [_982732, _982734, _982736, _982738] : [class_Orderings_Oorder(_982732), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982732, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_982732, _982734, _982736)), c_SetInterval_Oord__class_OgreaterThanLessThan(_982732, _982736, _982738)) = c_Orderings_Obot__class_Obot(tc_fun(_982732, tc_HOL_Obool)))], (10881 ^ _782464) ^ [_982859, _982861, _982863, _982865] : [class_Orderings_Oorder(_982859), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982859, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_982859, _982861, _982863)), c_SetInterval_Oord__class_OatLeastAtMost(_982859, _982863, _982865)) = c_Orderings_Obot__class_Obot(tc_fun(_982859, tc_HOL_Obool)))], (10887 ^ _782464) ^ [_982986, _982988] : [class_Orderings_Olinorder(_982986), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982986, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_982986), _982988)), hAPP(hAPP(c_Set_Oinsert(_982986), _982988), c_Orderings_Obot__class_Obot(tc_fun(_982986, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_982986), _982988))], (10893 ^ _782464) ^ [_983129, _983131, _983133, _983135] : [class_Orderings_Oorder(_983129), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983129, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_983129, _983131, _983133)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_983129, _983133), _983135)) = c_Orderings_Obot__class_Obot(tc_fun(_983129, tc_HOL_Obool)))], (10899 ^ _782464) ^ [_983260, _983262] : [-(c_Set_Othe__elem(_983260, hAPP(hAPP(c_Set_Oinsert(_983260), _983262), c_Orderings_Obot__class_Obot(tc_fun(_983260, tc_HOL_Obool)))) = _983262)], (10901 ^ _782464) ^ [_983322, _983324, _983326, _983328, _983330, _983332] : [hBOOL(hAPP(hAPP(c_member(_983322), _983324), _983326)), -(hAPP(c_Set_Oimage(_983322, _983328, c_Fun_Ofun__upd(_983322, _983328, _983330, _983324, _983332)), _983326) = hAPP(hAPP(c_Set_Oinsert(_983328), _983332), hAPP(c_Set_Oimage(_983322, _983328, _983330), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983322, tc_HOL_Obool)), _983326), hAPP(hAPP(c_Set_Oinsert(_983322), _983324), c_Orderings_Obot__class_Obot(tc_fun(_983322, tc_HOL_Obool)))))))], (10907 ^ _782464) ^ [_983519, _983521, _983523, _983525, _983527, _983529] : [-(hBOOL(hAPP(hAPP(c_member(_983519), _983521), _983523))), -(hAPP(c_Set_Oimage(_983519, _983525, c_Fun_Ofun__upd(_983519, _983525, _983527, _983521, _983529)), _983523) = hAPP(c_Set_Oimage(_983519, _983525, _983527), _983523))], (10913 ^ _782464) ^ [_983592, _983594, _983596] : [10915 ^ _782464 : [(10916 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_983592, tc_HOL_Obool)), 10914 ^ [_983592, _983594, _983596]), _983594)))], (10918 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983592, tc_HOL_Obool)), 10914 ^ [_983592, _983594, _983596]), _983596))]], -(_983594 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_983592, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983592, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_983592, tc_HOL_Obool), _983594)), _983596)))], (10926 ^ _782464) ^ [_983854, _983856, _983858, _983860] : [class_Orderings_Olinorder(_983854), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983854), _983856), _983858)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983854), _983858), _983860)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_983854, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_983854, _983856, _983858)), c_SetInterval_Oord__class_OatLeastAtMost(_983854, _983858, _983860)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_983854, _983856, _983860))], (10940 ^ _782464) ^ [_984119, _984121, _984123] : [class_Orderings_Olinorder(_984119), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984119), _984121), _984123)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984119, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_984119, _984121, _984123)), hAPP(hAPP(c_Set_Oinsert(_984119), _984123), c_Orderings_Obot__class_Obot(tc_fun(_984119, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_984119, _984121, _984123))], (10950 ^ _782464) ^ [_984328, _984330, _984332, _984334] : [class_Orderings_Olinorder(_984328), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984328), _984330), _984332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984328), _984332), _984334)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984328, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_984328, _984330, _984332)), c_SetInterval_Oord__class_OgreaterThanLessThan(_984328, _984332, _984334)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_984328, _984330), _984334))], (10964 ^ _782464) ^ [_984597, _984599, _984601] : [class_Orderings_Olinorder(_984597), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984597), _984599), _984601)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984597, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_984597), _984599), c_Orderings_Obot__class_Obot(tc_fun(_984597, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_984597, _984599, _984601)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_984597, _984599), _984601))], (10974 ^ _782464) ^ [_984810, _984812, _984814, _984816] : [c_Orderings_Oorder__class_Omono(tc_fun(_984810, tc_HOL_Obool), tc_fun(_984810, tc_HOL_Obool), _984812), hBOOL(hAPP(hAPP(c_member(_984810), _984814), _984816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984810, tc_HOL_Obool)), _984816), hAPP(_984812, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984810, tc_HOL_Obool)), _984816), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_984810, tc_HOL_Obool), _984812))))), -(hBOOL(hAPP(hAPP(c_member(_984810), _984814), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_984810, tc_HOL_Obool), _984812))))], (10988 ^ _782464) ^ [_985117, _985119, _985121, _985123, _985125] : [_985117 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_985119, tc_HOL_Obool), _985121), c_Orderings_Oorder__class_Omono(tc_fun(_985119, tc_HOL_Obool), tc_fun(_985119, tc_HOL_Obool), _985121), hBOOL(hAPP(hAPP(c_member(_985119), _985123), _985125)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985119, tc_HOL_Obool)), _985125), hAPP(_985121, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985119, tc_HOL_Obool)), _985125), _985117)))), -(hBOOL(hAPP(hAPP(c_member(_985119), _985123), _985117)))], (11006 ^ _782464) ^ [_985476, _985478, _985480, _985482] : [-(c_Fun_Ofun__upd(_985476, _985478, _985480, _985482, hAPP(_985480, _985482)) = _985480)], (11008 ^ _782464) ^ [_985514, _985516] : [class_Orderings_Opreorder(_985514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985514), _985516), _985516))], (11014 ^ _782464) ^ [_985604, _985606, _985608] : [class_Orderings_Olinorder(_985604), 11017 ^ _782464 : [(11028 ^ _782464) ^ [] : [11029 ^ _782464 : [(11030 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985604), _985606), _985608))], (11032 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985604), _985608), _985606))]], _985606 = _985608], (11018 ^ _782464) ^ [] : [-(_985606 = _985608), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985604), _985606), _985608))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985604), _985608), _985606)))]]], (11036 ^ _782464) ^ [_985858, _985860, _985862] : [class_Orderings_Olinorder(_985858), 11039 ^ _782464 : [(11050 ^ _782464) ^ [] : [11051 ^ _782464 : [(11052 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985858), _985862), _985860))], (11054 ^ _782464) ^ [] : [_985860 = _985862]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985858), _985860), _985862))], (11040 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985858), _985860), _985862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985858), _985862), _985860))), -(_985860 = _985862)]]], (11058 ^ _782464) ^ [_986112, _986114, _986116] : [class_Orderings_Olinorder(_986112), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986112), _986114), _986116))), -(_986114 = _986116), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986112), _986116), _986114)))], (11072 ^ _782464) ^ [_986243, _986245, _986247] : [class_Orderings_Olinorder(_986243), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986243), _986245), _986247))), 11079 ^ _782464 : [(11080 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986243), _986247), _986245))), -(_986247 = _986245)], (11086 ^ _782464) ^ [] : [_986247 = _986245, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986243), _986247), _986245))]]], (11092 ^ _782464) ^ [_986502, _986504, _986506] : [class_Orderings_Olinorder(_986502), -(_986504 = _986506), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986502), _986504), _986506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986502), _986506), _986504)))], (11106 ^ _782464) ^ [_986637, _986639, _986641] : [class_Orderings_Oorder(_986637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986637), _986639), _986641)), _986639 = _986641], (11116 ^ _782464) ^ [_986783, _986785, _986787] : [class_Orderings_Opreorder(_986783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986783), _986785), _986787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986783), _986787), _986785))], (11126 ^ _782464) ^ [_986943, _986945, _986947] : [class_Orderings_Opreorder(_986943), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986943), _986945), _986947)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986943), _986947), _986945))], (11136 ^ _782464) ^ [_987103, _987105, _987107] : [class_Orderings_Oorder(_987103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987103), _987105), _987107)), _987105 = _987107], (11146 ^ _782464) ^ [_987249, _987251, _987253] : [class_Orderings_Oorder(_987249), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987249), _987251), _987253)), _987253 = _987251], (11156 ^ _782464) ^ [_987395, _987397, _987399] : [class_Orderings_Opreorder(_987395), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987395), _987397), _987399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987395), _987399), _987397))], (11166 ^ _782464) ^ [_987555, _987557, _987559] : [class_Orderings_Oorder(_987555), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987555), _987557), _987559)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987555), _987559), _987557))], (11176 ^ _782464) ^ [_987715, _987717, _987719, _987721] : [class_Orderings_Oord(_987715), _987717 = _987719, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987715), _987719), _987721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987715), _987717), _987721)))], (11190 ^ _782464) ^ [_987934, _987936, _987938, _987940] : [class_Orderings_Oorder(_987934), _987936 = _987938, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987934), _987940), _987938)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987934), _987940), _987936)))], (11204 ^ _782464) ^ [_988153, _988155, _988157, _988159] : [class_Orderings_Oord(_988153), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988153), _988155), _988157)), _988157 = _988159, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988153), _988155), _988159)))], (11218 ^ _782464) ^ [_988372, _988374, _988376, _988378] : [class_Orderings_Oorder(_988372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988372), _988374), _988376)), _988374 = _988378, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988372), _988378), _988376)))], (11232 ^ _782464) ^ [_988591, _988593, _988595, _988597] : [class_Orderings_Opreorder(_988591), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988591), _988593), _988595)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988591), _988595), _988597)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988591), _988593), _988597)))], (11246 ^ _782464) ^ [_988824, _988826, _988828, _988830] : [class_Orderings_Oorder(_988824), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988824), _988826), _988828)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988824), _988830), _988826)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988824), _988830), _988828)))], (11260 ^ _782464) ^ [_989057, _989059, _989061] : [class_Orderings_Opreorder(_989057), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989057), _989059), _989061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989057), _989061), _989059))], (11270 ^ _782464) ^ [_989217, _989219, _989221] : [class_Orderings_Olinorder(_989217), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989217), _989219), _989221))), -(_989219 = _989221), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989217), _989221), _989219)))], (11284 ^ _782464) ^ [_989376, _989378, _989380, _989382, _989384] : [c_Fun_Ofun__upd(_989376, _989378, _989380, _989382, _989384) = _989380, -(hAPP(_989380, _989382) = _989384)], (11290 ^ _782464) ^ [_989473, _989475, _989477, _989479, _989481] : [hAPP(_989477, _989479) = _989481, -(c_Fun_Ofun__upd(_989473, _989475, _989477, _989479, _989481) = _989477)], (11296 ^ _782464) ^ [_989576, _989578, _989580, _989582, _989584, _989586] : [-(c_Fun_Ofun__upd(_989576, _989578, c_Fun_Ofun__upd(_989576, _989578, _989580, _989582, _989584), _989582, _989586) = c_Fun_Ofun__upd(_989576, _989578, _989580, _989582, _989586))], (11298 ^ _782464) ^ [_989627, _989629, _989631, _989633, _989635] : [-(hAPP(c_Fun_Ofun__upd(_989627, _989629, _989631, _989633, _989635), _989633) = _989635)], (11300 ^ _782464) ^ [_989688, _989690, _989692, _989694, _989696, _989698] : [_989688 = _989690, -(hAPP(c_Fun_Ofun__upd(_989692, _989694, _989696, _989690, _989698), _989688) = _989698)], (11306 ^ _782464) ^ [_989785, _989787, _989789, _989791, _989793, _989795] : [-(_989785 = _989787), -(hAPP(c_Fun_Ofun__upd(_989789, _989791, _989793, _989787, _989795), _989785) = hAPP(_989793, _989785))], (11312 ^ _782464) ^ [_989839, _989841, _989843, _989845, _989847, _989849, _989851] : [-(_989839 = _989841), -(c_Fun_Ofun__upd(_989843, _989845, c_Fun_Ofun__upd(_989843, _989845, _989847, _989839, _989849), _989841, _989851) = c_Fun_Ofun__upd(_989843, _989845, c_Fun_Ofun__upd(_989843, _989845, _989847, _989841, _989851), _989839, _989849))], (11318 ^ _782464) ^ [_989905, _989907, _989909, _989911, _989913, _989915] : [-(_989905 = _989907), -(hAPP(c_Fun_Ofun__upd(_989909, _989911, _989913, _989907, _989915), _989905) = hAPP(_989913, _989905))], (11324 ^ _782464) ^ [_989961, _989963, _989965, _989967, _989969] : [hAPP(_989961, _989963) = _989965, -(c_Fun_Ofun__upd(_989967, _989969, _989961, _989963, _989965) = _989961)], (11330 ^ _782464) ^ [_990062, _990064, _990066] : [class_Orderings_Olinorder(_990062), 11333 ^ _782464 : [(11334 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990062, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_990062), _990064)), hAPP(c_SetInterval_Oord__class_OlessThan(_990062), _990066))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990062), _990064), _990066)))], (11340 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990062), _990064), _990066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990062, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_990062), _990064)), hAPP(c_SetInterval_Oord__class_OlessThan(_990062), _990066))))]]], (11346 ^ _782464) ^ [_990375, _990377, _990379, _990381, _990383, _990385] : [_990375 = _990377, -(hAPP(c_Fun_Ofun__upd(_990379, _990381, _990383, _990377, _990385), _990375) = _990385)], (11352 ^ _782464) ^ [_990472, _990474, _990476, _990478, _990480, _990482] : [-(_990472 = _990474), -(hAPP(c_Fun_Ofun__upd(_990476, _990478, _990480, _990474, _990482), _990472) = hAPP(_990480, _990472))], (11358 ^ _782464) ^ [_990530, _990532, _990534, _990536, _990538] : [class_Orderings_Oorder(_990530), 11361 ^ _782464 : [(11362 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990530, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_990530, _990532, _990534)), c_SetInterval_Oord__class_OatLeastAtMost(_990530, _990536, _990538))), 11365 ^ _782464 : [(11380 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990536), _990538)))], (11366 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990532), _990534)), 11369 ^ _782464 : [(11370 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990536), _990532)))], (11372 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990534), _990538)))], (11374 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990530), _990536), _990532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990530), _990534), _990538)))]]]]], (11382 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990530, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_990530, _990532, _990534)), c_SetInterval_Oord__class_OatLeastAtMost(_990530, _990536, _990538)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990536), _990538)), 11385 ^ _782464 : [(11386 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990532), _990534)))], (11388 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990536), _990532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990530), _990534), _990538)), 11395 ^ _782464 : [(11396 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990530), _990536), _990532))], (11398 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990530), _990534), _990538))]]]]]]], (11404 ^ _782464) ^ [_991301, _991303, _991305, _991307] : [class_Orderings_Oord(_991301), 11407 ^ _782464 : [(11408 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991303, _991301)), _991305), _991307)), 11411 ^ _782464 : [(11412 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991303, _991301)), _991305), _991307)))], (11414 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991303, _991301)), _991307), _991305))]]], (11416 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991303, _991301)), _991305), _991307))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991303, _991301)), _991305), _991307)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991303, _991301)), _991307), _991305)))]]], (11426 ^ _782464) ^ [_991693, _991695, _991697] : [class_Orderings_Olinorder(_991693), 11429 ^ _782464 : [(11430 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991693), _991695), _991697))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991693), _991697), _991695)))], (11436 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991693), _991697), _991695)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991693), _991695), _991697))]]], (11442 ^ _782464) ^ [_991902, _991904, _991906] : [class_Orderings_Olinorder(_991902), 11445 ^ _782464 : [(11446 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991902), _991904), _991906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991902), _991906), _991904)))], (11452 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991902), _991906), _991904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991902), _991904), _991906))]]], (11458 ^ _782464) ^ [_992111, _992113, _992115] : [class_Orderings_Olinorder(_992111), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992111), _992113), _992115))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992111), _992115), _992113)))], (11468 ^ _782464) ^ [_992229, _992231, _992233] : [class_Orderings_Oorder(_992229), 11471 ^ _782464 : [(11472 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992229), _992231), _992233)), 11475 ^ _782464 : [(11476 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992229), _992231), _992233)))], (11478 ^ _782464) ^ [] : [_992231 = _992233]]], (11480 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992229), _992231), _992233))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992229), _992231), _992233)), -(_992231 = _992233)]]], (11490 ^ _782464) ^ [_992565, _992567, _992569] : [class_Orderings_Opreorder(_992565), 11493 ^ _782464 : [(11494 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992565), _992567), _992569)), 11497 ^ _782464 : [(11498 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992565), _992567), _992569)))], (11500 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992565), _992569), _992567))]]], (11502 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992565), _992567), _992569))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992565), _992567), _992569)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992565), _992569), _992567)))]]], (11512 ^ _782464) ^ [_992922, _992924, _992926] : [class_Orderings_Oorder(_992922), 11515 ^ _782464 : [(11526 ^ _782464) ^ [] : [11527 ^ _782464 : [(11528 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992922), _992924), _992926))], (11530 ^ _782464) ^ [] : [_992924 = _992926]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992922), _992924), _992926)))], (11516 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992922), _992924), _992926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992922), _992924), _992926))), -(_992924 = _992926)]]], (11534 ^ _782464) ^ [_993220, _993222, _993224] : [class_Orderings_Olinorder(_993220), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993220), _993222), _993224))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993220), _993224), _993222)))], (11544 ^ _782464) ^ [_993340, _993342, _993344] : [class_Orderings_Olinorder(_993340), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993340), _993342), _993344))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993340), _993344), _993342)))], (11554 ^ _782464) ^ [_993460, _993462, _993464] : [class_Orderings_Olinorder(_993460), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993460), _993462), _993464))), 11561 ^ _782464 : [(11562 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993460), _993462), _993464)), -(_993462 = _993464)], (11568 ^ _782464) ^ [] : [_993462 = _993464, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993460), _993462), _993464)))]]], (11574 ^ _782464) ^ [_993763, _993765, _993767] : [class_Orderings_Oorder(_993763), -(_993765 = _993767), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993763), _993765), _993767)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993763), _993765), _993767)))], (11588 ^ _782464) ^ [_993979, _993981, _993983] : [class_Orderings_Oorder(_993979), -(_993981 = _993983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993979), _993983), _993981)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993979), _993983), _993981)))], (11602 ^ _782464) ^ [_994195, _994197, _994199] : [class_Orderings_Olinorder(_994195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994195), _994197), _994199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994195), _994199), _994197))], (11612 ^ _782464) ^ [_994355, _994357, _994359] : [class_Orderings_Opreorder(_994355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994355), _994357), _994359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994355), _994357), _994359)))], (11622 ^ _782464) ^ [_994514, _994516, _994518] : [class_Orderings_Olinorder(_994514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994514), _994516), _994518)), 11629 ^ _782464 : [(11630 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994514), _994516), _994518))), -(_994516 = _994518)], (11636 ^ _782464) ^ [] : [_994516 = _994518, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994514), _994516), _994518))]]], (11642 ^ _782464) ^ [_994770, _994772, _994774] : [class_Orderings_Oorder(_994770), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994770), _994772), _994774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994770), _994772), _994774))), -(_994772 = _994774)], (11656 ^ _782464) ^ [_994942, _994944, _994946] : [class_Orderings_Oorder(_994942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994942), _994944), _994946)), -(_994944 = _994946), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994942), _994944), _994946)))], (11670 ^ _782464) ^ [_995116, _995118, _995120] : [class_Orderings_Oorder(_995116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995116), _995118), _995120)), -(_995120 = _995118), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995116), _995118), _995120)))], (11684 ^ _782464) ^ [_995290, _995292, _995294, _995296] : [class_Orderings_Opreorder(_995290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995290), _995292), _995294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995290), _995294), _995296)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995290), _995292), _995296)))], (11698 ^ _782464) ^ [_995523, _995525, _995527, _995529] : [class_Orderings_Oorder(_995523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995523), _995525), _995527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995523), _995529), _995525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995523), _995529), _995527)))], (11712 ^ _782464) ^ [_995756, _995758, _995760, _995762] : [class_Orderings_Opreorder(_995756), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995756), _995758), _995760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995756), _995760), _995762)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995756), _995758), _995762)))], (11726 ^ _782464) ^ [_995989, _995991, _995993, _995995] : [class_Orderings_Oorder(_995989), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995989), _995991), _995993)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995989), _995995), _995991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995989), _995995), _995993)))], (11740 ^ _782464) ^ [_996222, _996224, _996226, _996228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_996222, tc_HOL_Obool)), _996224), _996226)), hBOOL(hAPP(hAPP(c_member(_996222), _996228), _996224)), -(hBOOL(hAPP(hAPP(c_member(_996222), _996228), _996226)))], (11750 ^ _782464) ^ [_996419, _996421] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_996419, tc_HOL_Obool)), _996421), c_Orderings_Obot__class_Obot(tc_fun(_996419, tc_HOL_Obool))))], (11752 ^ _782464) ^ [_996459, _996461, _996463, _996465, _996467] : [class_Groups_Oordered__ab__group__add(_996459), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_996459), _996461), _996463) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_996459), _996465), _996467), 11759 ^ _782464 : [(11760 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996459), _996461), _996463)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996459), _996465), _996467)))], (11766 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996459), _996465), _996467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996459), _996461), _996463)))]]], (11772 ^ _782464) ^ [_996814, _996816, _996818, _996820] : [class_Lattices_Osemilattice__sup(_996814), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996814), _996816), _996818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996814), _996816), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996814), _996818), _996820))))], (11782 ^ _782464) ^ [_996993, _996995, _996997, _996999] : [class_Lattices_Osemilattice__sup(_996993), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996993), _996995), _996997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996993), _996995), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996993), _996999), _996997))))], (11792 ^ _782464) ^ [_997172, _997174, _997176, _997178] : [class_Lattices_Osemilattice__inf(_997172), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997172), _997174), _997176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997172), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_997172), _997174), _997178)), _997176)))], (11802 ^ _782464) ^ [_997351, _997353, _997355, _997357] : [class_Lattices_Osemilattice__inf(_997351), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997351), _997353), _997355)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997351), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_997351), _997357), _997353)), _997355)))], (11812 ^ _782464) ^ [_997530, _997532, _997534] : [class_Groups_Oordered__ab__group__add(_997530), 11815 ^ _782464 : [(11816 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997530), hAPP(c_Groups_Ouminus__class_Ouminus(_997530), _997532)), hAPP(c_Groups_Ouminus__class_Ouminus(_997530), _997534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997530), _997534), _997532)))], (11822 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997530), _997534), _997532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997530), hAPP(c_Groups_Ouminus__class_Ouminus(_997530), _997532)), hAPP(c_Groups_Ouminus__class_Ouminus(_997530), _997534))))]]], (11828 ^ _782464) ^ [_997813, _997815, _997817] : [class_Groups_Oordered__ab__group__add(_997813), 11831 ^ _782464 : [(11832 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997813), hAPP(c_Groups_Ouminus__class_Ouminus(_997813), _997815)), _997817)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997813), hAPP(c_Groups_Ouminus__class_Ouminus(_997813), _997817)), _997815)))], (11838 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997813), hAPP(c_Groups_Ouminus__class_Ouminus(_997813), _997817)), _997815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997813), hAPP(c_Groups_Ouminus__class_Ouminus(_997813), _997815)), _997817)))]]], (11844 ^ _782464) ^ [_998096, _998098, _998100] : [class_Groups_Oordered__ab__group__add(_998096), 11847 ^ _782464 : [(11848 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998096), _998098), hAPP(c_Groups_Ouminus__class_Ouminus(_998096), _998100))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998096), _998100), hAPP(c_Groups_Ouminus__class_Ouminus(_998096), _998098))))], (11854 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998096), _998100), hAPP(c_Groups_Ouminus__class_Ouminus(_998096), _998098))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998096), _998098), hAPP(c_Groups_Ouminus__class_Ouminus(_998096), _998100))))]]], (11860 ^ _782464) ^ [_998397, _998399, _998401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998397, tc_HOL_Obool)), _998399), _998401)), 11863 ^ _782464 : [(11864 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998397, tc_HOL_Obool)), _998399), _998401)))], (11866 ^ _782464) ^ [] : [_998399 = _998401]]], (11868 ^ _782464) ^ [_998546, _998548, _998550] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998546, tc_HOL_Obool)), _998548), _998550))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998546, tc_HOL_Obool)), _998548), _998550)), -(_998548 = _998550)], (11888 ^ _782464) ^ [_998870, _998872, _998874] : [11889 ^ _782464 : [(11890 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998870, tc_HOL_Obool)), _998872), _998874))], (11892 ^ _782464) ^ [] : [_998872 = _998874]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998870, tc_HOL_Obool)), _998872), _998874)))], (11878 ^ _782464) ^ [_998742, _998744, _998746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998742, tc_HOL_Obool)), _998744), _998746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998742, tc_HOL_Obool)), _998744), _998746))), -(_998744 = _998746)], (11896 ^ _782464) ^ [_999029, _999031, _999033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999029, tc_HOL_Obool)), _999031), _999033)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999029, tc_HOL_Obool)), _999031), _999033)))], (11902 ^ _782464) ^ [_999148, _999150, _999152, _999154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999148, tc_HOL_Obool)), _999150), _999152)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999148, tc_HOL_Obool)), _999152), _999154)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999148, tc_HOL_Obool)), _999150), _999154)))], (11912 ^ _782464) ^ [_999345, _999347, _999349, _999351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999345, tc_HOL_Obool)), _999347), _999349)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999345, tc_HOL_Obool)), _999349), _999351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999345, tc_HOL_Obool)), _999347), _999351)))], (11922 ^ _782464) ^ [_999542, _999544, _999546, _999548, _999550] : [class_Orderings_Olinorder(_999542), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999542), _999544), _999546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999542), _999548), _999550)), 11933 ^ _782464 : [(11934 ^ _782464) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999542, _999544), _999546) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999542, _999548), _999550), 11937 ^ _782464 : [(11938 ^ _782464) ^ [] : [-(_999544 = _999548)], (11940 ^ _782464) ^ [] : [-(_999546 = _999550)]]], (11942 ^ _782464) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999542, _999544), _999546) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999542, _999548), _999550)), _999544 = _999548, _999546 = _999550]]], (11952 ^ _782464) ^ [_1000023, _1000025, _1000027, _1000029, _1000031] : [class_Orderings_Olinorder(_1000023), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000023, _1000025), _1000027) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000023, _1000029), _1000031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000023), _1000025), _1000027)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000023), _1000029), _1000031)), -(_1000025 = _1000029)], (11970 ^ _782464) ^ [_1000330, _1000332, _1000334, _1000336, _1000338] : [class_Orderings_Olinorder(_1000330), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000330, _1000332), _1000334) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000330, _1000336), _1000338), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000330), _1000332), _1000334)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000330), _1000336), _1000338)), -(_1000334 = _1000338)], (11988 ^ _782464) ^ [_1000637, _1000639, _1000641] : [class_Complete__Lattice_Ocomplete__lattice(_1000637), class_Orderings_Olinorder(_1000637), 11995 ^ _782464 : [(11996 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000637), _1000639), c_Complete__Lattice_OSup__class_OSup(_1000637, _1000641))), 12000 ^ _782464 : [(12001 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1000637), 11999 ^ [_1000637, _1000639, _1000641]), _1000641)))], (12003 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000637), _1000639), 11999 ^ [_1000637, _1000639, _1000641])))]]], (12005 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000637), _1000639), c_Complete__Lattice_OSup__class_OSup(_1000637, _1000641)))), 12006 ^ _782464 : [(12007 ^ _782464) ^ [_1000943] : [hBOOL(hAPP(hAPP(c_member(_1000637), _1000943), _1000641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000637), _1000639), _1000943))]]]]], (12015 ^ _782464) ^ [_1001097, _1001099, _1001101] : [class_Complete__Lattice_Ocomplete__lattice(_1001097), class_Orderings_Olinorder(_1001097), 12022 ^ _782464 : [(12023 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001097), c_Complete__Lattice_OInf__class_OInf(_1001097, _1001099)), _1001101)), 12027 ^ _782464 : [(12028 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001097), 12026 ^ [_1001097, _1001099, _1001101]), _1001099)))], (12030 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001097), 12026 ^ [_1001097, _1001099, _1001101]), _1001101)))]]], (12032 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001097), c_Complete__Lattice_OInf__class_OInf(_1001097, _1001099)), _1001101))), 12033 ^ _782464 : [(12034 ^ _782464) ^ [_1001403] : [hBOOL(hAPP(hAPP(c_member(_1001097), _1001403), _1001099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001097), _1001403), _1001101))]]]]], (12042 ^ _782464) ^ [_1001557, _1001559, _1001561, _1001563, _1001565] : [class_Complete__Lattice_Ocomplete__lattice(_1001557), class_Orderings_Olinorder(_1001557), 12049 ^ _782464 : [(12050 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001557), _1001559), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001561, _1001557), _1001563), _1001565))), 12054 ^ _782464 : [(12055 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001561), 12053 ^ [_1001557, _1001559, _1001561, _1001563, _1001565]), _1001563)))], (12057 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001557), _1001559), hAPP(_1001565, 12053 ^ [_1001557, _1001559, _1001561, _1001563, _1001565]))))]]], (12059 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001557), _1001559), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001561, _1001557), _1001563), _1001565)))), 12060 ^ _782464 : [(12061 ^ _782464) ^ [_1001905] : [hBOOL(hAPP(hAPP(c_member(_1001561), _1001905), _1001563)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001557), _1001559), hAPP(_1001565, _1001905)))]]]]], (12069 ^ _782464) ^ [_1002075, _1002077, _1002079, _1002081, _1002083] : [class_Complete__Lattice_Ocomplete__lattice(_1002075), class_Orderings_Olinorder(_1002075), 12076 ^ _782464 : [(12077 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002075), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1002077, _1002075), _1002079), _1002081)), _1002083)), 12081 ^ _782464 : [(12082 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002077), 12080 ^ [_1002075, _1002077, _1002079, _1002081, _1002083]), _1002079)))], (12084 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002075), hAPP(_1002081, 12080 ^ [_1002075, _1002077, _1002079, _1002081, _1002083])), _1002083)))]]], (12086 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002075), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1002077, _1002075), _1002079), _1002081)), _1002083))), 12087 ^ _782464 : [(12088 ^ _782464) ^ [_1002423] : [hBOOL(hAPP(hAPP(c_member(_1002077), _1002423), _1002079)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002075), hAPP(_1002081, _1002423)), _1002083))]]]]], (12096 ^ _782464) ^ [_1002593, _1002595, _1002597] : [class_Complete__Lattice_Ocomplete__lattice(_1002593), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002593), _1002595), hAPP(_1002597, _1002595))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002593), _1002595), c_Inductive_Ocomplete__lattice__class_Ogfp(_1002593, _1002597))))], (12106 ^ _782464) ^ [_1002764, _1002766, _1002768, _1002770, _1002772] : [class_Orderings_Oorder(_1002764), class_Orderings_Olinorder(_1002766), c_Orderings_Oorder__class_Ostrict__mono(_1002766, _1002764, _1002768), 12117 ^ _782464 : [(12118 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002764), hAPP(_1002768, _1002770)), hAPP(_1002768, _1002772))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002766), _1002770), _1002772)))], (12124 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002766), _1002770), _1002772)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002764), hAPP(_1002768, _1002770)), hAPP(_1002768, _1002772))))]]], (12130 ^ _782464) ^ [_1003165, _1003167, _1003169, _1003171, _1003173] : [class_Orderings_Oorder(_1003165), class_Orderings_Oorder(_1003167), c_Orderings_Oorder__class_Ostrict__mono(_1003167, _1003165, _1003169), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003167), _1003171), _1003173)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003165), hAPP(_1003169, _1003171)), hAPP(_1003169, _1003173))))], (12148 ^ _782464) ^ [_1003462, _1003464, _1003466] : [class_Orderings_Owellorder(_1003462), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003462), _1003464), c_Orderings_Oord__class_OLeast(_1003462, _1003466))), hBOOL(hAPP(_1003466, _1003464))], (12158 ^ _782464) ^ [_1003618, _1003620, _1003622] : [class_Complete__Lattice_Ocomplete__lattice(_1003618), _1003620 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1003618, _1003622), c_Orderings_Oorder__class_Omono(_1003618, _1003618, _1003622), -(_1003620 = hAPP(_1003622, _1003620))], (12172 ^ _782464) ^ [_1003817, _1003819] : [class_Complete__Lattice_Ocomplete__lattice(_1003817), c_Orderings_Oorder__class_Omono(_1003817, _1003817, _1003819), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_1003817, _1003819) = hAPP(_1003819, c_Inductive_Ocomplete__lattice__class_Ogfp(_1003817, _1003819)))], (12182 ^ _782464) ^ [_1003964, _1003966, _1003968] : [class_Orderings_Oorder(_1003964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003964), _1003966), _1003968)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1003964, _1003968, _1003966) = c_Orderings_Obot__class_Obot(tc_fun(_1003964, tc_HOL_Obool)))], (12192 ^ _782464) ^ [_1004127, _1004129, _1004131] : [class_Orderings_Oorder(_1004127), 12195 ^ _782464 : [(12196 ^ _782464) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1004127, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004127, _1004129), _1004131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004127), _1004129), _1004131))], (12202 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004127), _1004129), _1004131))), -(c_Orderings_Obot__class_Obot(tc_fun(_1004127, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004127, _1004129), _1004131))]]], (12208 ^ _782464) ^ [_1004352, _1004354, _1004356] : [class_Orderings_Oorder(_1004352), 12211 ^ _782464 : [(12212 ^ _782464) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004352, _1004354), _1004356) = c_Orderings_Obot__class_Obot(tc_fun(_1004352, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004352), _1004354), _1004356))], (12218 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004352), _1004354), _1004356))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004352, _1004354), _1004356) = c_Orderings_Obot__class_Obot(tc_fun(_1004352, tc_HOL_Obool)))]]], (12224 ^ _782464) ^ [_1004577, _1004579, _1004581] : [class_Orderings_Oord(_1004577), 12227 ^ _782464 : [(12228 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1004577), _1004579), hAPP(c_SetInterval_Oord__class_OlessThan(_1004577), _1004581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004577), _1004579), _1004581)))], (12234 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004577), _1004579), _1004581)), -(hBOOL(hAPP(hAPP(c_member(_1004577), _1004579), hAPP(c_SetInterval_Oord__class_OlessThan(_1004577), _1004581))))]]], (12240 ^ _782464) ^ [_1004845, _1004847, _1004849] : [class_Orderings_Oorder(_1004845), 12243 ^ _782464 : [(12244 ^ _782464) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1004845, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1004845, _1004847, _1004849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004845), _1004847), _1004849))], (12250 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004845), _1004847), _1004849))), 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tc_HOL_Obool), tc_fun(tc_fun(_1009905, tc_HOL_Obool), tc_fun(_1009905, tc_HOL_Obool)), tc_fun(_1009905, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009905, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1009905, tc_HOL_Obool), tc_fun(_1009905, tc_HOL_Obool), tc_fun(_1009905, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009905, tc_HOL_Obool), tc_fun(tc_fun(_1009905, tc_HOL_Obool), tc_fun(_1009905, tc_HOL_Obool)), tc_fun(_1009905, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009905, tc_HOL_Obool))), _1009907)), _1009911))), _1009903))))), -(hBOOL(hAPP(hAPP(c_member(_1009905), _1009909), _1009903)))], (12512 ^ _782464) ^ [_1010448, _1010450, _1010452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010448, tc_HOL_Obool)), _1010450), hAPP(_1010452, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010448, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010448, tc_HOL_Obool), tc_fun(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), tc_fun(_1010448, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010448, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010448, tc_HOL_Obool), tc_fun(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), tc_fun(_1010448, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010448, tc_HOL_Obool))), _1010452)), _1010450))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010448, tc_HOL_Obool), _1010452)))))), c_Orderings_Oorder__class_Omono(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), _1010452), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010448, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010448, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010448, tc_HOL_Obool), tc_fun(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), tc_fun(_1010448, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010448, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010448, tc_HOL_Obool), tc_fun(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), tc_fun(_1010448, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010448, tc_HOL_Obool))), _1010452)), _1010450))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010448, tc_HOL_Obool), _1010452)))), hAPP(_1010452, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010448, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010448, tc_HOL_Obool), tc_fun(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), tc_fun(_1010448, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010448, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010448, tc_HOL_Obool), tc_fun(tc_fun(_1010448, tc_HOL_Obool), tc_fun(_1010448, tc_HOL_Obool)), tc_fun(_1010448, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010448, tc_HOL_Obool))), _1010452)), _1010450))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010448, tc_HOL_Obool), _1010452)))))))], (12522 ^ _782464) ^ [_1011307, _1011309] : [-(c_Set_Othe__elem(_1011307, _1011309) = c_HOL_OThe(_1011307, hAPP(hAPP(c_COMBB(tc_fun(_1011307, tc_HOL_Obool), tc_HOL_Obool, _1011307), hAPP(c_fequal, _1011309)), hAPP(hAPP(c_COMBC(_1011307, tc_fun(_1011307, tc_HOL_Obool), tc_fun(_1011307, tc_HOL_Obool)), c_Set_Oinsert(_1011307)), c_Orderings_Obot__class_Obot(tc_fun(_1011307, tc_HOL_Obool))))))], (12524 ^ _782464) ^ [_1011377, _1011379, _1011381, _1011383, _1011385, _1011387, _1011389] : [hBOOL(hAPP(hAPP(c_member(_1011377), _1011379), _1011381)), c_Nitpick_Ofold__graph_H(_1011377, _1011383, _1011385, _1011387, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011377, tc_HOL_Obool)), _1011381), hAPP(hAPP(c_Set_Oinsert(_1011377), _1011379), c_Orderings_Obot__class_Obot(tc_fun(_1011377, tc_HOL_Obool)))), _1011389), -(c_Nitpick_Ofold__graph_H(_1011377, _1011383, _1011385, _1011387, _1011381, hAPP(hAPP(_1011385, _1011379), _1011389)))], (12534 ^ _782464) ^ [_1011615, _1011617, _1011619] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011615, tc_HOL_Obool)), _1011617), _1011619))), 12540 ^ _782464 : [(12541 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011615, tc_HOL_Obool)), 12539 ^ [_1011615, _1011617, _1011619]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1011615, tc_HOL_Obool)), _1011617), _1011619))))], (12544 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011615, tc_HOL_Obool)), 12542 ^ [_1011615, _1011617, _1011619]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1011615, tc_HOL_Obool)), _1011617), _1011619))))], (12546 ^ _782464) ^ [] : [12539 ^ [_1011615, _1011617, _1011619] = 12542 ^ [_1011615, _1011617, _1011619]], (12548 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011615, tc_HOL_Obool)), 12539 ^ [_1011615, _1011617, _1011619]), 12542 ^ [_1011615, _1011617, _1011619]) = c_Orderings_Obot__class_Obot(tc_fun(_1011615, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011615, tc_HOL_Obool)), _1011617), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1011615, tc_HOL_Obool), _1011619)) = c_Orderings_Obot__class_Obot(tc_fun(_1011615, tc_HOL_Obool)))], (12552 ^ _782464) ^ [_1012209, _1012211, _1012213, _1012215] : [class_Complete__Lattice_Ocomplete__lattice(_1012209), _1012211 = c_Inductive_Ocomplete__lattice__class_Olfp(_1012209, _1012213), c_Orderings_Oorder__class_Omono(_1012209, _1012209, _1012213), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012209), hAPP(_1012213, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012209), _1012211), _1012215))), _1012215)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012209), _1012211), _1012215)))], (12570 ^ _782464) ^ [_1012514, _1012516, _1012518] : [class_Complete__Lattice_Ocomplete__lattice(_1012514), c_Orderings_Oorder__class_Omono(_1012514, _1012514, _1012516), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012514), hAPP(_1012516, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012514), c_Inductive_Ocomplete__lattice__class_Olfp(_1012514, _1012516)), _1012518))), _1012518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012514), c_Inductive_Ocomplete__lattice__class_Olfp(_1012514, _1012516)), _1012518)))], (12584 ^ _782464) ^ [_1012787, _1012789, _1012791, _1012793, _1012795] : [c_Fun_Oinj__on(_1012787, _1012789, _1012791, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012787, tc_HOL_Obool)), _1012793), _1012795)), 12587 ^ _782464 : [(12588 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1012787, _1012789, _1012791, _1012793))], (12590 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1012787, _1012789, _1012791, _1012795))], (12592 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012789, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1012787, _1012789, _1012791), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012787, tc_HOL_Obool)), _1012793), _1012795))), hAPP(c_Set_Oimage(_1012787, _1012789, _1012791), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012787, tc_HOL_Obool)), _1012795), _1012793))) = c_Orderings_Obot__class_Obot(tc_fun(_1012789, tc_HOL_Obool)))]]], (12594 ^ _782464) ^ [_1013054, _1013056, _1013058, _1013060, _1013062] : [-(c_Fun_Oinj__on(_1013054, _1013056, _1013058, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013054, tc_HOL_Obool)), _1013060), _1013062))), c_Fun_Oinj__on(_1013054, _1013056, _1013058, _1013060), c_Fun_Oinj__on(_1013054, _1013056, _1013058, _1013062), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013056, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1013054, _1013056, _1013058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013054, tc_HOL_Obool)), _1013060), _1013062))), hAPP(c_Set_Oimage(_1013054, _1013056, _1013058), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013054, tc_HOL_Obool)), _1013062), _1013060))) = c_Orderings_Obot__class_Obot(tc_fun(_1013056, tc_HOL_Obool))], (12608 ^ _782464) ^ [_1013393, _1013395, _1013397] : [-(c_Fun_Oinj__on(_1013393, _1013395, _1013397, c_Orderings_Obot__class_Obot(tc_fun(_1013393, tc_HOL_Obool))))], (12610 ^ _782464) ^ [_1013427, _1013429] : [class_Groups_Oordered__ab__group__add(_1013427), -(c_Fun_Oinj__on(_1013427, _1013427, c_Groups_Ouminus__class_Ouminus(_1013427), _1013429))], (12616 ^ _782464) ^ [_1013510, _1013512, _1013514, _1013516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013510, tc_HOL_Obool)), _1013512), _1013514)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013510, tc_HOL_Obool)), _1013514), _1013516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013510, tc_HOL_Obool)), _1013512), _1013516)))], (12626 ^ _782464) ^ [_1013707, _1013709, _1013711, _1013713] : [c_Fun_Oinj__on(_1013707, _1013709, _1013711, c_Orderings_Otop__class_Otop(tc_fun(_1013707, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1013707, tc_fun(_1013713, _1013709), hAPP(hAPP(c_COMBB(_1013709, tc_fun(_1013713, _1013709), _1013707), c_COMBK(_1013709, _1013713)), _1013711), c_Orderings_Otop__class_Otop(tc_fun(_1013707, tc_HOL_Obool))))], (12650 ^ _782464) ^ [_1014260, _1014262, _1014264, _1014266] : [12652 ^ _782464 : [(12653 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014260), 12651 ^ [_1014260, _1014262, _1014264, _1014266]), _1014266)))], (12656 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014260), 12654 ^ [_1014260, _1014262, _1014264, _1014266]), _1014266)))], (12658 ^ _782464) ^ [] : [-(hAPP(_1014264, 12651 ^ [_1014260, _1014262, _1014264, _1014266]) = hAPP(_1014264, 12654 ^ [_1014260, _1014262, _1014264, _1014266]))], (12660 ^ _782464) ^ [] : [12651 ^ [_1014260, _1014262, _1014264, _1014266] = 12654 ^ [_1014260, _1014262, _1014264, _1014266]]], -(c_Fun_Oinj__on(_1014260, _1014262, _1014264, _1014266))], (12632 ^ _782464) ^ [_1013875, _1013877, _1013879, _1013881] : [c_Fun_Oinj__on(_1013875, _1013877, _1013879, _1013881), 12635 ^ _782464 : [(12636 ^ _782464) ^ [_1013983] : [hBOOL(hAPP(hAPP(c_member(_1013875), _1013983), _1013881)), 12639 ^ _782464 : [(12640 ^ _782464) ^ [_1014085] : [hBOOL(hAPP(hAPP(c_member(_1013875), _1014085), _1013881)), hAPP(_1013879, _1013983) = hAPP(_1013879, _1014085), -(_1013983 = _1014085)]]]]], (12664 ^ _782464) ^ [_1014652, _1014654] : [-(c_Fun_Oinj__on(_1014652, _1014652, c_COMBI(_1014652), _1014654))], (12666 ^ _782464) ^ [_1014681, _1014683] : [class_Complete__Lattice_Ocomplete__lattice(_1014681), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1014681, hAPP(c_COMBK(_1014681, _1014681), _1014683)) = _1014683)], (12672 ^ _782464) ^ [_1014774, _1014776, _1014778, _1014780, _1014782, _1014784] : [c_Fun_Oinj__on(_1014774, _1014776, _1014778, _1014780), -(_1014782 = _1014784), hBOOL(hAPP(hAPP(c_member(_1014774), _1014782), _1014780)), hBOOL(hAPP(hAPP(c_member(_1014774), _1014784), _1014780)), hAPP(_1014778, _1014782) = hAPP(_1014778, _1014784)], (12690 ^ _782464) ^ [_1015087, _1015089, _1015091, _1015093, _1015095, _1015097] : [c_Fun_Oinj__on(_1015087, _1015089, _1015091, _1015093), hBOOL(hAPP(hAPP(c_member(_1015087), _1015095), _1015093)), hBOOL(hAPP(hAPP(c_member(_1015087), _1015097), _1015093)), 12701 ^ _782464 : [(12702 ^ _782464) ^ [] : [hAPP(_1015091, _1015095) = hAPP(_1015091, _1015097), -(_1015095 = _1015097)], (12708 ^ _782464) ^ [] : [_1015095 = _1015097, -(hAPP(_1015091, _1015095) = hAPP(_1015091, _1015097))]]], (12714 ^ _782464) ^ [_1015488, _1015490, _1015492, _1015494, _1015496, _1015498] : [c_Fun_Oinj__on(_1015488, _1015490, _1015492, _1015494), hAPP(_1015492, _1015496) = hAPP(_1015492, _1015498), hBOOL(hAPP(hAPP(c_member(_1015488), _1015496), _1015494)), hBOOL(hAPP(hAPP(c_member(_1015488), _1015498), _1015494)), -(_1015496 = _1015498)], (12732 ^ _782464) ^ [_1015797, _1015799, _1015801, _1015803, _1015805] : [c_Fun_Oinj__on(_1015797, _1015799, _1015801, _1015803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015797, tc_HOL_Obool)), _1015805), _1015803)), -(c_Fun_Oinj__on(_1015797, _1015799, _1015801, _1015805))], (12742 ^ _782464) ^ [_1015966, _1015968, _1015970, _1015972, _1015974] : [c_Fun_Oinj__on(_1015966, _1015968, _1015970, c_Orderings_Otop__class_Otop(tc_fun(_1015966, tc_HOL_Obool))), hAPP(_1015970, _1015972) = hAPP(_1015970, _1015974), -(_1015972 = _1015974)], (12752 ^ _782464) ^ [_1016133, _1016135, _1016137, _1016139, _1016141] : [c_Fun_Oinj__on(_1016133, _1016135, _1016137, c_Orderings_Otop__class_Otop(tc_fun(_1016133, tc_HOL_Obool))), 12755 ^ _782464 : [(12756 ^ _782464) ^ [] : [hAPP(_1016137, _1016139) = hAPP(_1016137, _1016141), -(_1016139 = _1016141)], (12762 ^ _782464) ^ [] : [_1016139 = _1016141, -(hAPP(_1016137, _1016139) = hAPP(_1016137, _1016141))]]], (12768 ^ _782464) ^ [_1016390, _1016392, _1016394, _1016396, _1016398] : [c_Fun_Oinj__on(_1016390, _1016392, _1016394, _1016396), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1016390, tc_HOL_Obool)), _1016398), _1016396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1016392, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1016390, _1016392, _1016394), _1016398)), hAPP(c_Set_Oimage(_1016390, _1016392, _1016394), _1016396))))], (12778 ^ _782464) ^ [_1016603, _1016605, _1016607, _1016609, _1016611] : [c_Fun_Oinj__on(_1016603, _1016605, _1016607, _1016609), c_Fun_Oinj__on(_1016603, _1016605, _1016607, _1016611), -(c_Fun_Oinj__on(_1016603, _1016605, _1016607, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016603, tc_HOL_Obool)), _1016609), _1016611)))], (12788 ^ _782464) ^ [_1016778, _1016780, _1016782, _1016784, _1016786] : [c_Fun_Oinj__on(_1016778, _1016780, _1016782, _1016784), -(c_Fun_Oinj__on(_1016778, _1016780, _1016782, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016778, tc_HOL_Obool)), _1016784), _1016786)))], (12794 ^ _782464) ^ [_1016891, _1016893, _1016895, _1016897] : [-(c_Nitpick_Ofold__graph_H(_1016891, _1016893, _1016895, _1016897, c_Orderings_Obot__class_Obot(tc_fun(_1016891, tc_HOL_Obool)), _1016897))], (12796 ^ _782464) ^ [_1016929, _1016931, _1016933, _1016935] : [-(c_Nitpick_Ofold__graph_H(_1016929, _1016931, _1016933, _1016935, c_Orderings_Obot__class_Obot(tc_fun(_1016929, tc_HOL_Obool)), _1016935))], (12798 ^ _782464) ^ [_1016967, _1016969, _1016971, _1016973] : [class_Orderings_Oorder(_1016967), class_Orderings_Olinorder(_1016969), c_Orderings_Oorder__class_Ostrict__mono(_1016969, _1016967, _1016971), -(c_Fun_Oinj__on(_1016969, _1016967, _1016971, _1016973))], (12812 ^ _782464) ^ [_1017164, _1017166, _1017168] : [class_Complete__Lattice_Ocomplete__lattice(_1017164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017164), hAPP(_1017166, _1017168)), _1017168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017164), c_Inductive_Ocomplete__lattice__class_Olfp(_1017164, _1017166)), _1017168)))], (12822 ^ _782464) ^ [_1017335, _1017337, _1017339, _1017341, _1017343] : [c_Fun_Oinj__on(_1017335, _1017337, _1017339, c_Orderings_Otop__class_Otop(tc_fun(_1017335, tc_HOL_Obool))), 12825 ^ _782464 : [(12826 ^ _782464) ^ [] : [hAPP(c_Set_Oimage(_1017335, _1017337, _1017339), _1017341) = hAPP(c_Set_Oimage(_1017335, _1017337, _1017339), _1017343), -(_1017341 = _1017343)], (12832 ^ _782464) ^ [] : [_1017341 = _1017343, -(hAPP(c_Set_Oimage(_1017335, _1017337, _1017339), _1017341) = hAPP(c_Set_Oimage(_1017335, _1017337, _1017339), _1017343))]]], (12838 ^ _782464) ^ [_1017616, _1017618, _1017620, _1017622, _1017624] : [c_Fun_Oinj__on(_1017616, _1017618, _1017620, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017616, tc_HOL_Obool)), _1017622), _1017624)), 12841 ^ _782464 : [(12842 ^ _782464) ^ [] : [hAPP(c_Set_Oimage(_1017616, _1017618, _1017620), _1017622) = hAPP(c_Set_Oimage(_1017616, _1017618, _1017620), _1017624), -(_1017622 = _1017624)], (12848 ^ _782464) ^ [] : [_1017622 = _1017624, -(hAPP(c_Set_Oimage(_1017616, _1017618, _1017620), _1017622) = hAPP(c_Set_Oimage(_1017616, _1017618, _1017620), _1017624))]]], (12854 ^ _782464) ^ [_1017909, _1017911] : [class_Complete__Lattice_Ocomplete__lattice(_1017909), c_Orderings_Oorder__class_Omono(_1017909, _1017909, _1017911), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1017909, _1017911) = hAPP(_1017911, c_Inductive_Ocomplete__lattice__class_Olfp(_1017909, _1017911)))], (12864 ^ _782464) ^ [_1018056, _1018058, _1018060] : [class_Complete__Lattice_Ocomplete__lattice(_1018056), _1018058 = c_Inductive_Ocomplete__lattice__class_Olfp(_1018056, _1018060), c_Orderings_Oorder__class_Omono(_1018056, _1018056, _1018060), -(_1018058 = hAPP(_1018060, _1018058))], (12878 ^ _782464) ^ [_1018255, _1018257, _1018259, _1018261] : [c_Fun_Oinj__on(_1018255, _1018257, _1018259, c_Orderings_Otop__class_Otop(tc_fun(_1018255, tc_HOL_Obool))), 12881 ^ _782464 : [(12882 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018257), _1018261), hAPP(c_Set_Oimage(_1018255, _1018257, _1018259), c_Orderings_Otop__class_Otop(tc_fun(_1018255, tc_HOL_Obool))))), 12886 ^ _782464 : [(12887 ^ _782464) ^ [] : [-(_1018261 = hAPP(_1018259, 12885 ^ [_1018255, _1018257, _1018259, _1018261]))], (12889 ^ _782464) ^ [_1018520] : [_1018261 = hAPP(_1018259, _1018520), -(_1018520 = 12885 ^ [_1018255, _1018257, _1018259, _1018261])]]], (12895 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018257), _1018261), hAPP(c_Set_Oimage(_1018255, _1018257, _1018259), c_Orderings_Otop__class_Otop(tc_fun(_1018255, tc_HOL_Obool)))))), 12896 ^ _782464 : [(12897 ^ _782464) ^ [_1018658] : [_1018261 = hAPP(_1018259, _1018658), 12901 ^ _782464 : [(12902 ^ _782464) ^ [] : [-(_1018261 = hAPP(_1018259, 12900 ^ [_1018255, _1018257, _1018259, _1018261, _1018658]))], (12904 ^ _782464) ^ [] : [12900 ^ [_1018255, _1018257, _1018259, _1018261, _1018658] = _1018658]]]]]]], (12908 ^ _782464) ^ [_1018886, _1018888, _1018890, _1018892, _1018894] : [c_Fun_Oinj__on(_1018886, _1018888, _1018890, c_Orderings_Otop__class_Otop(tc_fun(_1018886, tc_HOL_Obool))), 12911 ^ _782464 : [(12912 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018888), hAPP(_1018890, _1018892)), hAPP(c_Set_Oimage(_1018886, _1018888, _1018890), _1018894))), -(hBOOL(hAPP(hAPP(c_member(_1018886), _1018892), _1018894)))], (12918 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018886), _1018892), _1018894)), -(hBOOL(hAPP(hAPP(c_member(_1018888), hAPP(_1018890, _1018892)), hAPP(c_Set_Oimage(_1018886, _1018888, _1018890), _1018894))))]]], (12924 ^ _782464) ^ [_1019197, _1019199, _1019201, _1019203, _1019205] : [c_Fun_Oinj__on(_1019197, _1019199, _1019201, c_Orderings_Otop__class_Otop(tc_fun(_1019197, tc_HOL_Obool))), 12927 ^ _782464 : [(12928 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019199, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019197, _1019199, _1019201), _1019203)), hAPP(c_Set_Oimage(_1019197, _1019199, _1019201), _1019205))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019197, tc_HOL_Obool)), _1019203), _1019205)))], (12934 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019197, tc_HOL_Obool)), _1019203), _1019205)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019199, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019197, _1019199, _1019201), _1019203)), hAPP(c_Set_Oimage(_1019197, _1019199, _1019201), _1019205))))]]], (12940 ^ _782464) ^ [_1019538, _1019540, _1019542, _1019544, _1019546, _1019548] : [c_Fun_Oinj__on(_1019538, _1019540, _1019542, _1019544), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019538, tc_HOL_Obool)), _1019546), _1019544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019538, tc_HOL_Obool)), _1019548), _1019544)), -(hAPP(c_Set_Oimage(_1019538, _1019540, _1019542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019538, tc_HOL_Obool)), _1019546), _1019548)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019540, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019538, _1019540, _1019542), _1019546)), hAPP(c_Set_Oimage(_1019538, _1019540, _1019542), _1019548)))], (12954 ^ _782464) ^ [_1019873, _1019875, _1019877, _1019879, _1019881] : [c_Fun_Oinj__on(_1019873, _1019875, _1019877, c_Orderings_Otop__class_Otop(tc_fun(_1019873, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1019873, _1019875, _1019877), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019873, tc_HOL_Obool)), _1019879), _1019881)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019875, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019873, _1019875, _1019877), _1019879)), hAPP(c_Set_Oimage(_1019873, _1019875, _1019877), _1019881)))], (12960 ^ _782464) ^ [_1020056, _1020058, _1020060, _1020062, _1020064, _1020066] : [c_Fun_Oinj__on(_1020056, _1020058, _1020060, _1020062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020056, tc_HOL_Obool)), _1020064), _1020062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020056, tc_HOL_Obool)), _1020066), _1020062)), -(hAPP(c_Set_Oimage(_1020056, _1020058, _1020060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020056, tc_HOL_Obool)), _1020064), _1020066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020058, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1020056, _1020058, _1020060), _1020064)), hAPP(c_Set_Oimage(_1020056, _1020058, _1020060), _1020066)))], (12974 ^ _782464) ^ [_1020391, _1020393, _1020395, _1020397, _1020399] : [c_Fun_Oinj__on(_1020391, _1020393, _1020395, c_Orderings_Otop__class_Otop(tc_fun(_1020391, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1020391, _1020393, _1020395), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020391, tc_HOL_Obool)), _1020397), _1020399)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020393, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1020391, _1020393, _1020395), _1020397)), hAPP(c_Set_Oimage(_1020391, _1020393, _1020395), _1020399)))], (12980 ^ _782464) ^ [_1020574, _1020576, _1020578, _1020580, _1020582, _1020584] : [c_Fun_Oinj__on(_1020574, _1020576, _1020578, _1020580), -(hBOOL(hAPP(hAPP(c_member(_1020576), _1020582), hAPP(c_Set_Oimage(_1020574, _1020576, _1020578), _1020580)))), -(c_Fun_Oinj__on(_1020574, _1020576, c_Fun_Ofun__upd(_1020574, _1020576, _1020578, _1020584, _1020582), _1020580))], (12990 ^ _782464) ^ [_1020722] : [-(c_Fun_Oinj__on(_1020722, tc_fun(_1020722, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1020722, tc_fun(_1020722, tc_HOL_Obool), tc_fun(_1020722, tc_HOL_Obool)), c_Set_Oinsert(_1020722)), c_Orderings_Obot__class_Obot(tc_fun(_1020722, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1020722, tc_HOL_Obool))))], (12992 ^ _782464) ^ [_1020778, _1020780] : [class_Complete__Lattice_Ocomplete__lattice(_1020778), c_Orderings_Oorder__class_Omono(_1020778, _1020778, _1020780), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020778), c_Inductive_Ocomplete__lattice__class_Olfp(_1020778, _1020780)), hAPP(_1020780, c_Inductive_Ocomplete__lattice__class_Olfp(_1020778, _1020780)))))], (13002 ^ _782464) ^ [_1020939, _1020941] : [class_Complete__Lattice_Ocomplete__lattice(_1020939), c_Orderings_Oorder__class_Omono(_1020939, _1020939, _1020941), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020939), hAPP(_1020941, c_Inductive_Ocomplete__lattice__class_Olfp(_1020939, _1020941))), c_Inductive_Ocomplete__lattice__class_Olfp(_1020939, _1020941))))], (13012 ^ _782464) ^ [_1021100, _1021102, _1021104, _1021106] : [c_Fun_Oinj__on(_1021100, _1021102, _1021104, c_Orderings_Otop__class_Otop(tc_fun(_1021100, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021102, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021100, _1021102, _1021104), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021100, tc_HOL_Obool)), _1021106))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021102, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021100, _1021102, _1021104), _1021106)))))], (13018 ^ _782464) ^ [_1021299, _1021301, _1021303, _1021305, _1021307] : [c_Fun_Oinj__on(_1021299, _1021301, _1021303, hAPP(hAPP(c_Set_Oinsert(_1021299), _1021305), _1021307)), 13021 ^ _782464 : [(13022 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1021299, _1021301, _1021303, _1021307))], (13024 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021301), hAPP(_1021303, _1021305)), hAPP(c_Set_Oimage(_1021299, _1021301, _1021303), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021299, tc_HOL_Obool)), _1021307), hAPP(hAPP(c_Set_Oinsert(_1021299), _1021305), c_Orderings_Obot__class_Obot(tc_fun(_1021299, tc_HOL_Obool)))))))]]], (13026 ^ _782464) ^ [_1021518, _1021520, _1021522, _1021524, _1021526] : [-(c_Fun_Oinj__on(_1021518, _1021520, _1021522, hAPP(hAPP(c_Set_Oinsert(_1021518), _1021524), _1021526))), c_Fun_Oinj__on(_1021518, _1021520, _1021522, _1021526), -(hBOOL(hAPP(hAPP(c_member(_1021520), hAPP(_1021522, _1021524)), hAPP(c_Set_Oimage(_1021518, _1021520, _1021522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021518, tc_HOL_Obool)), _1021526), hAPP(hAPP(c_Set_Oinsert(_1021518), _1021524), c_Orderings_Obot__class_Obot(tc_fun(_1021518, tc_HOL_Obool))))))))], (13036 ^ _782464) ^ [_1021769, _1021771, _1021773, _1021775] : [-(_1021769 = c_Orderings_Obot__class_Obot(tc_fun(_1021771, tc_HOL_Obool))), 13039 ^ _782464 : [(13051 ^ _782464) ^ [] : [13052 ^ _782464 : [(13053 ^ _782464) ^ [_1022102] : [hAPP(c_Set_Oimage(_1021773, _1021771, _1022102), _1021775) = _1021769]], 13055 ^ _782464 : [(13056 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1021771, _1021773, 13054 ^ [_1021769, _1021771, _1021773, _1021775], _1021769))], (13058 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021773, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021771, _1021773, 13054 ^ [_1021769, _1021771, _1021773, _1021775]), _1021769)), _1021775)))]]], (13040 ^ _782464) ^ [] : [-(hAPP(c_Set_Oimage(_1021773, _1021771, 13047 ^ [_1021769, _1021771, _1021773, _1021775]), _1021775) = _1021769), 13041 ^ _782464 : [(13042 ^ _782464) ^ [_1021910] : [c_Fun_Oinj__on(_1021771, _1021773, _1021910, _1021769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021773, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021771, _1021773, _1021910), _1021769)), _1021775))]]]]], (13060 ^ _782464) ^ [_1022227, _1022229] : [-(c_Enum_Oenum__the(_1022227, _1022229) = c_HOL_OThe(_1022227, _1022229))], (13062 ^ _782464) ^ [_1022270, _1022272, _1022274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022270, tc_HOL_Obool)), _1022272), hAPP(hAPP(c_Set_Oinsert(_1022270), _1022274), c_Orderings_Obot__class_Obot(tc_fun(_1022270, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1022270, _1022274, _1022272) = _1022274)], (13068 ^ _782464) ^ [_1022397, _1022399, _1022401] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022397, tc_HOL_Obool)), _1022399), hAPP(hAPP(c_Set_Oinsert(_1022397), _1022401), c_Orderings_Obot__class_Obot(tc_fun(_1022397, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1022397, _1022401, _1022399) = c_HOL_OThe(_1022397, hAPP(hAPP(c_COMBC(_1022397, tc_fun(_1022397, tc_HOL_Obool), tc_HOL_Obool), c_member(_1022397)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022397, tc_HOL_Obool)), _1022399), hAPP(hAPP(c_Set_Oinsert(_1022397), _1022401), c_Orderings_Obot__class_Obot(tc_fun(_1022397, tc_HOL_Obool)))))))], (13074 ^ _782464) ^ [_1022536, _1022538, _1022540, _1022542, _1022544, _1022546, _1022548] : [c_Nitpick_Ofold__graph_H(_1022536, _1022538, _1022540, _1022542, _1022544, hAPP(hAPP(_1022540, _1022546), _1022548)), 13079 ^ _782464 : [(13080 ^ _782464) ^ [] : [-(_1022544 = c_Orderings_Obot__class_Obot(tc_fun(_1022536, tc_HOL_Obool)))], (13082 ^ _782464) ^ [] : [-(hAPP(hAPP(_1022540, _1022546), _1022548) = _1022542)]], 13085 ^ _782464 : [(13086 ^ _782464) ^ [] : [-(hAPP(hAPP(_1022540, _1022546), _1022548) = hAPP(hAPP(_1022540, 13083 ^ [_1022536, _1022538, _1022540, _1022542, _1022544, _1022546, _1022548]), 13084 ^ [_1022536, _1022538, _1022540, _1022542, _1022544, _1022546, _1022548]))], (13088 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1022536), 13083 ^ [_1022536, _1022538, _1022540, _1022542, _1022544, _1022546, _1022548]), _1022544)))], (13090 ^ _782464) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1022536, _1022538, _1022540, _1022542, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022536, tc_HOL_Obool)), _1022544), hAPP(hAPP(c_Set_Oinsert(_1022536), 13083 ^ [_1022536, _1022538, _1022540, _1022542, _1022544, _1022546, _1022548]), c_Orderings_Obot__class_Obot(tc_fun(_1022536, tc_HOL_Obool)))), 13084 ^ [_1022536, _1022538, _1022540, _1022542, _1022544, _1022546, _1022548]))]]], (13092 ^ _782464) ^ [_1022973, _1022975, _1022977, _1022979, _1022981, _1022983, _1022985] : [-(c_Nitpick_Ofold__graph_H(_1022973, _1022975, _1022977, _1022979, _1022981, hAPP(hAPP(_1022977, _1022983), _1022985))), 13093 ^ _782464 : [(13094 ^ _782464) ^ [] : [_1022981 = c_Orderings_Obot__class_Obot(tc_fun(_1022973, tc_HOL_Obool)), hAPP(hAPP(_1022977, _1022983), _1022985) = _1022979], (13100 ^ _782464) ^ [_1023202, _1023204] : [hAPP(hAPP(_1022977, _1022983), _1022985) = hAPP(hAPP(_1022977, _1023204), _1023202), hBOOL(hAPP(hAPP(c_member(_1022973), _1023204), _1022981)), c_Nitpick_Ofold__graph_H(_1022973, _1022975, _1022977, _1022979, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022973, tc_HOL_Obool)), _1022981), hAPP(hAPP(c_Set_Oinsert(_1022973), _1023204), c_Orderings_Obot__class_Obot(tc_fun(_1022973, tc_HOL_Obool)))), _1023202)]]], (13112 ^ _782464) ^ [_1023494, _1023496, _1023498, _1023500, _1023502, _1023504, _1023506, _1023508] : [c_Fun_Oinj__on(_1023494, _1023496, _1023498, _1023500), 13118 ^ _782464 : [(13119 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1023502), 13117 ^ [_1023494, _1023496, _1023498, _1023500, _1023502, _1023504, _1023506, _1023508]), _1023504)))], (13121 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023494, tc_HOL_Obool)), hAPP(_1023506, 13117 ^ [_1023494, _1023496, _1023498, _1023500, _1023502, _1023504, _1023506, _1023508])), _1023500))]], hBOOL(hAPP(hAPP(c_member(_1023502), _1023508), _1023504)), -(hAPP(c_Set_Oimage(_1023494, _1023496, _1023498), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023502, tc_fun(_1023494, tc_HOL_Obool)), _1023504), _1023506)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023502, tc_fun(_1023496, tc_HOL_Obool)), _1023504), hAPP(hAPP(c_COMBB(tc_fun(_1023494, tc_HOL_Obool), tc_fun(_1023496, tc_HOL_Obool), _1023502), c_Set_Oimage(_1023494, _1023496, _1023498)), _1023506)))], (13129 ^ _782464) ^ [_1023983, _1023985, _1023987, _1023989, _1023991, _1023993] : [c_Fun_Oinj__on(_1023983, _1023985, _1023987, _1023989), hBOOL(hAPP(hAPP(c_member(_1023985), _1023991), hAPP(c_Set_Oimage(_1023983, _1023985, _1023987), _1023989))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023983, tc_HOL_Obool)), _1023989), _1023993)), -(hBOOL(hAPP(hAPP(c_member(_1023983), hAPP(c_Fun_Othe__inv__into(_1023983, _1023985, _1023989, _1023987), _1023991)), _1023993)))], (13143 ^ _782464) ^ [_1024270, _1024272, _1024274, _1024276] : [c_Fun_Oinj__on(_1024270, _1024272, _1024274, c_Orderings_Otop__class_Otop(tc_fun(_1024270, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024270, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1024270, _1024272, _1024274), hAPP(hAPP(c_Set_Oinsert(_1024272), _1024276), c_Orderings_Obot__class_Obot(tc_fun(_1024272, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1024270), c_HOL_OThe(_1024270, hAPP(hAPP(c_COMBC(_1024270, _1024272, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1024272, tc_fun(_1024272, tc_HOL_Obool), _1024270), c_fequal), _1024274)), _1024276))), c_Orderings_Obot__class_Obot(tc_fun(_1024270, tc_HOL_Obool))))))], (13149 ^ _782464) ^ [_1024502, _1024504, _1024506, _1024508] : [-(_1024502 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1024504, tc_HOL_Obool), tc_HOL_Obool))), 13155 ^ _782464 : [(13156 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1024504, tc_HOL_Obool)), 13154 ^ [_1024502, _1024504, _1024506, _1024508]), _1024502)))], (13158 ^ _782464) ^ [] : [c_Fun_Oinj__on(_1024504, _1024506, _1024508, 13154 ^ [_1024502, _1024504, _1024506, _1024508])]], -(c_Fun_Oinj__on(_1024504, _1024506, _1024508, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1024504, tc_HOL_Obool), _1024502)))], (13162 ^ _782464) ^ [_1024763, _1024765, _1024767, _1024769, _1024771, _1024773] : [hAPP(_1024763, _1024765) = _1024767, hBOOL(hAPP(hAPP(c_member(_1024769), _1024767), _1024771)), -(hBOOL(hAPP(hAPP(c_member(_1024773), _1024765), hAPP(c_Set_Ovimage(_1024773, _1024769, _1024763), _1024771))))], (13172 ^ _782464) ^ [_1024956, _1024958] : [-(hAPP(c_Set_Ovimage(_1024956, _1024956, c_COMBI(_1024956)), _1024958) = _1024958)], (13174 ^ _782464) ^ [_1025014, _1025016, _1025018, _1025020, _1025022] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1025014, _1025016, _1025018), _1025020), _1025022)), -(hBOOL(hAPP(_1025020, hAPP(_1025018, _1025022))))], (13180 ^ _782464) ^ [_1025121, _1025123, _1025125, _1025127, _1025129] : [hBOOL(hAPP(_1025127, hAPP(_1025125, _1025129))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1025121, _1025123, _1025125), _1025127), _1025129)))], (13186 ^ _782464) ^ [_1025258, _1025260, _1025262, _1025264, _1025266] : [hBOOL(hAPP(hAPP(c_member(_1025258), _1025260), hAPP(c_Set_Ovimage(_1025258, _1025262, _1025264), _1025266))), -(hBOOL(hAPP(hAPP(c_member(_1025262), hAPP(_1025264, _1025260)), _1025266)))], (13192 ^ _782464) ^ [_1025385, _1025387, _1025389, _1025391, _1025393] : [hBOOL(hAPP(hAPP(c_member(_1025389), hAPP(_1025391, _1025387)), _1025393)), -(hBOOL(hAPP(hAPP(c_member(_1025385), _1025387), hAPP(c_Set_Ovimage(_1025385, _1025389, _1025391), _1025393))))], (13198 ^ _782464) ^ [_1025518, _1025520, _1025522, _1025524, _1025526] : [hBOOL(hAPP(hAPP(c_member(_1025518), _1025520), hAPP(c_Set_Ovimage(_1025518, _1025522, _1025524), _1025526))), -(hBOOL(hAPP(hAPP(c_member(_1025522), hAPP(_1025524, _1025520)), _1025526)))], (13204 ^ _782464) ^ [_1025649, _1025651, _1025653, _1025655, _1025657] : [hBOOL(hAPP(hAPP(c_member(_1025649), hAPP(_1025651, _1025653)), _1025655)), -(hBOOL(hAPP(hAPP(c_member(_1025657), _1025653), hAPP(c_Set_Ovimage(_1025657, _1025649, _1025651), _1025655))))], (13210 ^ _782464) ^ [_1025780, _1025782, _1025784] : [-(hAPP(c_Set_Ovimage(_1025780, _1025782, _1025784), c_Orderings_Obot__class_Obot(tc_fun(_1025782, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1025780, tc_HOL_Obool)))], (13212 ^ _782464) ^ [_1025824, _1025826, _1025828, _1025830, _1025832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025824, tc_HOL_Obool)), _1025826), _1025828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025830, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1025830, _1025824, _1025832), _1025826)), hAPP(c_Set_Ovimage(_1025830, _1025824, _1025832), _1025828))))], (13218 ^ _782464) ^ [_1025975, _1025977, _1025979] : [-(hAPP(c_Set_Ovimage(_1025975, _1025977, _1025979), c_Orderings_Otop__class_Otop(tc_fun(_1025977, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1025975, tc_HOL_Obool)))], (13220 ^ _782464) ^ [_1026019, _1026021, _1026023, _1026025, _1026027] : [-(hAPP(c_Set_Ovimage(_1026019, _1026021, _1026023), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1026021, tc_HOL_Obool)), _1026025), _1026027)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1026019, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026019, _1026021, _1026023), _1026025)), hAPP(c_Set_Ovimage(_1026019, _1026021, _1026023), _1026027)))], (13222 ^ _782464) ^ [_1026093, _1026095, _1026097, _1026099, _1026101] : [-(hAPP(c_Set_Ovimage(_1026093, _1026095, _1026097), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026095, tc_HOL_Obool)), _1026099), _1026101)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026093, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026093, _1026095, _1026097), _1026099)), hAPP(c_Set_Ovimage(_1026093, _1026095, _1026097), _1026101)))], (13224 ^ _782464) ^ [_1026167, _1026169, _1026171, _1026173, _1026175] : [-(hAPP(c_Set_Ovimage(_1026167, _1026169, _1026171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026169, tc_HOL_Obool)), _1026173), _1026175)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026167, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026167, _1026169, _1026171), _1026173)), hAPP(c_Set_Ovimage(_1026167, _1026169, _1026171), _1026175)))], (13226 ^ _782464) ^ [_1026241, _1026243, _1026245, _1026247] : [-(hAPP(c_Set_Ovimage(_1026241, _1026243, _1026245), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026243, tc_HOL_Obool)), _1026247)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026241, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026241, _1026243, _1026245), _1026247)))], (13228 ^ _782464) ^ [_1026300, _1026302, _1026304, _1026306, _1026308, _1026310] : [-(hAPP(c_Set_Ovimage(_1026300, _1026302, _1026304), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026306, tc_fun(_1026302, tc_HOL_Obool)), _1026308), _1026310)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026306, tc_fun(_1026300, tc_HOL_Obool)), _1026308), hAPP(hAPP(c_COMBB(tc_fun(_1026302, tc_HOL_Obool), tc_fun(_1026300, tc_HOL_Obool), _1026306), c_Set_Ovimage(_1026300, _1026302, _1026304)), _1026310)))], (13230 ^ _782464) ^ [_1026384, _1026386, _1026388, _1026390, _1026392, _1026394] : [-(hAPP(c_Set_Ovimage(_1026384, _1026386, _1026388), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026390, tc_fun(_1026386, tc_HOL_Obool)), _1026392), _1026394)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026390, tc_fun(_1026384, tc_HOL_Obool)), _1026392), hAPP(hAPP(c_COMBB(tc_fun(_1026386, tc_HOL_Obool), tc_fun(_1026384, tc_HOL_Obool), _1026390), c_Set_Ovimage(_1026384, _1026386, _1026388)), _1026394)))], (13232 ^ _782464) ^ [_1026468, _1026470, _1026472, _1026474] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026468, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1026470, _1026468, _1026472), hAPP(c_Set_Ovimage(_1026470, _1026468, _1026472), _1026474))), _1026474)))], (13234 ^ _782464) ^ [_1026521, _1026523, _1026525, _1026527] : [hAPP(c_Set_Oimage(_1026521, _1026523, _1026525), c_Orderings_Otop__class_Otop(tc_fun(_1026521, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1026523, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1026521, _1026523, _1026525), hAPP(c_Set_Ovimage(_1026521, _1026523, _1026525), _1026527)) = _1026527)], (13240 ^ _782464) ^ [_1026664, _1026666, _1026668, _1026670] : [-(hAPP(c_Set_Ovimage(_1026664, _1026666, _1026668), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1026666, tc_HOL_Obool), _1026670)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1026666, tc_HOL_Obool), tc_fun(_1026664, tc_HOL_Obool)), _1026670), c_Set_Ovimage(_1026664, _1026666, _1026668)))], (13242 ^ _782464) ^ [_1026749, _1026751, _1026753, _1026755, _1026757] : [hBOOL(hAPP(hAPP(c_member(_1026749), _1026751), hAPP(c_Set_Ovimage(_1026749, _1026753, _1026755), hAPP(hAPP(c_Set_Oinsert(_1026753), _1026757), c_Orderings_Obot__class_Obot(tc_fun(_1026753, tc_HOL_Obool)))))), -(hAPP(_1026755, _1026751) = _1026757)], (13248 ^ _782464) ^ [_1026888, _1026890, _1026892, _1026894, _1026896] : [hAPP(_1026894, _1026890) = _1026896, -(hBOOL(hAPP(hAPP(c_member(_1026888), _1026890), hAPP(c_Set_Ovimage(_1026888, _1026892, _1026894), hAPP(hAPP(c_Set_Oinsert(_1026892), _1026896), c_Orderings_Obot__class_Obot(tc_fun(_1026892, tc_HOL_Obool)))))))], (13254 ^ _782464) ^ [_1027033, _1027035, _1027037, _1027039, _1027041] : [-(hAPP(c_Set_Ovimage(_1027033, _1027035, _1027037), hAPP(hAPP(c_Set_Oinsert(_1027035), _1027039), _1027041)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027033, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1027033, _1027035, _1027037), hAPP(hAPP(c_Set_Oinsert(_1027035), _1027039), c_Orderings_Obot__class_Obot(tc_fun(_1027035, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1027033, _1027035, _1027037), _1027041)))], (13256 ^ _782464) ^ [_1027117, _1027119, _1027121, _1027123, _1027125] : [hAPP(c_Set_Oimage(_1027117, _1027119, _1027121), c_Orderings_Otop__class_Otop(tc_fun(_1027117, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1027119, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027117, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1027117, _1027119, _1027121), _1027123)), _1027125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027119, tc_HOL_Obool)), _1027123), hAPP(c_Set_Oimage(_1027117, _1027119, _1027121), _1027125))))], (13266 ^ _782464) ^ [_1027360, _1027362, _1027364, _1027366] : [-(hAPP(c_Set_Oimage(_1027360, _1027362, _1027364), hAPP(c_Set_Ovimage(_1027360, _1027362, _1027364), _1027366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027362, tc_HOL_Obool)), _1027366), hAPP(c_Set_Oimage(_1027360, _1027362, _1027364), c_Orderings_Otop__class_Otop(tc_fun(_1027360, tc_HOL_Obool)))))], (13268 ^ _782464) ^ [_1027426, _1027428, _1027430, _1027432] : [c_Fun_Oinj__on(_1027426, _1027428, _1027430, c_Orderings_Otop__class_Otop(tc_fun(_1027426, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1027426, _1027428, _1027430), hAPP(c_Set_Oimage(_1027426, _1027428, _1027430), _1027432)) = _1027432)], (13274 ^ _782464) ^ [_1027564, _1027566, _1027568, _1027570] : [hBOOL(hAPP(hAPP(c_member(_1027564), _1027566), _1027568)), -(hAPP(c_Set_Ovimage(_1027570, _1027564, hAPP(c_COMBK(_1027564, _1027570), _1027566)), _1027568) = c_Orderings_Otop__class_Otop(tc_fun(_1027570, tc_HOL_Obool)))], (13280 ^ _782464) ^ [_1027689, _1027691, _1027693, _1027695] : [-(hBOOL(hAPP(hAPP(c_member(_1027689), _1027691), _1027693))), -(hAPP(c_Set_Ovimage(_1027695, _1027689, hAPP(c_COMBK(_1027689, _1027695), _1027691)), _1027693) = c_Orderings_Obot__class_Obot(tc_fun(_1027695, tc_HOL_Obool)))], (13286 ^ _782464) ^ [_1027756, _1027758, _1027760, _1027762] : [-(hAPP(c_Set_Ovimage(_1027756, _1027758, _1027760), _1027762) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1027758, tc_fun(_1027756, tc_HOL_Obool)), _1027762), hAPP(hAPP(c_COMBB(tc_fun(_1027758, tc_HOL_Obool), tc_fun(_1027756, tc_HOL_Obool), _1027758), c_Set_Ovimage(_1027756, _1027758, _1027760)), hAPP(hAPP(c_COMBC(_1027758, tc_fun(_1027758, tc_HOL_Obool), tc_fun(_1027758, tc_HOL_Obool)), c_Set_Oinsert(_1027758)), c_Orderings_Obot__class_Obot(tc_fun(_1027758, tc_HOL_Obool))))))], (13288 ^ _782464) ^ [_1027847, _1027849, _1027851, _1027853, _1027855] : [c_Fun_Oinj__on(_1027847, _1027849, _1027851, _1027853), hBOOL(hAPP(hAPP(c_member(_1027847), _1027855), _1027853)), -(hAPP(c_Fun_Othe__inv__into(_1027847, _1027849, _1027853, _1027851), hAPP(_1027851, _1027855)) = _1027855)], (13298 ^ _782464) ^ [_1028028, _1028030, _1028032, _1028034, _1028036, _1028038] : [c_Fun_Oinj__on(_1028028, _1028030, _1028032, _1028034), hAPP(_1028032, _1028036) = _1028038, hBOOL(hAPP(hAPP(c_member(_1028028), _1028036), _1028034)), -(hAPP(c_Fun_Othe__inv__into(_1028028, _1028030, _1028034, _1028032), _1028038) = _1028036)], (13312 ^ _782464) ^ [_1028273, _1028275, _1028277, _1028279] : [c_Fun_Oinj__on(_1028273, _1028275, _1028277, c_Orderings_Otop__class_Otop(tc_fun(_1028273, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1028273, _1028275, c_Orderings_Otop__class_Otop(tc_fun(_1028273, tc_HOL_Obool)), _1028277), hAPP(_1028277, _1028279)) = _1028279)], (13318 ^ _782464) ^ [_1028400, _1028402, _1028404, _1028406] : [c_Fun_Oinj__on(_1028400, _1028402, _1028404, _1028406), -(hAPP(c_Set_Oimage(_1028402, _1028400, c_Fun_Othe__inv__into(_1028400, _1028402, _1028406, _1028404)), hAPP(c_Set_Oimage(_1028400, _1028402, _1028404), _1028406)) = _1028406)], (13324 ^ _782464) ^ [_1028523, _1028525, _1028527, _1028529] : [c_Fun_Oinj__on(_1028523, _1028525, _1028527, _1028529), -(c_Fun_Oinj__on(_1028525, _1028523, c_Fun_Othe__inv__into(_1028523, _1028525, _1028529, _1028527), hAPP(c_Set_Oimage(_1028523, _1028525, _1028527), _1028529)))], (13330 ^ _782464) ^ [_1028636, _1028638, _1028640, _1028642, _1028644] : [c_Fun_Oinj__on(_1028636, _1028638, _1028640, c_Orderings_Otop__class_Otop(tc_fun(_1028636, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028638, tc_HOL_Obool)), _1028642), hAPP(c_Set_Oimage(_1028636, _1028638, _1028640), _1028644))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028636, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1028636, _1028638, _1028640), _1028642)), _1028644)))], (13340 ^ _782464) ^ [_1028859, _1028861, _1028863, _1028865, _1028867] : [-(hAPP(c_Fun_Othe__inv__into(_1028859, _1028861, _1028863, _1028865), _1028867) = c_HOL_OThe(_1028859, hAPP(hAPP(c_COMBS(_1028859, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1028859), c_fconj), hAPP(hAPP(c_COMBC(_1028859, tc_fun(_1028859, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028859)), _1028863))), hAPP(hAPP(c_COMBC(_1028859, _1028861, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1028861, tc_fun(_1028861, tc_HOL_Obool), _1028859), c_fequal), _1028865)), _1028867))))], (13342 ^ _782464) ^ [_1028980, _1028982, _1028984, _1028986, _1028988, _1028990] : [hBOOL(hAPP(hAPP(c_member(_1028980), _1028982), _1028984)), 13345 ^ _782464 : [(13346 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1028980), _1028986), _1028984)), -(hAPP(c_Set_Ovimage(_1028988, _1028980, hAPP(hAPP(c_COMBC(_1028988, _1028980, _1028980), hAPP(hAPP(c_COMBC(_1028988, _1028980, tc_fun(_1028980, _1028980)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1028980, tc_fun(_1028980, _1028980)), _1028988), c_If(_1028980)), hAPP(hAPP(c_COMBC(_1028988, tc_fun(_1028988, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028988)), _1028990))), _1028982)), _1028986)), _1028984) = c_Orderings_Otop__class_Otop(tc_fun(_1028988, tc_HOL_Obool)))], (13352 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1028980), _1028986), _1028984))), -(hAPP(c_Set_Ovimage(_1028988, _1028980, hAPP(hAPP(c_COMBC(_1028988, _1028980, _1028980), hAPP(hAPP(c_COMBC(_1028988, _1028980, tc_fun(_1028980, _1028980)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1028980, tc_fun(_1028980, _1028980)), _1028988), c_If(_1028980)), hAPP(hAPP(c_COMBC(_1028988, tc_fun(_1028988, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028988)), _1028990))), _1028982)), _1028986)), _1028984) = _1028990)]]], (13358 ^ _782464) ^ [_1029471, _1029473, _1029475, _1029477, _1029479, _1029481] : [-(hBOOL(hAPP(hAPP(c_member(_1029471), _1029473), _1029475))), 13361 ^ _782464 : [(13362 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1029471), _1029477), _1029475)), -(hAPP(c_Set_Ovimage(_1029479, _1029471, hAPP(hAPP(c_COMBC(_1029479, _1029471, _1029471), hAPP(hAPP(c_COMBC(_1029479, _1029471, tc_fun(_1029471, _1029471)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1029471, tc_fun(_1029471, _1029471)), _1029479), c_If(_1029471)), hAPP(hAPP(c_COMBC(_1029479, tc_fun(_1029479, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029479)), _1029481))), _1029473)), _1029477)), _1029475) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1029479, tc_HOL_Obool)), _1029481))], (13368 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1029471), _1029477), _1029475))), -(hAPP(c_Set_Ovimage(_1029479, _1029471, hAPP(hAPP(c_COMBC(_1029479, _1029471, _1029471), hAPP(hAPP(c_COMBC(_1029479, _1029471, tc_fun(_1029471, _1029471)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1029471, tc_fun(_1029471, _1029471)), _1029479), c_If(_1029471)), hAPP(hAPP(c_COMBC(_1029479, tc_fun(_1029479, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029479)), _1029481))), _1029473)), _1029477)), _1029475) = c_Orderings_Obot__class_Obot(tc_fun(_1029479, tc_HOL_Obool)))]]], (13374 ^ _782464) ^ [_1029976, _1029978, _1029980, _1029982, _1029984] : [c_Fun_Oinj__on(_1029976, _1029978, _1029980, _1029982), hBOOL(hAPP(hAPP(c_member(_1029978), _1029984), hAPP(c_Set_Oimage(_1029976, _1029978, _1029980), _1029982))), -(hAPP(_1029980, hAPP(c_Fun_Othe__inv__into(_1029976, _1029978, _1029982, _1029980), _1029984)) = _1029984)], (13384 ^ _782464) ^ [_1030171, _1030173, _1030175, _1030177] : [class_Orderings_Oorder(_1030171), class_Enum_Oenum(_1030173), 13391 ^ _782464 : [(13392 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1030173, _1030171)), _1030175), _1030177)), 13395 ^ _782464 : [(13396 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1030173, _1030171)), _1030175), _1030177)))], (13398 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1030173), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1030173), c_fNot), hAPP(hAPP(c_COMBS(_1030173, _1030171, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1030171, tc_fun(_1030171, tc_HOL_Obool), _1030173), c_fequal), _1030175)), _1030177)))))]]], (13400 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1030173, _1030171)), _1030175), _1030177))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1030173, _1030171)), _1030175), _1030177)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1030173), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1030173), c_fNot), hAPP(hAPP(c_COMBS(_1030173, _1030171, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1030171, tc_fun(_1030171, tc_HOL_Obool), _1030173), c_fequal), _1030175)), _1030177))))]]], (13410 ^ _782464) ^ [_1030690, _1030692, _1030694, _1030696, _1030698, _1030700] : [-(_1030690 = c_Orderings_Obot__class_Obot(tc_fun(_1030692, tc_HOL_Obool))), 13416 ^ _782464 : [(13417 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1030692), 13415 ^ [_1030690, _1030692, _1030694, _1030696, _1030698, _1030700]), _1030690)))], (13419 ^ _782464) ^ [] : [c_Fun_Oinj__on(_1030694, _1030696, _1030698, hAPP(_1030700, 13415 ^ [_1030690, _1030692, _1030694, _1030696, _1030698, _1030700]))]], -(c_Fun_Oinj__on(_1030694, _1030696, _1030698, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030692, tc_fun(_1030694, tc_HOL_Obool)), _1030690), _1030700)))], (13423 ^ _782464) ^ [_1030982] : [-(c_Finite__Set_Ofun__left__comm__idem(_1030982, tc_fun(_1030982, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1030982, tc_HOL_Obool), tc_fun(tc_fun(_1030982, tc_HOL_Obool), tc_fun(_1030982, tc_HOL_Obool)), _1030982), hAPP(c_COMBC(tc_fun(_1030982, tc_HOL_Obool), tc_fun(_1030982, tc_HOL_Obool), tc_fun(_1030982, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1030982, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1030982, tc_fun(_1030982, tc_HOL_Obool), tc_fun(_1030982, tc_HOL_Obool)), c_Set_Oinsert(_1030982)), c_Orderings_Obot__class_Obot(tc_fun(_1030982, tc_HOL_Obool))))))], (13425 ^ _782464) ^ [_1031075, _1031077] : [-(c_HOL_OThe(_1031075, hAPP(hAPP(c_COMBC(_1031075, _1031075, tc_HOL_Obool), c_fequal), _1031077)) = _1031077)], (13427 ^ _782464) ^ [_1031113, _1031115] : [-(c_HOL_OThe(_1031113, hAPP(c_fequal, _1031115)) = _1031115)], (13429 ^ _782464) ^ [_1031144, _1031146, _1031148, _1031150, _1031152, _1031154, _1031156] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1031144, _1031146, _1031148, _1031150, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031144, tc_HOL_Obool)), _1031152), hAPP(hAPP(c_Set_Oinsert(_1031144), _1031154), c_Orderings_Obot__class_Obot(tc_fun(_1031144, tc_HOL_Obool))))), _1031156)), hBOOL(hAPP(hAPP(c_member(_1031144), _1031154), _1031152)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1031144, _1031146, _1031148, _1031150, _1031152), hAPP(hAPP(_1031148, _1031154), _1031156))))], (13439 ^ _782464) ^ [_1031399, _1031401, _1031403, _1031405] : [hBOOL(hAPP(hAPP(c_member(_1031399), _1031401), hAPP(c_Set_Oimage(_1031403, _1031399, _1031405), c_Orderings_Otop__class_Otop(tc_fun(_1031403, tc_HOL_Obool))))), -(_1031401 = hAPP(_1031405, 13442 ^ [_1031399, _1031401, _1031403, _1031405]))], (13446 ^ _782464) ^ [_1031565, _1031567, _1031569, _1031571] : [c_Partial__Function_Omk__less(_1031565, _1031567, _1031569, _1031571), 13449 ^ _782464 : [(13450 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1031567, _1031569), _1031571)))], (13452 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1031567, _1031571), _1031569))]]], (13454 ^ _782464) ^ [_1031700, _1031702, _1031704, _1031706] : [-(c_Partial__Function_Omk__less(_1031700, _1031702, _1031704, _1031706)), hBOOL(hAPP(hAPP(_1031702, _1031704), _1031706)), -(hBOOL(hAPP(hAPP(_1031702, _1031706), _1031704)))], (13464 ^ _782464) ^ [_1031866, _1031868] : [class_Enum_Oenum(_1031866), 13467 ^ _782464 : [(13468 ^ _782464) ^ [] : [13469 ^ _782464 : [(13470 ^ _782464) ^ [_1031968] : [hBOOL(hAPP(_1031868, _1031968))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1031866), _1031868)))], (13474 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1031866), _1031868)), -(hBOOL(hAPP(_1031868, 13477 ^ [_1031866, _1031868])))]]], (13481 ^ _782464) ^ [_1032109, _1032111] : [class_Enum_Oenum(_1032109), 13484 ^ _782464 : [(13485 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1032109), _1032111)), -(hBOOL(hAPP(_1032111, 13488 ^ [_1032109, _1032111])))], (13492 ^ _782464) ^ [] : [13493 ^ _782464 : [(13494 ^ _782464) ^ [_1032289] : [hBOOL(hAPP(_1032111, _1032289))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1032109), _1032111)))]]], (13498 ^ _782464) ^ [_1032352, _1032354, _1032356, _1032358, _1032360] : [c_Finite__Set_Ofun__left__comm__idem(_1032352, _1032354, _1032356), -(hAPP(hAPP(_1032356, _1032358), hAPP(hAPP(_1032356, _1032358), _1032360)) = hAPP(hAPP(_1032356, _1032358), _1032360))], (13504 ^ _782464) ^ [_1032473, _1032475, _1032477, _1032479, _1032481] : [c_Finite__Set_Ofun__left__comm__idem(_1032473, _1032475, _1032477), -(c_Finite__Set_Ofun__left__comm__idem(_1032479, _1032475, hAPP(hAPP(c_COMBB(_1032473, tc_fun(_1032475, _1032475), _1032479), _1032477), _1032481)))], (13510 ^ _782464) ^ [_1032586, _1032588, _1032590, _1032592] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032586, _1032588, _1032590, _1032592, c_Orderings_Obot__class_Obot(tc_fun(_1032586, tc_HOL_Obool))), _1032592)))], (13512 ^ _782464) ^ [_1032628, _1032630, _1032632, _1032634] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032628, _1032630, _1032632, _1032634, c_Orderings_Obot__class_Obot(tc_fun(_1032628, tc_HOL_Obool))), _1032634)))], (13514 ^ _782464) ^ [_1032670, _1032672, _1032674, _1032676, _1032678] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032670, _1032672, _1032674, _1032676, c_Orderings_Obot__class_Obot(tc_fun(_1032670, tc_HOL_Obool))), _1032678)), -(_1032678 = _1032676)], (13520 ^ _782464) ^ [_1032779] : [-(c_Finite__Set_Ofun__left__comm__idem(_1032779, tc_fun(_1032779, tc_HOL_Obool), c_Set_Oinsert(_1032779)))], (13522 ^ _782464) ^ [_1032808] : [class_Lattices_Osemilattice__sup(_1032808), -(c_Finite__Set_Ofun__left__comm__idem(_1032808, _1032808, c_Lattices_Osemilattice__sup__class_Osup(_1032808)))], (13528 ^ _782464) ^ [_1032887] : [class_Lattices_Osemilattice__inf(_1032887), -(c_Finite__Set_Ofun__left__comm__idem(_1032887, _1032887, c_Lattices_Osemilattice__inf__class_Oinf(_1032887)))], (13534 ^ _782464) ^ [_1032965, _1032967, _1032969, _1032971, _1032973, _1032975, _1032977] : [-(hBOOL(hAPP(hAPP(c_member(_1032965), _1032967), _1032969))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032965, _1032971, _1032973, _1032975, _1032969), _1032977)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032965, _1032971, _1032973, _1032975, hAPP(hAPP(c_Set_Oinsert(_1032965), _1032967), _1032969)), hAPP(hAPP(_1032973, _1032967), _1032977))))], (13544 ^ _782464) ^ [_1033179, _1033181, _1033183, _1033185, _1033187] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033179, _1033179, _1033181, _1033183, _1033185), _1033187)), -(hBOOL(hAPP(hAPP(c_member(_1033179), _1033183), _1033185))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1033179, _1033181, hAPP(hAPP(c_Set_Oinsert(_1033179), _1033183), _1033185)), _1033187)))], (13554 ^ _782464) ^ [_1033335, _1033337, _1033339, _1033341, _1033343] : [class_Groups_Oab__semigroup__mult(_1033335), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033335, _1033335, c_Groups_Otimes__class_Otimes(_1033335), _1033337, _1033339), _1033341)), hBOOL(hAPP(hAPP(c_member(_1033335), _1033343), _1033339)), -(hBOOL(hAPP(hAPP(c_member(_1033335), _1033337), _1033339))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033335, _1033335, c_Groups_Otimes__class_Otimes(_1033335), _1033343, hAPP(hAPP(c_Set_Oinsert(_1033335), _1033337), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033335, tc_HOL_Obool)), _1033339), hAPP(hAPP(c_Set_Oinsert(_1033335), _1033343), c_Orderings_Obot__class_Obot(tc_fun(_1033335, tc_HOL_Obool)))))), _1033341)))], (13572 ^ _782464) ^ [_1033679, _1033681, _1033683, _1033685, _1033687] : [c_Fun_Obij__betw(_1033679, _1033681, _1033683, c_Orderings_Otop__class_Otop(tc_fun(_1033679, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1033681, tc_HOL_Obool))), 13575 ^ _782464 : [(13576 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033679, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1033679, _1033681, _1033683), _1033685)), _1033687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033681, tc_HOL_Obool)), _1033685), hAPP(c_Set_Oimage(_1033679, _1033681, _1033683), _1033687))))], (13582 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033681, tc_HOL_Obool)), _1033685), hAPP(c_Set_Oimage(_1033679, _1033681, _1033683), _1033687))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033679, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1033679, _1033681, _1033683), _1033685)), _1033687)))]]], (13588 ^ _782464) ^ [_1034032, _1034034, _1034036] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1034032, tc_HOL_Obool)), _1034034), _1034036)), -(hBOOL(hAPP(hAPP(c_member(_1034032), 13591 ^ [_1034032, _1034034, _1034036]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1034032, tc_HOL_Obool)), _1034036), _1034034))))], (13595 ^ _782464) ^ [_1034181, _1034183, _1034185, _1034187, _1034189, _1034191, _1034193] : [c_Fun_Oinj__on(_1034181, _1034183, _1034185, hAPP(c_Set_Oimage(_1034187, _1034181, _1034189), _1034191)), c_Fun_Oinj__on(_1034187, _1034181, _1034189, _1034191), hBOOL(hAPP(hAPP(c_member(_1034183), _1034193), hAPP(c_Set_Oimage(_1034181, _1034183, _1034185), hAPP(c_Set_Oimage(_1034187, _1034181, _1034189), _1034191)))), -(hAPP(c_Fun_Othe__inv__into(_1034187, _1034183, _1034191, hAPP(c_Fun_Ocomp(_1034181, _1034183, _1034187, _1034185), _1034189)), _1034193) = hAPP(hAPP(c_Fun_Ocomp(_1034181, _1034187, _1034183, c_Fun_Othe__inv__into(_1034187, _1034181, _1034191, _1034189)), c_Fun_Othe__inv__into(_1034181, _1034183, hAPP(c_Set_Oimage(_1034187, _1034181, _1034189), _1034191), _1034185)), _1034193))], (13609 ^ _782464) ^ [_1034565, _1034567, _1034569, _1034571, _1034573, _1034575] : [hBOOL(hAPP(hAPP(c_member(_1034565), _1034567), _1034569)), -(hAPP(c_Fun_Ooverride__on(_1034565, _1034571, _1034573, _1034575, _1034569), _1034567) = hAPP(_1034575, _1034567))], (13615 ^ _782464) ^ [_1034682, _1034684, _1034686, _1034688, _1034690, _1034692] : [-(hBOOL(hAPP(hAPP(c_member(_1034682), _1034684), _1034686))), -(hAPP(c_Fun_Ooverride__on(_1034682, _1034688, _1034690, _1034692, _1034686), _1034684) = hAPP(_1034690, _1034684))], (13621 ^ _782464) ^ [_1034747, _1034749, _1034751, _1034753, _1034755, _1034757] : [13623 ^ _782464 : [(13624 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034747), 13622 ^ [_1034747, _1034749, _1034751, _1034753, _1034755, _1034757]), _1034749)))], (13626 ^ _782464) ^ [] : [hAPP(_1034751, 13622 ^ [_1034747, _1034749, _1034751, _1034753, _1034755, _1034757]) = hAPP(_1034753, 13622 ^ [_1034747, _1034749, _1034751, _1034753, _1034755, _1034757])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034747, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1034747, _1034755, _1034751), _1034757)), _1034749) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034747, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1034747, _1034755, _1034753), _1034757)), _1034749))], (13630 ^ _782464) ^ [_1035038, _1035040, _1035042, _1035044] : [c_Finite__Set_Ofolding__one(_1035038, _1035040, _1035042), -(hAPP(_1035042, hAPP(hAPP(c_Set_Oinsert(_1035038), _1035044), c_Orderings_Obot__class_Obot(tc_fun(_1035038, tc_HOL_Obool)))) = _1035044)], (13636 ^ _782464) ^ [_1035153, _1035155, _1035157, _1035159, _1035161, _1035163] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035153, _1035155, _1035157, hAPP(c_COMBK(_1035155, _1035153), _1035159)), _1035161), _1035163) = _1035159)], (13638 ^ _782464) ^ [_1035203, _1035205, _1035207, _1035209, _1035211, _1035213, _1035215] : [hAPP(c_Fun_Ocomp(_1035203, _1035205, _1035207, _1035209), _1035211) = _1035213, -(hAPP(_1035209, hAPP(_1035211, _1035215)) = hAPP(_1035213, _1035215))], (13644 ^ _782464) ^ [_1035324, _1035326] : [class_Lattices_Oab__semigroup__idem__mult(_1035324), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035324), _1035326), _1035326) = _1035326)], (13650 ^ _782464) ^ [_1035415, _1035417] : [class_Lattices_Oab__semigroup__idem__mult(_1035415), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035415), _1035417), _1035417) = _1035417)], (13656 ^ _782464) ^ [_1035506, _1035508, _1035510] : [class_Lattices_Oab__semigroup__idem__mult(_1035506), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035506), _1035508), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035506), _1035508), _1035510)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035506), _1035508), _1035510))], (13662 ^ _782464) ^ [_1035631, _1035633, _1035635, _1035637] : [class_Groups_Oab__semigroup__mult(_1035631), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035631), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035631), _1035633), _1035635)), _1035637) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035631), _1035633), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035631), _1035635), _1035637)))], (13668 ^ _782464) ^ [_1035774, _1035776, _1035778, _1035780, _1035782, _1035784] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035774, _1035776, _1035778, _1035780), _1035782), _1035784) = hAPP(_1035780, hAPP(_1035782, _1035784)))], (13670 ^ _782464) ^ [_1035824, _1035826, _1035828, _1035830, _1035832, _1035834, _1035836] : [-(hAPP(c_Fun_Ocomp(_1035824, _1035826, _1035828, _1035830), hAPP(c_Fun_Ocomp(_1035832, _1035824, _1035828, _1035834), _1035836)) = hAPP(c_Fun_Ocomp(_1035832, _1035826, _1035828, hAPP(c_Fun_Ocomp(_1035824, _1035826, _1035832, _1035830), _1035834)), _1035836))], (13672 ^ _782464) ^ [_1035891, _1035893, _1035895, _1035897, _1035899, _1035901] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035891, _1035893, _1035895, _1035897), _1035899), _1035901) = hAPP(_1035897, hAPP(_1035899, _1035901)))], (13674 ^ _782464) ^ [_1035941, _1035943, _1035945, _1035947, _1035949, _1035951, _1035953, _1035955, _1035957] : [hAPP(c_Fun_Ocomp(_1035941, _1035943, _1035945, _1035947), _1035949) = hAPP(c_Fun_Ocomp(_1035951, _1035943, _1035945, _1035953), _1035955), -(hAPP(_1035947, hAPP(_1035949, _1035957)) = hAPP(_1035953, hAPP(_1035955, _1035957)))], (13680 ^ _782464) ^ [_1036088, _1036090, _1036092, _1036094, _1036096, _1036098, _1036100, _1036102] : [hAPP(c_Fun_Ocomp(_1036088, _1036090, _1036092, _1036094), _1036096) = hAPP(c_Fun_Ocomp(_1036098, _1036090, _1036092, _1036100), _1036102), 13683 ^ _782464 : [(13684 ^ _782464) ^ [_1036203] : [-(hAPP(_1036094, hAPP(_1036096, _1036203)) = hAPP(_1036100, hAPP(_1036102, _1036203)))]]], (13686 ^ _782464) ^ [_1036242, _1036244, _1036246, _1036248, _1036250, _1036252, _1036254, _1036256] : [c_Fun_Obij__betw(_1036242, _1036244, _1036246, _1036248, _1036250), 13689 ^ _782464 : [(13690 ^ _782464) ^ [] : [c_Fun_Obij__betw(_1036244, _1036252, _1036254, _1036250, _1036256), -(c_Fun_Obij__betw(_1036242, _1036252, hAPP(c_Fun_Ocomp(_1036244, _1036252, _1036242, _1036254), _1036246), _1036248, _1036256))], (13696 ^ _782464) ^ [] : [c_Fun_Obij__betw(_1036242, _1036252, hAPP(c_Fun_Ocomp(_1036244, _1036252, _1036242, _1036254), _1036246), _1036248, _1036256), -(c_Fun_Obij__betw(_1036244, _1036252, _1036254, _1036250, _1036256))]]], (13702 ^ _782464) ^ [_1036533, _1036535, _1036537, _1036539, _1036541, _1036543, _1036545, _1036547] : [c_Fun_Obij__betw(_1036533, _1036535, _1036537, _1036539, _1036541), c_Fun_Obij__betw(_1036535, _1036543, _1036545, _1036541, _1036547), -(c_Fun_Obij__betw(_1036533, _1036543, hAPP(c_Fun_Ocomp(_1036535, _1036543, _1036533, _1036545), _1036537), _1036539, _1036547))], (13712 ^ _782464) ^ [_1036720, _1036722, _1036724, _1036726, _1036728] : [c_Fun_Obij__betw(_1036720, _1036722, _1036724, c_Orderings_Otop__class_Otop(tc_fun(_1036720, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036722, tc_HOL_Obool))), c_Fun_Obij__betw(_1036722, _1036726, _1036728, c_Orderings_Otop__class_Otop(tc_fun(_1036722, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036726, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1036720, _1036726, hAPP(c_Fun_Ocomp(_1036722, _1036726, _1036720, _1036728), _1036724), c_Orderings_Otop__class_Otop(tc_fun(_1036720, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036726, tc_HOL_Obool))))], (13722 ^ _782464) ^ [_1036955, _1036957, _1036959, _1036961, _1036963, _1036965, _1036967, _1036969] : [c_Fun_Obij__betw(_1036955, _1036957, _1036959, _1036961, _1036963), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1036955, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1036965, _1036955, _1036967), _1036969)), _1036961)), 13729 ^ _782464 : [(13730 ^ _782464) ^ [] : [c_Fun_Obij__betw(_1036965, _1036955, _1036967, _1036969, _1036961), -(c_Fun_Obij__betw(_1036965, _1036957, hAPP(c_Fun_Ocomp(_1036955, _1036957, _1036965, _1036959), _1036967), _1036969, _1036963))], (13736 ^ _782464) ^ [] : [c_Fun_Obij__betw(_1036965, _1036957, hAPP(c_Fun_Ocomp(_1036955, _1036957, _1036965, _1036959), _1036967), _1036969, _1036963), -(c_Fun_Obij__betw(_1036965, _1036955, _1036967, _1036969, _1036961))]]], (13742 ^ _782464) ^ [_1037344, _1037346, _1037348, _1037350, _1037352, _1037354] : [-(hAPP(c_Set_Oimage(_1037344, _1037346, hAPP(c_Fun_Ocomp(_1037348, _1037346, _1037344, _1037350), _1037352)), _1037354) = hAPP(c_Set_Oimage(_1037348, _1037346, _1037350), hAPP(c_Set_Oimage(_1037344, _1037348, _1037352), _1037354)))], (13744 ^ _782464) ^ [_1037406, _1037408, _1037410, _1037412, _1037414, _1037416] : [c_Fun_Oinj__on(_1037406, _1037408, hAPP(c_Fun_Ocomp(_1037410, _1037408, _1037406, _1037412), _1037414), _1037416), -(c_Fun_Oinj__on(_1037406, _1037410, _1037414, _1037416))], (13750 ^ _782464) ^ [_1037515, _1037517, _1037519, _1037521] : [c_Fun_Obij__betw(_1037515, _1037517, _1037519, _1037521, c_Orderings_Obot__class_Obot(tc_fun(_1037517, tc_HOL_Obool))), -(_1037521 = c_Orderings_Obot__class_Obot(tc_fun(_1037515, tc_HOL_Obool)))], (13756 ^ _782464) ^ [_1037622, _1037624, _1037626, _1037628] : [c_Fun_Obij__betw(_1037622, _1037624, _1037626, c_Orderings_Obot__class_Obot(tc_fun(_1037622, tc_HOL_Obool)), _1037628), -(_1037628 = c_Orderings_Obot__class_Obot(tc_fun(_1037624, tc_HOL_Obool)))], (13762 ^ _782464) ^ [_1037729, _1037731, _1037733, _1037735, _1037737, _1037739, _1037741] : [-(hAPP(c_Fun_Ocomp(_1037729, _1037731, _1037733, _1037735), c_Fun_Ofun__upd(_1037733, _1037729, _1037737, _1037739, _1037741)) = c_Fun_Ofun__upd(_1037733, _1037731, hAPP(c_Fun_Ocomp(_1037729, _1037731, _1037733, _1037735), _1037737), _1037739, hAPP(_1037735, _1037741)))], (13764 ^ _782464) ^ [_1037795, _1037797, _1037799, _1037801, _1037803, _1037805] : [-(hAPP(c_Set_Ovimage(_1037795, _1037797, hAPP(c_Fun_Ocomp(_1037799, _1037797, _1037795, _1037801), _1037803)), _1037805) = hAPP(c_Set_Ovimage(_1037795, _1037799, _1037803), hAPP(c_Set_Ovimage(_1037799, _1037797, _1037801), _1037805)))], (13766 ^ _782464) ^ [_1037857, _1037859, _1037861, _1037863, _1037865] : [c_Fun_Obij__betw(_1037857, _1037859, _1037861, _1037863, _1037865), -(c_Fun_Oinj__on(_1037857, _1037859, _1037861, _1037863))], (13772 ^ _782464) ^ [_1037950, _1037952, _1037954, _1037956] : [c_Finite__Set_Ofun__left__comm__idem(_1037950, _1037952, _1037954), -(hAPP(c_Fun_Ocomp(_1037952, _1037952, _1037952, hAPP(_1037954, _1037956)), hAPP(_1037954, _1037956)) = hAPP(_1037954, _1037956))], (13778 ^ _782464) ^ [_1038067, _1038069, _1038071, _1038073, _1038075] : [c_Fun_Obij__betw(_1038067, _1038069, _1038071, _1038073, _1038075), -(c_Fun_Obij__betw(_1038069, _1038067, c_Fun_Othe__inv__into(_1038067, _1038069, _1038073, _1038071), _1038075, _1038073))], (13784 ^ _782464) ^ [_1038172] : [class_Lattices_Oab__semigroup__idem__mult(_1038172), -(c_Finite__Set_Ofun__left__comm__idem(_1038172, _1038172, c_Groups_Otimes__class_Otimes(_1038172)))], (13790 ^ _782464) ^ [_1038251, _1038253, _1038255, _1038257, _1038259] : [hAPP(c_Set_Oimage(_1038251, _1038253, _1038255), c_Orderings_Otop__class_Otop(tc_fun(_1038251, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038253, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1038253, _1038257, _1038259), c_Orderings_Otop__class_Otop(tc_fun(_1038253, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038257, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1038251, _1038257, hAPP(c_Fun_Ocomp(_1038253, _1038257, _1038251, _1038259), _1038255)), c_Orderings_Otop__class_Otop(tc_fun(_1038251, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038257, tc_HOL_Obool)))], (13800 ^ _782464) ^ [_1038510, _1038512, _1038514, _1038516, _1038518, _1038520] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038510, tc_fun(_1038512, tc_HOL_Obool)), _1038514), hAPP(c_Fun_Ocomp(_1038516, tc_fun(_1038512, tc_HOL_Obool), _1038510, _1038518), _1038520)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038516, tc_fun(_1038512, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1038510, _1038516, _1038520), _1038514)), _1038518))], (13802 ^ _782464) ^ [_1038585, _1038587, _1038589, _1038591, _1038593] : [c_Fun_Oinj__on(_1038585, _1038587, _1038589, c_Orderings_Otop__class_Otop(tc_fun(_1038585, tc_HOL_Obool))), c_Fun_Oinj__on(_1038591, _1038585, _1038593, c_Orderings_Otop__class_Otop(tc_fun(_1038591, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1038591, _1038587, hAPP(c_Fun_Ocomp(_1038585, _1038587, _1038591, _1038589), _1038593), c_Orderings_Otop__class_Otop(tc_fun(_1038591, tc_HOL_Obool))))], (13812 ^ _782464) ^ [_1038784, _1038786, _1038788, _1038790, _1038792, _1038794] : [c_Fun_Oinj__on(_1038784, _1038786, hAPP(c_Fun_Ocomp(_1038788, _1038786, _1038784, _1038790), _1038792), _1038794), -(c_Fun_Oinj__on(_1038788, _1038786, _1038790, hAPP(c_Set_Oimage(_1038784, _1038788, _1038792), _1038794)))], (13818 ^ _782464) ^ [_1038907, _1038909, _1038911, _1038913, _1038915, _1038917] : [c_Fun_Oinj__on(_1038907, _1038909, _1038911, _1038913), c_Fun_Oinj__on(_1038909, _1038915, _1038917, hAPP(c_Set_Oimage(_1038907, _1038909, _1038911), _1038913)), -(c_Fun_Oinj__on(_1038907, _1038915, hAPP(c_Fun_Ocomp(_1038909, _1038915, _1038907, _1038917), _1038911), _1038913))], (13828 ^ _782464) ^ [_1039094, _1039096, _1039098, _1039100, _1039102, _1039104] : [c_Fun_Oinj__on(_1039094, _1039096, _1039098, _1039100), 13831 ^ _782464 : [(13832 ^ _782464) ^ [] : [c_Fun_Oinj__on(_1039096, _1039102, _1039104, hAPP(c_Set_Oimage(_1039094, _1039096, _1039098), _1039100)), -(c_Fun_Oinj__on(_1039094, _1039102, hAPP(c_Fun_Ocomp(_1039096, _1039102, _1039094, _1039104), _1039098), _1039100))], (13838 ^ _782464) ^ [] : [c_Fun_Oinj__on(_1039094, _1039102, hAPP(c_Fun_Ocomp(_1039096, _1039102, _1039094, _1039104), _1039098), _1039100), -(c_Fun_Oinj__on(_1039096, _1039102, _1039104, hAPP(c_Set_Oimage(_1039094, _1039096, _1039098), _1039100)))]]], (13844 ^ _782464) ^ [_1039386, _1039388, _1039390, _1039392, _1039394, _1039396, _1039398] : [c_Fun_Obij__betw(_1039386, _1039388, _1039390, _1039392, _1039394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039386, tc_HOL_Obool)), _1039396), _1039392)), hAPP(c_Set_Oimage(_1039386, _1039388, _1039390), _1039396) = _1039398, -(c_Fun_Obij__betw(_1039386, _1039388, _1039390, _1039396, _1039398))], (13858 ^ _782464) ^ [_1039643, _1039645, _1039647, _1039649] : [c_Fun_Obij__betw(_1039643, _1039645, _1039647, _1039649, c_Orderings_Otop__class_Otop(tc_fun(_1039645, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1039643, _1039645, _1039647), c_Orderings_Otop__class_Otop(tc_fun(_1039643, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1039645, tc_HOL_Obool)))], (13864 ^ _782464) ^ [_1039774, _1039776, _1039778] : [c_Fun_Obij__betw(_1039774, _1039776, _1039778, c_Orderings_Otop__class_Otop(tc_fun(_1039774, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039776, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1039774, _1039776, _1039778), c_Orderings_Otop__class_Otop(tc_fun(_1039774, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1039776, tc_HOL_Obool)))], (13870 ^ _782464) ^ [_1039913, _1039915, _1039917] : [c_Fun_Obij__betw(_1039913, _1039915, _1039917, c_Orderings_Otop__class_Otop(tc_fun(_1039913, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039915, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1039913, _1039915, _1039917, c_Orderings_Otop__class_Otop(tc_fun(_1039913, tc_HOL_Obool))))], (13876 ^ _782464) ^ [_1040032, _1040034, _1040036, _1040038] : [c_Fun_Oinj__on(_1040032, _1040034, _1040036, _1040038), -(c_Fun_Obij__betw(_1040032, _1040034, _1040036, _1040038, hAPP(c_Set_Oimage(_1040032, _1040034, _1040036), _1040038)))], (13882 ^ _782464) ^ [_1040161, _1040163, _1040165, _1040167, _1040169] : [c_Fun_Obij__betw(_1040161, _1040163, _1040165, _1040167, _1040169), 13885 ^ _782464 : [(13886 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1040161, _1040163, _1040165, _1040167))], (13888 ^ _782464) ^ [] : [-(hAPP(c_Set_Oimage(_1040161, _1040163, _1040165), _1040167) = _1040169)]]], (13890 ^ _782464) ^ [_1040290, _1040292, _1040294, _1040296, _1040298] : [-(c_Fun_Obij__betw(_1040290, _1040292, _1040294, _1040296, _1040298)), c_Fun_Oinj__on(_1040290, _1040292, _1040294, _1040296), hAPP(c_Set_Oimage(_1040290, _1040292, _1040294), _1040296) = _1040298], (13900 ^ _782464) ^ [_1040457, _1040459, _1040461, _1040463] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1040457, _1040459, _1040461), _1040463)), _1040461 = c_Orderings_Obot__class_Obot(tc_fun(_1040457, tc_HOL_Obool))], (13906 ^ _782464) ^ [_1040576, _1040578, _1040580] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1040576, _1040578, c_Orderings_Obot__class_Obot(tc_fun(_1040576, tc_HOL_Obool))), _1040580))], (13908 ^ _782464) ^ [_1040614, _1040616, _1040618, _1040620, _1040622, _1040624, _1040626] : [c_Fun_Obij__betw(_1040614, _1040616, _1040618, _1040620, _1040622), c_Fun_Obij__betw(_1040614, _1040616, _1040618, _1040624, _1040626), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040616, tc_HOL_Obool)), _1040622), _1040626) = c_Orderings_Obot__class_Obot(tc_fun(_1040616, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1040614, _1040616, _1040618, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040614, tc_HOL_Obool)), _1040620), _1040624), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040616, tc_HOL_Obool)), _1040622), _1040626)))], (13922 ^ _782464) ^ [_1040919, _1040921, _1040923, _1040925, _1040927, _1040929, _1040931] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040919, tc_HOL_Obool)), _1040921), _1040923) = c_Orderings_Obot__class_Obot(tc_fun(_1040919, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040925, tc_HOL_Obool)), _1040927), _1040929) = c_Orderings_Obot__class_Obot(tc_fun(_1040925, tc_HOL_Obool)), c_Fun_Obij__betw(_1040919, _1040925, _1040931, _1040921, _1040927), c_Fun_Obij__betw(_1040919, _1040925, _1040931, _1040923, _1040929), -(c_Fun_Obij__betw(_1040919, _1040925, _1040931, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040919, tc_HOL_Obool)), _1040921), _1040923), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040925, tc_HOL_Obool)), _1040927), _1040929)))], (13940 ^ _782464) ^ [_1041336, _1041338, _1041340] : [c_Fun_Obij__betw(_1041336, _1041338, _1041340, c_Orderings_Otop__class_Otop(tc_fun(_1041336, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041338, tc_HOL_Obool))), 13943 ^ _782464 : [(13944 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1041336, _1041338, _1041340, c_Orderings_Otop__class_Otop(tc_fun(_1041336, tc_HOL_Obool))))], (13946 ^ _782464) ^ [] : [-(hAPP(c_Set_Oimage(_1041336, _1041338, _1041340), c_Orderings_Otop__class_Otop(tc_fun(_1041336, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041338, tc_HOL_Obool)))]]], (13948 ^ _782464) ^ [_1041511, _1041513, _1041515] : [-(c_Fun_Obij__betw(_1041511, _1041513, _1041515, c_Orderings_Otop__class_Otop(tc_fun(_1041511, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041513, tc_HOL_Obool)))), c_Fun_Oinj__on(_1041511, _1041513, _1041515, c_Orderings_Otop__class_Otop(tc_fun(_1041511, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1041511, _1041513, _1041515), c_Orderings_Otop__class_Otop(tc_fun(_1041511, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041513, tc_HOL_Obool))], (13958 ^ _782464) ^ [_1041720, _1041722, _1041724] : [c_Fun_Oinj__on(_1041720, _1041722, _1041724, c_Orderings_Otop__class_Otop(tc_fun(_1041720, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1041720, _1041722, _1041724), c_Orderings_Otop__class_Otop(tc_fun(_1041720, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041722, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1041720, _1041722, _1041724, c_Orderings_Otop__class_Otop(tc_fun(_1041720, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041722, tc_HOL_Obool))))], (13968 ^ _782464) ^ [_1041927, _1041929, _1041931, _1041933, _1041935, _1041937] : [hBOOL(hAPP(hAPP(c_member(_1041927), _1041929), _1041931)), -(hAPP(c_Fun_Ooverride__on(_1041927, _1041933, _1041935, _1041937, _1041931), _1041929) = hAPP(_1041937, _1041929))], (13974 ^ _782464) ^ [_1042046, _1042048, _1042050, _1042052, _1042054, _1042056] : [-(hBOOL(hAPP(hAPP(c_member(_1042046), _1042048), _1042050))), -(hAPP(c_Fun_Ooverride__on(_1042046, _1042052, _1042054, _1042056, _1042050), _1042048) = hAPP(_1042054, _1042048))], (13980 ^ _782464) ^ [_1042109, _1042111, _1042113, _1042115] : [c_Fun_Obij__betw(_1042109, _1042111, _1042113, c_Orderings_Otop__class_Otop(tc_fun(_1042109, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1042111, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1042109, _1042111, _1042113), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042109, tc_HOL_Obool)), _1042115)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042111, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1042109, _1042111, _1042113), _1042115)))], (13986 ^ _782464) ^ [_1042276, _1042278, _1042280, _1042282] : [-(c_Fun_Ooverride__on(_1042276, _1042278, _1042280, _1042282, c_Orderings_Obot__class_Obot(tc_fun(_1042276, tc_HOL_Obool))) = _1042280)], (13988 ^ _782464) ^ [_1042316, _1042318, _1042320, _1042322, _1042324] : [class_Groups_Oab__semigroup__mult(_1042316), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042316, _1042316, c_Groups_Otimes__class_Otimes(_1042316), _1042318, _1042320), _1042322)), -(hBOOL(hAPP(hAPP(c_member(_1042316), _1042318), _1042320))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042316, _1042316, c_Groups_Otimes__class_Otimes(_1042316), _1042324, hAPP(hAPP(c_Set_Oinsert(_1042316), _1042318), _1042320)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042316), _1042324), _1042322))))], (14002 ^ _782464) ^ [_1042556, _1042558, _1042560, _1042562, _1042564, _1042566] : [c_Fun_Obij__betw(_1042556, _1042558, _1042560, c_Orderings_Otop__class_Otop(tc_fun(_1042556, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1042558, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1042556, _1042558, _1042560), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042562, tc_fun(_1042556, tc_HOL_Obool)), _1042564), _1042566)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042562, tc_fun(_1042558, tc_HOL_Obool)), _1042564), hAPP(hAPP(c_COMBB(tc_fun(_1042556, tc_HOL_Obool), tc_fun(_1042558, tc_HOL_Obool), _1042562), c_Set_Oimage(_1042556, _1042558, _1042560)), _1042566)))], (14008 ^ _782464) ^ [_1042790, _1042792, _1042794, _1042796] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1042790, _1042792, hAPP(hAPP(c_Set_Oinsert(_1042790), _1042794), c_Orderings_Obot__class_Obot(tc_fun(_1042790, tc_HOL_Obool)))), _1042796)), -(_1042794 = _1042796)], (14014 ^ _782464) ^ [_1042905, _1042907, _1042909, _1042911] : [_1042909 = _1042911, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1042905, _1042907, hAPP(hAPP(c_Set_Oinsert(_1042905), _1042909), c_Orderings_Obot__class_Obot(tc_fun(_1042905, tc_HOL_Obool)))), _1042911)))], (14020 ^ _782464) ^ [_1043026, _1043028, _1043030] : [class_Rings_Oring(_1043026), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1043026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043026), _1043028), _1043030)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043026), _1043028), hAPP(c_Groups_Ouminus__class_Ouminus(_1043026), _1043030)))], (14026 ^ _782464) ^ [_1043155, _1043157, _1043159] : [class_Rings_Oring(_1043155), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1043155), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043155), _1043157), _1043159)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043155), hAPP(c_Groups_Ouminus__class_Ouminus(_1043155), _1043157)), _1043159))], (14032 ^ _782464) ^ [_1043284, _1043286, _1043288] : [class_Rings_Oring(_1043284), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043284), hAPP(c_Groups_Ouminus__class_Ouminus(_1043284), _1043286)), _1043288) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043284), _1043286), hAPP(c_Groups_Ouminus__class_Ouminus(_1043284), _1043288)))], (14038 ^ _782464) ^ [_1043413, _1043415, _1043417] : [class_Rings_Oring(_1043413), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043413), hAPP(c_Groups_Ouminus__class_Ouminus(_1043413), _1043415)), hAPP(c_Groups_Ouminus__class_Ouminus(_1043413), _1043417)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043413), _1043415), _1043417))], (14044 ^ _782464) ^ [_1043542, _1043544, _1043546] : [class_Rings_Oidom(_1043542), 14047 ^ _782464 : [(14058 ^ _782464) ^ [] : [14059 ^ _782464 : [(14060 ^ _782464) ^ [] : [_1043544 = _1043546], (14062 ^ _782464) ^ [] : [_1043544 = hAPP(c_Groups_Ouminus__class_Ouminus(_1043542), _1043546)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043542), _1043544), _1043544) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043542), _1043546), _1043546))], (14048 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043542), _1043544), _1043544) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043542), _1043546), _1043546), -(_1043544 = _1043546), -(_1043544 = hAPP(c_Groups_Ouminus__class_Ouminus(_1043542), _1043546))]]], (14066 ^ _782464) ^ [_1043861, _1043863, _1043865, _1043867, _1043869] : [c_Finite__Set_Ofolding__one(_1043861, _1043863, _1043865), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043861), _1043867)), hBOOL(hAPP(hAPP(c_member(_1043861), _1043869), _1043867)), 14077 ^ _782464 : [(14078 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043861, tc_HOL_Obool)), _1043867), hAPP(hAPP(c_Set_Oinsert(_1043861), _1043869), c_Orderings_Obot__class_Obot(tc_fun(_1043861, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1043861, tc_HOL_Obool)), -(hAPP(_1043865, _1043867) = _1043869)], (14084 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043861, tc_HOL_Obool)), _1043867), hAPP(hAPP(c_Set_Oinsert(_1043861), _1043869), c_Orderings_Obot__class_Obot(tc_fun(_1043861, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1043861, tc_HOL_Obool))), -(hAPP(_1043865, _1043867) = hAPP(hAPP(_1043863, _1043869), hAPP(_1043865, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043861, tc_HOL_Obool)), _1043867), hAPP(hAPP(c_Set_Oinsert(_1043861), _1043869), c_Orderings_Obot__class_Obot(tc_fun(_1043861, tc_HOL_Obool)))))))]]], (14090 ^ _782464) ^ [_1044407, _1044409, _1044411, _1044413, _1044415] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1044407, _1044409, hAPP(hAPP(c_Set_Oinsert(_1044407), _1044411), _1044413)), _1044415)), 14095 ^ _782464 : [(14096 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1044407), _1044411), _1044413) = hAPP(hAPP(c_Set_Oinsert(_1044407), 14093 ^ [_1044407, _1044409, _1044411, _1044413, _1044415]), 14094 ^ [_1044407, _1044409, _1044411, _1044413, _1044415]))], (14098 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1044407, _1044407, _1044409, 14093 ^ [_1044407, _1044409, _1044411, _1044413, _1044415], 14094 ^ [_1044407, _1044409, _1044411, _1044413, _1044415]), _1044415)))], (14100 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1044407), 14093 ^ [_1044407, _1044409, _1044411, _1044413, _1044415]), 14094 ^ [_1044407, _1044409, _1044411, _1044413, _1044415]))]]], (14102 ^ _782464) ^ [_1044798, _1044800, _1044802, _1044804, _1044806] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1044798, _1044800, hAPP(hAPP(c_Set_Oinsert(_1044798), _1044802), _1044804)), _1044806))), 14103 ^ _782464 : [(14104 ^ _782464) ^ [_1044902, _1044904] : [hAPP(hAPP(c_Set_Oinsert(_1044798), _1044802), _1044804) = hAPP(hAPP(c_Set_Oinsert(_1044798), _1044904), _1044902), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1044798, _1044798, _1044800, _1044904, _1044902), _1044806)), -(hBOOL(hAPP(hAPP(c_member(_1044798), _1044904), _1044902)))]]], (14116 ^ _782464) ^ [_1045159, _1045161, _1045163, _1045165, _1045167] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1045159, _1045161, hAPP(hAPP(c_Set_Oinsert(_1045159), _1045163), _1045165)), _1045167)), 14121 ^ _782464 : [(14122 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1045159), _1045163), _1045165) = hAPP(hAPP(c_Set_Oinsert(_1045159), 14119 ^ [_1045159, _1045161, _1045163, _1045165, _1045167]), 14120 ^ [_1045159, _1045161, _1045163, _1045165, _1045167]))], (14124 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1045159, _1045159, _1045161, 14119 ^ [_1045159, _1045161, _1045163, _1045165, _1045167], 14120 ^ [_1045159, _1045161, _1045163, _1045165, _1045167]), _1045167)))], (14126 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1045159), 14119 ^ [_1045159, _1045161, _1045163, _1045165, _1045167]), 14120 ^ [_1045159, _1045161, _1045163, _1045165, _1045167]))]]], (14128 ^ _782464) ^ [_1045552] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045552), c_Orderings_Obot__class_Obot(tc_fun(_1045552, tc_HOL_Obool)))))], (14130 ^ _782464) ^ [_1045584, _1045586, _1045588] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045584), _1045586)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045584), hAPP(hAPP(c_Set_Oinsert(_1045584), _1045588), _1045586))))], (14136 ^ _782464) ^ [_1045695, _1045697, _1045699, _1045701] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045695), _1045697)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045699), hAPP(c_Set_Oimage(_1045695, _1045699, _1045701), _1045697))))], (14142 ^ _782464) ^ [_1045806, _1045808, _1045810] : [14143 ^ _782464 : [(14144 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045806), _1045808))], (14146 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045806), _1045810))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045806), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045806, tc_HOL_Obool)), _1045808), _1045810))))], (14150 ^ _782464) ^ [_1045969, _1045971, _1045973] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045969), _1045971)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045969), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1045969, tc_HOL_Obool)), _1045971), _1045973))))], (14156 ^ _782464) ^ [_1046086, _1046088] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046086), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1046086, tc_HOL_Obool), _1046088)))), 14157 ^ _782464 : [(14158 ^ _782464) ^ [_1046150] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1046086, tc_HOL_Obool)), _1046150), _1046088)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046086), _1046150))]]], (14166 ^ _782464) ^ [_1046294, _1046296, _1046298, _1046300] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046298), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1046294, tc_fun(_1046298, tc_HOL_Obool)), _1046296), _1046300)))), 14167 ^ _782464 : [(14168 ^ _782464) ^ [_1046368] : [hBOOL(hAPP(hAPP(c_member(_1046294), _1046368), _1046296)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046298), hAPP(_1046300, _1046368)))]]], (14176 ^ _782464) ^ [_1046537, _1046539] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046537, tc_HOL_Obool)), hAPP(c_Set_OPow(_1046537), _1046539))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046537), _1046539)))], (14182 ^ _782464) ^ [_1046642, _1046644] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046642), _1046644)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046642, tc_HOL_Obool)), hAPP(c_Set_OPow(_1046642), _1046644))))], (14188 ^ _782464) ^ [_1046753, _1046755] : [class_Finite__Set_Ofinite(_1046753), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046753), _1046755)))], (14194 ^ _782464) ^ [_1046836, _1046838] : [class_Finite__Set_Ofinite(_1046836), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046836), _1046838)))], (14200 ^ _782464) ^ [_1046919, _1046921] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046919), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1046919, tc_HOL_Obool), _1046921))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046919, tc_HOL_Obool)), _1046921)))], (14206 ^ _782464) ^ [_1047030, _1047032] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047030), c_Orderings_Otop__class_Otop(tc_fun(_1047030, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047032), c_Orderings_Otop__class_Otop(tc_fun(_1047032, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1047030, _1047032)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1047030, _1047032), tc_HOL_Obool)))))], (14216 ^ _782464) ^ [_1047240, _1047242] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1047240, _1047242)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1047240, _1047242), tc_HOL_Obool)))), 14219 ^ _782464 : [(14220 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047240), c_Orderings_Otop__class_Otop(tc_fun(_1047240, tc_HOL_Obool)))))], (14222 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047242), c_Orderings_Otop__class_Otop(tc_fun(_1047242, tc_HOL_Obool)))))]]], (14224 ^ _782464) ^ [_1047405, _1047407] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1047405, _1047407)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1047405, _1047407), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047405), c_Orderings_Otop__class_Otop(tc_fun(_1047405, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047407), c_Orderings_Otop__class_Otop(tc_fun(_1047407, tc_HOL_Obool))))], (14234 ^ _782464) ^ [_1047614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1047614)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1047614), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047614), c_Orderings_Otop__class_Otop(tc_fun(_1047614, tc_HOL_Obool)))))], (14240 ^ _782464) ^ [_1047729] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047729), c_Orderings_Otop__class_Otop(tc_fun(_1047729, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1047729)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1047729), tc_HOL_Obool)))))], (14246 ^ _782464) ^ [_1047850] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047850), c_Orderings_Obot__class_Obot(tc_fun(_1047850, tc_HOL_Obool)))))], (14248 ^ _782464) ^ [_1047900, _1047902, _1047904] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047900), hAPP(hAPP(c_Set_Oinsert(_1047900), _1047902), _1047904))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047900), _1047904)))], (14254 ^ _782464) ^ [_1048007, _1048009, _1048011] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048007), _1048011)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048007), hAPP(hAPP(c_Set_Oinsert(_1048007), _1048009), _1048011))))], (14260 ^ _782464) ^ [_1048120, _1048122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1048120, _1048122)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1048120, _1048122), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048122), c_Orderings_Otop__class_Otop(tc_fun(_1048122, tc_HOL_Obool)))))], (14266 ^ _782464) ^ [_1048245, _1048247, _1048249] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048245, tc_HOL_Obool)), _1048247), _1048249)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048245), _1048249)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048245), _1048247)))], (14276 ^ _782464) ^ [_1048414, _1048416, _1048418] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048414), _1048416)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048414, tc_HOL_Obool)), _1048418), _1048416)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048414), _1048418)))], (14286 ^ _782464) ^ [_1048583] : [class_Finite__Set_Ofinite(_1048583), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048583), c_Orderings_Otop__class_Otop(tc_fun(_1048583, tc_HOL_Obool)))))], (14292 ^ _782464) ^ [_1048692, _1048694, _1048696] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048692), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048692, tc_HOL_Obool)), _1048694), _1048696))), 14295 ^ _782464 : [(14296 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048692), _1048694)))], (14298 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048692), _1048696)))]]], (14300 ^ _782464) ^ [_1048839, _1048841, _1048843] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048839), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048839, tc_HOL_Obool)), _1048841), _1048843)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048839), _1048841)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048839), _1048843))], (14310 ^ _782464) ^ [_1049020, _1049022, _1049024] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049020), _1049022)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1049020), _1049024)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049020), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1049020, tc_HOL_Obool)), _1049022), _1049024))))], (14320 ^ _782464) ^ [_1049199, _1049201, _1049203] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049199), _1049201)), 14323 ^ _782464 : [(14324 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049199, tc_HOL_Obool)), _1049203), _1049201))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049199), _1049203)))], (14330 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049199), _1049203)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049199), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049199, tc_HOL_Obool)), _1049203), _1049201))))]]], (14336 ^ _782464) ^ [_1049477, _1049479, _1049481, _1049483] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049477), _1049479)), 14339 ^ _782464 : [(14350 ^ _782464) ^ [] : [14352 ^ _782464 : [(14353 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049477), 14351 ^ [_1049477, _1049479, _1049481, _1049483]), _1049479)))], (14355 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049481), hAPP(_1049483, 14351 ^ [_1049477, _1049479, _1049481, _1049483])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049481), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049477, tc_fun(_1049481, tc_HOL_Obool)), _1049479), _1049483))))], (14340 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049481), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049477, tc_fun(_1049481, tc_HOL_Obool)), _1049479), _1049483))), 14343 ^ _782464 : [(14344 ^ _782464) ^ [_1049661] : [hBOOL(hAPP(hAPP(c_member(_1049477), _1049661), _1049479)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049481), hAPP(_1049483, _1049661))))]]]]], (14359 ^ _782464) ^ [_1049952, _1049954, _1049956, _1049958, _1049960] : [c_Fun_Obij__betw(_1049952, _1049954, _1049956, _1049958, _1049960), 14362 ^ _782464 : [(14363 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049952), _1049958)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049954), _1049960)))], (14369 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049954), _1049960)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049952), _1049958)))]]], (14375 ^ _782464) ^ [_1050207, _1050209, _1050211, _1050213, _1050215, _1050217] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1050207, _1050209, _1050211, _1050213, _1050215), _1050217)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050207), _1050215)))], (14381 ^ _782464) ^ [_1050316, _1050318, _1050320, _1050322, _1050324] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050316), _1050318)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1050320, tc_HOL_Obool)), _1050322), hAPP(c_Set_Oimage(_1050316, _1050320, _1050324), _1050318))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050320), _1050322)))], (14391 ^ _782464) ^ [_1050528, _1050530, _1050532, _1050534] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050528, tc_HOL_Obool)), _1050530), hAPP(hAPP(c_Set_Oinsert(_1050528), _1050532), _1050534)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050528), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050528, tc_HOL_Obool)), _1050530), _1050534))))], (14397 ^ _782464) ^ [_1050681, _1050683, _1050685, _1050687] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050681, tc_HOL_Obool)), _1050683), _1050687))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050681), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050681, tc_HOL_Obool)), _1050683), hAPP(hAPP(c_Set_Oinsert(_1050681), _1050685), _1050687)))))], (14403 ^ _782464) ^ [_1050840, _1050842, _1050844, _1050846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050840), hAPP(c_Set_Oimage(_1050842, _1050840, _1050844), _1050846))), c_Fun_Oinj__on(_1050842, _1050840, _1050844, _1050846), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050842), _1050846)))], (14413 ^ _782464) ^ [_1051011, _1051013] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051011), _1051013)), 14416 ^ _782464 : [(14417 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051011), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1051011, tc_HOL_Obool)), _1051013))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051011), c_Orderings_Otop__class_Otop(tc_fun(_1051011, tc_HOL_Obool)))))], (14423 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051011), c_Orderings_Otop__class_Otop(tc_fun(_1051011, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051011), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1051011, tc_HOL_Obool)), _1051013))))]]], (14429 ^ _782464) ^ [_1051289, _1051291, _1051293, _1051295, _1051297] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051289), hAPP(c_Set_Oimage(_1051291, _1051289, _1051293), c_Orderings_Otop__class_Otop(tc_fun(_1051291, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051295), hAPP(c_Set_Oimage(_1051291, _1051295, hAPP(hAPP(c_COMBB(_1051289, _1051295, _1051291), _1051297), _1051293)), c_Orderings_Otop__class_Otop(tc_fun(_1051291, tc_HOL_Obool))))))], (14435 ^ _782464) ^ [_1051456, _1051458, _1051460] : [class_Rings_Olinordered__idom(_1051456), -(_1051458 = _1051460), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051456), _1051458), _1051460))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051456), _1051460), _1051458)))], (14449 ^ _782464) ^ [_1051591, _1051593, _1051595] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051591), _1051593)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051591, tc_HOL_Obool)), _1051593), hAPP(c_Set_Oimage(_1051591, _1051591, _1051595), _1051593))), -(c_Fun_Oinj__on(_1051591, _1051591, _1051595, _1051593))], (14459 ^ _782464) ^ [_1051770, _1051772, _1051774] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051770), _1051772)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051770, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1051770, _1051770, _1051774), _1051772)), _1051772)), c_Fun_Oinj__on(_1051770, _1051770, _1051774, _1051772), -(hAPP(c_Set_Oimage(_1051770, _1051770, _1051774), _1051772) = _1051772)], (14473 ^ _782464) ^ [_1052017, _1052019] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052017), c_Orderings_Otop__class_Otop(tc_fun(_1052017, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1052017, _1052017, _1052019), c_Orderings_Otop__class_Otop(tc_fun(_1052017, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052017, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1052017, _1052017, _1052019, c_Orderings_Otop__class_Otop(tc_fun(_1052017, tc_HOL_Obool))))], (14483 ^ _782464) ^ [_1052212, _1052214] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052212), c_Orderings_Otop__class_Otop(tc_fun(_1052212, tc_HOL_Obool)))), c_Fun_Oinj__on(_1052212, _1052212, _1052214, c_Orderings_Otop__class_Otop(tc_fun(_1052212, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1052212, _1052212, _1052214), c_Orderings_Otop__class_Otop(tc_fun(_1052212, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052212, tc_HOL_Obool)))], (14493 ^ _782464) ^ [_1052407, _1052409, _1052411, _1052413] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052407), hAPP(c_Set_Ovimage(_1052407, _1052409, _1052411), _1052413))), hAPP(c_Set_Oimage(_1052407, _1052409, _1052411), c_Orderings_Otop__class_Otop(tc_fun(_1052407, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052409, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052409), _1052413)))], (14503 ^ _782464) ^ [_1052608, _1052610, _1052612, _1052614] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052608), _1052610)), c_Fun_Oinj__on(_1052612, _1052608, _1052614, c_Orderings_Otop__class_Otop(tc_fun(_1052612, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052612), hAPP(c_Set_Ovimage(_1052612, _1052608, _1052614), _1052610))))], (14513 ^ _782464) ^ [_1052789, _1052791, _1052793, _1052795] : [c_Fun_Obij__betw(_1052789, _1052791, _1052793, c_Orderings_Otop__class_Otop(tc_fun(_1052789, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1052791, tc_HOL_Obool))), 14516 ^ _782464 : [(14517 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052789), hAPP(c_Set_Ovimage(_1052789, _1052791, _1052793), _1052795))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052791), _1052795)))], (14523 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052791), _1052795)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052789), hAPP(c_Set_Ovimage(_1052789, _1052791, _1052793), _1052795))))]]], (14529 ^ _782464) ^ [_1053079, _1053081, _1053083, _1053085, _1053087] : [c_Finite__Set_Ofolding__one(_1053079, _1053081, _1053083), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053079), _1053085)), -(hBOOL(hAPP(hAPP(c_member(_1053079), _1053087), _1053085))), -(_1053085 = c_Orderings_Obot__class_Obot(tc_fun(_1053079, tc_HOL_Obool))), -(hAPP(_1053083, hAPP(hAPP(c_Set_Oinsert(_1053079), _1053087), _1053085)) = hAPP(hAPP(_1053081, _1053087), hAPP(_1053083, _1053085)))], (14547 ^ _782464) ^ [_1053324, _1053326, _1053328, _1053330, _1053332] : [c_Finite__Set_Ofolding__one(_1053324, _1053326, _1053328), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053324), _1053330)), 14554 ^ _782464 : [(14555 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053324, tc_HOL_Obool)), _1053330), hAPP(hAPP(c_Set_Oinsert(_1053324), _1053332), c_Orderings_Obot__class_Obot(tc_fun(_1053324, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1053324, tc_HOL_Obool)), -(hAPP(_1053328, hAPP(hAPP(c_Set_Oinsert(_1053324), _1053332), _1053330)) = _1053332)], (14561 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053324, tc_HOL_Obool)), _1053330), hAPP(hAPP(c_Set_Oinsert(_1053324), _1053332), c_Orderings_Obot__class_Obot(tc_fun(_1053324, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1053324, tc_HOL_Obool))), -(hAPP(_1053328, hAPP(hAPP(c_Set_Oinsert(_1053324), _1053332), _1053330)) = hAPP(hAPP(_1053326, _1053332), hAPP(_1053328, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053324, tc_HOL_Obool)), _1053330), hAPP(hAPP(c_Set_Oinsert(_1053324), _1053332), c_Orderings_Obot__class_Obot(tc_fun(_1053324, tc_HOL_Obool)))))))]]], (14567 ^ _782464) ^ [_1053806, _1053808, _1053810, _1053812, _1053814] : [c_Finite__Set_Ofolding__one(_1053806, _1053808, _1053810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053806), _1053812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053806), _1053814)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053806, tc_HOL_Obool)), _1053812), _1053814) = c_Orderings_Obot__class_Obot(tc_fun(_1053806, tc_HOL_Obool))), -(hAPP(hAPP(_1053808, hAPP(_1053810, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1053806, tc_HOL_Obool)), _1053812), _1053814))), hAPP(_1053810, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053806, tc_HOL_Obool)), _1053812), _1053814))) = hAPP(hAPP(_1053808, hAPP(_1053810, _1053812)), hAPP(_1053810, _1053814)))], (14585 ^ _782464) ^ [_1054162, _1054164, _1054166, _1054168, _1054170] : [c_Finite__Set_Ofolding__one(_1054162, _1054164, _1054166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054162), _1054168)), -(_1054168 = c_Orderings_Obot__class_Obot(tc_fun(_1054162, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054162), _1054170)), -(_1054170 = c_Orderings_Obot__class_Obot(tc_fun(_1054162, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054162, tc_HOL_Obool)), _1054168), _1054170) = c_Orderings_Obot__class_Obot(tc_fun(_1054162, tc_HOL_Obool)), -(hAPP(_1054166, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054162, tc_HOL_Obool)), _1054168), _1054170)) = hAPP(hAPP(_1054164, hAPP(_1054166, _1054168)), hAPP(_1054166, _1054170)))], (14611 ^ _782464) ^ [_1054663, _1054665, _1054667, _1054669, _1054671, _1054673] : [c_Finite__Set_Ofolding(_1054663, _1054665, _1054667, _1054669), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054663), _1054671)), hBOOL(hAPP(hAPP(c_member(_1054663), _1054673), _1054671)), -(hAPP(_1054669, _1054671) = hAPP(c_Fun_Ocomp(_1054665, _1054665, _1054665, hAPP(_1054669, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054663, tc_HOL_Obool)), _1054671), hAPP(hAPP(c_Set_Oinsert(_1054663), _1054673), c_Orderings_Obot__class_Obot(tc_fun(_1054663, tc_HOL_Obool)))))), hAPP(_1054667, _1054673)))], (14625 ^ _782464) ^ [_1054976, _1054978, _1054980, _1054982, _1054984, _1054986, _1054988, _1054990] : [c_Finite__Set_Ofolding__image__simple(_1054976, _1054978, _1054980, _1054982, _1054984, _1054986), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054978), _1054988)), hBOOL(hAPP(hAPP(c_member(_1054978), _1054990), _1054988)), -(hAPP(_1054986, _1054988) = hAPP(hAPP(_1054980, hAPP(_1054984, _1054990)), hAPP(_1054986, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054978, tc_HOL_Obool)), _1054988), hAPP(hAPP(c_Set_Oinsert(_1054978), _1054990), c_Orderings_Obot__class_Obot(tc_fun(_1054978, tc_HOL_Obool)))))))], (14639 ^ _782464) ^ [_1055301, _1055303, _1055305, _1055307, _1055309, _1055311, _1055313, _1055315] : [c_Finite__Set_Ofolding__image(_1055301, _1055303, _1055305, _1055307, _1055309), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055303), _1055311)), c_Fun_Oinj__on(_1055303, _1055303, _1055313, _1055311), -(hAPP(hAPP(_1055309, _1055315), hAPP(c_Set_Oimage(_1055303, _1055303, _1055313), _1055311)) = hAPP(hAPP(_1055309, hAPP(c_Fun_Ocomp(_1055303, _1055301, _1055303, _1055315), _1055313)), _1055311))], (14653 ^ _782464) ^ [_1055590, _1055592, _1055594, _1055596, _1055598, _1055600] : [c_Finite__Set_Ofolding(_1055590, _1055592, _1055594, _1055596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055590), _1055598)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055590), _1055600)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055590, tc_HOL_Obool)), _1055598), _1055600) = c_Orderings_Obot__class_Obot(tc_fun(_1055590, tc_HOL_Obool)), -(hAPP(_1055596, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055590, tc_HOL_Obool)), _1055598), _1055600)) = hAPP(c_Fun_Ocomp(_1055592, _1055592, _1055592, hAPP(_1055596, _1055598)), hAPP(_1055596, _1055600)))], (14671 ^ _782464) ^ [_1055963, _1055965, _1055967, _1055969, _1055971, _1055973] : [c_Finite__Set_Ofolding(_1055963, _1055965, _1055967, _1055969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055963), _1055971)), -(hAPP(_1055969, hAPP(hAPP(c_Set_Oinsert(_1055963), _1055973), _1055971)) = hAPP(c_Fun_Ocomp(_1055965, _1055965, _1055965, hAPP(_1055969, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055963, tc_HOL_Obool)), _1055971), hAPP(hAPP(c_Set_Oinsert(_1055963), _1055973), c_Orderings_Obot__class_Obot(tc_fun(_1055963, tc_HOL_Obool)))))), hAPP(_1055967, _1055973)))], (14681 ^ _782464) ^ [_1056218, _1056220, _1056222, _1056224, _1056226, _1056228, _1056230, _1056232] : [c_Finite__Set_Ofolding__image__simple(_1056218, _1056220, _1056222, _1056224, _1056226, _1056228), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056220), _1056230)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056220), _1056232)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056220, tc_HOL_Obool)), _1056230), _1056232) = c_Orderings_Obot__class_Obot(tc_fun(_1056220, tc_HOL_Obool)), -(hAPP(_1056228, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056220, tc_HOL_Obool)), _1056230), _1056232)) = hAPP(hAPP(_1056222, hAPP(_1056228, _1056230)), hAPP(_1056228, _1056232)))], (14699 ^ _782464) ^ [_1056607, _1056609, _1056611, _1056613, _1056615, _1056617, _1056619, _1056621] : [c_Finite__Set_Ofolding__image__simple(_1056607, _1056609, _1056611, _1056613, _1056615, _1056617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056609), _1056619)), -(hAPP(_1056617, hAPP(hAPP(c_Set_Oinsert(_1056609), _1056621), _1056619)) = hAPP(hAPP(_1056611, hAPP(_1056615, _1056621)), hAPP(_1056617, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056609, tc_HOL_Obool)), _1056619), hAPP(hAPP(c_Set_Oinsert(_1056609), _1056621), c_Orderings_Obot__class_Obot(tc_fun(_1056609, tc_HOL_Obool)))))))], (14709 ^ _782464) ^ [_1056870, _1056872, _1056874] : [class_Lattices_Olattice(_1056870), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056870), _1056872)), hBOOL(hAPP(hAPP(c_member(_1056870), _1056874), _1056872)), 14720 ^ _782464 : [(14721 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056870, tc_HOL_Obool)), _1056872), hAPP(hAPP(c_Set_Oinsert(_1056870), _1056874), c_Orderings_Obot__class_Obot(tc_fun(_1056870, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1056870, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1056870, _1056872) = _1056874)], (14727 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056870, tc_HOL_Obool)), _1056872), hAPP(hAPP(c_Set_Oinsert(_1056870), _1056874), c_Orderings_Obot__class_Obot(tc_fun(_1056870, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1056870, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1056870, _1056872) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1056870), _1056874), c_Big__Operators_Olattice__class_OInf__fin(_1056870, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056870, tc_HOL_Obool)), _1056872), hAPP(hAPP(c_Set_Oinsert(_1056870), _1056874), c_Orderings_Obot__class_Obot(tc_fun(_1056870, tc_HOL_Obool)))))))]]], (14733 ^ _782464) ^ [_1057376, _1057378, _1057380, _1057382, _1057384, _1057386, _1057388, _1057390, _1057392, _1057394, _1057396] : [c_Finite__Set_Ofolding(_1057376, _1057378, _1057380, _1057382), -(hAPP(c_Fun_Ocomp(_1057384, _1057386, _1057388, _1057390), hAPP(c_Fun_Ocomp(_1057392, _1057384, _1057388, _1057394), _1057396)) = hAPP(c_Fun_Ocomp(_1057392, _1057386, _1057388, hAPP(c_Fun_Ocomp(_1057384, _1057386, _1057392, _1057390), _1057394)), _1057396))], (14739 ^ _782464) ^ [_1057539, _1057541, _1057543, _1057545, _1057547, _1057549] : [c_Finite__Set_Ofolding(_1057539, _1057541, _1057543, _1057545), -(hAPP(c_Fun_Ocomp(_1057541, _1057541, _1057541, hAPP(_1057543, _1057547)), hAPP(_1057543, _1057549)) = hAPP(c_Fun_Ocomp(_1057541, _1057541, _1057541, hAPP(_1057543, _1057549)), hAPP(_1057543, _1057547)))], (14745 ^ _782464) ^ [_1057684, _1057686, _1057688, _1057690, _1057692, _1057694, _1057696, _1057698] : [c_Finite__Set_Ofolding(_1057684, _1057686, _1057688, _1057690), -(hAPP(c_Fun_Ocomp(_1057686, _1057686, _1057692, hAPP(_1057688, _1057694)), hAPP(c_Fun_Ocomp(_1057686, _1057686, _1057692, hAPP(_1057688, _1057696)), _1057698)) = hAPP(c_Fun_Ocomp(_1057686, _1057686, _1057692, hAPP(_1057688, _1057696)), hAPP(c_Fun_Ocomp(_1057686, _1057686, _1057692, hAPP(_1057688, _1057694)), _1057698)))], (14751 ^ _782464) ^ [_1057865, _1057867, _1057869, _1057871, _1057873, _1057875] : [c_Finite__Set_Ofolding__image__simple(_1057865, _1057867, _1057869, _1057871, _1057873, _1057875), -(hAPP(_1057875, c_Orderings_Obot__class_Obot(tc_fun(_1057867, tc_HOL_Obool))) = _1057871)], (14757 ^ _782464) ^ [_1057974, _1057976] : [class_Lattices_Olattice(_1057974), -(c_Big__Operators_Olattice__class_OInf__fin(_1057974, hAPP(hAPP(c_Set_Oinsert(_1057974), _1057976), c_Orderings_Obot__class_Obot(tc_fun(_1057974, tc_HOL_Obool)))) = _1057976)], (14763 ^ _782464) ^ [_1058081, _1058083, _1058085, _1058087, _1058089, _1058091, _1058093, _1058095] : [c_Finite__Set_Ofolding__image(_1058081, _1058083, _1058085, _1058087, _1058089), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058083), _1058091)), -(hAPP(hAPP(_1058089, hAPP(hAPP(c_COMBS(_1058083, _1058081, _1058081), hAPP(hAPP(c_COMBB(_1058081, tc_fun(_1058081, _1058081), _1058083), _1058085), _1058093)), _1058095)), _1058091) = hAPP(hAPP(_1058085, hAPP(hAPP(_1058089, _1058093), _1058091)), hAPP(hAPP(_1058089, _1058095), _1058091)))], (14773 ^ _782464) ^ [_1058342, _1058344, _1058346, _1058348, _1058350, _1058352, _1058354, _1058356] : [c_Finite__Set_Ofolding(_1058342, _1058344, _1058346, _1058348), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058342), _1058350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058342), _1058352)), -(hAPP(c_Fun_Ocomp(_1058344, _1058344, _1058354, hAPP(_1058348, _1058352)), hAPP(c_Fun_Ocomp(_1058344, _1058344, _1058354, hAPP(_1058348, _1058350)), _1058356)) = hAPP(c_Fun_Ocomp(_1058344, _1058344, _1058354, hAPP(_1058348, _1058350)), hAPP(c_Fun_Ocomp(_1058344, _1058344, _1058354, hAPP(_1058348, _1058352)), _1058356)))], (14787 ^ _782464) ^ [_1058667, _1058669, _1058671, _1058673, _1058675, _1058677] : [c_Finite__Set_Ofolding(_1058667, _1058669, _1058671, _1058673), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058667), _1058675)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058667), _1058677)), -(hAPP(c_Fun_Ocomp(_1058669, _1058669, _1058669, hAPP(_1058673, _1058677)), hAPP(_1058673, _1058675)) = hAPP(c_Fun_Ocomp(_1058669, _1058669, _1058669, hAPP(_1058673, _1058675)), hAPP(_1058673, _1058677)))], (14801 ^ _782464) ^ [_1058948, _1058950, _1058952, _1058954, _1058956, _1058958, _1058960, _1058962] : [c_Finite__Set_Ofolding(_1058948, _1058950, _1058952, _1058954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058948), _1058956)), -(hAPP(c_Fun_Ocomp(_1058950, _1058950, _1058958, hAPP(_1058952, _1058960)), hAPP(c_Fun_Ocomp(_1058950, _1058950, _1058958, hAPP(_1058954, _1058956)), _1058962)) = hAPP(c_Fun_Ocomp(_1058950, _1058950, _1058958, hAPP(_1058954, _1058956)), hAPP(c_Fun_Ocomp(_1058950, _1058950, _1058958, hAPP(_1058952, _1058960)), _1058962)))], (14811 ^ _782464) ^ [_1059201, _1059203, _1059205, _1059207, _1059209, _1059211] : [c_Finite__Set_Ofolding(_1059201, _1059203, _1059205, _1059207), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059201), _1059209)), -(hAPP(c_Fun_Ocomp(_1059203, _1059203, _1059203, hAPP(_1059205, _1059211)), hAPP(_1059207, _1059209)) = hAPP(c_Fun_Ocomp(_1059203, _1059203, _1059203, hAPP(_1059207, _1059209)), hAPP(_1059205, _1059211)))], (14821 ^ _782464) ^ [_1059414, _1059416, _1059418] : [class_Lattices_Olattice(_1059414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059414), _1059416)), hBOOL(hAPP(hAPP(c_member(_1059414), _1059418), _1059416)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059414), _1059418), c_Big__Operators_Olattice__class_OInf__fin(_1059414, _1059416)) = _1059418)], (14835 ^ _782464) ^ [_1059643, _1059645, _1059647] : [class_Lattices_Olattice(_1059643), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059643), _1059645)), hBOOL(hAPP(hAPP(c_member(_1059643), _1059647), _1059645)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1059643), _1059647), c_Big__Operators_Olattice__class_OInf__fin(_1059643, _1059645)) = c_Big__Operators_Olattice__class_OInf__fin(_1059643, _1059645))], (14849 ^ _782464) ^ [_1059878, _1059880] : [class_Complete__Lattice_Ocomplete__lattice(_1059878), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059878), _1059880)), -(_1059880 = c_Orderings_Obot__class_Obot(tc_fun(_1059878, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1059878, _1059880) = c_Complete__Lattice_OInf__class_OInf(_1059878, _1059880))], (14863 ^ _782464) ^ [_1060050, _1060052, _1060054] : [class_Lattices_Olattice(_1060050), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060050), _1060052)), -(_1060052 = c_Orderings_Obot__class_Obot(tc_fun(_1060050, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060050, hAPP(hAPP(c_Set_Oinsert(_1060050), _1060054), _1060052)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060050), _1060054), c_Big__Operators_Olattice__class_OInf__fin(_1060050, _1060052)))], (14877 ^ _782464) ^ [_1060258, _1060260, _1060262] : [class_Lattices_Olattice(_1060258), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060258), _1060260)), -(_1060262 = c_Orderings_Obot__class_Obot(tc_fun(_1060258, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060258, tc_HOL_Obool)), _1060262), _1060260)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060258), c_Big__Operators_Olattice__class_OInf__fin(_1060258, _1060262)), c_Big__Operators_Olattice__class_OInf__fin(_1060258, _1060260)) = c_Big__Operators_Olattice__class_OInf__fin(_1060258, _1060260))], (14895 ^ _782464) ^ [_1060572, _1060574, _1060576] : [class_Lattices_Olattice(_1060572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060572), _1060574)), -(_1060574 = c_Orderings_Obot__class_Obot(tc_fun(_1060572, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060572), _1060576)), -(_1060576 = c_Orderings_Obot__class_Obot(tc_fun(_1060572, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060572, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060572, tc_HOL_Obool)), _1060574), _1060576)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060572), c_Big__Operators_Olattice__class_OInf__fin(_1060572, _1060574)), c_Big__Operators_Olattice__class_OInf__fin(_1060572, _1060576)))], (14917 ^ _782464) ^ [_1060921, _1060923, _1060925, _1060927, _1060929, _1060931, _1060933, _1060935] : [c_Finite__Set_Ofolding__image__simple(_1060921, _1060923, _1060925, _1060927, _1060929, _1060931), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060923), _1060933)), -(hBOOL(hAPP(hAPP(c_member(_1060923), _1060935), _1060933))), -(hAPP(_1060931, hAPP(hAPP(c_Set_Oinsert(_1060923), _1060935), _1060933)) = hAPP(hAPP(_1060925, hAPP(_1060929, _1060935)), hAPP(_1060931, _1060933)))], (14931 ^ _782464) ^ [_1061165, _1061167, _1061169, _1061171, _1061173, _1061175, _1061177, _1061179] : [c_Finite__Set_Ofolding__image__simple(_1061165, _1061167, _1061169, _1061171, _1061173, _1061175), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061167), _1061177)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061167), _1061179)), -(hAPP(hAPP(_1061169, hAPP(_1061175, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061167, tc_HOL_Obool)), _1061177), _1061179))), hAPP(_1061175, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061167, tc_HOL_Obool)), _1061177), _1061179))) = hAPP(hAPP(_1061169, hAPP(_1061175, _1061177)), hAPP(_1061175, _1061179)))], (14945 ^ _782464) ^ [_1061498, _1061500, _1061502] : [class_Lattices_Olattice(_1061498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061498), _1061500)), -(hBOOL(hAPP(hAPP(c_member(_1061498), _1061502), _1061500))), -(_1061500 = c_Orderings_Obot__class_Obot(tc_fun(_1061498, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061498, hAPP(hAPP(c_Set_Oinsert(_1061498), _1061502), _1061500)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061498), _1061502), c_Big__Operators_Olattice__class_OInf__fin(_1061498, _1061500)))], (14963 ^ _782464) ^ [_1061735, _1061737, _1061739] : [class_Lattices_Olattice(_1061735), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061735), _1061737)), 14970 ^ _782464 : [(14971 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061735, tc_HOL_Obool)), _1061737), hAPP(hAPP(c_Set_Oinsert(_1061735), _1061739), c_Orderings_Obot__class_Obot(tc_fun(_1061735, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1061735, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1061735, hAPP(hAPP(c_Set_Oinsert(_1061735), _1061739), _1061737)) = _1061739)], (14977 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061735, tc_HOL_Obool)), _1061737), hAPP(hAPP(c_Set_Oinsert(_1061735), _1061739), c_Orderings_Obot__class_Obot(tc_fun(_1061735, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1061735, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061735, hAPP(hAPP(c_Set_Oinsert(_1061735), _1061739), _1061737)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061735), _1061739), c_Big__Operators_Olattice__class_OInf__fin(_1061735, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061735, tc_HOL_Obool)), _1061737), hAPP(hAPP(c_Set_Oinsert(_1061735), _1061739), c_Orderings_Obot__class_Obot(tc_fun(_1061735, tc_HOL_Obool)))))))]]], (14983 ^ _782464) ^ [_1062205, _1062207, _1062209] : [class_Lattices_Olattice(_1062205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062205), _1062207)), -(_1062207 = c_Orderings_Obot__class_Obot(tc_fun(_1062205, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062205), _1062209)), -(_1062209 = c_Orderings_Obot__class_Obot(tc_fun(_1062205, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062205, tc_HOL_Obool)), _1062207), _1062209) = c_Orderings_Obot__class_Obot(tc_fun(_1062205, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1062205, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062205, tc_HOL_Obool)), _1062207), _1062209)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062205), c_Big__Operators_Olattice__class_OInf__fin(_1062205, _1062207)), c_Big__Operators_Olattice__class_OInf__fin(_1062205, _1062209)))], (15009 ^ _782464) ^ [_1062682, _1062684, _1062686] : [class_Lattices_Olattice(_1062682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062682), _1062684)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062682), _1062686)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062682, tc_HOL_Obool)), _1062684), _1062686) = c_Orderings_Obot__class_Obot(tc_fun(_1062682, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062682), c_Big__Operators_Olattice__class_OInf__fin(_1062682, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062682, tc_HOL_Obool)), _1062684), _1062686))), c_Big__Operators_Olattice__class_OInf__fin(_1062682, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062682, tc_HOL_Obool)), _1062684), _1062686))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062682), c_Big__Operators_Olattice__class_OInf__fin(_1062682, _1062684)), c_Big__Operators_Olattice__class_OInf__fin(_1062682, _1062686)))], (15027 ^ _782464) ^ [_1063030, _1063032, _1063034, _1063036, _1063038, _1063040] : [c_Finite__Set_Ofolding(_1063030, _1063032, _1063034, _1063036), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063030), _1063038)), -(hBOOL(hAPP(hAPP(c_member(_1063030), _1063040), _1063038))), -(hAPP(_1063036, hAPP(hAPP(c_Set_Oinsert(_1063030), _1063040), _1063038)) = hAPP(c_Fun_Ocomp(_1063032, _1063032, _1063032, hAPP(_1063036, _1063038)), hAPP(_1063034, _1063040)))], (15041 ^ _782464) ^ [_1063266, _1063268, _1063270, _1063272, _1063274, _1063276] : [c_Finite__Set_Ofolding(_1063266, _1063268, _1063270, _1063272), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063266), _1063274)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063266), _1063276)), -(hAPP(c_Fun_Ocomp(_1063268, _1063268, _1063268, hAPP(_1063272, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063266, tc_HOL_Obool)), _1063274), _1063276))), hAPP(_1063272, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063266, tc_HOL_Obool)), _1063274), _1063276))) = hAPP(c_Fun_Ocomp(_1063268, _1063268, _1063268, hAPP(_1063272, _1063274)), hAPP(_1063272, _1063276)))], (15055 ^ _782464) ^ [_1063591, _1063593] : [class_Lattices_Olattice(_1063591), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063591), _1063593)), -(_1063593 = c_Orderings_Obot__class_Obot(tc_fun(_1063591, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1063591), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063591), 15068 ^ [_1063591, _1063593]), 15069 ^ [_1063591, _1063593])), hAPP(hAPP(c_Set_Oinsert(_1063591), 15068 ^ [_1063591, _1063593]), hAPP(hAPP(c_Set_Oinsert(_1063591), 15069 ^ [_1063591, _1063593]), c_Orderings_Obot__class_Obot(tc_fun(_1063591, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1063591), c_Big__Operators_Olattice__class_OInf__fin(_1063591, _1063593)), _1063593)))], (15075 ^ _782464) ^ [_1064035, _1064037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1064035, tc_HOL_Obool)), _1064037)), 15081 ^ _782464 : [(15082 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1064035, tc_HOL_Obool)), 15080 ^ [_1064035, _1064037]), _1064037)))], (15084 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064035), 15080 ^ [_1064035, _1064037]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1064035), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1064035, tc_HOL_Obool), _1064037))))], (15088 ^ _782464) ^ [_1064294, _1064296, _1064298] : [class_Lattices_Olattice(_1064294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064294), _1064296)), hBOOL(hAPP(hAPP(c_member(_1064294), _1064298), _1064296)), 15099 ^ _782464 : [(15100 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064294, tc_HOL_Obool)), _1064296), hAPP(hAPP(c_Set_Oinsert(_1064294), _1064298), c_Orderings_Obot__class_Obot(tc_fun(_1064294, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1064294, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1064294, _1064296) = _1064298)], (15106 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064294, tc_HOL_Obool)), _1064296), hAPP(hAPP(c_Set_Oinsert(_1064294), _1064298), c_Orderings_Obot__class_Obot(tc_fun(_1064294, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1064294, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1064294, _1064296) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064294), _1064298), c_Big__Operators_Olattice__class_OSup__fin(_1064294, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064294, tc_HOL_Obool)), _1064296), hAPP(hAPP(c_Set_Oinsert(_1064294), _1064298), c_Orderings_Obot__class_Obot(tc_fun(_1064294, tc_HOL_Obool)))))))]]], (15112 ^ _782464) ^ [_1064800, _1064802, _1064804, _1064806, _1064808, _1064810] : [c_Finite__Set_Ofolding__idem(_1064800, _1064802, _1064804, _1064806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064800), _1064808)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064800), _1064810)), -(hAPP(_1064806, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064800, tc_HOL_Obool)), _1064808), _1064810)) = hAPP(c_Fun_Ocomp(_1064802, _1064802, _1064802, hAPP(_1064806, _1064808)), hAPP(_1064806, _1064810)))], (15126 ^ _782464) ^ [_1065081, _1065083, _1065085, _1065087, _1065089, _1065091] : [c_Finite__Set_Ofolding__idem(_1065081, _1065083, _1065085, _1065087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065081), _1065089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1065081, tc_HOL_Obool)), _1065091), _1065089)), -(hAPP(c_Fun_Ocomp(_1065083, _1065083, _1065083, hAPP(_1065087, _1065089)), hAPP(_1065087, _1065091)) = hAPP(_1065087, _1065089))], (15140 ^ _782464) ^ [_1065352, _1065354, _1065356, _1065358, _1065360, _1065362] : [c_Finite__Set_Ofolding__idem(_1065352, _1065354, _1065356, _1065358), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065352), _1065360)), -(hAPP(_1065358, hAPP(hAPP(c_Set_Oinsert(_1065352), _1065362), _1065360)) = hAPP(c_Fun_Ocomp(_1065354, _1065354, _1065354, hAPP(_1065358, _1065360)), hAPP(_1065356, _1065362)))], (15150 ^ _782464) ^ [_1065559, _1065561, _1065563, _1065565] : [c_Finite__Set_Ofolding__one(_1065559, _1065561, _1065563), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065559), _1065565)), -(_1065565 = c_Orderings_Obot__class_Obot(tc_fun(_1065559, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1065559), hAPP(hAPP(_1065561, 15163 ^ [_1065559, _1065561, _1065563, _1065565]), 15164 ^ [_1065559, _1065561, _1065563, _1065565])), hAPP(hAPP(c_Set_Oinsert(_1065559), 15163 ^ [_1065559, _1065561, _1065563, _1065565]), hAPP(hAPP(c_Set_Oinsert(_1065559), 15164 ^ [_1065559, _1065561, _1065563, _1065565]), c_Orderings_Obot__class_Obot(tc_fun(_1065559, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1065559), hAPP(_1065563, _1065565)), _1065565)))], (15170 ^ _782464) ^ [_1066045, _1066047, _1066049, _1066051, _1066053, _1066055] : [c_Finite__Set_Ofolding__idem(_1066045, _1066047, _1066049, _1066051), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066045), _1066053)), hBOOL(hAPP(hAPP(c_member(_1066045), _1066055), _1066053)), -(hAPP(c_Fun_Ocomp(_1066047, _1066047, _1066047, hAPP(_1066051, _1066053)), hAPP(_1066049, _1066055)) = hAPP(_1066051, _1066053))], (15184 ^ _782464) ^ [_1066310, _1066312] : [class_Lattices_Olattice(_1066310), -(c_Big__Operators_Olattice__class_OSup__fin(_1066310, hAPP(hAPP(c_Set_Oinsert(_1066310), _1066312), c_Orderings_Obot__class_Obot(tc_fun(_1066310, tc_HOL_Obool)))) = _1066312)], (15190 ^ _782464) ^ [_1066417, _1066419, _1066421, _1066423, _1066425, _1066427, _1066429] : [c_Finite__Set_Ofolding__idem(_1066417, _1066419, _1066421, _1066423), -(hAPP(c_Fun_Ocomp(_1066419, _1066419, _1066425, hAPP(_1066421, _1066427)), hAPP(c_Fun_Ocomp(_1066419, _1066419, _1066425, hAPP(_1066421, _1066427)), _1066429)) = hAPP(c_Fun_Ocomp(_1066419, _1066419, _1066425, hAPP(_1066421, _1066427)), _1066429))], (15196 ^ _782464) ^ [_1066574, _1066576, _1066578, _1066580, _1066582] : [c_Finite__Set_Ofolding__idem(_1066574, _1066576, _1066578, _1066580), -(hAPP(c_Fun_Ocomp(_1066576, _1066576, _1066576, hAPP(_1066578, _1066582)), hAPP(_1066578, _1066582)) = hAPP(_1066578, _1066582))], (15202 ^ _782464) ^ [_1066695, _1066697, _1066699] : [class_Lattices_Olattice(_1066695), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066695), _1066697)), hBOOL(hAPP(hAPP(c_member(_1066695), _1066699), _1066697)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066695), _1066699), c_Big__Operators_Olattice__class_OSup__fin(_1066695, _1066697)) = c_Big__Operators_Olattice__class_OSup__fin(_1066695, _1066697))], (15216 ^ _782464) ^ [_1066930, _1066932, _1066934] : [class_Lattices_Olattice(_1066930), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066930), _1066932)), hBOOL(hAPP(hAPP(c_member(_1066930), _1066934), _1066932)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066930), _1066934), c_Big__Operators_Olattice__class_OSup__fin(_1066930, _1066932)) = _1066934)], (15230 ^ _782464) ^ [_1067159, _1067161] : [class_Complete__Lattice_Ocomplete__lattice(_1067159), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067159), _1067161)), -(_1067161 = c_Orderings_Obot__class_Obot(tc_fun(_1067159, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067159, _1067161) = c_Complete__Lattice_OSup__class_OSup(_1067159, _1067161))], (15244 ^ _782464) ^ [_1067331, _1067333, _1067335] : [class_Lattices_Olattice(_1067331), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067331), _1067333)), -(_1067333 = c_Orderings_Obot__class_Obot(tc_fun(_1067331, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067331, hAPP(hAPP(c_Set_Oinsert(_1067331), _1067335), _1067333)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067331), _1067335), c_Big__Operators_Olattice__class_OSup__fin(_1067331, _1067333)))], (15258 ^ _782464) ^ [_1067539, _1067541, _1067543] : [class_Lattices_Olattice(_1067539), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067539), _1067541)), -(_1067543 = c_Orderings_Obot__class_Obot(tc_fun(_1067539, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1067539, tc_HOL_Obool)), _1067543), _1067541)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067539), c_Big__Operators_Olattice__class_OSup__fin(_1067539, _1067543)), c_Big__Operators_Olattice__class_OSup__fin(_1067539, _1067541)) = c_Big__Operators_Olattice__class_OSup__fin(_1067539, _1067541))], (15276 ^ _782464) ^ [_1067853, _1067855, _1067857] : [class_Lattices_Olattice(_1067853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067853), _1067855)), -(_1067855 = c_Orderings_Obot__class_Obot(tc_fun(_1067853, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067853), _1067857)), -(_1067857 = c_Orderings_Obot__class_Obot(tc_fun(_1067853, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067853, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1067853, tc_HOL_Obool)), _1067855), _1067857)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067853), c_Big__Operators_Olattice__class_OSup__fin(_1067853, _1067855)), c_Big__Operators_Olattice__class_OSup__fin(_1067853, _1067857)))], (15298 ^ _782464) ^ [_1068202, _1068204] : [class_Lattices_Olattice(_1068202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068202), _1068204)), -(_1068204 = c_Orderings_Obot__class_Obot(tc_fun(_1068202, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068202), c_Big__Operators_Olattice__class_OInf__fin(_1068202, _1068204)), c_Big__Operators_Olattice__class_OSup__fin(_1068202, _1068204))))], (15312 ^ _782464) ^ [_1068388, _1068390, _1068392] : [class_Lattices_Olattice(_1068388), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068388), _1068390)), -(hBOOL(hAPP(hAPP(c_member(_1068388), _1068392), _1068390))), -(_1068390 = c_Orderings_Obot__class_Obot(tc_fun(_1068388, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1068388, hAPP(hAPP(c_Set_Oinsert(_1068388), _1068392), _1068390)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068388), _1068392), c_Big__Operators_Olattice__class_OSup__fin(_1068388, _1068390)))], (15330 ^ _782464) ^ [_1068625, _1068627, _1068629] : [class_Lattices_Olattice(_1068625), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068625), _1068627)), 15337 ^ _782464 : [(15338 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068625, tc_HOL_Obool)), _1068627), hAPP(hAPP(c_Set_Oinsert(_1068625), _1068629), c_Orderings_Obot__class_Obot(tc_fun(_1068625, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068625, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1068625, hAPP(hAPP(c_Set_Oinsert(_1068625), _1068629), _1068627)) = _1068629)], (15344 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068625, tc_HOL_Obool)), _1068627), hAPP(hAPP(c_Set_Oinsert(_1068625), _1068629), c_Orderings_Obot__class_Obot(tc_fun(_1068625, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068625, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1068625, hAPP(hAPP(c_Set_Oinsert(_1068625), _1068629), _1068627)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068625), _1068629), c_Big__Operators_Olattice__class_OSup__fin(_1068625, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068625, tc_HOL_Obool)), _1068627), hAPP(hAPP(c_Set_Oinsert(_1068625), _1068629), c_Orderings_Obot__class_Obot(tc_fun(_1068625, tc_HOL_Obool)))))))]]], (15350 ^ _782464) ^ [_1069095, _1069097, _1069099] : [class_Lattices_Olattice(_1069095), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069095), _1069097)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069095), _1069099)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069095, tc_HOL_Obool)), _1069097), _1069099) = c_Orderings_Obot__class_Obot(tc_fun(_1069095, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069095), c_Big__Operators_Olattice__class_OSup__fin(_1069095, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069095, tc_HOL_Obool)), _1069097), _1069099))), c_Big__Operators_Olattice__class_OSup__fin(_1069095, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069095, tc_HOL_Obool)), _1069097), _1069099))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069095), c_Big__Operators_Olattice__class_OSup__fin(_1069095, _1069097)), c_Big__Operators_Olattice__class_OSup__fin(_1069095, _1069099)))], (15368 ^ _782464) ^ [_1069443, _1069445, _1069447] : [class_Lattices_Olattice(_1069443), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069443), _1069445)), -(_1069445 = c_Orderings_Obot__class_Obot(tc_fun(_1069443, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069443), _1069447)), -(_1069447 = c_Orderings_Obot__class_Obot(tc_fun(_1069443, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069443, tc_HOL_Obool)), _1069445), _1069447) = c_Orderings_Obot__class_Obot(tc_fun(_1069443, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1069443, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069443, tc_HOL_Obool)), _1069445), _1069447)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069443), c_Big__Operators_Olattice__class_OSup__fin(_1069443, _1069445)), c_Big__Operators_Olattice__class_OSup__fin(_1069443, _1069447)))], (15394 ^ _782464) ^ [_1069920, _1069922] : [class_Lattices_Olattice(_1069920), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069920), _1069922)), -(_1069922 = c_Orderings_Obot__class_Obot(tc_fun(_1069920, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1069920), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069920), 15407 ^ [_1069920, _1069922]), 15408 ^ [_1069920, _1069922])), hAPP(hAPP(c_Set_Oinsert(_1069920), 15407 ^ [_1069920, _1069922]), hAPP(hAPP(c_Set_Oinsert(_1069920), 15408 ^ [_1069920, _1069922]), c_Orderings_Obot__class_Obot(tc_fun(_1069920, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1069920), c_Big__Operators_Olattice__class_OSup__fin(_1069920, _1069922)), _1069922)))], (15414 ^ _782464) ^ [_1070364, _1070366, _1070368] : [class_Lattices_Olattice(_1070364), hAPP(_1070366, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070364), 15419 ^ [_1070364, _1070366, _1070368]), 15420 ^ [_1070364, _1070366, _1070368])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070364), hAPP(_1070366, 15419 ^ [_1070364, _1070366, _1070368])), hAPP(_1070366, 15420 ^ [_1070364, _1070366, _1070368])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070364), _1070368)), -(_1070368 = c_Orderings_Obot__class_Obot(tc_fun(_1070364, tc_HOL_Obool))), -(hAPP(_1070366, c_Big__Operators_Olattice__class_OInf__fin(_1070364, _1070368)) = c_Big__Operators_Olattice__class_OInf__fin(_1070364, hAPP(c_Set_Oimage(_1070364, _1070364, _1070366), _1070368)))], (15434 ^ _782464) ^ [_1070767, _1070769, _1070771] : [class_Lattices_Olattice(_1070767), hAPP(_1070769, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070767), 15439 ^ [_1070767, _1070769, _1070771]), 15440 ^ [_1070767, _1070769, _1070771])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070767), hAPP(_1070769, 15439 ^ [_1070767, _1070769, _1070771])), hAPP(_1070769, 15440 ^ [_1070767, _1070769, _1070771])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070767), _1070771)), -(_1070771 = c_Orderings_Obot__class_Obot(tc_fun(_1070767, tc_HOL_Obool))), -(hAPP(_1070769, c_Big__Operators_Olattice__class_OSup__fin(_1070767, _1070771)) = c_Big__Operators_Olattice__class_OSup__fin(_1070767, hAPP(c_Set_Oimage(_1070767, _1070767, _1070769), _1070771)))], (15454 ^ _782464) ^ [_1071170, _1071172, _1071174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071170), _1071172)), hBOOL(hAPP(_1071174, _1071172)), 15465 ^ _782464 : [(15466 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1071170), 15464 ^ [_1071170, _1071172, _1071174])))], (15468 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071170), 15463 ^ [_1071170, _1071172, _1071174]), 15464 ^ [_1071170, _1071172, _1071174])))], (15470 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1071174, 15464 ^ [_1071170, _1071172, _1071174])))], (15472 ^ _782464) ^ [] : [hBOOL(hAPP(_1071174, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1071170, tc_HOL_Obool)), 15464 ^ [_1071170, _1071172, _1071174]), hAPP(hAPP(c_Set_Oinsert(_1071170), 15463 ^ [_1071170, _1071172, _1071174]), c_Orderings_Obot__class_Obot(tc_fun(_1071170, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1071174, c_Orderings_Obot__class_Obot(tc_fun(_1071170, tc_HOL_Obool)))))], (15476 ^ _782464) ^ [_1071695, _1071697, _1071699, _1071701, _1071703] : [c_Finite__Set_Ofolding__one__idem(_1071695, _1071697, _1071699), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071695), _1071701)), -(_1071701 = c_Orderings_Obot__class_Obot(tc_fun(_1071695, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071695), _1071703)), -(_1071703 = c_Orderings_Obot__class_Obot(tc_fun(_1071695, tc_HOL_Obool))), -(hAPP(_1071699, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071695, tc_HOL_Obool)), _1071701), _1071703)) = hAPP(hAPP(_1071697, hAPP(_1071699, _1071701)), hAPP(_1071699, _1071703)))], (15498 ^ _782464) ^ [_1072060, _1072062, _1072064, _1072066] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1072060), _1072062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072060, tc_HOL_Obool)), _1072062), _1072064)), hBOOL(hAPP(_1072066, c_Orderings_Obot__class_Obot(tc_fun(_1072060, tc_HOL_Obool)))), 15513 ^ _782464 : [(15514 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1072060), 15512 ^ [_1072060, _1072062, _1072064, _1072066])))], (15516 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072060), 15511 ^ [_1072060, _1072062, _1072064, _1072066]), _1072064)))], (15518 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1072060), 15511 ^ [_1072060, _1072062, _1072064, _1072066]), 15512 ^ [_1072060, _1072062, _1072064, _1072066]))], (15520 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1072066, 15512 ^ [_1072060, _1072062, _1072064, _1072066])))], (15522 ^ _782464) ^ [] : [hBOOL(hAPP(_1072066, hAPP(hAPP(c_Set_Oinsert(_1072060), 15511 ^ [_1072060, _1072062, _1072064, _1072066]), 15512 ^ [_1072060, _1072062, _1072064, _1072066])))]], -(hBOOL(hAPP(_1072066, _1072062)))], (15526 ^ _782464) ^ [_1072725, _1072727, _1072729, _1072731, _1072733] : [c_Finite__Set_Ofolding__one__idem(_1072725, _1072727, _1072729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1072725), _1072731)), -(_1072733 = c_Orderings_Obot__class_Obot(tc_fun(_1072725, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072725, tc_HOL_Obool)), _1072733), _1072731)), -(hAPP(hAPP(_1072727, hAPP(_1072729, _1072733)), hAPP(_1072729, _1072731)) = hAPP(_1072729, _1072731))], (15544 ^ _782464) ^ [_1073055, _1073057, _1073059, _1073061, _1073063] : [c_Finite__Set_Ofolding__one__idem(_1073055, _1073057, _1073059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073055), _1073061)), -(_1073061 = c_Orderings_Obot__class_Obot(tc_fun(_1073055, tc_HOL_Obool))), -(hAPP(_1073059, hAPP(hAPP(c_Set_Oinsert(_1073055), _1073063), _1073061)) = hAPP(hAPP(_1073057, _1073063), hAPP(_1073059, _1073061)))], (15558 ^ _782464) ^ [_1073271, _1073273, _1073275, _1073277] : [c_Finite__Set_Ofolding__one__idem(_1073271, _1073273, _1073275), -(hAPP(hAPP(_1073273, _1073277), _1073277) = _1073277)], (15564 ^ _782464) ^ [_1073366, _1073368, _1073370, _1073372, _1073374] : [c_Finite__Set_Ofolding__one__idem(_1073366, _1073368, _1073370), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073366), _1073372)), hBOOL(hAPP(hAPP(c_member(_1073366), _1073374), _1073372)), -(hAPP(hAPP(_1073368, _1073374), hAPP(_1073370, _1073372)) = hAPP(_1073370, _1073372))], (15578 ^ _782464) ^ [_1073613, _1073615, _1073617, _1073619] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073613), _1073615)), -(hAPP(c_Set_Oimage(_1073613, _1073617, _1073619), _1073615) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1073617, tc_HOL_Obool), _1073613, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073617, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1073613, tc_fun(_1073617, tc_HOL_Obool), tc_fun(_1073617, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1073617, tc_fun(tc_fun(_1073617, tc_HOL_Obool), tc_fun(_1073617, tc_HOL_Obool)), _1073613), c_Set_Oinsert(_1073617)), _1073619)), c_Orderings_Obot__class_Obot(tc_fun(_1073617, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1073617, tc_HOL_Obool))), _1073615))], (15584 ^ _782464) ^ [_1073852, _1073854, _1073856] : [class_Groups_Oab__semigroup__mult(_1073852), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073852), _1073854)), -(_1073854 = c_Orderings_Obot__class_Obot(tc_fun(_1073852, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073852), _1073856)), -(_1073856 = c_Orderings_Obot__class_Obot(tc_fun(_1073852, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073852, tc_HOL_Obool)), _1073854), _1073856) = c_Orderings_Obot__class_Obot(tc_fun(_1073852, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1073852, c_Groups_Otimes__class_Otimes(_1073852)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073852, tc_HOL_Obool)), _1073854), _1073856)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073852), hAPP(c_Finite__Set_Ofold1(_1073852, c_Groups_Otimes__class_Otimes(_1073852)), _1073854)), hAPP(c_Finite__Set_Ofold1(_1073852, c_Groups_Otimes__class_Otimes(_1073852)), _1073856)))], (15610 ^ _782464) ^ [_1074359, _1074361, _1074363, _1074365, _1074367] : [c_Finite__Set_Ofolding__one__idem(_1074359, _1074361, _1074363), hAPP(_1074365, hAPP(hAPP(_1074361, 15615 ^ [_1074359, _1074361, _1074363, _1074365, _1074367]), 15616 ^ [_1074359, _1074361, _1074363, _1074365, _1074367])) = hAPP(hAPP(_1074361, hAPP(_1074365, 15615 ^ [_1074359, _1074361, _1074363, _1074365, _1074367])), hAPP(_1074365, 15616 ^ [_1074359, _1074361, _1074363, _1074365, _1074367])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074359), _1074367)), -(_1074367 = c_Orderings_Obot__class_Obot(tc_fun(_1074359, tc_HOL_Obool))), -(hAPP(_1074365, hAPP(_1074363, _1074367)) = hAPP(_1074363, hAPP(c_Set_Oimage(_1074359, _1074359, _1074365), _1074367)))], (15630 ^ _782464) ^ [_1074794, _1074796, _1074798, _1074800, _1074802, _1074804, _1074806, _1074808] : [c_Finite__Set_Ofolding__image__simple(_1074794, _1074796, _1074798, _1074800, _1074802, _1074804), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074796), _1074806)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074796), _1074808)), 15644 ^ _782464 : [(15645 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1074796), 15643 ^ [_1074794, _1074796, _1074798, _1074800, _1074802, _1074804, _1074806, _1074808]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074796, tc_HOL_Obool)), _1074806), _1074808))))], (15647 ^ _782464) ^ [] : [hAPP(_1074802, 15643 ^ [_1074794, _1074796, _1074798, _1074800, _1074802, _1074804, _1074806, _1074808]) = _1074800]], -(hAPP(_1074804, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074796, tc_HOL_Obool)), _1074806), _1074808)) = hAPP(hAPP(_1074798, hAPP(_1074804, _1074806)), hAPP(_1074804, _1074808)))], (15651 ^ _782464) ^ [_1075295, _1075297, _1075299] : [class_Groups_Oab__semigroup__mult(_1075295), -(_1075297 = c_Orderings_Obot__class_Obot(tc_fun(_1075295, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075295), _1075297)), -(hBOOL(hAPP(hAPP(c_member(_1075295), _1075299), _1075297))), -(hAPP(c_Finite__Set_Ofold1(_1075295, c_Groups_Otimes__class_Otimes(_1075295)), hAPP(hAPP(c_Set_Oinsert(_1075295), _1075299), _1075297)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075295), _1075299), hAPP(c_Finite__Set_Ofold1(_1075295, c_Groups_Otimes__class_Otimes(_1075295)), _1075297)))], (15669 ^ _782464) ^ [_1075594, _1075596, _1075598, _1075600, _1075602, _1075604, _1075606] : [class_Groups_Oab__semigroup__mult(_1075594), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075596), _1075598)), c_Fun_Oinj__on(_1075596, _1075600, _1075602, _1075598), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075594, _1075600, c_Groups_Otimes__class_Otimes(_1075594)), _1075604), _1075606), hAPP(c_Set_Oimage(_1075596, _1075600, _1075602), _1075598)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075594, _1075596, c_Groups_Otimes__class_Otimes(_1075594)), hAPP(c_Fun_Ocomp(_1075600, _1075594, _1075596, _1075604), _1075602)), _1075606), _1075598))], (15683 ^ _782464) ^ [_1075905, _1075907, _1075909, _1075911] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075905), _1075907)), 15689 ^ _782464 : [(15690 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1075905), 15688 ^ [_1075905, _1075907, _1075909, _1075911]), _1075907)))], (15692 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075909), hAPP(_1075911, 15688 ^ [_1075905, _1075907, _1075909, _1075911])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075909), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1075905, tc_fun(_1075909, tc_HOL_Obool)), _1075907), _1075911))))], (15696 ^ _782464) ^ [_1076192, _1076194, _1076196, _1076198, _1076200] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076192, _1076194, _1076196), _1076198), _1076200), c_Orderings_Obot__class_Obot(tc_fun(_1076194, tc_HOL_Obool))) = _1076200)], (15698 ^ _782464) ^ [_1076241, _1076243, _1076245, _1076247] : [_1076241 = c_Finite__Set_Ofold1(_1076243, _1076245), -(hAPP(_1076241, hAPP(hAPP(c_Set_Oinsert(_1076243), _1076247), c_Orderings_Obot__class_Obot(tc_fun(_1076243, tc_HOL_Obool)))) = _1076247)], (15704 ^ _782464) ^ [_1076360, _1076362, _1076364] : [-(hAPP(c_Finite__Set_Ofold1(_1076360, _1076362), hAPP(hAPP(c_Set_Oinsert(_1076360), _1076364), c_Orderings_Obot__class_Obot(tc_fun(_1076360, tc_HOL_Obool)))) = _1076364)], (15706 ^ _782464) ^ [_1076406, _1076408, _1076410, _1076412, _1076414, _1076416, _1076418] : [c_Finite__Set_Ofolding__image__simple(_1076406, _1076408, _1076410, _1076412, _1076414, _1076416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076408), _1076418)), -(hAPP(_1076416, _1076418) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076406, _1076408, _1076410), _1076414), _1076412), _1076418))], (15716 ^ _782464) ^ [_1076603, _1076605, _1076607, _1076609, _1076611, _1076613, _1076615] : [c_Finite__Set_Ofolding__image(_1076603, _1076605, _1076607, _1076609, _1076611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076605), _1076613)), -(hAPP(hAPP(_1076611, _1076615), _1076613) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076603, _1076605, _1076607), _1076615), _1076609), _1076613))], (15726 ^ _782464) ^ [_1076804, _1076806, _1076808, _1076810] : [c_Finite__Set_Ofolding__one(_1076804, _1076806, _1076808), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076804), _1076810)), -(hAPP(_1076808, _1076810) = hAPP(c_Finite__Set_Ofold1(_1076804, _1076806), _1076810))], (15736 ^ _782464) ^ [_1076969, _1076971, _1076973] : [-(hAPP(c_Finite__Set_Ofold1(_1076969, _1076971), _1076973) = c_HOL_OThe(_1076969, c_Finite__Set_Ofold1Set(_1076969, _1076971, _1076973)))], (15738 ^ _782464) ^ [_1077009, _1077011] : [class_Lattices_Olattice(_1077009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077009), _1077011)), -(c_Big__Operators_Olattice__class_OSup__fin(_1077009, _1077011) = hAPP(c_Finite__Set_Ofold1(_1077009, c_Lattices_Osemilattice__sup__class_Osup(_1077009)), _1077011))], (15748 ^ _782464) ^ [_1077166, _1077168] : [class_Lattices_Olattice(_1077166), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077166), _1077168)), -(c_Big__Operators_Olattice__class_OInf__fin(_1077166, _1077168) = hAPP(c_Finite__Set_Ofold1(_1077166, c_Lattices_Osemilattice__inf__class_Oinf(_1077166)), _1077168))], (15758 ^ _782464) ^ [_1077323, _1077325, _1077327, _1077329, _1077331, _1077333] : [class_Groups_Oab__semigroup__mult(_1077323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077325), _1077327)), -(hBOOL(hAPP(hAPP(c_member(_1077325), _1077329), _1077327))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1077323, _1077325, c_Groups_Otimes__class_Otimes(_1077323)), _1077331), _1077333), hAPP(hAPP(c_Set_Oinsert(_1077325), _1077329), _1077327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077323), hAPP(_1077331, _1077329)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1077323, _1077325, c_Groups_Otimes__class_Otimes(_1077323)), _1077331), _1077333), _1077327)))], (15772 ^ _782464) ^ [_1077601, _1077603, _1077605] : [class_Lattices_Osemilattice__inf(_1077601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077601), _1077603)), hBOOL(hAPP(hAPP(c_member(_1077601), _1077605), _1077603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077601), hAPP(c_Finite__Set_Ofold1(_1077601, c_Lattices_Osemilattice__inf__class_Oinf(_1077601)), _1077603)), _1077605)))], (15786 ^ _782464) ^ [_1077838, _1077840, _1077842] : [class_Lattices_Osemilattice__inf(_1077838), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077838), _1077840)), -(_1077840 = c_Orderings_Obot__class_Obot(tc_fun(_1077838, tc_HOL_Obool))), 15797 ^ _782464 : [(15808 ^ _782464) ^ [] : [15810 ^ _782464 : [(15811 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1077838), 15809 ^ [_1077838, _1077840, _1077842]), _1077840)))], (15813 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077838), _1077842), 15809 ^ [_1077838, _1077840, _1077842]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077838), _1077842), hAPP(c_Finite__Set_Ofold1(_1077838, c_Lattices_Osemilattice__inf__class_Oinf(_1077838)), _1077840))))], (15798 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077838), _1077842), hAPP(c_Finite__Set_Ofold1(_1077838, c_Lattices_Osemilattice__inf__class_Oinf(_1077838)), _1077840))), 15801 ^ _782464 : [(15802 ^ _782464) ^ [_1078131] : [hBOOL(hAPP(hAPP(c_member(_1077838), _1078131), _1077840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077838), _1077842), _1078131)))]]]]], (15817 ^ _782464) ^ [_1078416, _1078418, _1078420] : [class_Lattices_Oab__semigroup__idem__mult(_1078416), -(_1078418 = c_Orderings_Obot__class_Obot(tc_fun(_1078416, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078416), _1078418)), -(hAPP(c_Finite__Set_Ofold1(_1078416, c_Groups_Otimes__class_Otimes(_1078416)), hAPP(hAPP(c_Set_Oinsert(_1078416), _1078420), _1078418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078416), _1078420), hAPP(c_Finite__Set_Ofold1(_1078416, c_Groups_Otimes__class_Otimes(_1078416)), _1078418)))], (15831 ^ _782464) ^ [_1078686, _1078688, _1078690] : [class_Lattices_Oab__semigroup__idem__mult(_1078686), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078686), _1078688)), -(_1078688 = c_Orderings_Obot__class_Obot(tc_fun(_1078686, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078686), _1078690)), -(_1078690 = c_Orderings_Obot__class_Obot(tc_fun(_1078686, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1078686, c_Groups_Otimes__class_Otimes(_1078686)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078686, tc_HOL_Obool)), _1078688), _1078690)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078686), hAPP(c_Finite__Set_Ofold1(_1078686, c_Groups_Otimes__class_Otimes(_1078686)), _1078688)), hAPP(c_Finite__Set_Ofold1(_1078686, c_Groups_Otimes__class_Otimes(_1078686)), _1078690)))], (15853 ^ _782464) ^ [_1079065, _1079067, _1079069, _1079071] : [c_Big__Operators_Osemilattice__big(_1079065, _1079067, _1079069), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079065), _1079071)), -(hAPP(_1079069, _1079071) = hAPP(c_Finite__Set_Ofold1(_1079065, _1079067), _1079071))], (15863 ^ _782464) ^ [_1079230, _1079232, _1079234, _1079236, _1079238, _1079240, _1079242] : [c_Big__Operators_Ocomm__monoid__big(_1079230, _1079232, _1079234, _1079236, _1079238), 15866 ^ _782464 : [(15867 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1079232), _1079240)), -(hAPP(hAPP(_1079238, _1079242), _1079240) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1079230, _1079232, _1079234), _1079242), _1079236), _1079240))], (15873 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1079232), _1079240))), -(hAPP(hAPP(_1079238, _1079242), _1079240) = _1079236)]]], (15879 ^ _782464) ^ [_1079498, _1079500] : [class_Groups_Oab__semigroup__mult(_1079498), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079498), _1079500)), -(_1079500 = c_Orderings_Obot__class_Obot(tc_fun(_1079498, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1079498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079498), 15892 ^ [_1079498, _1079500]), 15893 ^ [_1079498, _1079500])), hAPP(hAPP(c_Set_Oinsert(_1079498), 15892 ^ [_1079498, _1079500]), hAPP(hAPP(c_Set_Oinsert(_1079498), 15893 ^ [_1079498, _1079500]), c_Orderings_Obot__class_Obot(tc_fun(_1079498, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1079498), hAPP(c_Finite__Set_Ofold1(_1079498, c_Groups_Otimes__class_Otimes(_1079498)), _1079500)), _1079500)))], (15899 ^ _782464) ^ [_1079952, _1079954, _1079956] : [class_Lattices_Oab__semigroup__idem__mult(_1079952), hAPP(_1079954, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079952), 15904 ^ [_1079952, _1079954, _1079956]), 15905 ^ [_1079952, _1079954, _1079956])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079952), hAPP(_1079954, 15904 ^ [_1079952, _1079954, _1079956])), hAPP(_1079954, 15905 ^ [_1079952, _1079954, _1079956])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079952), _1079956)), -(_1079956 = c_Orderings_Obot__class_Obot(tc_fun(_1079952, tc_HOL_Obool))), -(hAPP(_1079954, hAPP(c_Finite__Set_Ofold1(_1079952, c_Groups_Otimes__class_Otimes(_1079952)), _1079956)) = hAPP(c_Finite__Set_Ofold1(_1079952, c_Groups_Otimes__class_Otimes(_1079952)), hAPP(c_Set_Oimage(_1079952, _1079952, _1079954), _1079956)))], (15919 ^ _782464) ^ [_1080375, _1080377, _1080379, _1080381, _1080383] : [class_Groups_Ocomm__monoid__mult(_1080375), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080377), _1080379)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080377), _1080381)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1080377, tc_HOL_Obool)), _1080379), _1080381) = c_Orderings_Obot__class_Obot(tc_fun(_1080377, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080375, _1080377, c_Groups_Otimes__class_Otimes(_1080375)), _1080383), c_Groups_Oone__class_Oone(_1080375)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080377, tc_HOL_Obool)), _1080379), _1080381)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080375), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080375, _1080377, c_Groups_Otimes__class_Otimes(_1080375)), _1080383), c_Groups_Oone__class_Oone(_1080375)), _1080379)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080375, _1080377, c_Groups_Otimes__class_Otimes(_1080375)), _1080383), c_Groups_Oone__class_Oone(_1080375)), _1080381)))], (15937 ^ _782464) ^ [_1080818, _1080820, _1080822, _1080824, _1080826] : [class_Groups_Oab__group__add(_1080818), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080820), _1080822)), 15944 ^ _782464 : [(15945 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1080820), _1080824), _1080822)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080820, _1080818), _1080826), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080820, tc_HOL_Obool)), _1080822), hAPP(hAPP(c_Set_Oinsert(_1080820), _1080824), c_Orderings_Obot__class_Obot(tc_fun(_1080820, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080818), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080820, _1080818), _1080826), _1080822)), hAPP(_1080826, _1080824)))], (15951 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1080820), _1080824), _1080822))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080820, _1080818), _1080826), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080820, tc_HOL_Obool)), _1080822), hAPP(hAPP(c_Set_Oinsert(_1080820), _1080824), c_Orderings_Obot__class_Obot(tc_fun(_1080820, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080820, _1080818), _1080826), _1080822))]]], (15957 ^ _782464) ^ [_1081288, _1081290, _1081292, _1081294, _1081296] : [class_Rings_Oring(_1081288), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081290), _1081292)), hBOOL(hAPP(hAPP(c_member(_1081290), _1081294), _1081292)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081290, _1081288), _1081296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1081290, tc_HOL_Obool)), _1081292), hAPP(hAPP(c_Set_Oinsert(_1081290), _1081294), c_Orderings_Obot__class_Obot(tc_fun(_1081290, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1081288), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081290, _1081288), _1081296), _1081292)), hAPP(_1081296, _1081294)))], (15971 ^ _782464) ^ [_1081613, _1081615] : [class_Groups_Oone(_1081613), 15974 ^ _782464 : [(15975 ^ _782464) ^ [] : [c_Groups_Oone__class_Oone(_1081613) = _1081615, -(_1081615 = c_Groups_Oone__class_Oone(_1081613))], (15981 ^ _782464) ^ [] : [_1081615 = c_Groups_Oone__class_Oone(_1081613), -(c_Groups_Oone__class_Oone(_1081613) = _1081615)]]], (15987 ^ _782464) ^ [_1081830, _1081832, _1081834, _1081836, _1081838, _1081840] : [class_Groups_Ocomm__monoid__add(_1081830), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081832, _1081830), hAPP(hAPP(c_COMBC(_1081832, tc_fun(_1081834, tc_HOL_Obool), _1081830), hAPP(hAPP(c_COMBB(tc_fun(_1081834, _1081830), tc_fun(tc_fun(_1081834, tc_HOL_Obool), _1081830), _1081832), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081834, _1081830)), _1081836)), _1081838)), _1081840) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081834, _1081830), hAPP(hAPP(c_COMBC(_1081834, tc_fun(_1081832, tc_HOL_Obool), _1081830), hAPP(hAPP(c_COMBB(tc_fun(_1081832, _1081830), tc_fun(tc_fun(_1081832, tc_HOL_Obool), _1081830), _1081834), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081832, _1081830)), hAPP(c_COMBC(_1081832, _1081834, _1081830), _1081836))), _1081840)), _1081838))], (15993 ^ _782464) ^ [_1082103, _1082105, _1082107, _1082109, _1082111] : [class_Groups_Oab__group__add(_1082103), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082105), _1082107)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082107), _1082109)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082103), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082103), _1082111), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082105), _1082109))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082103), _1082111), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082105), _1082107))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082103), _1082111), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082107), _1082109)))], (16007 ^ _782464) ^ [_1082426, _1082428] : [class_Groups_Omonoid__mult(_1082426), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082426), c_Groups_Oone__class_Oone(_1082426)), _1082428) = _1082428)], (16013 ^ _782464) ^ [_1082521, _1082523] : [class_Groups_Ocomm__monoid__mult(_1082521), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082521), c_Groups_Oone__class_Oone(_1082521)), _1082523) = _1082523)], (16019 ^ _782464) ^ [_1082616, _1082618] : [class_Groups_Omonoid__mult(_1082616), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082616), _1082618), c_Groups_Oone__class_Oone(_1082616)) = _1082618)], (16025 ^ _782464) ^ [_1082711, _1082713] : [class_Groups_Ocomm__monoid__mult(_1082711), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082711), _1082713), c_Groups_Oone__class_Oone(_1082711)) = _1082713)], (16031 ^ _782464) ^ [_1082806, _1082808, _1082810, _1082812, _1082814] : [class_Rings_Osemiring__0(_1082806), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082806), _1082808), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082810, _1082806), _1082812), _1082814)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082810, _1082806), hAPP(hAPP(c_COMBB(_1082806, _1082806, _1082810), hAPP(c_Groups_Otimes__class_Otimes(_1082806), _1082808)), _1082812)), _1082814))], (16037 ^ _782464) ^ [_1082969, _1082971, _1082973, _1082975, _1082977] : [class_Rings_Osemiring__0(_1082969), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082969), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082971, _1082969), _1082973), _1082975)), _1082977) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082971, _1082969), hAPP(hAPP(c_COMBC(_1082971, _1082969, _1082969), hAPP(hAPP(c_COMBB(_1082969, tc_fun(_1082969, _1082969), _1082971), c_Groups_Otimes__class_Otimes(_1082969)), _1082973)), _1082977)), _1082975))], (16043 ^ _782464) ^ [_1083152, _1083154, _1083156, _1083158, _1083160, _1083162, _1083164] : [class_Rings_Osemiring__0(_1083152), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083152), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083154, _1083152), _1083156), _1083158)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083160, _1083152), _1083162), _1083164)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083154, _1083152), hAPP(hAPP(c_COMBC(_1083154, tc_fun(_1083160, tc_HOL_Obool), _1083152), hAPP(hAPP(c_COMBB(tc_fun(_1083160, _1083152), tc_fun(tc_fun(_1083160, tc_HOL_Obool), _1083152), _1083154), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083160, _1083152)), hAPP(hAPP(c_COMBC(_1083154, tc_fun(_1083160, _1083152), tc_fun(_1083160, _1083152)), hAPP(hAPP(c_COMBB(tc_fun(_1083152, _1083152), tc_fun(tc_fun(_1083160, _1083152), tc_fun(_1083160, _1083152)), _1083154), c_COMBB(_1083152, _1083152, _1083160)), hAPP(hAPP(c_COMBB(_1083152, tc_fun(_1083152, _1083152), _1083154), c_Groups_Otimes__class_Otimes(_1083152)), _1083156))), _1083162))), _1083164)), _1083158))], (16049 ^ _782464) ^ [_1083491, _1083493, _1083495, _1083497, _1083499] : [class_Groups_Oab__group__add(_1083491), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083493, _1083491), hAPP(hAPP(c_COMBS(_1083493, _1083491, _1083491), hAPP(hAPP(c_COMBB(_1083491, tc_fun(_1083491, _1083491), _1083493), c_Groups_Ominus__class_Ominus(_1083491)), _1083495)), _1083497)), _1083499) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083491), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083493, _1083491), _1083495), _1083499)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083493, _1083491), _1083497), _1083499)))], (16055 ^ _782464) ^ [_1083692, _1083694, _1083696, _1083698] : [class_Groups_Oab__group__add(_1083692), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083694, _1083692), hAPP(hAPP(c_COMBB(_1083692, _1083692, _1083694), c_Groups_Ouminus__class_Ouminus(_1083692)), _1083696)), _1083698) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083692), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083694, _1083692), _1083696), _1083698)))], (16061 ^ _782464) ^ [_1083841, _1083843, _1083845] : [class_Rings_Olinordered__semidom(_1083841), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083841), c_Groups_Oone__class_Oone(_1083841)), _1083843)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083841), c_Groups_Oone__class_Oone(_1083841)), _1083845)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083841), c_Groups_Oone__class_Oone(_1083841)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083841), _1083843), _1083845))))], (16075 ^ _782464) ^ [_1084096, _1084098] : [class_Rings_Oring__1__no__zero__divisors(_1084096), 16078 ^ _782464 : [(16089 ^ _782464) ^ [] : [16090 ^ _782464 : [(16091 ^ _782464) ^ [] : [_1084098 = c_Groups_Oone__class_Oone(_1084096)], (16093 ^ _782464) ^ [] : [_1084098 = hAPP(c_Groups_Ouminus__class_Ouminus(_1084096), c_Groups_Oone__class_Oone(_1084096))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084096), _1084098), _1084098) = c_Groups_Oone__class_Oone(_1084096))], (16079 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084096), _1084098), _1084098) = c_Groups_Oone__class_Oone(_1084096), -(_1084098 = c_Groups_Oone__class_Oone(_1084096)), -(_1084098 = hAPP(c_Groups_Ouminus__class_Ouminus(_1084096), c_Groups_Oone__class_Oone(_1084096)))]]], (16097 ^ _782464) ^ [_1084403, _1084405, _1084407, _1084409] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084403), _1084405)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084403, tc_HOL_Obool)), _1084405), _1084407)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084403, tc_Nat_Onat), _1084409), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084403, tc_HOL_Obool)), _1084407), _1084405)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084403, tc_Nat_Onat), _1084409), _1084407)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084403, tc_Nat_Onat), _1084409), _1084405)))], (16107 ^ _782464) ^ [_1084656, _1084658, _1084660, _1084662, _1084664, _1084666] : [class_Groups_Ocomm__monoid__add(_1084656), c_Fun_Oinj__on(_1084658, _1084660, _1084662, _1084664), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084660, _1084656), _1084666), hAPP(c_Set_Oimage(_1084658, _1084660, _1084662), _1084664)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084658, _1084656), hAPP(c_Fun_Ocomp(_1084660, _1084656, _1084658, _1084666), _1084662)), _1084664))], (16117 ^ _782464) ^ [_1084869, _1084871, _1084873, _1084875, _1084877] : [class_Groups_Ocomm__monoid__mult(_1084869), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084871), _1084873)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084869, _1084871, c_Groups_Otimes__class_Otimes(_1084869)), hAPP(hAPP(c_COMBS(_1084871, _1084869, _1084869), hAPP(hAPP(c_COMBB(_1084869, tc_fun(_1084869, _1084869), _1084871), c_Groups_Otimes__class_Otimes(_1084869)), _1084875)), _1084877)), c_Groups_Oone__class_Oone(_1084869)), _1084873) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084869), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084869, _1084871, c_Groups_Otimes__class_Otimes(_1084869)), _1084875), c_Groups_Oone__class_Oone(_1084869)), _1084873)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084869, _1084871, c_Groups_Otimes__class_Otimes(_1084869)), _1084877), c_Groups_Oone__class_Oone(_1084869)), _1084873)))], (16127 ^ _782464) ^ [_1085199, _1085201, _1085203, _1085205] : [hBOOL(hAPP(hAPP(c_member(_1085199), _1085201), _1085203)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085199, tc_Nat_Onat), _1085205), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085199, tc_HOL_Obool)), _1085203), hAPP(hAPP(c_Set_Oinsert(_1085199), _1085201), c_Orderings_Obot__class_Obot(tc_fun(_1085199, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085199, tc_Nat_Onat), _1085205), _1085203)), hAPP(_1085205, _1085201)))], (16133 ^ _782464) ^ [_1085390, _1085392, _1085394, _1085396] : [-(hBOOL(hAPP(hAPP(c_member(_1085390), _1085392), _1085394))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085390, tc_Nat_Onat), _1085396), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085390, tc_HOL_Obool)), _1085394), hAPP(hAPP(c_Set_Oinsert(_1085390), _1085392), c_Orderings_Obot__class_Obot(tc_fun(_1085390, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085390, tc_Nat_Onat), _1085396), _1085394))], (16139 ^ _782464) ^ [_1085481, _1085483, _1085485, _1085487, _1085489] : [class_Groups_Oab__group__add(_1085481), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085483), _1085485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1085483, tc_HOL_Obool)), _1085487), _1085485)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085483, _1085481), _1085489), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085483, tc_HOL_Obool)), _1085485), _1085487)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085481), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085483, _1085481), _1085489), _1085485)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085483, _1085481), _1085489), _1085487)))], (16153 ^ _782464) ^ [_1085798, _1085800, _1085802, _1085804, _1085806] : [class_Groups_Ocomm__monoid__add(_1085798), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085800), _1085802)), c_Fun_Oinj__on(_1085800, _1085800, _1085804, _1085802), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085800, _1085798), _1085806), hAPP(c_Set_Oimage(_1085800, _1085800, _1085804), _1085802)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085800, _1085798), hAPP(c_Fun_Ocomp(_1085800, _1085798, _1085800, _1085806), _1085804)), _1085802))], (16167 ^ _782464) ^ [_1086073, _1086075, _1086077, _1086079, _1086081, _1086083, _1086085] : [c_Big__Operators_Ocomm__monoid__big(_1086073, _1086075, _1086077, _1086079, _1086081), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1086075), _1086083))), -(hAPP(hAPP(_1086081, _1086085), _1086083) = _1086079)], (16177 ^ _782464) ^ [_1086201, _1086203, _1086205, _1086207, _1086209] : [class_Groups_Ocomm__monoid__mult(_1086201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086203), _1086205)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086203), _1086207)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086201), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086201, _1086203, c_Groups_Otimes__class_Otimes(_1086201)), _1086209), c_Groups_Oone__class_Oone(_1086201)), _1086205)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086201, _1086203, c_Groups_Otimes__class_Otimes(_1086201)), _1086209), c_Groups_Oone__class_Oone(_1086201)), _1086207)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086201), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086201, _1086203, c_Groups_Otimes__class_Otimes(_1086201)), _1086209), c_Groups_Oone__class_Oone(_1086201)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086203, tc_HOL_Obool)), _1086205), _1086207))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086201, _1086203, c_Groups_Otimes__class_Otimes(_1086201)), _1086209), c_Groups_Oone__class_Oone(_1086201)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086203, tc_HOL_Obool)), _1086205), _1086207))))], (16191 ^ _782464) ^ [_1086626, _1086628] : [class_Rings_Ocomm__ring__1(_1086626), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1086626), _1086628) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086626), hAPP(c_Groups_Ouminus__class_Ouminus(_1086626), c_Groups_Oone__class_Oone(_1086626))), _1086628))], (16197 ^ _782464) ^ [_1086741, _1086743, _1086745, _1086747, _1086749] : [class_Groups_Ocomm__monoid__mult(_1086741), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086743), _1086745)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086743), _1086747)), 16211 ^ _782464 : [(16212 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1086743), 16210 ^ [_1086741, _1086743, _1086745, _1086747, _1086749]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086743, tc_HOL_Obool)), _1086745), _1086747))))], (16214 ^ _782464) ^ [] : [hAPP(_1086749, 16210 ^ [_1086741, _1086743, _1086745, _1086747, _1086749]) = c_Groups_Oone__class_Oone(_1086741)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086741, _1086743, c_Groups_Otimes__class_Otimes(_1086741)), _1086749), c_Groups_Oone__class_Oone(_1086741)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086743, tc_HOL_Obool)), _1086745), _1086747)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086741), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086741, _1086743, c_Groups_Otimes__class_Otimes(_1086741)), _1086749), c_Groups_Oone__class_Oone(_1086741)), _1086745)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086741, _1086743, c_Groups_Otimes__class_Otimes(_1086741)), _1086749), c_Groups_Oone__class_Oone(_1086741)), _1086747)))], (16218 ^ _782464) ^ [_1087284, _1087286] : [class_Rings_Ocomm__semiring__1(_1087284), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087284), c_Groups_Oone__class_Oone(_1087284)), _1087286) = _1087286)], (16224 ^ _782464) ^ [_1087379, _1087381] : [class_Rings_Ocomm__semiring__1(_1087379), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087379), _1087381), c_Groups_Oone__class_Oone(_1087379)) = _1087381)], (16230 ^ _782464) ^ [_1087474, _1087476, _1087478, _1087480, _1087482] : [class_Groups_Ocomm__monoid__add(_1087474), class_Groups_Oordered__cancel__ab__semigroup__add(_1087474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087476), _1087478)), -(_1087478 = c_Orderings_Obot__class_Obot(tc_fun(_1087476, tc_HOL_Obool))), 16248 ^ _782464 : [(16249 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087476), 16247 ^ [_1087474, _1087476, _1087478, _1087480, _1087482]), _1087478)))], (16251 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087474), hAPP(_1087480, 16247 ^ [_1087474, _1087476, _1087478, _1087480, _1087482])), hAPP(_1087482, 16247 ^ [_1087474, _1087476, _1087478, _1087480, _1087482])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087474), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087476, _1087474), _1087480), _1087478)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087476, _1087474), _1087482), _1087478))))], (16255 ^ _782464) ^ [_1088005, _1088007, _1088009, _1088011, _1088013] : [class_Groups_Ocomm__monoid__add(_1088005), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088007), _1088009)), hBOOL(hAPP(hAPP(c_member(_1088007), _1088011), _1088009)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088007, _1088005), _1088013), _1088009) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088005), hAPP(_1088013, _1088011)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088007, _1088005), _1088013), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088007, tc_HOL_Obool)), _1088009), hAPP(hAPP(c_Set_Oinsert(_1088007), _1088011), c_Orderings_Obot__class_Obot(tc_fun(_1088007, tc_HOL_Obool)))))))], (16269 ^ _782464) ^ [_1088330, _1088332, _1088334, _1088336, _1088338] : [class_Groups_Ocomm__monoid__add(_1088330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088332), _1088334)), hBOOL(hAPP(hAPP(c_member(_1088332), _1088336), _1088334)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088332, _1088330), _1088338), _1088334) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088330), hAPP(_1088338, _1088336)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088332, _1088330), _1088338), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088332, tc_HOL_Obool)), _1088334), hAPP(hAPP(c_Set_Oinsert(_1088332), _1088336), c_Orderings_Obot__class_Obot(tc_fun(_1088332, tc_HOL_Obool)))))))], (16283 ^ _782464) ^ [_1088655, _1088657] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088655), _1088657))))], (16285 ^ _782464) ^ [_1088688, _1088690, _1088692, _1088694, _1088696] : [class_Groups_Ocomm__monoid__add(_1088688), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088690), _1088692)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088692), _1088694)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088688), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088688), _1088696), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088690), _1088692))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088688), _1088696), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088692), _1088694))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088688), _1088696), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088690), _1088694)))], (16299 ^ _782464) ^ [_1089011, _1089013, _1089015, _1089017, _1089019] : [class_Groups_Ocomm__monoid__add(_1089011), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089013), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089015), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089011), _1089017), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089013, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089015), _1089019))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089011), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089011), _1089017), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089013, _1089015))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089011), _1089017), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089015), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089015), _1089019)))))], (16309 ^ _782464) ^ [_1089302, _1089304, _1089306, _1089308, _1089310] : [class_Groups_Ocomm__monoid__add(_1089302), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089302), _1089304), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089306), _1089308)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089310), _1089308))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089302), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1089302, tc_Nat_Onat), _1089304), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1089308))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1089306), _1089310)))], (16315 ^ _782464) ^ [_1089493, _1089495, _1089497, _1089499, _1089501] : [class_Groups_Ocomm__monoid__add(_1089493), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089493), _1089495), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089497), _1089499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089501), _1089499))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089493), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1089493, tc_Nat_Onat), _1089495), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1089499))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089497, _1089501)))], (16321 ^ _782464) ^ [_1089676, _1089678, _1089680, _1089682] : [class_Groups_Ocomm__monoid__add(_1089676), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089678), _1089680)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089676), _1089682), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089678, _1089680)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089676), hAPP(_1089682, _1089678)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089676), _1089682), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1089678, _1089680))))], (16342 ^ _782464) ^ [_1090094] : [16344 ^ _782464 : [(16345 ^ _782464) ^ [_1090170] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 16343 ^ [_1090094, _1090170]), _1090094)))], (16347 ^ _782464) ^ [_1090204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 16343 ^ [_1090094, _1090204]), _1090204))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1090094)))], (16331 ^ _782464) ^ [_1089907] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1089907)), 16335 ^ _782464 : [(16336 ^ _782464) ^ [_1089987] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1089987), _1089907)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089987), 16334 ^ [_1089907])))]]], (16351 ^ _782464) ^ [_1090273, _1090275, _1090277, _1090279, _1090281] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1090273), 16354 ^ _782464 : [(16365 ^ _782464) ^ [] : [16366 ^ _782464 : [(16367 ^ _782464) ^ [] : [_1090275 = _1090279], (16369 ^ _782464) ^ [] : [_1090277 = _1090281]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090275), _1090277)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090279), _1090281)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090275), _1090281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090279), _1090277)))], (16355 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090275), _1090277)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090279), _1090281)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090273), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090275), _1090281)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090273), _1090279), _1090277)), -(_1090275 = _1090279), -(_1090277 = _1090281)]]], (16373 ^ _782464) ^ [_1090685, _1090687, _1090689, _1090691] : [class_Rings_Ocomm__semiring__1(_1090685), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090685), _1090687), _1090689)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090685), _1090691), _1090689)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090685), _1090687), _1090691)), _1090689))], (16379 ^ _782464) ^ [_1090844, _1090846, _1090848, _1090850] : [class_Rings_Ocomm__semiring__1(_1090844), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090844), _1090846), _1090848)), _1090850) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090844), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090844), _1090846), _1090850)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090844), _1090848), _1090850)))], (16385 ^ _782464) ^ [_1091003, _1091005, _1091007, _1091009, _1091011] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1091003), 16388 ^ _782464 : [(16399 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091005), _1091009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091007), _1091011)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091005), _1091011)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091007), _1091009))), 16402 ^ _782464 : [(16403 ^ _782464) ^ [] : [_1091005 = _1091007], (16405 ^ _782464) ^ [] : [_1091009 = _1091011]]], (16389 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091005), _1091009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091007), _1091011)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091005), _1091011)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091003), _1091007), _1091009)), -(_1091005 = _1091007), -(_1091009 = _1091011)]]], (16407 ^ _782464) ^ [_1091421, _1091423, _1091425, _1091427] : [class_Rings_Ocomm__semiring__1(_1091421), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091421), _1091423), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091421), _1091425), _1091427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091421), _1091423), _1091425)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091421), _1091423), _1091427)))], (16413 ^ _782464) ^ [_1091580, _1091582, _1091584] : [-(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)), _1091580)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091582), _1091584)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091582), _1091580)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091584), _1091580)))], (16415 ^ _782464) ^ [_1091641, _1091643, _1091645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091641), _1091643)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091641), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091643), _1091645)) = 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, _1091641), _1091643)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091643), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091643), _1091645))))], (16421 ^ _782464) ^ [_1091802, _1091804, _1091806, _1091808] : [class_Groups_Ocancel__semigroup__add(_1091802), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091802), _1091804), _1091806) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091802), _1091808), _1091806), -(_1091804 = _1091808)], (16431 ^ _782464) ^ [_1091969, _1091971, _1091973, _1091975] : [class_Groups_Ocancel__ab__semigroup__add(_1091969), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091969), _1091971), _1091973) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091969), _1091971), _1091975), -(_1091973 = _1091975)], (16441 ^ _782464) ^ [_1092136, _1092138, _1092140, _1092142] : [class_Groups_Ocancel__semigroup__add(_1092136), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092136), _1092138), _1092140) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092136), _1092138), _1092142), -(_1092140 = _1092142)], (16451 ^ _782464) ^ [_1092303, _1092305, _1092307, _1092309] : [class_Groups_Ocancel__semigroup__add(_1092303), 16454 ^ _782464 : [(16455 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092303), _1092305), _1092307) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092303), _1092309), _1092307), -(_1092305 = _1092309)], (16461 ^ _782464) ^ [] : [_1092305 = _1092309, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092303), _1092305), _1092307) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092303), _1092309), _1092307))]]], (16467 ^ _782464) ^ [_1092568, _1092570, _1092572, _1092574] : [class_Groups_Ocancel__semigroup__add(_1092568), 16470 ^ _782464 : [(16471 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092568), _1092570), _1092572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092568), _1092570), _1092574), -(_1092572 = _1092574)], (16477 ^ _782464) ^ [] : [_1092572 = _1092574, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092568), _1092570), _1092572) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092568), _1092570), _1092574))]]], (16483 ^ _782464) ^ [_1092833, _1092835, _1092837, _1092839] : [class_Groups_Oab__semigroup__add(_1092833), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092833), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092833), _1092835), _1092837)), _1092839) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092833), _1092835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092833), _1092837), _1092839)))], (16489 ^ _782464) ^ [_1092976, _1092978, _1092980] : [class_Rings_Ocomm__semiring__1(_1092976), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092976), _1092978), _1092980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092976), _1092980), _1092978))], (16495 ^ _782464) ^ [_1093085, _1093087, _1093089, _1093091] : [class_Rings_Ocomm__semiring__1(_1093085), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093085), _1093087), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093085), _1093089), _1093091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093085), _1093089), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093085), _1093087), _1093091)))], (16501 ^ _782464) ^ [_1093228, _1093230, _1093232, _1093234] : [class_Rings_Ocomm__semiring__1(_1093228), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093228), _1093230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093228), _1093232), _1093234)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093228), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093228), _1093230), _1093232)), _1093234))], (16507 ^ _782464) ^ [_1093371, _1093373, _1093375, _1093377] : [class_Rings_Ocomm__semiring__1(_1093371), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093371), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093371), _1093373), _1093375)), _1093377) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093371), _1093373), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093371), _1093375), _1093377)))], (16513 ^ _782464) ^ [_1093514, _1093516, _1093518, _1093520] : [class_Rings_Ocomm__semiring__1(_1093514), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093514), _1093516), _1093518)), _1093520) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093514), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093514), _1093516), _1093520)), _1093518))], (16519 ^ _782464) ^ [_1093657, _1093659, _1093661, _1093663, _1093665] : [class_Rings_Ocomm__semiring__1(_1093657), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093657), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093657), _1093659), _1093661)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093657), _1093663), _1093665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093657), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093657), _1093659), _1093663)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093657), _1093661), _1093665)))], (16525 ^ _782464) ^ [_1093834, _1093836, _1093838, _1093840] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1093834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093834), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093834), _1093836), _1093838)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093834), _1093836), _1093840))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093834), _1093838), _1093840)))], (16535 ^ _782464) ^ [_1094029, _1094031, _1094033, _1094035] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1094029), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094029), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094029), _1094031), _1094033)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094029), _1094035), _1094033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094029), _1094031), _1094035)))], (16545 ^ _782464) ^ [_1094224, _1094226, _1094228, _1094230, _1094232] : [class_Groups_Oordered__ab__semigroup__add(_1094224), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094224), _1094226), _1094228)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094224), _1094230), _1094232)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094224), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094224), _1094226), _1094230)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094224), _1094228), _1094232))))], (16559 ^ _782464) ^ [_1094495, _1094497, _1094499, _1094501] : [class_Groups_Oordered__ab__semigroup__add(_1094495), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094495), _1094497), _1094499)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094495), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094495), _1094501), _1094497)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094495), _1094501), _1094499))))], (16569 ^ _782464) ^ [_1094690, _1094692, _1094694, _1094696] : [class_Groups_Oordered__ab__semigroup__add(_1094690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094690), _1094692), _1094694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094690), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094690), _1094692), _1094696)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094690), _1094694), _1094696))))], (16579 ^ _782464) ^ [_1094885, _1094887, _1094889, _1094891] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1094885), 16582 ^ _782464 : [(16583 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094885), _1094887), _1094889)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094885), _1094887), _1094891))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094885), _1094889), _1094891)))], (16589 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094885), _1094889), _1094891)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094885), _1094887), _1094889)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094885), _1094887), _1094891))))]]], (16595 ^ _782464) ^ [_1095192, _1095194, _1095196, _1095198] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095192), 16598 ^ _782464 : [(16599 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095192), _1095194), _1095196)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095192), _1095198), _1095196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095192), _1095194), _1095198)))], (16605 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095192), _1095194), _1095198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095192), _1095194), _1095196)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095192), _1095198), _1095196))))]]], (16611 ^ _782464) ^ [_1095499, _1095501, _1095503, _1095505] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095499), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095499), _1095501), _1095503)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095499), _1095501), _1095505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095499), _1095503), _1095505)))], (16621 ^ _782464) ^ [_1095694, _1095696, _1095698, _1095700] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095694), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095694), _1095696), _1095698)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095694), _1095700), _1095698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095694), _1095696), _1095700)))], (16631 ^ _782464) ^ [_1095889, _1095891, _1095893, _1095895, _1095897] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1095889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095889), _1095891), _1095893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095889), _1095895), _1095897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095889), _1095891), _1095895)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095889), _1095893), _1095897))))], (16645 ^ _782464) ^ [_1096160, _1096162, _1096164, _1096166] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1096160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096160), _1096162), _1096164)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096160), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096160), _1096166), _1096162)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096160), _1096166), _1096164))))], (16655 ^ _782464) ^ [_1096355, _1096357, _1096359, _1096361] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1096355), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096355), _1096357), _1096359)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096355), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096355), _1096357), _1096361)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096355), _1096359), _1096361))))], (16665 ^ _782464) ^ [_1096550, _1096552, _1096554, _1096556] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1096550), 16668 ^ _782464 : [(16669 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096550), _1096552), _1096554)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096550), _1096552), _1096556))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096550), _1096554), _1096556)))], (16675 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096550), _1096554), _1096556)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096550), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096550), _1096552), _1096554)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096550), _1096552), _1096556))))]]], (16681 ^ _782464) ^ [_1096857, _1096859, _1096861, _1096863] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1096857), 16684 ^ _782464 : [(16685 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096857), _1096859), _1096861)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096857), _1096863), _1096861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096857), _1096859), _1096863)))], (16691 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096857), _1096859), _1096863)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096857), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096857), _1096859), _1096861)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096857), _1096863), _1096861))))]]], (16697 ^ _782464) ^ [_1097164, _1097166, _1097168, _1097170, _1097172] : [class_Rings_Osemiring(_1097164), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097164), _1097166), _1097168)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097164), _1097170), _1097168)), _1097172)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097164), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097164), _1097166), _1097170)), _1097168)), _1097172))], (16703 ^ _782464) ^ [_1097357, _1097359, _1097361, _1097363] : [class_Rings_Ocomm__semiring(_1097357), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097357), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097357), _1097359), _1097361)), _1097363) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097357), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097357), _1097359), _1097363)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097357), _1097361), _1097363)))], (16709 ^ _782464) ^ [_1097516, _1097518, _1097520] : [class_Groups_Ogroup__add(_1097516), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097516), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097516), _1097518), _1097520)), _1097520) = _1097518)], (16715 ^ _782464) ^ [_1097625, _1097627, _1097629] : [class_Groups_Ogroup__add(_1097625), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097625), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097625), _1097627), _1097629)), _1097629) = _1097627)], (16721 ^ _782464) ^ [_1097734, _1097736, _1097738] : [class_Groups_Oab__group__add(_1097734), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097734), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097734), _1097736), _1097738)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097734), hAPP(c_Groups_Ouminus__class_Ouminus(_1097734), _1097736)), hAPP(c_Groups_Ouminus__class_Ouminus(_1097734), _1097738)))], (16727 ^ _782464) ^ [_1097873, _1097875, _1097877] : [class_Groups_Ogroup__add(_1097873), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097873), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097873), _1097875), _1097877)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097873), hAPP(c_Groups_Ouminus__class_Ouminus(_1097873), _1097877)), hAPP(c_Groups_Ouminus__class_Ouminus(_1097873), _1097875)))], (16733 ^ _782464) ^ [_1098012, _1098014, _1098016] : [class_Groups_Ogroup__add(_1098012), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098012), _1098014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098012), hAPP(c_Groups_Ouminus__class_Ouminus(_1098012), _1098014)), _1098016)) = _1098016)], (16739 ^ _782464) ^ [_1098131, _1098133, _1098135] : [class_Groups_Ogroup__add(_1098131), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098131), hAPP(c_Groups_Ouminus__class_Ouminus(_1098131), _1098133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098131), _1098133), _1098135)) = _1098135)], (16745 ^ _782464) ^ [_1098250, _1098252, _1098254] : [class_Rings_Ocomm__semiring__1(_1098250), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098250), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098250), _1098252), _1098254)), _1098254) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098250), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098250), _1098252), c_Groups_Oone__class_Oone(_1098250))), _1098254))], (16751 ^ _782464) ^ [_1098395, _1098397, _1098399] : [class_Rings_Ocomm__semiring__1(_1098395), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098395), _1098397), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098395), _1098399), _1098397)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098395), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098395), _1098399), c_Groups_Oone__class_Oone(_1098395))), _1098397))], (16757 ^ _782464) ^ [_1098540, _1098542] : [class_Rings_Ocomm__semiring__1(_1098540), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098540), _1098542), _1098542) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098540), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098540), c_Groups_Oone__class_Oone(_1098540)), c_Groups_Oone__class_Oone(_1098540))), _1098542))], (16763 ^ _782464) ^ [_1098671, _1098673, _1098675] : [class_Rings_Ocomm__ring__1(_1098671), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1098671), _1098673), _1098675) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098671), _1098673), hAPP(c_Groups_Ouminus__class_Ouminus(_1098671), _1098675)))], (16769 ^ _782464) ^ [_1098790, _1098792, _1098794, _1098796, _1098798] : [class_Groups_Ocomm__monoid__add(_1098790), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098792, _1098790), hAPP(hAPP(c_COMBS(_1098792, _1098790, _1098790), hAPP(hAPP(c_COMBB(_1098790, tc_fun(_1098790, _1098790), _1098792), c_Groups_Oplus__class_Oplus(_1098790)), _1098794)), _1098796)), _1098798) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098790), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098792, _1098790), _1098794), _1098798)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098792, _1098790), _1098796), _1098798)))], (16775 ^ _782464) ^ [_1098991, _1098993, _1098995, _1098997, _1098999] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1098991), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098991), _1098993), _1098995)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098991), _1098997), _1098999)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098991), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098991), _1098993), _1098997)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098991), _1098995), _1098999))))], (16789 ^ _782464) ^ [_1099262, _1099264, _1099266, _1099268, _1099270] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1099262), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099262), _1099264), _1099266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099262), _1099268), _1099270)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099262), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099262), _1099264), _1099268)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099262), _1099266), _1099270))))], (16803 ^ _782464) ^ [_1099533, _1099535] : [class_Rings_Olinordered__semidom(_1099533), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099533), _1099535), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099533), _1099535), c_Groups_Oone__class_Oone(_1099533)))))], (16809 ^ _782464) ^ [_1099642, _1099644, _1099646, _1099648, _1099650, _1099652] : [class_Rings_Oring(_1099642), 16812 ^ _782464 : [(16813 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099642), _1099644), _1099646)), _1099648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099642), _1099650), _1099646)), _1099652), -(_1099648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099642), _1099650), _1099644)), _1099646)), _1099652))], (16819 ^ _782464) ^ [] : [_1099648 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099642), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099642), _1099650), _1099644)), _1099646)), _1099652), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099642), _1099644), _1099646)), _1099648) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099642), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099642), _1099650), _1099646)), _1099652))]]], (16825 ^ _782464) ^ [_1100039, _1100041, _1100043, _1100045, _1100047, _1100049] : [class_Rings_Oring(_1100039), 16828 ^ _782464 : [(16829 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100039), _1100041), _1100043)), _1100045) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100039), _1100047), _1100043)), _1100049), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100039), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100039), _1100041), _1100047)), _1100043)), _1100045) = _1100049)], (16835 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100039), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100039), _1100041), _1100047)), _1100043)), _1100045) = _1100049, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100039), _1100041), _1100043)), _1100045) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100039), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100039), _1100047), _1100043)), _1100049))]]], (16841 ^ _782464) ^ [_1100436, _1100438, _1100440] : [class_Groups_Ogroup__add(_1100436), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100436), _1100438), _1100440) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100436), _1100438), hAPP(c_Groups_Ouminus__class_Ouminus(_1100436), _1100440)))], (16847 ^ _782464) ^ [_1100555, _1100557, _1100559] : [class_Groups_Oab__group__add(_1100555), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100555), _1100557), _1100559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100555), _1100557), hAPP(c_Groups_Ouminus__class_Ouminus(_1100555), _1100559)))], (16853 ^ _782464) ^ [_1100674, _1100676, _1100678] : [class_Groups_Ogroup__add(_1100674), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100674), _1100676), hAPP(c_Groups_Ouminus__class_Ouminus(_1100674), _1100678)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100674), _1100676), _1100678))], (16859 ^ _782464) ^ [_1100793, _1100795, _1100797, _1100799, _1100801] : [class_Groups_Ocomm__monoid__add(_1100793), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100795), _1100797)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100795, _1100793), hAPP(hAPP(c_COMBS(_1100795, _1100793, _1100793), hAPP(hAPP(c_COMBB(_1100793, tc_fun(_1100793, _1100793), _1100795), c_Groups_Oplus__class_Oplus(_1100793)), _1100799)), _1100801)), _1100797) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100793), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100795, _1100793), _1100799), _1100797)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100795, _1100793), _1100801), _1100797)))], (16869 ^ _782464) ^ [_1101060, _1101062, _1101064, _1101066, _1101068, _1101070] : [class_Rings_Oordered__ring(_1101060), 16872 ^ _782464 : [(16873 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101060), _1101062), _1101064)), _1101066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101060), _1101068), _1101064)), _1101070))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101060), _1101062), _1101068)), _1101064)), _1101066)), _1101070)))], (16879 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101060), _1101062), _1101068)), _1101064)), _1101066)), _1101070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101060), _1101062), _1101064)), _1101066)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101060), _1101068), _1101064)), _1101070))))]]], (16885 ^ _782464) ^ [_1101499, _1101501, _1101503, _1101505, _1101507, _1101509] : [class_Rings_Oordered__ring(_1101499), 16888 ^ _782464 : [(16889 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101499), _1101501), _1101503)), _1101505)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101499), _1101507), _1101503)), _1101509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101499), _1101505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101499), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101499), _1101507), _1101501)), _1101503)), _1101509))))], (16895 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101499), _1101505), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101499), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101499), _1101507), _1101501)), _1101503)), _1101509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101499), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101499), _1101501), _1101503)), _1101505)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101499), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101499), _1101507), _1101503)), _1101509))))]]], (16901 ^ _782464) ^ [_1101938, _1101940, _1101942, _1101944, _1101946, _1101948] : [class_Rings_Oordered__ring(_1101938), 16904 ^ _782464 : [(16905 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101938), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101938), _1101940), _1101942)), _1101944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101938), _1101946), _1101942)), _1101948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101938), _1101944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101938), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101938), _1101946), _1101940)), _1101942)), _1101948))))], (16911 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101938), _1101944), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101938), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101938), _1101946), _1101940)), _1101942)), _1101948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101938), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101938), _1101940), _1101942)), _1101944)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101938), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101938), _1101946), _1101942)), _1101948))))]]], (16917 ^ _782464) ^ [_1102377, _1102379, _1102381, _1102383, _1102385, _1102387] : [class_Rings_Oordered__ring(_1102377), 16920 ^ _782464 : [(16921 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102377), _1102379), _1102381)), _1102383)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102377), _1102385), _1102381)), _1102387))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1102377), _1102379), _1102385)), _1102381)), _1102383)), _1102387)))], (16927 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102377), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1102377), _1102379), _1102385)), _1102381)), _1102383)), _1102387)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1102377), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102377), _1102379), _1102381)), _1102383)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1102377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1102377), _1102385), _1102381)), _1102387))))]]], (16933 ^ _782464) ^ [_1102816, _1102818, _1102820, _1102822] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1102816), _1102818)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1102816), _1102820)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102816, tc_Nat_Onat), _1102822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1102816, tc_HOL_Obool)), _1102818), _1102820)) = 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(_1102816, tc_Nat_Onat), _1102822), _1102818)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102816, tc_Nat_Onat), _1102822), _1102820))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1102816, tc_Nat_Onat), _1102822), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1102816, tc_HOL_Obool)), _1102818), _1102820))))], (16943 ^ _782464) ^ [_1103109, _1103111, _1103113] : [class_Rings_Ocomm__semiring__1(_1103109), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1103109), 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hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1105848, tc_HOL_Obool)), _1105850), _1105852))))], (17075 ^ _782464) ^ [_1106207, _1106209, _1106211, _1106213, _1106215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106207), _1106209)), 17078 ^ _782464 : [(17079 ^ _782464) ^ [] : [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), _1106207), _1106211)), _1106213)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106209), _1106211)), _1106215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1106213), 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), _1106209), _1106207)), _1106211)), _1106215))))], (17085 ^ _782464) ^ [] : 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106598), _1106602)), _1106606))))]]], (17107 ^ _782464) ^ [_1106989, _1106991, _1106993, _1106995, _1106997] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106989), _1106991)), 17110 ^ _782464 : [(17111 ^ _782464) ^ [] : [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), _1106991), _1106993)), _1106995)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106989), _1106993)), _1106997))), -(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), _1106991), _1106989)), _1106993)), _1106995)), _1106997)))], (17117 ^ 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1107583), _1107581)), _1107585)), _1107587) = _1107589)], (17139 ^ _782464) ^ [] : [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), _1107583), _1107581)), _1107585)), _1107587) = _1107589, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107583), _1107585)), _1107587) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107581), _1107585)), _1107589))]]], (17145 ^ _782464) ^ [_1107942, _1107944, _1107946, _1107948, _1107950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107942), _1107944)), 17148 ^ _782464 : [(17149 ^ _782464) ^ [] : [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), _1107942), _1107946)), _1107948)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107944), _1107946)), _1107950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107948), 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), _1107944), _1107942)), _1107946)), _1107950))))], (17155 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107948), 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), _1107944), _1107942)), _1107946)), _1107950))), -(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), _1107942), _1107946)), _1107948)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107944), _1107946)), _1107950))))]]], (17161 ^ _782464) ^ [_1108333, _1108335, _1108337, _1108339, _1108341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108333), _1108335)), -(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), _1108333), _1108337)), _1108339)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108335), _1108337)), _1108341)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1108339), 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), _1108335), _1108333)), _1108337)), _1108341)))], (17167 ^ _782464) ^ [_1108534, _1108536] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1108534, _1108536))))], (17169 ^ _782464) ^ [_1108565] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1108565))))], (17171 ^ _782464) ^ [_1108593] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1108593))))], (17173 ^ _782464) ^ [_1108621, _1108623] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108621, _1108623))))], (17175 ^ _782464) ^ [_1108652, _1108654] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1108652, _1108654))))], (17177 ^ _782464) ^ [_1108683, _1108685, _1108687, _1108689] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108683), _1108685)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108687), _1108685)), _1108689)) = 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), _1108683), _1108687)), _1108685)), _1108689))], (17179 ^ _782464) ^ [_1108754, _1108756, _1108758, _1108760] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1108754, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1108756)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1108754, tc_HOL_Obool), tc_Nat_Onat), _1108758), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1108760))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1108754, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108760, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108756), _1108760))), _1108758))], (17181 ^ _782464) ^ [_1108836, _1108838, _1108840] : [-(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)), _1108836)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108838, _1108840)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108838), _1108836), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108840), _1108836)))], (17194 ^ _782464) ^ [_1109092] : [17196 ^ _782464 : [(17197 ^ _782464) ^ [_1109168] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17195 ^ [_1109092, _1109168]), _1109092)))], (17199 ^ _782464) ^ [_1109202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17195 ^ [_1109092, _1109202]), _1109202))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1109092)))], (17183 ^ _782464) ^ [_1108905] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1108905)), 17187 ^ _782464 : [(17188 ^ _782464) ^ [_1108985] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1108985), _1108905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108985), 17186 ^ [_1108905])))]]], (17203 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (17205 ^ _782464) ^ [_1109295, _1109297, _1109299, _1109301, _1109303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109295), _1109297)), 17208 ^ _782464 : [(17209 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109295), _1109299)), _1109301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109297), _1109299)), _1109303), -(_1109301 = 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), _1109297), _1109295)), _1109299)), _1109303))], (17215 ^ _782464) ^ [] : [_1109301 = 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), _1109297), _1109295)), _1109299)), _1109303), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109295), _1109299)), _1109301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109297), _1109299)), _1109303))]]], (17221 ^ _782464) ^ [_1109656, _1109658, _1109660] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109656), _1109658)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109658), _1109660)), _1109656) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109658), _1109656)), _1109660))], (17227 ^ _782464) ^ [_1109793, _1109795, _1109797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109793), _1109795)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109795), _1109793)), _1109797) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109795), _1109797)), _1109793))], (17233 ^ _782464) ^ [_1109930, _1109932, _1109934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109930), _1109932)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109934), _1109932)), _1109930) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109934), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109932), _1109930)))], (17239 ^ _782464) ^ [_1110067, _1110069, _1110071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110067), _1110069)), 17242 ^ _782464 : [(17243 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110069), _1110067) = _1110071, -(_1110069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110071), _1110067))], (17249 ^ _782464) ^ [] : [_1110069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110071), _1110067), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110069), _1110067) = _1110071)]]], (17255 ^ _782464) ^ [_1110326, _1110328] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110326), _1110328)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110328), _1110326)), _1110326) = _1110328)], (17261 ^ _782464) ^ [_1110437, _1110439, _1110441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110437), _1110439)), 17264 ^ _782464 : [(17265 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110439), _1110437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110441), _1110437)), _1110439)))], (17271 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110441), _1110437)), _1110439)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110441), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110439), _1110437))))]]], (17277 ^ _782464) ^ [_1110726, _1110728, _1110730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110726), _1110728)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110730), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110728), _1110726)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110730), _1110728)), _1110726))], (17283 ^ _782464) ^ [] : [-(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)))], (17285 ^ _782464) ^ [] : [-(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)))], (17287 ^ _782464) ^ [] : [-(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)))], (17289 ^ _782464) ^ [] : [-(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)))], (17291 ^ _782464) ^ [_1110944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110944), _1110944))], (17303 ^ _782464) ^ [_1111030, _1111032] : [17304 ^ _782464 : [(17305 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111030), _1111032))], (17307 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111032), _1111030))]], _1111030 = _1111032], (17293 ^ _782464) ^ [_1110981, _1110983] : [-(_1110981 = _1110983), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110981), _1110983))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110983), _1110981)))], (17311 ^ _782464) ^ [_1111164, _1111166] : [-(_1111164 = _1111166), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111164), _1111166))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111166), _1111164)))], (17321 ^ _782464) ^ [_1111226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111226), _1111226))], (17323 ^ _782464) ^ [_1111254, _1111256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111254), _1111256)), _1111256 = _1111254], (17329 ^ _782464) ^ [_1111342, _1111344] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111342), _1111344)), _1111342 = _1111344], (17335 ^ _782464) ^ [_1111430, _1111432, _1111434] : [17336 ^ _782464 : [(17337 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111430), _1111432)))], (17339 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1111434, _1111432), _1111430))]], 17342 ^ _782464 : [(17343 ^ _782464) ^ [] : [-(_1111430 = _1111432)], (17345 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1111434, _1111432), _1111430))]], 17348 ^ _782464 : [(17349 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111432), _1111430)))], (17351 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1111434, _1111432), _1111430))]], -(hBOOL(hAPP(hAPP(_1111434, _1111432), _1111430)))], (17355 ^ _782464) ^ [_1111794, _1111796, _1111798] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111794), _1111796) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111798), _1111796), -(_1111794 = _1111798)], (17361 ^ _782464) ^ [_1111893, _1111895, _1111897] : [_1111893 = _1111897, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111893), _1111895) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111897), _1111895))], (17367 ^ _782464) ^ [_1112016, _1112018, _1112020] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112016), _1112018) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112016), _1112020), -(_1112018 = _1112020)], (17373 ^ _782464) ^ [_1112115, _1112117, _1112119] : [_1112117 = _1112119, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112115), _1112117) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112115), _1112119))], (17379 ^ _782464) ^ [_1112220, _1112222, _1112224] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112220), _1112222)), _1112224) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112220), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112222), _1112224)))], (17381 ^ _782464) ^ [_1112271, _1112273, _1112275] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112271), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112273), _1112275)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112273), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112271), _1112275)))], (17383 ^ _782464) ^ [_1112322, _1112324] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112322), _1112324) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112324), _1112322))], (17385 ^ _782464) ^ [_1112359] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112359), _1112359)))], (17387 ^ _782464) ^ [_1112383, _1112385] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112383), _1112385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112385), _1112383)))], (17393 ^ _782464) ^ [_1112429, _1112431] : [_1112429 = _1112431, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112429), _1112431)))], (17399 ^ _782464) ^ [_1112516, _1112518, _1112520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112516), _1112518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112518), _1112520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112516), _1112520)))], (17409 ^ _782464) ^ [_1112679, _1112681] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112679), _1112681)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112681), _1112679)), -(_1112679 = _1112681)], (17419 ^ _782464) ^ [_1112828, _1112830, _1112832] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112828), _1112830)), _1112832) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112828), _1112832)), _1112830))], (17421 ^ _782464) ^ [_1112879, _1112881, _1112883] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112879), _1112881)), _1112883) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112881), _1112883)))], (17423 ^ _782464) ^ [_1112930, _1112932] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112930), _1112932) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112932), _1112930))], (17425 ^ _782464) ^ [_1112967, _1112969] : [-(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)), _1112967), _1112969))], (17427 ^ _782464) ^ [_1112997, _1112999, _1113001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112997), _1112999)), _1113001)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112997), _1113001)))], (17433 ^ _782464) ^ [_1113108, _1113110, _1113112, _1113114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113108), _1113110)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113112), _1113110) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113108), _1113114), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113112), _1113114)))], (17443 ^ _782464) ^ [_1113289, _1113291, _1113293, _1113295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113289), _1113291)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113293), _1113295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113289), _1113293)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113291), _1113295))))], (17453 ^ _782464) ^ [_1113480, _1113482, _1113484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113480), _1113482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113480), _1113484)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113482), _1113484))))], (17459 ^ _782464) ^ [_1113603, _1113605, _1113607] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113603), _1113605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113603), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113607), _1113605))))], (17465 ^ _782464) ^ [_1113714, _1113716, _1113718] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113714), _1113716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113716), _1113718))))], (17471 ^ _782464) ^ [_1113843, _1113845, _1113847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113843), _1113845)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113843), _1113847))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113845), _1113847)))], (17477 ^ _782464) ^ [_1113962, _1113964, _1113966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113964), _1113966)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113962), _1113964)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113962), _1113966))))], (17483 ^ _782464) ^ [_1114099, _1114101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114099), _1114101)), _1114101))], (17485 ^ _782464) ^ [_1114147, _1114149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114147), _1114149)), _1114147))], (17487 ^ _782464) ^ [_1114198, _1114200] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114198), _1114200)), 17490 ^ _782464 : [(17491 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114198), _1114200)))], (17493 ^ _782464) ^ [] : [_1114198 = _1114200]]], (17495 ^ _782464) ^ [_1114325, _1114327] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114325), _1114327))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114325), _1114327)), -(_1114325 = _1114327)], (17515 ^ _782464) ^ [_1114600, _1114602] : [17516 ^ _782464 : [(17517 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114600), _1114602))], (17519 ^ _782464) ^ [] : [_1114600 = _1114602]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114600), _1114602)))], (17505 ^ _782464) ^ [_1114494, _1114496] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114494), _1114496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114494), _1114496))), -(_1114494 = _1114496)], (17523 ^ _782464) ^ [_1114737, _1114739] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114737), _1114739)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114737), _1114739)))], (17529 ^ _782464) ^ [_1114834, _1114836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114834), _1114836)), -(_1114834 = _1114836), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114834), _1114836)))], (17539 ^ _782464) ^ [_1114946, _1114948] : [17540 ^ _782464 : [(17541 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114946), _1114948))], (17543 ^ _782464) ^ [] : [_1114946 = _1114948]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114946), _1114948)))], (17547 ^ _782464) ^ [_1115081, _1115083] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115081), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115083), _1115081))))], (17549 ^ _782464) ^ [_1115117, _1115119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115117), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115117), _1115119))))], (17551 ^ _782464) ^ [_1115168, _1115170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115168), _1115170)), -(_1115170 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115168), 17554 ^ [_1115168, _1115170]))], (17558 ^ _782464) ^ [_1115275, _1115277] : [17559 ^ _782464 : [(17560 ^ _782464) ^ [_1115325] : [_1115277 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115275), _1115325)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115275), _1115277)))], (17564 ^ _782464) ^ [_1115407, _1115409, _1115411] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115407), _1115409)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115407), _1115411))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115409), _1115411)))], (17570 ^ _782464) ^ [_1115526, _1115528, _1115530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115528), _1115530)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115526), _1115528)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115526), _1115530))))], (17576 ^ _782464) ^ [_1115651, _1115653, _1115655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115651), _1115653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115653), _1115655))))], (17582 ^ _782464) ^ [_1115762, _1115764, _1115766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115762), _1115764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115766), _1115764))))], (17588 ^ _782464) ^ [_1115873, _1115875, _1115877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115873), _1115875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115873), _1115877)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115875), _1115877))))], (17594 ^ _782464) ^ [_1115996, _1115998, _1116000, _1116002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115996), _1115998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116000), _1116002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115996), _1116000)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115998), _1116002))))], (17604 ^ _782464) ^ [_1116187, _1116189, _1116191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116187), _1116189)), _1116191)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116189), _1116191)))], (17610 ^ _782464) ^ [_1116298, _1116300, _1116302] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116298), _1116300)), _1116302)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116298), _1116302)))], (17616 ^ _782464) ^ [_1116409, _1116411, _1116413] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116409), _1116411)), _1116413)), 17619 ^ _782464 : [(17620 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116409), _1116413)))], (17622 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116411), _1116413)))]]], (17624 ^ _782464) ^ [_1116560, _1116562, _1116564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116560), _1116562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116560), _1116564)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116564), _1116562)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116564), _1116560))))], (17634 ^ _782464) ^ [_1116747, _1116749, _1116751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116747), _1116749)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116747), _1116751)), _1116749)))], (17640 ^ _782464) ^ [_1116858, _1116860] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116858), _1116860)), _1116860) = _1116858)], (17642 ^ _782464) ^ [_1116895, _1116897] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116895), _1116897)), _1116895) = _1116897)], (17644 ^ _782464) ^ [_1116932, _1116934, _1116936] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116932), _1116934)), _1116936) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116934), _1116936)))], (17646 ^ _782464) ^ [_1116983, _1116985, _1116987] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116983), _1116985)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116983), _1116987)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116985), _1116987))], (17648 ^ _782464) ^ [_1117034, _1117036, _1117038] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117034), _1117036)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117038), _1117036)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117034), _1117038))], (17650 ^ _782464) ^ [_1117085, _1117087, _1117089] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117087), _1117089)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117085), _1117087)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117085), _1117089)))], (17652 ^ _782464) ^ [_1117142, _1117144, _1117146] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117142), _1117144)), _1117146) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117142), _1117146)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117144), _1117146)))], (17654 ^ _782464) ^ [_1117199, _1117201] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117199), _1117201)), _1117199)))], (17656 ^ _782464) ^ [_1117235, _1117237, _1117239] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117235), _1117237)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117239), _1117237)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117239), _1117235))))], (17662 ^ _782464) ^ [_1117358, _1117360, _1117362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117358), _1117360)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117358), _1117362)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117360), _1117362))))], (17668 ^ _782464) ^ [_1117481, _1117483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117481), _1117483)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117483), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117483), _1117481)) = _1117481)], (17674 ^ _782464) ^ [_1117592, _1117594, _1117596] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117592), _1117594)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117592), _1117596)), 17681 ^ _782464 : [(17682 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117594), _1117592) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117596), _1117592), -(_1117594 = _1117596)], (17688 ^ _782464) ^ [] : [_1117594 = _1117596, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117594), _1117592) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117596), _1117592))]]], (17694 ^ _782464) ^ [_1117915, _1117917, _1117919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117915), _1117917)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117915), _1117919)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117917), _1117915)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117919), _1117915)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117917), _1117919))], (17704 ^ _782464) ^ [_1118116, _1118118, _1118120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118116), _1118118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118116), _1118120)), 17711 ^ _782464 : [(17712 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118118), _1118116)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118120), _1118116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118118), _1118120)))], (17718 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118118), _1118120)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118118), _1118116)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118120), _1118116))))]]], (17724 ^ _782464) ^ [_1118469, _1118471, _1118473, _1118475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118469), _1118471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118473), _1118475)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118469), _1118473)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118471), _1118475))))], (17734 ^ _782464) ^ [_1118660, _1118662, _1118664] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118660), _1118662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118664), _1118660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118664), _1118662))))], (17740 ^ _782464) ^ [_1118783, _1118785, _1118787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118783), _1118785)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118783), _1118787)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118785), _1118787))))], (17746 ^ _782464) ^ [_1118906] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118906), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118906), _1118906)))))], (17748 ^ _782464) ^ [_1118946] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118946), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118946), _1118946))))], (17750 ^ _782464) ^ [_1118980, _1118982, _1118984] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118980), _1118982)), _1118984) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118980), _1118984)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118982), _1118984)))], (17752 ^ _782464) ^ [_1119037, _1119039, _1119041] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119037), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119039), _1119041)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119037), _1119039)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119037), _1119041)))], (17754 ^ _782464) ^ [_1119094] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1119094) = _1119094)], (17756 ^ _782464) ^ [_1119135, _1119137] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119135), _1119137), 17759 ^ _782464 : [(17760 ^ _782464) ^ [] : [-(_1119135 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17762 ^ _782464) ^ [] : [-(_1119137 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17764 ^ _782464) ^ [_1119246, _1119248] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119246), _1119248)), _1119246 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1119248 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (17774 ^ _782464) ^ [_1119389] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119389), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1119389)], (17776 ^ _782464) ^ [_1119433, _1119435] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119433), _1119435) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17779 ^ _782464 : [(17780 ^ _782464) ^ [] : [-(_1119433 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17782 ^ _782464) ^ [] : [-(_1119435 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17784 ^ _782464) ^ [_1119544, _1119546] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119544), _1119546) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1119544 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1119546 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (17794 ^ _782464) ^ [_1119683, _1119685] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119683), _1119685))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119685), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119683), _1119685)) = _1119683)], (17800 ^ _782464) ^ [_1119754, _1119756, _1119758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119754), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119756), _1119758))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119754), _1119758)), _1119756)))], (17806 ^ _782464) ^ [_1119873, _1119875, _1119877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119873), _1119877)), _1119875)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119873), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119875), _1119877))))], (17812 ^ _782464) ^ [_1119998, _1120000, _1120002] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119998), _1120000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119998), _1120002)), 17819 ^ _782464 : [(17820 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120000), _1119998)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120002), _1119998))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120000), _1120002)))], (17826 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120000), _1120002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120000), _1119998)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120002), _1119998))))]]], (17832 ^ _782464) ^ [_1120351, _1120353, _1120355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120351), _1120353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120355), _1120351)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120351), _1120355)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120353), _1120355))))], (17842 ^ _782464) ^ [_1120538, _1120540, _1120542] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120538), _1120540)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120542), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120540), _1120538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120542), _1120538)), _1120540))], (17848 ^ _782464) ^ [_1120693, _1120695, _1120697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120693), _1120695)), _1120697)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120693), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120697), _1120695))))], (17854 ^ _782464) ^ [_1120812, _1120814, _1120816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120816), _1120814))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120812), _1120814)), _1120816)))], (17860 ^ _782464) ^ [_1120937, _1120939, _1120941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120937), _1120939)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120941), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120939), _1120941)), _1120937))))], (17866 ^ _782464) ^ [_1121060, _1121062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121060), _1121062)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121060), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121062), _1121060)) = _1121062)], (17872 ^ _782464) ^ [_1121171, _1121173, _1121175, _1121177] : [class_Rings_Ocomm__semiring__1(_1121171), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121171), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121171), c_Groups_Oone__class_Oone(_1121171)), c_Groups_Oone__class_Oone(_1121171))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121171), hAPP(hAPP(c_COMBB(_1121171, _1121171, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1121171), _1121173)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1121171, _1121171), hAPP(hAPP(c_COMBB(_1121171, tc_fun(_1121171, _1121171), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1121171)), c_Nat_Osemiring__1__class_Oof__nat(_1121171))), _1121175))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1121177))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121171), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121171), _1121177)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121171), _1121173), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121171), _1121173), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121171), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121177), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1121175)))))], (17878 ^ _782464) ^ [_1121494, _1121496, _1121498, _1121500] : [class_Groups_Oab__group__add(_1121494), 17881 ^ _782464 : [(17882 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121496), _1121498)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121494), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1121494, _1121494), hAPP(hAPP(c_COMBB(_1121494, tc_fun(_1121494, _1121494), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1121494)), _1121500)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1121494, tc_Nat_Onat), _1121500), 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, _1121496, _1121498)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1121494), hAPP(_1121500, _1121496)), hAPP(_1121500, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121498), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (17888 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121496), _1121498))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121494), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1121494, _1121494), hAPP(hAPP(c_COMBB(_1121494, tc_fun(_1121494, _1121494), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1121494)), _1121500)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1121494, tc_Nat_Onat), _1121500), 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, _1121496, _1121498)) = c_Groups_Ozero__class_Ozero(_1121494))]]], (17894 ^ _782464) ^ [_1121932, _1121934, _1121936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121932), _1121934)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121932), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121934), _1121936))))], (17900 ^ _782464) ^ [_1122043, _1122045, _1122047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122043), _1122045)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122047), _1122045))))], (17906 ^ _782464) ^ [_1122154, _1122156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122154), _1122156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122154), _1122156)))], (17912 ^ _782464) ^ [_1122251, _1122253, _1122255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122251), _1122253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122255), _1122253))))], (17918 ^ _782464) ^ [_1122362, _1122364, _1122366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122362), _1122364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122362), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122364), _1122366))))], (17924 ^ _782464) ^ [_1122482] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122482), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17926 ^ _782464) ^ [_1122510] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122510)))], (17928 ^ _782464) ^ [_1122535, _1122537] : [class_Rings_Olinordered__semidom(_1122535), 17931 ^ _782464 : [(17932 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122535), c_Groups_Ozero__class_Ozero(_1122535)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122535), _1122537))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122537)))], (17938 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122535), c_Groups_Ozero__class_Ozero(_1122535)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122535), _1122537))))]]], (17944 ^ _782464) ^ [_1122788, _1122790] : [class_Rings_Olinordered__semidom(_1122788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122788), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122788), _1122790)), c_Groups_Ozero__class_Ozero(_1122788)))], (17950 ^ _782464) ^ [_1122892] : [class_Rings_Osemiring__1(_1122892), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122892), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1122892))], (17956 ^ _782464) ^ [_1122979, _1122981, _1122983] : [class_Nat_Osemiring__char__0(_1122979), 17959 ^ _782464 : [(17960 ^ _782464) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122979), _1122981) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122979), _1122983), -(_1122981 = _1122983)], (17966 ^ _782464) ^ [] : [_1122981 = _1122983, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122979), _1122981) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122979), _1122983))]]], (17972 ^ _782464) ^ [_1123220, _1123222] : [class_Rings_Olinordered__semidom(_1123220), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123220), c_Groups_Ozero__class_Ozero(_1123220)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1123220), _1123222))))], (17978 ^ _782464) ^ [_1123323, _1123325] : [class_Rings_Olinordered__semidom(_1123323), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123323), c_Groups_Ozero__class_Ozero(_1123323)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1123323), _1123325))))], (17984 ^ _782464) ^ [_1123426, _1123428] : [class_Groups_Ozero(_1123426), 17987 ^ _782464 : [(17988 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(_1123426) = _1123428, -(_1123428 = c_Groups_Ozero__class_Ozero(_1123426))], (17994 ^ _782464) ^ [] : [_1123428 = c_Groups_Ozero__class_Ozero(_1123426), -(c_Groups_Ozero__class_Ozero(_1123426) = _1123428)]]], (18000 ^ _782464) ^ [_1123643, _1123645, _1123647] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1123643), 18003 ^ _782464 : [(18004 ^ _782464) ^ [] : [_1123645 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123643), _1123645), _1123647), -(_1123647 = c_Groups_Ozero__class_Ozero(_1123643))], (18010 ^ _782464) ^ [] : [_1123647 = c_Groups_Ozero__class_Ozero(_1123643), -(_1123645 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123643), _1123645), _1123647))]]], (18016 ^ _782464) ^ [_1123884, _1123886] : [class_Rings_Ocomm__semiring__1(_1123884), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123884), _1123886), c_Groups_Ozero__class_Ozero(_1123884)) = _1123886)], (18022 ^ _782464) ^ [_1123979, _1123981] : [class_Rings_Ocomm__semiring__1(_1123979), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123979), c_Groups_Ozero__class_Ozero(_1123979)), _1123981) = _1123981)], (18028 ^ _782464) ^ [_1124074, _1124076] : [class_Groups_Omonoid__add(_1124074), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124074), c_Groups_Ozero__class_Ozero(_1124074)), _1124076) = _1124076)], (18034 ^ _782464) ^ [_1124169, _1124171] : [class_Groups_Ocomm__monoid__add(_1124169), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124169), c_Groups_Ozero__class_Ozero(_1124169)), _1124171) = _1124171)], (18040 ^ _782464) ^ [_1124264, _1124266] : [class_Groups_Olinordered__ab__group__add(_1124264), 18043 ^ _782464 : [(18044 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(_1124264) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124264), _1124266), _1124266), -(_1124266 = c_Groups_Ozero__class_Ozero(_1124264))], (18050 ^ _782464) ^ [] : [_1124266 = c_Groups_Ozero__class_Ozero(_1124264), -(c_Groups_Ozero__class_Ozero(_1124264) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124264), _1124266), _1124266))]]], (18056 ^ _782464) ^ [_1124505, _1124507] : [class_Groups_Omonoid__add(_1124505), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124505), _1124507), c_Groups_Ozero__class_Ozero(_1124505)) = _1124507)], (18062 ^ _782464) ^ [_1124600, _1124602] : [class_Groups_Ocomm__monoid__add(_1124600), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124600), _1124602), c_Groups_Ozero__class_Ozero(_1124600)) = _1124602)], (18068 ^ _782464) ^ [_1124695, _1124697] : [class_Rings_Omult__zero(_1124695), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124695), c_Groups_Ozero__class_Ozero(_1124695)), _1124697) = c_Groups_Ozero__class_Ozero(_1124695))], (18074 ^ _782464) ^ [_1124794, _1124796] : [class_Rings_Omult__zero(_1124794), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124794), _1124796), c_Groups_Ozero__class_Ozero(_1124794)) = c_Groups_Ozero__class_Ozero(_1124794))], (18080 ^ _782464) ^ [_1124893, _1124895, _1124897] : [class_Rings_Oring__no__zero__divisors(_1124893), 18083 ^ _782464 : [(18094 ^ _782464) ^ [] : [18095 ^ _782464 : [(18096 ^ _782464) ^ [] : [_1124895 = c_Groups_Ozero__class_Ozero(_1124893)], (18098 ^ _782464) ^ [] : [_1124897 = c_Groups_Ozero__class_Ozero(_1124893)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124893), _1124895), _1124897) = c_Groups_Ozero__class_Ozero(_1124893))], (18084 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124893), _1124895), _1124897) = c_Groups_Ozero__class_Ozero(_1124893), -(_1124895 = c_Groups_Ozero__class_Ozero(_1124893)), -(_1124897 = c_Groups_Ozero__class_Ozero(_1124893))]]], (18102 ^ _782464) ^ [_1125191, _1125193, _1125195] : [class_Rings_Ono__zero__divisors(_1125191), -(_1125193 = c_Groups_Ozero__class_Ozero(_1125191)), -(_1125195 = c_Groups_Ozero__class_Ozero(_1125191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125191), _1125193), _1125195) = c_Groups_Ozero__class_Ozero(_1125191)], (18116 ^ _782464) ^ [_1125411, _1125413, _1125415] : [class_Rings_Ono__zero__divisors(_1125411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125411), _1125413), _1125415) = c_Groups_Ozero__class_Ozero(_1125411), -(_1125413 = c_Groups_Ozero__class_Ozero(_1125411)), -(_1125415 = c_Groups_Ozero__class_Ozero(_1125411))], (18130 ^ _782464) ^ [_1125583, _1125585] : [class_Rings_Ocomm__semiring__1(_1125583), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125583), c_Groups_Ozero__class_Ozero(_1125583)), _1125585) = c_Groups_Ozero__class_Ozero(_1125583))], (18136 ^ _782464) ^ [_1125682, _1125684] : [class_Rings_Ocomm__semiring__1(_1125682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125682), _1125684), c_Groups_Ozero__class_Ozero(_1125682)) = c_Groups_Ozero__class_Ozero(_1125682))], (18142 ^ _782464) ^ [_1125781, _1125783] : [class_Groups_Ogroup__add(_1125781), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125781), _1125783), c_Groups_Ozero__class_Ozero(_1125781)) = _1125783)], (18148 ^ _782464) ^ [_1125876, _1125878] : [class_Groups_Ogroup__add(_1125876), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125876), _1125878), _1125878) = c_Groups_Ozero__class_Ozero(_1125876))], (18154 ^ _782464) ^ [_1125971, _1125973, _1125975] : [class_Groups_Oab__group__add(_1125971), 18157 ^ _782464 : [(18158 ^ _782464) ^ [] : [_1125973 = _1125975, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125971), _1125973), _1125975) = c_Groups_Ozero__class_Ozero(_1125971))], (18164 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125971), _1125973), _1125975) = c_Groups_Ozero__class_Ozero(_1125971), -(_1125973 = _1125975)]]], (18170 ^ _782464) ^ [_1126212, _1126214, _1126216] : [class_Groups_Ogroup__add(_1126212), 18173 ^ _782464 : [(18174 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126212), _1126214), _1126216) = c_Groups_Ozero__class_Ozero(_1126212), -(_1126214 = _1126216)], (18180 ^ _782464) ^ [] : [_1126214 = _1126216, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126212), _1126214), _1126216) = c_Groups_Ozero__class_Ozero(_1126212))]]], (18186 ^ _782464) ^ [_1126453] : [class_Rings_Ozero__neq__one(_1126453), c_Groups_Oone__class_Oone(_1126453) = c_Groups_Ozero__class_Ozero(_1126453)], (18192 ^ _782464) ^ [_1126535] : [class_Rings_Ozero__neq__one(_1126535), c_Groups_Ozero__class_Ozero(_1126535) = c_Groups_Oone__class_Oone(_1126535)], (18198 ^ _782464) ^ [_1126617, _1126619] : [class_Groups_Olinordered__ab__group__add(_1126617), 18201 ^ _782464 : [(18202 ^ _782464) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1126617), _1126619) = _1126619, -(_1126619 = c_Groups_Ozero__class_Ozero(_1126617))], (18208 ^ _782464) ^ [] : [_1126619 = c_Groups_Ozero__class_Ozero(_1126617), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126617), _1126619) = _1126619)]]], (18214 ^ _782464) ^ [_1126843, _1126845] : [class_Groups_Ogroup__add(_1126843), 18217 ^ _782464 : [(18218 ^ _782464) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1126843), _1126845) = c_Groups_Ozero__class_Ozero(_1126843), -(_1126845 = c_Groups_Ozero__class_Ozero(_1126843))], (18224 ^ _782464) ^ [] : [_1126845 = c_Groups_Ozero__class_Ozero(_1126843), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126843), _1126845) = c_Groups_Ozero__class_Ozero(_1126843))]]], (18230 ^ _782464) ^ [_1127075, _1127077] : [class_Groups_Olinordered__ab__group__add(_1127075), 18233 ^ _782464 : [(18234 ^ _782464) ^ [] : [_1127077 = hAPP(c_Groups_Ouminus__class_Ouminus(_1127075), _1127077), -(_1127077 = c_Groups_Ozero__class_Ozero(_1127075))], (18240 ^ _782464) ^ [] : [_1127077 = c_Groups_Ozero__class_Ozero(_1127075), -(_1127077 = hAPP(c_Groups_Ouminus__class_Ouminus(_1127075), _1127077))]]], (18246 ^ _782464) ^ [_1127301, _1127303] : [class_Groups_Ogroup__add(_1127301), 18249 ^ _782464 : [(18250 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(_1127301) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127301), _1127303), -(c_Groups_Ozero__class_Ozero(_1127301) = _1127303)], (18256 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(_1127301) = _1127303, -(c_Groups_Ozero__class_Ozero(_1127301) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127301), _1127303))]]], (18262 ^ _782464) ^ [_1127533] : [class_Groups_Ogroup__add(_1127533), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127533), c_Groups_Ozero__class_Ozero(_1127533)) = c_Groups_Ozero__class_Ozero(_1127533))], (18268 ^ _782464) ^ [_1127633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127633), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18270 ^ _782464) ^ [_1127667] : [-(_1127667 = 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)), _1127667)))], (18276 ^ _782464) ^ [_1127699] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1127699)), _1127699 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18282 ^ _782464) ^ [_1127790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127790), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18284 ^ _782464) ^ [_1127818, _1127820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127818), _1127820)), _1127820 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18290 ^ _782464) ^ [_1127902] : [-(_1127902 = 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)), _1127902)))], (18296 ^ _782464) ^ [_1127938, _1127940] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1127938), _1127940) = _1127938, -(_1127940 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18302 ^ _782464) ^ [_1128042, _1128044] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128042), _1128044) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18305 ^ _782464 : [(18306 ^ _782464) ^ [] : [-(_1128042 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18308 ^ _782464) ^ [] : [-(_1128044 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18310 ^ _782464) ^ [_1128153, _1128155] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128153), _1128155) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128153 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1128155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18320 ^ _782464) ^ [_1128296] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128296), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1128296)], (18322 ^ _782464) ^ [_1128325] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128325) = _1128325)], (18324 ^ _782464) ^ [_1128351] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128351)))], (18326 ^ _782464) ^ [_1128388] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128388), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1128388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18332 ^ _782464) ^ [_1128469] : [_1128469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128469), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18338 ^ _782464) ^ [_1128556] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128556) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18340 ^ _782464) ^ [_1128582] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128582), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1128582)], (18342 ^ _782464) ^ [_1128611] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128611), _1128611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18344 ^ _782464) ^ [_1128640, _1128642] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128640), _1128642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128642), _1128640) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1128640 = _1128642)], (18364 ^ _782464) ^ [_1128923, _1128925, _1128927] : [18365 ^ _782464 : [(18366 ^ _782464) ^ [] : [_1128923 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18368 ^ _782464) ^ [] : [_1128925 = _1128927]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128923), _1128925) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128923), _1128927))], (18354 ^ _782464) ^ [_1128811, _1128813, _1128815] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128811), _1128813) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128811), _1128815), -(_1128811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1128813 = _1128815)], (18382 ^ _782464) ^ [_1129196, _1129198, _1129200] : [18383 ^ _782464 : [(18384 ^ _782464) ^ [] : [_1129196 = _1129200], (18386 ^ _782464) ^ [] : [_1129198 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129196), _1129198) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129200), _1129198))], (18372 ^ _782464) ^ [_1129084, _1129086, _1129088] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129084), _1129086) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129088), _1129086), -(_1129084 = _1129088), -(_1129086 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18400 ^ _782464) ^ [_1129469, _1129471, _1129473] : [18401 ^ _782464 : [(18402 ^ _782464) ^ [] : [_1129471 = _1129473], (18404 ^ _782464) ^ [] : [_1129469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129469), _1129471) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129469), _1129473))], (18390 ^ _782464) ^ [_1129357, _1129359, _1129361] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129357), _1129359) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129357), _1129361), -(_1129359 = _1129361), -(_1129357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18418 ^ _782464) ^ [_1129725, _1129727] : [18419 ^ _782464 : [(18420 ^ _782464) ^ [] : [_1129725 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18422 ^ _782464) ^ [] : [_1129727 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129725), _1129727) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18408 ^ _782464) ^ [_1129627, _1129629] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129627), _1129629) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1129627 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1129629 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18426 ^ _782464) ^ [_1129854] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129854), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18428 ^ _782464) ^ [_1129883] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1129883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18430 ^ _782464) ^ [_1129909] : [class_Nat_Osemiring__char__0(_1129909), -(c_Fun_Oinj__on(tc_Nat_Onat, _1129909, c_Nat_Osemiring__1__class_Oof__nat(_1129909), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (18436 ^ _782464) ^ [_1129990] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1129990), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (18438 ^ _782464) ^ [] : [-(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)))], (18440 ^ _782464) ^ [] : [-(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)))], (18442 ^ _782464) ^ [] : [-(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))))], (18444 ^ _782464) ^ [_1130073, _1130075, _1130077] : [class_Groups_Ocomm__monoid__add(_1130073), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1130075, _1130073), hAPP(c_COMBK(_1130073, _1130075), c_Groups_Ozero__class_Ozero(_1130073))), _1130077) = c_Groups_Ozero__class_Ozero(_1130073))], (18450 ^ _782464) ^ [_1130188, _1130190, _1130192] : [class_Rings_Olinordered__semidom(_1130188), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130188), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130188), _1130190)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130188), _1130192))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130190), _1130192)))], (18460 ^ _782464) ^ [_1130363, _1130365, _1130367] : [class_Rings_Olinordered__semidom(_1130363), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130365), _1130367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130363), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130363), _1130365)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130363), _1130367))))], (18470 ^ _782464) ^ [_1130538, _1130540, _1130542] : [class_Rings_Olinordered__semidom(_1130538), 18473 ^ _782464 : [(18474 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130538), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130538), _1130540)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130538), _1130542))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130540), _1130542)))], (18480 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130540), _1130542)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130538), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130538), _1130540)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130538), _1130542))))]]], (18486 ^ _782464) ^ [_1130815, _1130817, _1130819] : [class_Rings_Olinordered__semidom(_1130815), 18489 ^ _782464 : [(18490 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130815), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130815), _1130817)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130815), _1130819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130817), _1130819)))], (18496 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130817), _1130819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130815), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130815), _1130817)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130815), _1130819))))]]], (18502 ^ _782464) ^ [_1131092, _1131094, _1131096] : [class_Rings_Osemiring__1(_1131092), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131092), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1131094), _1131096)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131092), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131092), _1131094)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131092), _1131096)))], (18508 ^ _782464) ^ [_1131227, _1131229] : [class_Groups_Olinordered__ab__group__add(_1131227), 18511 ^ _782464 : [(18512 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131227), c_Groups_Ozero__class_Ozero(_1131227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131227), _1131229), _1131229))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131227), c_Groups_Ozero__class_Ozero(_1131227)), _1131229)))], (18518 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131227), c_Groups_Ozero__class_Ozero(_1131227)), _1131229)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131227), c_Groups_Ozero__class_Ozero(_1131227)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131227), _1131229), _1131229))))]]], (18524 ^ _782464) ^ [_1131510, _1131512] : [class_Groups_Olinordered__ab__group__add(_1131510), 18527 ^ _782464 : [(18528 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131510), _1131512), _1131512)), c_Groups_Ozero__class_Ozero(_1131510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131510), _1131512), c_Groups_Ozero__class_Ozero(_1131510))))], (18534 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131510), _1131512), c_Groups_Ozero__class_Ozero(_1131510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131510), _1131512), _1131512)), c_Groups_Ozero__class_Ozero(_1131510))))]]], (18540 ^ _782464) ^ [_1131793, _1131795, _1131797] : [class_Groups_Oordered__comm__monoid__add(_1131793), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131793), c_Groups_Ozero__class_Ozero(_1131793)), _1131795)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131793), c_Groups_Ozero__class_Ozero(_1131793)), _1131797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131793), c_Groups_Ozero__class_Ozero(_1131793)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131793), _1131795), _1131797))))], (18554 ^ _782464) ^ [_1132048, _1132050, _1132052] : [class_Groups_Oordered__comm__monoid__add(_1132048), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132048), c_Groups_Ozero__class_Ozero(_1132048)), _1132050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132048), c_Groups_Ozero__class_Ozero(_1132048)), _1132052)), 18565 ^ _782464 : [(18566 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132048), _1132050), _1132052) = c_Groups_Ozero__class_Ozero(_1132048), 18569 ^ _782464 : [(18570 ^ _782464) ^ [] : [-(_1132050 = c_Groups_Ozero__class_Ozero(_1132048))], (18572 ^ _782464) ^ [] : [-(_1132052 = c_Groups_Ozero__class_Ozero(_1132048))]]], (18574 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132048), _1132050), _1132052) = c_Groups_Ozero__class_Ozero(_1132048)), _1132050 = c_Groups_Ozero__class_Ozero(_1132048), _1132052 = c_Groups_Ozero__class_Ozero(_1132048)]]], (18584 ^ _782464) ^ [_1132519, _1132521, _1132523, _1132525] : [class_Groups_Oordered__comm__monoid__add(_1132519), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132519), c_Groups_Ozero__class_Ozero(_1132519)), _1132521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132519), _1132523), _1132525)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132519), _1132523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132519), _1132521), _1132525))))], (18598 ^ _782464) ^ [_1132772, _1132774, _1132776, _1132778] : [class_Groups_Oordered__comm__monoid__add(_1132772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132772), c_Groups_Ozero__class_Ozero(_1132772)), _1132774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132772), _1132776), _1132778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132772), _1132776), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132772), _1132778), _1132774))))], (18612 ^ _782464) ^ [_1133025, _1133027, _1133029] : [class_Groups_Oordered__comm__monoid__add(_1133025), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133025), _1133027), c_Groups_Ozero__class_Ozero(_1133025))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133025), _1133029), c_Groups_Ozero__class_Ozero(_1133025))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133025), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1133025), _1133027), _1133029)), c_Groups_Ozero__class_Ozero(_1133025))))], (18626 ^ _782464) ^ [_1133280, _1133282, _1133284] : [class_Rings_Oordered__cancel__semiring(_1133280), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133280), _1133282), _1133284)), c_Groups_Ozero__class_Ozero(_1133280)))), 18631 ^ _782464 : [(18632 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133280), c_Groups_Ozero__class_Ozero(_1133280)), _1133282)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133280), _1133284), c_Groups_Ozero__class_Ozero(_1133280)))], (18638 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133280), _1133282), c_Groups_Ozero__class_Ozero(_1133280))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133280), c_Groups_Ozero__class_Ozero(_1133280)), _1133284))]]], (18646 ^ _782464) ^ [_1133656, _1133658, _1133660] : [class_Rings_Oordered__ring(_1133656), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133656), c_Groups_Ozero__class_Ozero(_1133656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133656), _1133658), _1133660)))), 18651 ^ _782464 : [(18652 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133656), c_Groups_Ozero__class_Ozero(_1133656)), _1133658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133656), c_Groups_Ozero__class_Ozero(_1133656)), _1133660))], (18658 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133656), _1133658), c_Groups_Ozero__class_Ozero(_1133656))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133656), _1133660), c_Groups_Ozero__class_Ozero(_1133656)))]]], (18666 ^ _782464) ^ [_1134032, _1134034, _1134036, _1134038, _1134040] : [class_Rings_Oordered__semiring(_1134032), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134032), _1134034), _1134036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134032), _1134038), _1134040)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134032), c_Groups_Ozero__class_Ozero(_1134032)), _1134036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134032), c_Groups_Ozero__class_Ozero(_1134032)), _1134038)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134032), _1134034), _1134038)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134032), _1134036), _1134040))))], (18688 ^ _782464) ^ [_1134455, _1134457, _1134459, _1134461, _1134463] : [class_Rings_Oordered__semiring(_1134455), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134455), _1134457), _1134459)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134455), _1134461), _1134463)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134455), c_Groups_Ozero__class_Ozero(_1134455)), _1134457)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134455), c_Groups_Ozero__class_Ozero(_1134455)), _1134461)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134455), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134455), _1134457), _1134461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134455), _1134459), _1134463))))], (18710 ^ _782464) ^ [_1134878, _1134880, _1134882, _1134884] : [class_Rings_Oordered__ring(_1134878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134878), _1134880), _1134882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134878), _1134884), c_Groups_Ozero__class_Ozero(_1134878))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134878), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134878), _1134884), _1134882)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134878), _1134884), _1134880))))], (18724 ^ _782464) ^ [_1135147, _1135149, _1135151, _1135153] : [class_Rings_Oordered__ring(_1135147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135147), _1135149), _1135151)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135147), _1135153), c_Groups_Ozero__class_Ozero(_1135147))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135147), _1135151), _1135153)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135147), _1135149), _1135153))))], (18738 ^ _782464) ^ [_1135416, _1135418, _1135420, _1135422] : [class_Rings_Oordered__comm__semiring(_1135416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135416), _1135418), _1135420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135416), c_Groups_Ozero__class_Ozero(_1135416)), _1135422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135416), _1135422), _1135418)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135416), _1135422), _1135420))))], (18752 ^ _782464) ^ [_1135685, _1135687, _1135689, _1135691] : [class_Rings_Oordered__semiring(_1135685), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135685), _1135687), _1135689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135685), c_Groups_Ozero__class_Ozero(_1135685)), _1135691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135685), _1135691), _1135687)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135685), _1135691), _1135689))))], (18766 ^ _782464) ^ [_1135954, _1135956, _1135958, _1135960] : [class_Rings_Oordered__semiring(_1135954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135954), _1135956), _1135958)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135954), c_Groups_Ozero__class_Ozero(_1135954)), _1135960)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135954), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135954), _1135956), _1135960)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135954), _1135958), _1135960))))], (18780 ^ _782464) ^ [_1136223, _1136225, _1136227] : [class_Rings_Oordered__ring(_1136223), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136223), _1136225), c_Groups_Ozero__class_Ozero(_1136223))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136223), _1136227), c_Groups_Ozero__class_Ozero(_1136223))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136223), c_Groups_Ozero__class_Ozero(_1136223)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136223), _1136225), _1136227))))], (18794 ^ _782464) ^ [_1136478, _1136480, _1136482] : [class_Rings_Oordered__cancel__semiring(_1136478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136478), _1136480), c_Groups_Ozero__class_Ozero(_1136478))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136478), c_Groups_Ozero__class_Ozero(_1136478)), _1136482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136478), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136478), _1136480), _1136482)), c_Groups_Ozero__class_Ozero(_1136478))))], (18808 ^ _782464) ^ [_1136733, _1136735, _1136737] : [class_Rings_Oordered__cancel__semiring(_1136733), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136733), c_Groups_Ozero__class_Ozero(_1136733)), _1136735)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136733), _1136737), c_Groups_Ozero__class_Ozero(_1136733))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136733), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136733), _1136737), _1136735)), c_Groups_Ozero__class_Ozero(_1136733))))], (18822 ^ _782464) ^ [_1136988, _1136990, _1136992] : [class_Rings_Oordered__cancel__semiring(_1136988), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136988), c_Groups_Ozero__class_Ozero(_1136988)), _1136990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136988), _1136992), c_Groups_Ozero__class_Ozero(_1136988))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136988), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136988), _1136990), _1136992)), c_Groups_Ozero__class_Ozero(_1136988))))], (18836 ^ _782464) ^ [_1137243, _1137245, _1137247] : [class_Rings_Oordered__cancel__semiring(_1137243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137243), c_Groups_Ozero__class_Ozero(_1137243)), _1137245)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137243), c_Groups_Ozero__class_Ozero(_1137243)), _1137247)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137243), c_Groups_Ozero__class_Ozero(_1137243)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137243), _1137245), _1137247))))], (18850 ^ _782464) ^ [_1137498, _1137500, _1137502] : [class_Rings_Olinordered__ring__strict(_1137498), 18853 ^ _782464 : [(18854 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137498), _1137500), _1137502)), c_Groups_Ozero__class_Ozero(_1137498))), 18859 ^ _782464 : [(18860 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), c_Groups_Ozero__class_Ozero(_1137498)), _1137500)))], (18862 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), _1137502), c_Groups_Ozero__class_Ozero(_1137498))))]], 18863 ^ _782464 : [(18864 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), _1137500), c_Groups_Ozero__class_Ozero(_1137498))))], (18866 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), c_Groups_Ozero__class_Ozero(_1137498)), _1137502)))]]], (18868 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137498), _1137500), _1137502)), c_Groups_Ozero__class_Ozero(_1137498)))), 18869 ^ _782464 : [(18870 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), c_Groups_Ozero__class_Ozero(_1137498)), _1137500)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), _1137502), c_Groups_Ozero__class_Ozero(_1137498)))], (18876 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), _1137500), c_Groups_Ozero__class_Ozero(_1137498))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137498), c_Groups_Ozero__class_Ozero(_1137498)), _1137502))]]]]], (18884 ^ _782464) ^ [_1138088, _1138090, _1138092] : [class_Rings_Olinordered__ring__strict(_1138088), 18887 ^ _782464 : [(18888 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), c_Groups_Ozero__class_Ozero(_1138088)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138088), _1138090), _1138092))), 18893 ^ _782464 : [(18894 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), c_Groups_Ozero__class_Ozero(_1138088)), _1138090)))], (18896 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), c_Groups_Ozero__class_Ozero(_1138088)), _1138092)))]], 18897 ^ _782464 : [(18898 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), _1138090), c_Groups_Ozero__class_Ozero(_1138088))))], (18900 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), _1138092), c_Groups_Ozero__class_Ozero(_1138088))))]]], (18902 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), c_Groups_Ozero__class_Ozero(_1138088)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138088), _1138090), _1138092)))), 18903 ^ _782464 : [(18904 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), c_Groups_Ozero__class_Ozero(_1138088)), _1138090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), c_Groups_Ozero__class_Ozero(_1138088)), _1138092))], (18910 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), _1138090), c_Groups_Ozero__class_Ozero(_1138088))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138088), _1138092), c_Groups_Ozero__class_Ozero(_1138088)))]]]]], (18918 ^ _782464) ^ [_1138678, _1138680] : [class_Rings_Olinordered__ring(_1138678), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138678), c_Groups_Ozero__class_Ozero(_1138678)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138678), _1138680), _1138680))))], (18924 ^ _782464) ^ [_1138787, _1138789, _1138791, _1138793] : [class_Rings_Olinordered__semidom(_1138787), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138787), c_Groups_Ozero__class_Ozero(_1138787)), _1138789)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138787), _1138791), _1138793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138787), _1138791), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138787), _1138789), _1138793))))], (18938 ^ _782464) ^ [_1139040, _1139042] : [class_Groups_Olinordered__ab__group__add(_1139040), 18941 ^ _782464 : [(18942 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139040), c_Groups_Ozero__class_Ozero(_1139040)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139040), _1139042), _1139042))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139040), c_Groups_Ozero__class_Ozero(_1139040)), _1139042)))], (18948 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139040), c_Groups_Ozero__class_Ozero(_1139040)), _1139042)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139040), c_Groups_Ozero__class_Ozero(_1139040)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139040), _1139042), _1139042))))]]], (18954 ^ _782464) ^ [_1139323, _1139325] : [class_Groups_Olinordered__ab__group__add(_1139323), 18957 ^ _782464 : [(18958 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139323), _1139325), _1139325)), c_Groups_Ozero__class_Ozero(_1139323))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139323), _1139325), c_Groups_Ozero__class_Ozero(_1139323))))], (18964 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139323), _1139325), c_Groups_Ozero__class_Ozero(_1139323))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139323), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139323), _1139325), _1139325)), c_Groups_Ozero__class_Ozero(_1139323))))]]], (18970 ^ _782464) ^ [_1139606, _1139608, _1139610] : [class_Groups_Oordered__comm__monoid__add(_1139606), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139606), c_Groups_Ozero__class_Ozero(_1139606)), _1139608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139606), c_Groups_Ozero__class_Ozero(_1139606)), _1139610)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139606), c_Groups_Ozero__class_Ozero(_1139606)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139606), _1139608), _1139610))))], (18984 ^ _782464) ^ [_1139861, _1139863, _1139865] : [class_Groups_Oordered__comm__monoid__add(_1139861), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139861), _1139863), c_Groups_Ozero__class_Ozero(_1139861))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139861), _1139865), c_Groups_Ozero__class_Ozero(_1139861))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139861), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139861), _1139863), _1139865)), c_Groups_Ozero__class_Ozero(_1139861))))], (18998 ^ _782464) ^ [_1140116, _1140118, _1140120, _1140122] : [class_Rings_Olinordered__ring__strict(_1140116), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140116), _1140118), _1140120)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140116), _1140122), c_Groups_Ozero__class_Ozero(_1140116))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140116), _1140122), _1140120)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140116), _1140122), _1140118))))], (19012 ^ _782464) ^ [_1140385, _1140387, _1140389, _1140391] : [class_Rings_Olinordered__ring__strict(_1140385), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140385), _1140387), _1140389)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140385), _1140391), c_Groups_Ozero__class_Ozero(_1140385))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140385), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140385), _1140389), _1140391)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140385), _1140387), _1140391))))], (19026 ^ _782464) ^ [_1140654, _1140656, _1140658, _1140660] : [class_Rings_Olinordered__comm__semiring__strict(_1140654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140654), _1140656), _1140658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140654), c_Groups_Ozero__class_Ozero(_1140654)), _1140660)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140654), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140654), _1140660), _1140656)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140654), _1140660), _1140658))))], (19040 ^ _782464) ^ [_1140923, _1140925, _1140927, _1140929] : [class_Rings_Olinordered__semiring__strict(_1140923), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140923), _1140925), _1140927)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140923), c_Groups_Ozero__class_Ozero(_1140923)), _1140929)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140923), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140923), _1140929), _1140925)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140923), _1140929), _1140927))))], (19054 ^ _782464) ^ [_1141192, _1141194, _1141196, _1141198] : [class_Rings_Olinordered__semiring__strict(_1141192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141192), _1141194), _1141196)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141192), c_Groups_Ozero__class_Ozero(_1141192)), _1141198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141192), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141192), _1141194), _1141198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141192), _1141196), _1141198))))], (19068 ^ _782464) ^ [_1141461, _1141463, _1141465] : [class_Rings_Olinordered__ring__strict(_1141461), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141461), _1141463), c_Groups_Ozero__class_Ozero(_1141461))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141461), _1141465), c_Groups_Ozero__class_Ozero(_1141461))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141461), c_Groups_Ozero__class_Ozero(_1141461)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141461), _1141463), _1141465))))], (19082 ^ _782464) ^ [_1141716, _1141718, _1141720] : [class_Rings_Olinordered__semiring__strict(_1141716), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141716), _1141718), c_Groups_Ozero__class_Ozero(_1141716))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141716), c_Groups_Ozero__class_Ozero(_1141716)), _1141720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141716), _1141718), _1141720)), c_Groups_Ozero__class_Ozero(_1141716))))], (19096 ^ _782464) ^ [_1141971, _1141973, _1141975, _1141977] : [class_Rings_Olinordered__ring__strict(_1141971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141971), _1141973), c_Groups_Ozero__class_Ozero(_1141971))), 19103 ^ _782464 : [(19104 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141971), _1141973), _1141975)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141971), _1141973), _1141977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141971), _1141977), _1141975)))], (19110 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141971), _1141977), _1141975)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141971), _1141973), _1141975)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141971), _1141973), _1141977))))]]], (19116 ^ _782464) ^ [_1142352, _1142354, _1142356] : [class_Rings_Olinordered__semiring__strict(_1142352), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142352), c_Groups_Ozero__class_Ozero(_1142352)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142352), _1142354), _1142356))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142352), c_Groups_Ozero__class_Ozero(_1142352)), _1142356)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142352), c_Groups_Ozero__class_Ozero(_1142352)), _1142354)))], (19130 ^ _782464) ^ [_1142607, _1142609, _1142611] : [class_Rings_Olinordered__semiring__strict(_1142607), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142607), c_Groups_Ozero__class_Ozero(_1142607)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142607), _1142609), _1142611))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142607), c_Groups_Ozero__class_Ozero(_1142607)), _1142609)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142607), c_Groups_Ozero__class_Ozero(_1142607)), _1142611)))], (19144 ^ _782464) ^ [_1142862, _1142864, _1142866] : [class_Rings_Olinordered__semiring__strict(_1142862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142862), c_Groups_Ozero__class_Ozero(_1142862)), _1142864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142862), _1142866), c_Groups_Ozero__class_Ozero(_1142862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142862), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142862), _1142866), _1142864)), c_Groups_Ozero__class_Ozero(_1142862))))], (19158 ^ _782464) ^ [_1143117, _1143119, _1143121] : [class_Rings_Olinordered__semiring__strict(_1143117), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143117), c_Groups_Ozero__class_Ozero(_1143117)), _1143119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143117), _1143121), c_Groups_Ozero__class_Ozero(_1143117))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143117), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143117), _1143119), _1143121)), c_Groups_Ozero__class_Ozero(_1143117))))], (19172 ^ _782464) ^ [_1143372, _1143374, _1143376] : [class_Rings_Olinordered__semiring__strict(_1143372), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143372), c_Groups_Ozero__class_Ozero(_1143372)), _1143374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143372), c_Groups_Ozero__class_Ozero(_1143372)), _1143376)), 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hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143627), _1143629), _1143633))))]]], (19206 ^ _782464) ^ [_1144008, _1144010, _1144012, _1144014] : [class_Rings_Olinordered__ring__strict(_1144008), 19209 ^ _782464 : [(19210 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144008), _1144010), _1144012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144008), _1144010), _1144014))), 19215 ^ _782464 : [(19216 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), c_Groups_Ozero__class_Ozero(_1144008)), _1144010)))], (19218 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), _1144012), _1144014)))]], 19219 ^ _782464 : [(19220 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), _1144010), c_Groups_Ozero__class_Ozero(_1144008))))], (19222 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), _1144014), _1144012)))]]], (19224 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144008), _1144010), _1144012)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144008), _1144010), _1144014)))), 19225 ^ _782464 : [(19226 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), c_Groups_Ozero__class_Ozero(_1144008)), _1144010)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), _1144012), _1144014))], (19232 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), _1144010), c_Groups_Ozero__class_Ozero(_1144008))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144008), _1144014), _1144012))]]]]], (19240 ^ _782464) ^ [_1144614, _1144616, _1144618, _1144620] : [class_Rings_Olinordered__ring__strict(_1144614), 19243 ^ _782464 : [(19244 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144614), _1144616), _1144618)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144614), _1144620), _1144618))), 19249 ^ _782464 : [(19250 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), c_Groups_Ozero__class_Ozero(_1144614)), _1144618)))], (19252 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), _1144616), _1144620)))]], 19253 ^ _782464 : [(19254 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), _1144618), c_Groups_Ozero__class_Ozero(_1144614))))], (19256 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), _1144620), _1144616)))]]], (19258 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144614), _1144616), _1144618)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144614), _1144620), _1144618)))), 19259 ^ _782464 : [(19260 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), c_Groups_Ozero__class_Ozero(_1144614)), _1144618)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), _1144616), _1144620))], (19266 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), _1144618), c_Groups_Ozero__class_Ozero(_1144614))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144614), _1144620), _1144616))]]]]], (19274 ^ _782464) ^ [_1145220, _1145222] : [class_Rings_Olinordered__ring(_1145220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145220), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145220), _1145222), _1145222)), c_Groups_Ozero__class_Ozero(_1145220)))], (19280 ^ _782464) ^ [_1145330, _1145332, _1145334] : [class_Rings_Osemiring__1(_1145330), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145330), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145332), _1145334)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145330), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145330), _1145332)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145330), _1145334)))], (19286 ^ _782464) ^ [_1145465, _1145467, _1145469] : [class_Groups_Oordered__ab__group__add(_1145465), 19289 ^ _782464 : [(19290 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145465), _1145467), _1145469)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145465), _1145467), _1145469)), c_Groups_Ozero__class_Ozero(_1145465))))], (19296 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145465), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145465), _1145467), _1145469)), c_Groups_Ozero__class_Ozero(_1145465))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145465), _1145467), _1145469)))]]], (19302 ^ _782464) ^ [_1145748, _1145750, _1145752] : [class_Groups_Oordered__ab__group__add(_1145748), 19305 ^ _782464 : [(19306 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145748), _1145750), _1145752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145748), 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-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147835), c_Groups_Ozero__class_Ozero(_1147835)), _1147837)))], (19434 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147835), c_Groups_Ozero__class_Ozero(_1147835)), _1147837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147835), hAPP(c_Groups_Ouminus__class_Ouminus(_1147835), _1147837)), _1147837)))]]], (19440 ^ _782464) ^ [_1148103, _1148105] : [class_Groups_Oordered__ab__group__add(_1148103), 19443 ^ _782464 : [(19444 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148103), hAPP(c_Groups_Ouminus__class_Ouminus(_1148103), _1148105)), c_Groups_Ozero__class_Ozero(_1148103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148103), c_Groups_Ozero__class_Ozero(_1148103)), _1148105)))], (19450 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148103), c_Groups_Ozero__class_Ozero(_1148103)), _1148105)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148103), hAPP(c_Groups_Ouminus__class_Ouminus(_1148103), _1148105)), c_Groups_Ozero__class_Ozero(_1148103))))]]], (19456 ^ _782464) ^ [_1148377, _1148379] : [class_Groups_Oordered__ab__group__add(_1148377), 19459 ^ _782464 : [(19460 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148377), c_Groups_Ozero__class_Ozero(_1148377)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148377), _1148379))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148377), _1148379), c_Groups_Ozero__class_Ozero(_1148377))))], (19466 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148377), _1148379), c_Groups_Ozero__class_Ozero(_1148377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148377), c_Groups_Ozero__class_Ozero(_1148377)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148377), _1148379))))]]], (19472 ^ _782464) ^ [_1148651, _1148653] : [class_Rings_Olinordered__idom(_1148651), 19475 ^ _782464 : [(19476 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148651), _1148653), hAPP(c_Groups_Ouminus__class_Ouminus(_1148651), _1148653))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148651), _1148653), c_Groups_Ozero__class_Ozero(_1148651))))], (19482 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148651), _1148653), c_Groups_Ozero__class_Ozero(_1148651))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148651), _1148653), hAPP(c_Groups_Ouminus__class_Ouminus(_1148651), _1148653))))]]], (19488 ^ _782464) ^ [_1148919, _1148921, _1148923] : [class_Groups_Ogroup__add(_1148919), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148919), _1148921), _1148923) = c_Groups_Ozero__class_Ozero(_1148919), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1148919), _1148921) = _1148923)], (19498 ^ _782464) ^ [_1149080, _1149082] : [class_Groups_Oab__group__add(_1149080), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149080), hAPP(c_Groups_Ouminus__class_Ouminus(_1149080), _1149082)), _1149082) = c_Groups_Ozero__class_Ozero(_1149080))], (19504 ^ _782464) ^ [_1149185, _1149187] : [class_Groups_Ogroup__add(_1149185), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149185), hAPP(c_Groups_Ouminus__class_Ouminus(_1149185), _1149187)), _1149187) = c_Groups_Ozero__class_Ozero(_1149185))], (19510 ^ _782464) ^ [_1149290, _1149292, _1149294] : [class_Groups_Ogroup__add(_1149290), 19513 ^ _782464 : [(19514 ^ _782464) ^ [] : [_1149292 = hAPP(c_Groups_Ouminus__class_Ouminus(_1149290), _1149294), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149290), _1149292), _1149294) = c_Groups_Ozero__class_Ozero(_1149290))], (19520 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149290), _1149292), _1149294) = c_Groups_Ozero__class_Ozero(_1149290), -(_1149292 = hAPP(c_Groups_Ouminus__class_Ouminus(_1149290), _1149294))]]], (19526 ^ _782464) ^ [_1149546, _1149548] : [class_Groups_Ogroup__add(_1149546), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149546), _1149548), hAPP(c_Groups_Ouminus__class_Ouminus(_1149546), _1149548)) = c_Groups_Ozero__class_Ozero(_1149546))], (19532 ^ _782464) ^ [_1149651] : [class_Rings_Osemiring__1(_1149651), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149651), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1149651))], (19538 ^ _782464) ^ [_1149738, _1149740] : [class_Groups_Ogroup__add(_1149738), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149738), c_Groups_Ozero__class_Ozero(_1149738)), _1149740) = hAPP(c_Groups_Ouminus__class_Ouminus(_1149738), _1149740))], (19544 ^ _782464) ^ [_1149843, _1149845, _1149847] : [class_Groups_Ocomm__monoid__add(_1149843), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149845, _1149843), _1149847), c_Orderings_Obot__class_Obot(tc_fun(_1149845, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1149843))], (19550 ^ _782464) ^ [_1149952, _1149954, _1149956] : [class_Groups_Ocomm__monoid__add(_1149952), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149954, _1149952), _1149956), c_Orderings_Obot__class_Obot(tc_fun(_1149954, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1149952))], (19556 ^ _782464) ^ [_1150061, _1150063, _1150065, _1150067] : [class_Groups_Ocomm__monoid__add(_1150061), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150063), _1150065))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150063, _1150061), _1150067), _1150065) = c_Groups_Ozero__class_Ozero(_1150061))], (19566 ^ _782464) ^ [_1150185, _1150187, _1150189, _1150191] : [class_Groups_Ocomm__monoid__add(_1150185), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150187), _1150189))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150187, _1150185), _1150191), _1150189) = c_Groups_Ozero__class_Ozero(_1150185))], (19586 ^ _782464) ^ [_1150434, _1150436] : [19587 ^ _782464 : [(19588 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150434))], (19590 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150436))]], -(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), _1150434), _1150436))))], (19576 ^ _782464) ^ [_1150324, _1150326] : [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), _1150324), _1150326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150324))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150326)))], (19594 ^ _782464) ^ [_1150575, _1150577] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150575)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150577)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150577), _1150575)), _1150577)))], (19604 ^ _782464) ^ [_1150749, _1150751] : [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), _1150749), _1150751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150751), _1150749)))], (19610 ^ _782464) ^ [_1150848, _1150850] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150850), _1150848)), -(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), _1150848), _1150850))))], (19616 ^ _782464) ^ [_1150953, _1150955, _1150957] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150953)), 19619 ^ _782464 : [(19620 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150953), _1150955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150953), _1150957), -(_1150955 = _1150957)], (19626 ^ _782464) ^ [] : [_1150955 = _1150957, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150953), _1150955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150953), _1150957))]]], (19632 ^ _782464) ^ [_1151206, _1151208, _1151210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151206)), 19635 ^ _782464 : [(19636 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151206), _1151208)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151206), _1151210))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151208), _1151210)))], (19642 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151208), _1151210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151206), _1151208)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151206), _1151210))))]]], (19648 ^ _782464) ^ [_1151504, _1151506] : [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), _1151504), _1151506))), 19651 ^ _782464 : [(19652 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151504)))], (19654 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151506)))]]], (19656 ^ _782464) ^ [_1151627, _1151629] : [-(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), _1151627), _1151629)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151629))], (19666 ^ _782464) ^ [_1151800, _1151802, _1151804] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151800), _1151802)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151800), _1151804))), 19669 ^ _782464 : [(19670 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151800)))], (19672 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151802), _1151804)))]]], (19674 ^ _782464) ^ [_1151949, _1151951, _1151953] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151949), _1151951)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151949), _1151953)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151949)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151951), _1151953))], (19684 ^ _782464) ^ [_1152150, _1152152, _1152154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152150), _1152152)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152154), _1152152))), 19687 ^ _782464 : [(19688 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152152)))], (19690 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152150), _1152154)))]]], (19692 ^ _782464) ^ [_1152299, _1152301, _1152303] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152299), _1152301)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152303), _1152301)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152301)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152299), _1152303))], (19702 ^ _782464) ^ [_1152482, _1152484, _1152486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152482), _1152484)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152482), _1152486)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152484), _1152486))))], (19712 ^ _782464) ^ [_1152663, _1152665, _1152667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152663), _1152665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152667)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152667), _1152663)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152667), _1152665))))], (19722 ^ _782464) ^ [_1152844, _1152846] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1152844), _1152846)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19724 ^ _782464) ^ [_1152881, _1152883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152881), _1152883)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152881), _1152883) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19730 ^ _782464) ^ [_1152995, _1152997] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152995), _1152997) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152995), _1152997)))], (19736 ^ _782464) ^ [_1153090, _1153092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153090), _1153092)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1153090), _1153092) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19742 ^ _782464) ^ [_1153191, _1153193] : [_1153191 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153191), _1153193), -(_1153193 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1153191 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19752 ^ _782464) ^ [_1153293, _1153295, _1153297] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1153293), _1153295)), 19755 ^ _782464 : [(19766 ^ _782464) ^ [] : [19768 ^ _782464 : [(19769 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1153293), 19767 ^ [_1153293, _1153295, _1153297]), _1153295)))], (19771 ^ _782464) ^ [] : [hAPP(_1153297, 19767 ^ [_1153293, _1153295, _1153297]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153293, tc_Nat_Onat), _1153297), _1153295) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19756 ^ _782464) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153293, tc_Nat_Onat), _1153297), _1153295) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19759 ^ _782464 : [(19760 ^ _782464) ^ [_1153455] : [hBOOL(hAPP(hAPP(c_member(_1153293), _1153455), _1153295)), -(hAPP(_1153297, _1153455) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (19775 ^ _782464) ^ [_1153713] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153713) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1153713))], (19777 ^ _782464) ^ [_1153742] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1153742) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1153742))], (19779 ^ _782464) ^ [_1153772, _1153774, _1153776] : [class_Groups_Oordered__comm__monoid__add(_1153772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153772), c_Groups_Ozero__class_Ozero(_1153772)), _1153774)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153772), c_Groups_Ozero__class_Ozero(_1153772)), _1153776)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153772), c_Groups_Ozero__class_Ozero(_1153772)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153772), _1153774), _1153776))))], (19793 ^ _782464) ^ [_1154027, _1154029, _1154031] : [class_Groups_Oordered__comm__monoid__add(_1154027), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154027), c_Groups_Ozero__class_Ozero(_1154027)), _1154029)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154027), c_Groups_Ozero__class_Ozero(_1154027)), _1154031)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154027), c_Groups_Ozero__class_Ozero(_1154027)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154027), _1154029), _1154031))))], (19807 ^ _782464) ^ [_1154282, _1154284, _1154286, _1154288] : [class_Groups_Oordered__comm__monoid__add(_1154282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154282), c_Groups_Ozero__class_Ozero(_1154282)), _1154284)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154282), _1154286), _1154288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154282), _1154286), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154282), _1154284), _1154288))))], (19821 ^ _782464) ^ [_1154535, _1154537, _1154539, _1154541] : [class_Groups_Oordered__comm__monoid__add(_1154535), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154535), c_Groups_Ozero__class_Ozero(_1154535)), _1154537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154535), _1154539), _1154541)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154535), _1154539), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154535), _1154537), _1154541))))], (19835 ^ _782464) ^ [_1154788, _1154790, _1154792] : [class_Groups_Oordered__comm__monoid__add(_1154788), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154788), _1154790), c_Groups_Ozero__class_Ozero(_1154788))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154788), _1154792), c_Groups_Ozero__class_Ozero(_1154788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154788), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154788), _1154790), _1154792)), c_Groups_Ozero__class_Ozero(_1154788))))], (19849 ^ _782464) ^ [_1155043, _1155045, _1155047] : [class_Groups_Oordered__comm__monoid__add(_1155043), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155043), _1155045), c_Groups_Ozero__class_Ozero(_1155043))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155043), _1155047), c_Groups_Ozero__class_Ozero(_1155043))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155043), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155043), _1155045), _1155047)), c_Groups_Ozero__class_Ozero(_1155043))))], (19863 ^ _782464) ^ [_1155298, _1155300, _1155302, _1155304] : [class_Rings_Olinordered__ring__strict(_1155298), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155298), c_Groups_Ozero__class_Ozero(_1155298)), _1155300)), 19870 ^ _782464 : [(19871 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155298), _1155300), _1155302)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155298), _1155300), _1155304))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155298), _1155302), _1155304)))], (19877 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155298), _1155302), _1155304)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155298), _1155300), _1155302)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155298), _1155300), _1155304))))]]], (19883 ^ _782464) ^ [_1155679, _1155681, _1155683, _1155685] : [class_Rings_Olinordered__ring__strict(_1155679), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155679), _1155681), c_Groups_Ozero__class_Ozero(_1155679))), 19890 ^ _782464 : [(19891 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155679), _1155681), _1155683)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155679), _1155681), _1155685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155679), _1155685), _1155683)))], (19897 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155679), _1155685), _1155683)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155679), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155679), _1155681), _1155683)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155679), _1155681), _1155685))))]]], (19903 ^ _782464) ^ [_1156060, _1156062, _1156064, _1156066, _1156068] : [class_Rings_Olinordered__semiring__strict(_1156060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156060), _1156062), _1156064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156060), _1156066), _1156068)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156060), c_Groups_Ozero__class_Ozero(_1156060)), _1156064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156060), c_Groups_Ozero__class_Ozero(_1156060)), _1156066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156060), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156060), _1156062), _1156066)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156060), _1156064), _1156068))))], (19925 ^ _782464) ^ [_1156483, _1156485, _1156487, _1156489, _1156491] : [class_Rings_Olinordered__semiring__strict(_1156483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156483), _1156485), _1156487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156483), _1156489), _1156491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156483), c_Groups_Ozero__class_Ozero(_1156483)), _1156485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156483), c_Groups_Ozero__class_Ozero(_1156483)), _1156489)), 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hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157752), c_Groups_Ozero__class_Ozero(_1157752)), _1157756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157752), _1157754), _1157758)))], (20005 ^ _782464) ^ [_1158021, _1158023, _1158025, _1158027] : [class_Rings_Olinordered__semiring__strict(_1158021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158021), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158021), _1158023), _1158025)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158021), _1158027), _1158025))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158021), c_Groups_Ozero__class_Ozero(_1158021)), _1158025)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158021), _1158023), _1158027)))], (20019 ^ _782464) ^ [_1158290, _1158292, _1158294, _1158296] : [class_Rings_Olinordered__semiring(_1158290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158290), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158290), _1158292), _1158294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158290), _1158292), _1158296))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158290), c_Groups_Ozero__class_Ozero(_1158290)), _1158292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158290), _1158294), _1158296)))], (20033 ^ _782464) ^ [_1158559, _1158561, _1158563, _1158565] : [class_Rings_Olinordered__semiring__strict(_1158559), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158559), _1158561), _1158563)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158559), _1158561), _1158565))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158559), c_Groups_Ozero__class_Ozero(_1158559)), _1158561)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158559), _1158563), _1158565)))], (20047 ^ _782464) ^ [_1158828, _1158830, _1158832, _1158834] : [class_Rings_Olinordered__semiring__strict(_1158828), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158828), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158828), _1158830), _1158832)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158828), _1158834), _1158832))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158828), c_Groups_Ozero__class_Ozero(_1158828)), _1158832)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158828), _1158830), _1158834)))], (20061 ^ _782464) ^ [_1159097, _1159099, _1159101, _1159103] : [class_Rings_Olinordered__semiring__strict(_1159097), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159097), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159097), _1159099), _1159101)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159097), _1159099), _1159103))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159097), c_Groups_Ozero__class_Ozero(_1159097)), _1159099)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159097), _1159101), _1159103)))], (20075 ^ _782464) ^ [_1159366, _1159368, _1159370] : [class_Rings_Olinordered__idom(_1159366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159366), c_Groups_Ozero__class_Ozero(_1159366)), _1159368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159366), c_Groups_Ozero__class_Ozero(_1159366)), _1159370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159366), _1159370), c_Groups_Oone__class_Oone(_1159366))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159366), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159366), _1159368), _1159370)), _1159368)))], (20093 ^ _782464) ^ [_1159689, _1159691, _1159693] : [class_Rings_Olinordered__idom(_1159689), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159689), c_Groups_Ozero__class_Ozero(_1159689)), _1159691)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159689), c_Groups_Ozero__class_Ozero(_1159689)), _1159693)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159689), _1159693), c_Groups_Oone__class_Oone(_1159689))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159689), 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hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160630), _1160632)))), 20146 ^ _782464 : [(20147 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160630), _1160632)))], (20149 ^ _782464) ^ [] : [hBOOL(hAPP(_1160628, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20151 ^ _782464 : [(20152 ^ _782464) ^ [] : [-(_1160630 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160632), 20150 ^ [_1160628, _1160630, _1160632]))], (20154 ^ _782464) ^ [] : [hBOOL(hAPP(_1160628, 20150 ^ [_1160628, _1160630, _1160632]))]]], (20127 ^ _782464) ^ [_1160344, _1160346, _1160348] : [hBOOL(hAPP(_1160344, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160346), _1160348))), 20130 ^ _782464 : [(20131 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160346), _1160348)), -(hBOOL(hAPP(_1160344, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20137 ^ _782464) ^ [_1160529] : [_1160346 = 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[hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160933), _1160935)), -(hBOOL(hAPP(_1160931, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20168 ^ _782464) ^ [_1161122] : [_1160933 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160935), _1161122), -(hBOOL(hAPP(_1160931, _1161122)))]]], (20189 ^ _782464) ^ [_1161516, _1161518, _1161520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161516)), 20192 ^ _782464 : [(20193 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161516), _1161518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161516), _1161520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161518), _1161520)))], (20199 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161518), _1161520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161516), _1161518)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161516), _1161520))))]]], (20215 ^ _782464) ^ [_1161994, _1161996, _1161998] : [20216 ^ _782464 : [(20217 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161996)))], (20219 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161994), _1161998))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161994), _1161996)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161998), _1161996))))], (20205 ^ _782464) ^ [_1161817, _1161819, _1161821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161817), _1161819)), 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_1162680), _1162678) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20255 ^ _782464 : [(20256 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1162676), 20254 ^ [_1162676, _1162678, _1162680]), _1162678)))], (20258 ^ _782464) ^ [] : [-(hAPP(_1162680, 20254 ^ [_1162676, _1162678, _1162680]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20260 ^ _782464) ^ [_1162996] : [hBOOL(hAPP(hAPP(c_member(_1162676), _1162996), _1162678)), -(20254 ^ [_1162676, _1162678, _1162680] = _1162996), -(hAPP(_1162680, _1162996) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20270 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1162676, tc_Nat_Onat), _1162680), _1162678) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 20271 ^ _782464 : [(20272 ^ _782464) ^ [_1163157] : [hBOOL(hAPP(hAPP(c_member(_1162676), _1163157), _1162678)), hAPP(_1162680, _1163157) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20280 ^ _782464 : [(20281 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1162676), 20279 ^ [_1162676, _1162678, _1162680, _1163157]), _1162678)))], (20283 ^ _782464) ^ [] : [_1163157 = 20279 ^ [_1162676, _1162678, _1162680, _1163157]], (20285 ^ _782464) ^ [] : [hAPP(_1162680, 20279 ^ [_1162676, _1162678, _1162680, _1163157]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (20289 ^ _782464) ^ [_1163510, _1163512, _1163514, _1163516, _1163518] : [class_Groups_Ocomm__monoid__add(_1163510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1163512), _1163514)), 20296 ^ _782464 : [(20297 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1163512), _1163516), _1163514)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163512, _1163510), hAPP(hAPP(c_COMBC(_1163512, _1163510, _1163510), hAPP(hAPP(c_COMBS(_1163512, _1163510, tc_fun(_1163510, _1163510)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163510, tc_fun(_1163510, _1163510)), _1163512), c_If(_1163510)), hAPP(c_fequal, _1163516))), _1163518)), c_Groups_Ozero__class_Ozero(_1163510))), _1163514) = hAPP(_1163518, _1163516))], (20303 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1163512), _1163516), _1163514))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163512, _1163510), hAPP(hAPP(c_COMBC(_1163512, _1163510, _1163510), hAPP(hAPP(c_COMBS(_1163512, _1163510, tc_fun(_1163510, _1163510)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163510, tc_fun(_1163510, _1163510)), _1163512), c_If(_1163510)), hAPP(c_fequal, _1163516))), _1163518)), c_Groups_Ozero__class_Ozero(_1163510))), _1163514) = c_Groups_Ozero__class_Ozero(_1163510))]]], (20309 ^ _782464) ^ [_1164020, _1164022, _1164024, _1164026, _1164028] : [class_Groups_Ocomm__monoid__add(_1164020), hBOOL(hAPP(c_Finite__Set_Ofinite(_1164022), _1164024)), 20316 ^ _782464 : [(20317 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1164022), _1164026), _1164024)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1164022, _1164020), hAPP(hAPP(c_COMBC(_1164022, _1164020, _1164020), hAPP(hAPP(c_COMBS(_1164022, _1164020, tc_fun(_1164020, _1164020)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1164020, tc_fun(_1164020, _1164020)), _1164022), c_If(_1164020)), hAPP(hAPP(c_COMBC(_1164022, _1164022, tc_HOL_Obool), c_fequal), _1164026))), _1164028)), c_Groups_Ozero__class_Ozero(_1164020))), _1164024) = hAPP(_1164028, _1164026))], (20323 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1164022), _1164026), _1164024))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1164022, _1164020), hAPP(hAPP(c_COMBC(_1164022, _1164020, _1164020), hAPP(hAPP(c_COMBS(_1164022, _1164020, tc_fun(_1164020, _1164020)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1164020, tc_fun(_1164020, _1164020)), _1164022), c_If(_1164020)), hAPP(hAPP(c_COMBC(_1164022, _1164022, tc_HOL_Obool), c_fequal), _1164026))), _1164028)), c_Groups_Ozero__class_Ozero(_1164020))), _1164024) = c_Groups_Ozero__class_Ozero(_1164020))]]], (20329 ^ _782464) ^ [_1164558, _1164560, _1164562, _1164564, _1164566, _1164568] : [class_Rings_Olinordered__semiring__1(_1164558), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164558), _1164560), _1164562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164558), _1164564), _1164562)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164558), c_Groups_Ozero__class_Ozero(_1164558)), _1164566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164558), c_Groups_Ozero__class_Ozero(_1164558)), _1164568)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164558), _1164566), _1164568) = c_Groups_Oone__class_Oone(_1164558), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164558), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164558), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164558), _1164566), _1164560)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164558), _1164568), _1164564))), _1164562)))], (20355 ^ _782464) ^ [_1165087, _1165089] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165087, 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(_1165087, tc_HOL_Obool)), tc_fun(_1165087, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1165087, tc_HOL_Obool)), tc_fun(_1165087, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165087, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1165089)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165087, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1165089))], (20357 ^ _782464) ^ [_1165183, _1165185, _1165187, _1165189] : [class_Groups_Ocomm__monoid__add(_1165183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165185), _1165187)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165185, _1165183), _1165189), _1165187) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1165183, _1165185, c_Groups_Oplus__class_Oplus(_1165183)), _1165189), c_Groups_Ozero__class_Ozero(_1165183)), _1165187))], (20367 ^ _782464) ^ [_1165378, _1165380, _1165382, _1165384] : [class_Groups_Ocomm__monoid__add(_1165378), 20370 ^ _782464 : [(20371 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165380), _1165382)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165380, _1165378), _1165384), _1165382) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1165378, _1165380, c_Groups_Oplus__class_Oplus(_1165378)), _1165384), c_Groups_Ozero__class_Ozero(_1165378)), _1165382))], (20377 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1165380), _1165382))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165380, _1165378), _1165384), _1165382) = c_Groups_Ozero__class_Ozero(_1165378))]]], (20383 ^ _782464) ^ [_1165650, _1165652, _1165654, _1165656, _1165658] : [class_Groups_Ocomm__monoid__add(_1165650), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165652), _1165654)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165652, _1165650), _1165656), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1165652, tc_HOL_Obool)), _1165654), _1165658)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165652, _1165650), hAPP(hAPP(c_COMBC(_1165652, _1165650, _1165650), hAPP(hAPP(c_COMBS(_1165652, _1165650, tc_fun(_1165650, _1165650)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165650, tc_fun(_1165650, _1165650)), _1165652), c_If(_1165650)), hAPP(hAPP(c_COMBC(_1165652, tc_fun(_1165652, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165652)), _1165658))), _1165656)), c_Groups_Ozero__class_Ozero(_1165650))), _1165654))], (20393 ^ _782464) ^ [_1165971, _1165973, _1165975, _1165977, _1165979, _1165981] : [class_Rings_Olinordered__semiring__1__strict(_1165971), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165971), _1165973), _1165975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165971), _1165977), _1165975)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165971), c_Groups_Ozero__class_Ozero(_1165971)), _1165979)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165971), c_Groups_Ozero__class_Ozero(_1165971)), _1165981)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165971), _1165979), _1165981) = c_Groups_Oone__class_Oone(_1165971), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165971), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165971), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165971), _1165979), _1165973)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165971), _1165981), _1165977))), _1165975)))], (20419 ^ _782464) ^ [_1166512, _1166514, _1166516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166512), _1166514)), -(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)), _1166512)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166516), _1166514)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166516), _1166512)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166514), _1166512)))], (20425 ^ _782464) ^ [_1166664, _1166666, _1166668] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166664), _1166666))), 20428 ^ _782464 : [(20429 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166668), _1166666)), -(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)), _1166664)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166668), _1166666)) = 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))))], (20435 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166668), _1166666))), -(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)), _1166664)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166668), _1166666)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (20441 ^ _782464) ^ [_1166933, _1166935, _1166937] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1166933, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1166935)), _1166937) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1166933, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1166933, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1166935)), _1166937)), hAPP(_1166937, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20443 ^ _782464) ^ [_1167005, _1167007] : [class_Rings_Ocomm__semiring__1(_1167005), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167005), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167005), c_Groups_Oone__class_Oone(_1167005)), c_Groups_Oone__class_Oone(_1167005))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1167005), c_Nat_Osemiring__1__class_Oof__nat(_1167005)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1167007))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167005), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1167005), _1167007)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167005), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1167005), _1167007)), c_Groups_Oone__class_Oone(_1167005))))], (20449 ^ _782464) ^ [_1167215, _1167217] : [_1167215 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167215), _1167217) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20455 ^ _782464) ^ [_1167298, _1167300] : [-(_1167298 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167298), _1167300) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1167300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167298), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1167300)))], (20461 ^ _782464) ^ [_1167360, _1167362, _1167364] : [class_Rings_Olinordered__ring(_1167360), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167360), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167360), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167360), _1167362), _1167362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167360), _1167364), _1167364))), c_Groups_Ozero__class_Ozero(_1167360)))], (20467 ^ _782464) ^ [_1167504, _1167506, _1167508] : [class_Rings_Olinordered__ring__strict(_1167504), 20470 ^ _782464 : [(20481 ^ _782464) ^ [] : [20482 ^ _782464 : [(20483 ^ _782464) ^ [] : [-(_1167506 = c_Groups_Ozero__class_Ozero(_1167504))], (20485 ^ _782464) ^ [] : [-(_1167508 = c_Groups_Ozero__class_Ozero(_1167504))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167504), c_Groups_Ozero__class_Ozero(_1167504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167504), _1167506), _1167506)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167504), _1167508), _1167508)))))], (20471 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167504), c_Groups_Ozero__class_Ozero(_1167504)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167504), _1167506), _1167506)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167504), _1167508), _1167508)))), _1167506 = c_Groups_Ozero__class_Ozero(_1167504), _1167508 = c_Groups_Ozero__class_Ozero(_1167504)]]], (20489 ^ _782464) ^ [_1167879, _1167881, _1167883] : [class_Rings_Olinordered__ring(_1167879), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167879), c_Groups_Ozero__class_Ozero(_1167879)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167879), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167879), _1167881), _1167881)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167879), _1167883), _1167883)))))], (20495 ^ _782464) ^ [_1168022, _1168024, _1168026] : [class_Rings_Olinordered__ring__strict(_1168022), 20498 ^ _782464 : [(20499 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168022), _1168024), _1168024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168022), _1168026), _1168026))), c_Groups_Ozero__class_Ozero(_1168022))), 20502 ^ _782464 : [(20503 ^ _782464) ^ [] : [-(_1168024 = c_Groups_Ozero__class_Ozero(_1168022))], (20505 ^ _782464) ^ [] : [-(_1168026 = c_Groups_Ozero__class_Ozero(_1168022))]]], (20507 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1168022), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1168022), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168022), _1168024), _1168024)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1168022), _1168026), _1168026))), c_Groups_Ozero__class_Ozero(_1168022)))), _1168024 = c_Groups_Ozero__class_Ozero(_1168022), _1168026 = c_Groups_Ozero__class_Ozero(_1168022)]]], (20517 ^ _782464) ^ [_1168418, _1168420, _1168422, _1168424] : [class_Rings_Osemiring__1(_1168418), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168418), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168420, tc_Nat_Onat), _1168422), _1168424)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168420, _1168418), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1168418, _1168420), c_Nat_Osemiring__1__class_Oof__nat(_1168418)), _1168422)), _1168424))], (20523 ^ _782464) ^ [_1168567, _1168569] : [class_Rings_Osemiring__1(_1168567), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168567), _1168569) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1168567, hAPP(hAPP(c_COMBC(_1168567, _1168567, _1168567), c_Groups_Oplus__class_Oplus(_1168567)), c_Groups_Oone__class_Oone(_1168567)), _1168569, c_Groups_Ozero__class_Ozero(_1168567)))], (20529 ^ _782464) ^ [_1168694, _1168696, _1168698] : [class_Rings_Osemiring__1(_1168694), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1168694, _1168696, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1168698) = _1168698)], (20535 ^ _782464) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20537 ^ _782464) ^ [_1168814, _1168816] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168814)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168816)))), 20540 ^ _782464 : [(20541 ^ _782464) ^ [] : [-(_1168814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20543 ^ _782464) ^ [] : [-(_1168816 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20545 ^ _782464) ^ [_1168941, _1168943] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168941)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168943))))), _1168941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1168943 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20555 ^ _782464) ^ [_1169112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169112)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1169112 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20561 ^ _782464) ^ [_1169199] : [_1169199 = 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), _1169199)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20567 ^ _782464) ^ [_1169304] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169304) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1169304 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20573 ^ _782464) ^ [_1169381] : [_1169381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169381) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20579 ^ _782464) ^ [] : [-(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))], (20581 ^ _782464) ^ [_1169497, _1169499] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169497)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169499), 20584 ^ _782464 : [(20585 ^ _782464) ^ [] : [-(_1169497 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20587 ^ _782464) ^ [] : [-(_1169499 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20589 ^ _782464) ^ [_1169614, _1169616] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169614)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169616)), _1169614 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1169616 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20599 ^ _782464) ^ [_1169778, _1169780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169778)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169780))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169778), _1169780)))], (20605 ^ _782464) ^ [_1169883, _1169885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169883), _1169885)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169883)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169885))))], (20611 ^ _782464) ^ [_1170006] : [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), _1170006))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170006)))], (20617 ^ _782464) ^ [_1170091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170091)), -(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), _1170091))))], (20623 ^ _782464) ^ [_1170182, _1170184, _1170186] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170182), _1170184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170186)), -(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), _1170186)), _1170182)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170186)), _1170184))))], (20633 ^ _782464) ^ [_1170375, _1170377] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170375)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170377)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1170375), _1170377)))], (20635 ^ _782464) ^ [_1170421, _1170423, _1170425] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170421)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170423)), _1170425)) = 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), _1170421), _1170423))), _1170425))], (20637 ^ _782464) ^ [_1170496, _1170498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170496)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170496), _1170498)))], (20643 ^ _782464) ^ [_1170601, _1170603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170601), _1170603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170601)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170603))))], (20649 ^ _782464) ^ [_1170712, _1170714] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170712), _1170714)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170712)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170714)))], (20651 ^ _782464) ^ [_1170758, _1170760] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170758)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170760)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170758), _1170760)))], (20653 ^ _782464) ^ [] : [-(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))], (20655 ^ _782464) ^ [] : [-(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))))], (20657 ^ _782464) ^ [_1170840, _1170842, _1170844] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170840, tc_Nat_Onat), _1170842), _1170844)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170840, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1170840), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1170842)), _1170844))], (20659 ^ _782464) ^ [_1170898, _1170900] : [class_Groups_Olinordered__ab__group__add(_1170898), 20662 ^ _782464 : [(20663 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170898), _1170900), _1170900) = c_Groups_Ozero__class_Ozero(_1170898), -(_1170900 = c_Groups_Ozero__class_Ozero(_1170898))], (20669 ^ _782464) ^ [] : [_1170900 = c_Groups_Ozero__class_Ozero(_1170898), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170898), _1170900), _1170900) = c_Groups_Ozero__class_Ozero(_1170898))]]], (20675 ^ _782464) ^ [_1171139, _1171141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1171139), _1171141)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1171141)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1171139)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171141), _1171139)))], (20681 ^ _782464) ^ [_1171268, _1171270] : [class_Rings_Olinordered__idom(_1171268), 20684 ^ _782464 : [(20685 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171268), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171268), _1171270), _1171270)), c_Groups_Ozero__class_Ozero(_1171268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171268), _1171270), c_Groups_Ozero__class_Ozero(_1171268))))], (20691 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171268), _1171270), c_Groups_Ozero__class_Ozero(_1171268))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171268), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171268), _1171270), _1171270)), c_Groups_Ozero__class_Ozero(_1171268))))]]], (20697 ^ _782464) ^ [_1171551, _1171553, _1171555] : [class_Rings_Olinordered__ring__strict(_1171551), 20700 ^ _782464 : [(20701 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171551), _1171553), _1171553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171551), _1171555), _1171555)) = c_Groups_Ozero__class_Ozero(_1171551), 20704 ^ _782464 : [(20705 ^ _782464) ^ [] : [-(_1171553 = c_Groups_Ozero__class_Ozero(_1171551))], (20707 ^ _782464) ^ [] : [-(_1171555 = c_Groups_Ozero__class_Ozero(_1171551))]]], (20709 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171551), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171551), _1171553), _1171553)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171551), _1171555), _1171555)) = c_Groups_Ozero__class_Ozero(_1171551)), _1171553 = c_Groups_Ozero__class_Ozero(_1171551), _1171555 = c_Groups_Ozero__class_Ozero(_1171551)]]], (20719 ^ _782464) ^ [_1171941, _1171943] : [20727 ^ _782464 : [(20728 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20726 ^ [_1171941, _1171943]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171941))))], (20730 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1171943, 20726 ^ [_1171941, _1171943])))]], 20720 ^ _782464 : [(20721 ^ _782464) ^ [_1172010] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172010), _1171941)), hBOOL(hAPP(_1171943, _1172010))]]], (20732 ^ _782464) ^ [_1172171, _1172173] : [20740 ^ _782464 : [(20741 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20739 ^ [_1172171, _1172173]), _1172171)))], (20743 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1172173, 20739 ^ [_1172171, _1172173])))]], 20733 ^ _782464 : [(20734 ^ _782464) ^ [_1172240] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1172240), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172171))), hBOOL(hAPP(_1172173, _1172240))]]], (20745 ^ _782464) ^ [_1172426, _1172428] : [20747 ^ _782464 : [(20748 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20746 ^ [_1172426, _1172428]), _1172426)))], (20750 ^ _782464) ^ [] : [hBOOL(hAPP(_1172428, 20746 ^ [_1172426, _1172428]))]], 20751 ^ _782464 : [(20752 ^ _782464) ^ [_1172577] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1172577), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172426))), -(hBOOL(hAPP(_1172428, _1172577)))]]], (20758 ^ _782464) ^ [_1172680, _1172682] : [20760 ^ _782464 : [(20761 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20759 ^ [_1172680, _1172682]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172680))))], (20763 ^ _782464) ^ [] : [hBOOL(hAPP(_1172682, 20759 ^ [_1172680, _1172682]))]], 20764 ^ _782464 : [(20765 ^ _782464) ^ [_1172835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172835), _1172680)), -(hBOOL(hAPP(_1172682, _1172835)))]]], (20771 ^ _782464) ^ [_1172951, _1172953] : [20779 ^ _782464 : [(20780 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20778 ^ [_1172951, _1172953]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172951))))], (20782 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1172953, 20778 ^ [_1172951, _1172953])))]], 20772 ^ _782464 : [(20773 ^ _782464) ^ [_1173019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173019), _1172951)), hBOOL(hAPP(_1172953, _1173019))]]], (20784 ^ _782464) ^ [_1173179, _1173181] : [20792 ^ _782464 : [(20793 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20791 ^ [_1173179, _1173181]), _1173179)))], (20795 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1173181, 20791 ^ [_1173179, _1173181])))]], 20785 ^ _782464 : [(20786 ^ _782464) ^ [_1173247] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173247), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173179))), hBOOL(hAPP(_1173181, _1173247))]]], (20797 ^ _782464) ^ [_1173431, _1173433] : [20799 ^ _782464 : [(20800 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20798 ^ [_1173431, _1173433]), _1173431)))], (20802 ^ _782464) ^ [] : [hBOOL(hAPP(_1173433, 20798 ^ [_1173431, _1173433]))]], 20803 ^ _782464 : [(20804 ^ _782464) ^ [_1173581] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173581), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173431))), -(hBOOL(hAPP(_1173433, _1173581)))]]], (20810 ^ _782464) ^ [_1173682, _1173684] : [20812 ^ _782464 : [(20813 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20811 ^ [_1173682, _1173684]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173682))))], (20815 ^ _782464) ^ [] : [hBOOL(hAPP(_1173684, 20811 ^ [_1173682, _1173684]))]], 20816 ^ _782464 : [(20817 ^ _782464) ^ [_1173835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173835), _1173682)), -(hBOOL(hAPP(_1173684, _1173835)))]]], (20839 ^ _782464) ^ [_1174243, _1174245, _1174247] : [-(hBOOL(hAPP(_1174243, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174245), _1174247))))), 20842 ^ _782464 : [(20843 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174247), _1174245)))], (20845 ^ _782464) ^ [] : [hBOOL(hAPP(_1174243, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174245)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174247))))]], 20846 ^ _782464 : [(20847 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174245), _1174247)))], (20849 ^ _782464) ^ [] : [hBOOL(hAPP(_1174243, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (20823 ^ _782464) ^ [_1173954, _1173956, _1173958] : [hBOOL(hAPP(_1173954, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1173956), _1173958)))), 20826 ^ _782464 : [(20827 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173958), _1173956)), -(hBOOL(hAPP(_1173954, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173956)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173958)))))], (20833 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173956), _1173958)), -(hBOOL(hAPP(_1173954, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (20853 ^ _782464) ^ [_1174518, _1174520, _1174522, _1174524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174518, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174518, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20854 ^ [_1174518, _1174520, _1174522, _1174524])), _1174520)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174518, 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), 20854 ^ [_1174518, _1174520, _1174522, _1174524]), _1174522))), _1174524))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174518, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174518, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1174520)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174518, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1174524))))], (20860 ^ _782464) ^ [_1174848, _1174850] : [-(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), _1174848))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174850))))], (20862 ^ _782464) ^ [_1174887] : [-(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), _1174887))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20864 ^ _782464) ^ [_1174921] : [-(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), _1174921))))], (20866 ^ _782464) ^ [_1174964, _1174966] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174964) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174966), -(_1174964 = _1174966)], (20872 ^ _782464) ^ [_1175049, _1175051] : [_1175049 = _1175051, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175049) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175051))], (20878 ^ _782464) ^ [] : [-(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))], (20880 ^ _782464) ^ [] : [-(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))))], (20882 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (20884 ^ _782464) ^ [_1175200, _1175202] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175200)), 20887 ^ _782464 : [(20888 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175200), _1175202) = c_Groups_Oone__class_Oone(tc_Int_Oint), 20891 ^ _782464 : [(20892 ^ _782464) ^ [] : [-(_1175200 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (20894 ^ _782464) ^ [] : [-(_1175202 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (20896 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175200), _1175202) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1175200 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1175202 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (20906 ^ _782464) ^ [_1175501, _1175503, _1175505] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175501), _1175503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175505)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175505), _1175501)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175505), _1175503))))], (20916 ^ _782464) ^ [_1175694, _1175696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175694)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175696))))], (20918 ^ _782464) ^ [_1175742] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175742)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20920 ^ _782464) ^ [_1175788, _1175790] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175788), _1175790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175788), _1175790)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20926 ^ _782464) ^ [_1175893, _1175895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175893), _1175895)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175893), _1175895)))], (20932 ^ _782464) ^ [_1176004] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176004), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1176004)], (20934 ^ _782464) ^ [_1176033] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176033) = _1176033)], (20936 ^ _782464) ^ [_1176074, _1176076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176074), _1176076)), -(_1176076 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176074), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20939 ^ [_1176074, _1176076])))], (20943 ^ _782464) ^ [_1176187, _1176189] : [20944 ^ _782464 : [(20945 ^ _782464) ^ [_1176240] : [_1176189 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176187), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1176240))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176187), _1176189)))], (20949 ^ _782464) ^ [_1176307] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176307)), _1176307) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20951 ^ _782464) ^ [_1176339, _1176341] : [-(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)), _1176339)), 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), _1176341), _1176339))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1176339), _1176341))], (20953 ^ _782464) ^ [_1176389] : [-(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)), _1176389))))], (20955 ^ _782464) ^ [_1176426] : [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)), _1176426)), _1176426) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20957 ^ _782464) ^ [_1176470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176470)))], (20963 ^ _782464) ^ [_1176549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176549)))], (20969 ^ _782464) ^ [_1176634] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176634)), -(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)), _1176634))))], (20975 ^ _782464) ^ [_1176735] : [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)), _1176735)), _1176735)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176735), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20981 ^ _782464) ^ [_1176844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176844), 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)), _1176844)), _1176844)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20987 ^ _782464) ^ [_1176968, _1176970] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176968), _1176970)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1176970, _1176968) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (20993 ^ _782464) ^ [_1177057, _1177059] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177057), _1177059))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1177059, _1177057) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1177059), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177059), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1177057)))], (20999 ^ _782464) ^ [_1177135, _1177137] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177135), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177137), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177135), _1177137)))], (21005 ^ _782464) ^ [_1177240, _1177242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177240), _1177242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177240), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177242), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21021 ^ _782464) ^ [_1177484, _1177486] : [21022 ^ _782464 : [(21023 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177484), _1177486))], (21025 ^ _782464) ^ [] : [_1177484 = _1177486]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177484), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177486), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21011 ^ _782464) ^ [_1177366, _1177368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177368), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177366), _1177368))), -(_1177366 = _1177368)], (21029 ^ _782464) ^ [_1177633, _1177635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177633), _1177635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177633), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177635)))], (21035 ^ _782464) ^ [_1177757, _1177759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177757), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177757), _1177759)))], (21041 ^ _782464) ^ [_1177862, _1177864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177862), _1177864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177862), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177864)))], (21047 ^ _782464) ^ [_1177988, _1177990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177988), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177990), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177988), _1177990)))], (21053 ^ _782464) ^ [_1178093, _1178095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178093), _1178095)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178093), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178095), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21059 ^ _782464) ^ [_1178204, _1178206, _1178208] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178204), _1178206)), _1178208) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178204), _1178208)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178206), _1178208)))], (21061 ^ _782464) ^ [_1178261, _1178263, _1178265] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178261), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178263), _1178265)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178261), _1178263)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178261), _1178265)))], (21063 ^ _782464) ^ [_1178318, _1178320, _1178322] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178318), _1178320)), _1178322) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178318), _1178322)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178320), _1178322)))], (21065 ^ _782464) ^ [_1178375, _1178377, _1178379] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178375), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178377), _1178379)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178375), _1178377)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178375), _1178379)))], (21067 ^ _782464) ^ [_1178432, _1178434] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178432), _1178434) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178432), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178434)))], (21069 ^ _782464) ^ [_1178472, _1178474] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178472), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178474)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178472), _1178474))], (21071 ^ _782464) ^ [_1178512, _1178514] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178512), _1178514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178512)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178514)))], (21073 ^ _782464) ^ [_1178558, _1178560, _1178562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178558), _1178560)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178562), _1178558)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178562), _1178560))))], (21079 ^ _782464) ^ [_1178681, _1178683] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178681), _1178683) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178683), _1178681))], (21081 ^ _782464) ^ [_1178718, _1178720, _1178722] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178718), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178720), _1178722)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178720), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178718), _1178722)))], (21083 ^ _782464) ^ [_1178769, _1178771, _1178773] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178769), _1178771)), _1178773) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178769), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178771), _1178773)))], (21085 ^ _782464) ^ [_1178835, _1178837] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178835), _1178837)), 21088 ^ _782464 : [(21089 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178835), _1178837)))], (21091 ^ _782464) ^ [] : [_1178835 = _1178837]]], (21093 ^ _782464) ^ [_1178962, _1178964] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178962), _1178964))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178962), _1178964)), -(_1178962 = _1178964)], (21103 ^ _782464) ^ [_1179116, _1179118, _1179120, _1179122] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179116), _1179118)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179120), _1179122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179116), _1179120)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179118), _1179122))))], (21113 ^ _782464) ^ [_1179307, _1179309, _1179311] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179307), _1179309)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179307), _1179311)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179309), _1179311))))], (21119 ^ _782464) ^ [_1179426, _1179428] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179426), _1179428))), -(_1179426 = _1179428), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179428), _1179426)))], (21129 ^ _782464) ^ [_1179479, _1179481] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179479)), _1179481) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179479), _1179481)))], (21131 ^ _782464) ^ [_1179522, _1179524] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179522), _1179524) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179524), _1179522))], (21133 ^ _782464) ^ [_1179559, _1179561, _1179563] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179559), _1179561)), _1179563) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179561), _1179563)))], (21135 ^ _782464) ^ [_1179610] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179610), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1179610)], (21137 ^ _782464) ^ [_1179639] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1179639) = _1179639)], (21139 ^ _782464) ^ [_1179665] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179665)) = _1179665)], (21141 ^ _782464) ^ [_1179694, _1179696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179694), _1179696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179696), _1179694)), -(_1179694 = _1179696)], (21151 ^ _782464) ^ [_1179843, _1179845, _1179847] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179843), _1179845)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179845), _1179847)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179843), _1179847)))], (21161 ^ _782464) ^ [_1180002, _1180004] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180002), _1180004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180004), _1180002)))], (21167 ^ _782464) ^ [_1180048] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180048), _1180048)))], (21169 ^ _782464) ^ [_1180076, _1180078] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180076), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1180078) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1180076, _1180078))], (21171 ^ _782464) ^ [_1180117, _1180119] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180117), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180119) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1180117, _1180119))], (21173 ^ _782464) ^ [_1180156, _1180158] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1180156), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180158), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1180156, _1180158))], (21175 ^ _782464) ^ [_1180197, _1180199, _1180201] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180197)), _1180197 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180199), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180197), _1180201)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180199), _1180197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180201)))], (21189 ^ _782464) ^ [_1180426, _1180428, _1180430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180426)), _1180426 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180428), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180426), _1180430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180428)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180430), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (21203 ^ _782464) ^ [_1180655, _1180657, _1180659] : [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), _1180655), _1180657)), _1180659))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180659), _1180655)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180655)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180657)))], (21217 ^ _782464) ^ [_1180888, _1180890, _1180892] : [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), _1180888), _1180890)), _1180892)), 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)), _1180892)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180890), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21231 ^ _782464) ^ [_1181127, _1181129, _1181131, _1181133, _1181135] : [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), _1181127), _1181129)), _1181131)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181127), _1181133)), _1181135))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181131), _1181127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181135), _1181127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181129), _1181133)))], (21249 ^ _782464) ^ [_1181476, _1181478, _1181480, _1181482, _1181484, _1181486] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181476), _1181478)), _1181480) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181482), _1181484)), _1181486), 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), _1181482), _1181484)), _1181486))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181486), _1181482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181480)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181482)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181482), _1181476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181478), _1181484)))], (21275 ^ _782464) ^ [_1181975, _1181977] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1181975, _1181977))))], (21277 ^ _782464) ^ [_1182006, _1182008] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1182006), _1182008))))], (21279 ^ _782464) ^ [_1182039, _1182041] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1182039, _1182041))))], (21281 ^ _782464) ^ [_1182070, _1182072] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1182070, _1182072))))], (21283 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (21285 ^ _782464) ^ [_1182125, _1182127, _1182129, _1182131, _1182133, _1182135] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182125), _1182127)), _1182129) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182131), _1182133)), _1182135), 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), _1182131), _1182133)), _1182135)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182129), _1182125)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182135)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182131)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182131), _1182125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182133), _1182127)))], (21311 ^ _782464) ^ [_1182630, _1182632, _1182634, _1182636, _1182638] : [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), _1182630), _1182632)), _1182634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182630), _1182636)), _1182638))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182638), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182630), _1182638)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182630), _1182634)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182636), _1182632)))], (21329 ^ _782464) ^ [] : [-(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))))], (21331 ^ _782464) ^ [_1183015] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1183015)), -(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)), _1183015))))], (21337 ^ _782464) ^ [_1183100] : [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)), _1183100))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1183100)))], (21343 ^ _782464) ^ [] : [-(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)))], (21345 ^ _782464) ^ [_1183209, _1183211] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183209)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183211)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183209), _1183211)))], (21347 ^ _782464) ^ [_1183255, _1183257] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183255)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183257)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1183255), _1183257)))], (21349 ^ _782464) ^ [_1183316, _1183318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183316)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183318))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183316), _1183318)))], (21355 ^ _782464) ^ [_1183421, _1183423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183421), _1183423)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183421)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183423))))], (21361 ^ _782464) ^ [_1183547, _1183549] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183547), _1183549)), -(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)), _1183547)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183549))))], (21367 ^ _782464) ^ [_1183652, _1183654] : [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)), _1183652)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183652), _1183654)))], (21373 ^ _782464) ^ [_1183778, _1183780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183778), _1183780)), -(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)), _1183778)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183780))))], (21379 ^ _782464) ^ [_1183883, _1183885] : [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)), _1183883)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183885))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183883), _1183885)))], (21385 ^ _782464) ^ [_1184009, _1184011] : [_1184009 = _1184011, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184009) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184011))], (21391 ^ _782464) ^ [_1184094, _1184096] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184094) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184096), -(_1184094 = _1184096)], (21397 ^ _782464) ^ [_1184200, _1184202] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184200), _1184202)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184200)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184202))))], (21403 ^ _782464) ^ [_1184305, _1184307] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184305)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184307))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184305), _1184307)))], (21409 ^ _782464) ^ [_1184431, _1184433] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184431) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184433), -(_1184431 = _1184433)], (21415 ^ _782464) ^ [_1184516, _1184518] : [_1184516 = _1184518, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184516) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184518))], (21421 ^ _782464) ^ [] : [-(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))))], (21423 ^ _782464) ^ [] : [-(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)))], (21425 ^ _782464) ^ [_1184643, _1184645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184645)), -(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), _1184643), _1184645))))], (21435 ^ _782464) ^ [_1184796] : [-(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), _1184796))))], (21448 ^ _782464) ^ [_1185006] : [21449 ^ _782464 : [(21450 ^ _782464) ^ [_1185063] : [hBOOL(hAPP(_1185006, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185063)))]], 21452 ^ _782464 : [(21453 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21451 ^ [_1185006])))], (21455 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1185006, 21451 ^ [_1185006])))]]], (21437 ^ _782464) ^ [_1184836] : [-(hBOOL(hAPP(_1184836, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21444 ^ [_1184836])))), 21438 ^ _782464 : [(21439 ^ _782464) ^ [_1184888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184888)), hBOOL(hAPP(_1184836, _1184888))]]], (21457 ^ _782464) ^ [_1185167] : [21459 ^ _782464 : [(21460 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21458 ^ [_1185167])))], (21462 ^ _782464) ^ [] : [hBOOL(hAPP(_1185167, 21458 ^ [_1185167]))]], 21463 ^ _782464 : [(21464 ^ _782464) ^ [_1185294] : [-(hBOOL(hAPP(_1185167, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185294))))]]], (21466 ^ _782464) ^ [_1185324] : [hBOOL(hAPP(_1185324, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21467 ^ [_1185324]))), 21470 ^ _782464 : [(21471 ^ _782464) ^ [_1185424] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185424)), -(hBOOL(hAPP(_1185324, _1185424)))]]], (21477 ^ _782464) ^ [] : [-(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))))], (21479 ^ _782464) ^ [_1185533, _1185535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185535)), -(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), _1185533), _1185535))))], (21489 ^ _782464) ^ [_1185701, _1185703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185701)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185701), _1185703)))], (21495 ^ _782464) ^ [_1185806, _1185808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185806), _1185808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185806)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185808))))], (21501 ^ _782464) ^ [_1185917, _1185919, _1185921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185917)), 21504 ^ _782464 : [(21505 ^ _782464) ^ [_1186051] : [21507 ^ _782464 : [(21508 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21506 ^ [_1185917, _1185919, _1185921, _1186051]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1185917))))], (21511 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21509 ^ [_1185917, _1185919, _1185921, _1186051]), _1185919)))], (21513 ^ _782464) ^ [] : [-(_1186051 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21509 ^ [_1185917, _1185919, _1185921, _1186051]), 21506 ^ [_1185917, _1185919, _1185921, _1186051]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185921), _1186051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185921), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186051), _1185917))))]]], (21521 ^ _782464) ^ [_1186325, _1186327, _1186329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186325)), 21524 ^ _782464 : [(21525 ^ _782464) ^ [_1186459] : [21527 ^ _782464 : [(21528 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21526 ^ [_1186325, _1186327, _1186329, _1186459]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1186325))))], (21531 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21529 ^ [_1186325, _1186327, _1186329, _1186459]), _1186327)))], (21533 ^ _782464) ^ [] : [-(_1186459 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21529 ^ [_1186325, _1186327, _1186329, _1186459]), 21526 ^ [_1186325, _1186327, _1186329, _1186459]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186459), _1186329)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1186459), _1186325)), _1186329)))]]], (21541 ^ _782464) ^ [_1186733, _1186735, _1186737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186733)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186735), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1186737)), 21548 ^ _782464 : [(21549 ^ _782464) ^ [_1186941] : [21551 ^ _782464 : [(21552 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21550 ^ [_1186733, _1186735, _1186737, _1186941]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1186733))))], (21555 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21553 ^ [_1186733, _1186735, _1186737, _1186941]), _1186737)))], (21557 ^ _782464) ^ [] : [-(_1186941 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21553 ^ [_1186733, _1186735, _1186737, _1186941]), 21550 ^ [_1186733, _1186735, _1186737, _1186941]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186941), _1186735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186941), _1186733)), _1186735)))]]], (21565 ^ _782464) ^ [_1187217, _1187219, _1187221] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187217)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1187219), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1187221)), 21572 ^ _782464 : [(21573 ^ _782464) ^ [_1187425] : [21575 ^ _782464 : [(21576 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21574 ^ [_1187217, _1187219, _1187221, _1187425]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1187217))))], (21579 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21577 ^ [_1187217, _1187219, _1187221, _1187425]), _1187221)))], (21581 ^ _782464) ^ [] : [-(_1187425 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21577 ^ [_1187217, _1187219, _1187221, _1187425]), 21574 ^ [_1187217, _1187219, _1187221, _1187425]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187219), _1187425)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187219), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1187425), _1187217))))]]], (21589 ^ _782464) ^ [_1187701, _1187703, _1187705, _1187707, _1187709] : [class_Groups_Oordered__comm__monoid__add(_1187701), hBOOL(hAPP(c_Finite__Set_Ofinite(_1187703), _1187705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1187703, tc_HOL_Obool)), _1187707), _1187705)), 21603 ^ _782464 : [(21604 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187703), 21602 ^ [_1187701, _1187703, _1187705, _1187707, _1187709]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1187703, tc_HOL_Obool)), _1187705), _1187707))))], (21606 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187701), c_Groups_Ozero__class_Ozero(_1187701)), hAPP(_1187709, 21602 ^ [_1187701, _1187703, _1187705, _1187707, _1187709])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187701), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187703, _1187701), _1187709), _1187707)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187703, _1187701), _1187709), _1187705))))], (21610 ^ _782464) ^ [_1188187, _1188189] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188187)), 21619 ^ _782464 : [(21620 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1188189, 21615 ^ [_1188187, _1188189])))], (21622 ^ _782464) ^ [] : [hBOOL(hAPP(_1188189, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21615 ^ [_1188187, _1188189]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 21616 ^ [_1188187, _1188189]), _1188187))))]], 21623 ^ _782464 : [(21624 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1188189, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21615 ^ [_1188187, _1188189]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 21616 ^ [_1188187, _1188189]), _1188187)))))], (21626 ^ _782464) ^ [] : [hBOOL(hAPP(_1188189, 21615 ^ [_1188187, _1188189]))]], 21627 ^ _782464 : [(21628 ^ _782464) ^ [] : [21629 ^ _782464 : [(21630 ^ _782464) ^ [_1188619] : [hBOOL(hAPP(_1188189, _1188619))]], 21632 ^ _782464 : [(21633 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21631 ^ [_1188187, _1188189]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188187))))], (21635 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1188189, 21631 ^ [_1188187, _1188189])))]]], (21637 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1188189, 21644 ^ [_1188187, _1188189]))), 21638 ^ _782464 : [(21639 ^ _782464) ^ [_1188734] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1188734), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188187))), hBOOL(hAPP(_1188189, _1188734))]]]]], (21648 ^ _782464) ^ [_1188881, _1188883, _1188885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188881)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1188883), _1188885)), 21655 ^ _782464 : [(21656 ^ _782464) ^ [_1189071] : [21658 ^ _782464 : [(21659 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21657 ^ [_1188881, _1188883, _1188885, _1189071]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188881))))], (21662 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21660 ^ [_1188881, _1188883, _1188885, _1189071]), _1188885)))], (21664 ^ _782464) ^ [] : [-(_1189071 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21660 ^ [_1188881, _1188883, _1188885, _1189071]), 21657 ^ [_1188881, _1188883, _1188885, _1189071]))]], -(_1189071 = _1188883), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1189071), _1188881) = _1188883]]], (21672 ^ _782464) ^ [_1189331, _1189333, _1189335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189331)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1189333), _1189335)), 21679 ^ _782464 : [(21680 ^ _782464) ^ [_1189521] : [21682 ^ _782464 : [(21683 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21681 ^ [_1189331, _1189333, _1189335, _1189521]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1189331))))], (21686 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21684 ^ [_1189331, _1189333, _1189335, _1189521]), _1189335)))], (21688 ^ _782464) ^ [] : [-(_1189521 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21684 ^ [_1189331, _1189333, _1189335, _1189521]), 21681 ^ [_1189331, _1189333, _1189335, _1189521]))]], -(_1189521 = _1189333), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1189521), _1189331) = _1189333]]], (21696 ^ _782464) ^ [_1189781, _1189783, _1189785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189781)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1189783), _1189785)), 21703 ^ _782464 : [(21704 ^ _782464) ^ [_1189977] : [21706 ^ _782464 : [(21707 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21705 ^ [_1189781, _1189783, _1189785, _1189977]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1189781))))], (21710 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21708 ^ [_1189781, _1189783, _1189785, _1189977]), _1189785)))], (21712 ^ _782464) ^ [] : [-(_1189977 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21708 ^ [_1189781, _1189783, _1189785, _1189977]), 21705 ^ [_1189781, _1189783, _1189785, _1189977]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189783), _1189977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189783), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1189977), _1189781))))]]], (21720 ^ _782464) ^ [_1190253, _1190255, _1190257] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190253)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1190255), _1190257)), 21727 ^ _782464 : [(21728 ^ _782464) ^ [_1190449] : [21730 ^ _782464 : [(21731 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21729 ^ [_1190253, _1190255, _1190257, _1190449]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1190253))))], (21734 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21732 ^ [_1190253, _1190255, _1190257, _1190449]), _1190257)))], (21736 ^ _782464) ^ [] : [-(_1190449 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21732 ^ [_1190253, _1190255, _1190257, _1190449]), 21729 ^ [_1190253, _1190255, _1190257, _1190449]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190449), _1190255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190449), _1190253)), _1190255)))]]], (21744 ^ _782464) ^ [_1190725, _1190727, _1190729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190725)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190727), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1190729)), 21754 ^ _782464 : [(21755 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21753 ^ [_1190725, _1190727, _1190729]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1190725))))], (21758 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21756 ^ [_1190725, _1190727, _1190729]), _1190729)))], (21760 ^ _782464) ^ [] : [-(_1190727 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21756 ^ [_1190725, _1190727, _1190729]), 21753 ^ [_1190725, _1190727, _1190729]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190727), _1190725) = _1190727)], (21764 ^ _782464) ^ [_1191064, _1191066, _1191068] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191064)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191066), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1191068)), 21774 ^ _782464 : [(21775 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21773 ^ [_1191064, _1191066, _1191068]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191064))))], (21778 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21776 ^ [_1191064, _1191066, _1191068]), _1191068)))], (21780 ^ _782464) ^ [] : [-(_1191066 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21776 ^ [_1191064, _1191066, _1191068]), 21773 ^ [_1191064, _1191066, _1191068]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191066), _1191064) = _1191066)], (21784 ^ _782464) ^ [_1191403, _1191405, _1191407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191403)), 21787 ^ _782464 : [(21788 ^ _782464) ^ [_1191537] : [21790 ^ _782464 : [(21791 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21789 ^ [_1191403, _1191405, _1191407, _1191537]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191403))))], (21794 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21792 ^ [_1191403, _1191405, _1191407, _1191537]), _1191405)))], (21796 ^ _782464) ^ [] : [-(_1191537 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21792 ^ [_1191403, _1191405, _1191407, _1191537]), 21789 ^ [_1191403, _1191405, _1191407, _1191537]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191407), _1191537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191407), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191537), _1191403))))]]], (21804 ^ _782464) ^ [_1191811, _1191813, _1191815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191811)), 21807 ^ _782464 : [(21808 ^ _782464) ^ [_1191945] : [21810 ^ _782464 : [(21811 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21809 ^ [_1191811, _1191813, _1191815, _1191945]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191811))))], (21814 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21812 ^ [_1191811, _1191813, _1191815, _1191945]), _1191813)))], (21816 ^ _782464) ^ [] : [-(_1191945 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21812 ^ [_1191811, _1191813, _1191815, _1191945]), 21809 ^ [_1191811, _1191813, _1191815, _1191945]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191945), _1191815)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191945), _1191811)), _1191815)))]]], (21824 ^ _782464) ^ [_1192219, _1192221, _1192223, _1192225, _1192227] : [class_Groups_Ocomm__monoid__add(_1192219), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192221), _1192223)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192221), _1192225)), 21838 ^ _782464 : [(21839 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192221), 21837 ^ [_1192219, _1192221, _1192223, _1192225, _1192227]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1192221, tc_HOL_Obool)), _1192223), _1192225))))], (21841 ^ _782464) ^ [] : [hAPP(_1192227, 21837 ^ [_1192219, _1192221, _1192223, _1192225, _1192227]) = c_Groups_Ozero__class_Ozero(_1192219)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192221, _1192219), _1192227), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1192221, tc_HOL_Obool)), _1192223), _1192225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192219), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192221, _1192219), _1192227), _1192223)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192221, _1192219), _1192227), _1192225)))], (21845 ^ _782464) ^ [_1192714, _1192716, _1192718, _1192720, _1192722] : [class_Groups_Ocomm__monoid__add(_1192714), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192716), _1192718)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192716), _1192720)), 21859 ^ _782464 : [(21860 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192716), 21858 ^ [_1192714, _1192716, _1192718, _1192720, _1192722]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1192716, tc_HOL_Obool)), _1192718), _1192720))))], (21862 ^ _782464) ^ [] : [hAPP(_1192722, 21858 ^ [_1192714, _1192716, _1192718, _1192720, _1192722]) = c_Groups_Ozero__class_Ozero(_1192714)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192716, _1192714), _1192722), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1192716, tc_HOL_Obool)), _1192718), _1192720)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192714), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192716, _1192714), _1192722), _1192718)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192716, _1192714), _1192722), _1192720)))], (21866 ^ _782464) ^ [_1193209, _1193211, _1193213, _1193215, _1193217] : [class_Groups_Ocomm__monoid__add(_1193209), class_Groups_Oordered__ab__semigroup__add(_1193209), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193211), _1193213)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1193211, tc_HOL_Obool)), _1193215), _1193213)), 21884 ^ _782464 : [(21885 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193211), 21883 ^ [_1193209, _1193211, _1193213, _1193215, _1193217]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1193211, tc_HOL_Obool)), _1193213), _1193215))))], (21887 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193209), c_Groups_Ozero__class_Ozero(_1193209)), hAPP(_1193217, 21883 ^ [_1193209, _1193211, _1193213, _1193215, _1193217])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193209), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193211, _1193209), _1193217), _1193215)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193211, _1193209), _1193217), _1193213))))], (21891 ^ _782464) ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763] : [class_Groups_Ocomm__monoid__add(_1193753), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193755), _1193757)), 21901 ^ _782464 : [(21902 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193755), 21900 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763]), _1193757)))], (21905 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193755), 21903 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763]), _1193757)))], (21907 ^ _782464) ^ [] : [21900 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763] = 21903 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763]], (21909 ^ _782464) ^ [] : [-(hAPP(_1193759, 21900 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763]) = hAPP(_1193759, 21903 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763]))], (21911 ^ _782464) ^ [] : [hAPP(_1193761, hAPP(_1193759, 21900 ^ [_1193753, _1193755, _1193757, _1193759, _1193761, _1193763])) = c_Groups_Ozero__class_Ozero(_1193753)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193763, _1193753), _1193761), hAPP(c_Set_Oimage(_1193755, _1193763, _1193759), _1193757)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193755, _1193753), hAPP(c_Fun_Ocomp(_1193763, _1193753, _1193755, _1193761), _1193759)), _1193757))], (21915 ^ _782464) ^ [_1194490, _1194492, _1194494, _1194496] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194490, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21916 ^ [_1194490, _1194492, _1194494, _1194496])), _1194492) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194490, 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), 21916 ^ [_1194490, _1194492, _1194494, _1194496]), _1194494))), _1194496), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194490, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194492) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194490, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194496))], (21922 ^ _782464) ^ [_1194770, _1194772, _1194774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194770, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194770, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21923 ^ [_1194770, _1194772, _1194774])), _1194772)), _1194774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194770, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194770, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194772)), _1194774)))], (21929 ^ _782464) ^ [_1195005, _1195007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195005), _1195007)), -(c_Nat__Transfer_Otsub(_1195007, _1195005) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1195007), _1195005))], (21935 ^ _782464) ^ [_1195104, _1195106] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195104), _1195106))), -(c_Nat__Transfer_Otsub(_1195106, _1195104) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21941 ^ _782464) ^ [_1195150, _1195152] : [class_Rings_Olinordered__idom(_1195150), hBOOL(hAPP(hAPP(c_member(_1195150), _1195152), c_Int_Oring__1__class_OInts(_1195150))), 21948 ^ _782464 : [(21949 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195150), c_Groups_Oone__class_Oone(_1195150)), _1195152)), _1195152)), c_Groups_Ozero__class_Ozero(_1195150))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195150), _1195152), c_Groups_Ozero__class_Ozero(_1195150))))], (21955 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195150), _1195152), c_Groups_Ozero__class_Ozero(_1195150))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195150), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195150), c_Groups_Oone__class_Oone(_1195150)), _1195152)), _1195152)), c_Groups_Ozero__class_Ozero(_1195150))))]]], (21961 ^ _782464) ^ [_1195533, _1195535, _1195537] : [-(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), _1195533)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1195535))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195537))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195537), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195533), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195533), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195537), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1195535)))))], (21963 ^ _782464) ^ [_1195614, _1195616, _1195618] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1195614), _1195616)), hBOOL(hAPP(hAPP(c_member(_1195614), _1195618), _1195616)), -(hAPP(c_Finite__Set_Ocard(_1195614), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195614, tc_HOL_Obool)), _1195616), hAPP(hAPP(c_Set_Oinsert(_1195614), _1195618), c_Orderings_Obot__class_Obot(tc_fun(_1195614, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1195614), _1195616)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21973 ^ _782464) ^ [_1195849] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195849), hAPP(c_Nat_OSuc, _1195849))))], (21975 ^ _782464) ^ [_1195880, _1195882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195880), _1195882)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195880)), hAPP(c_Nat_OSuc, _1195882))))], (21981 ^ _782464) ^ [_1195989] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1195989))))], (21983 ^ _782464) ^ [_1196017, _1196019] : [-(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, _1196017)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1196019))))], (21985 ^ _782464) ^ [_1196059] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1196059)) = hAPP(c_Nat_OSuc, _1196059))], (21987 ^ _782464) ^ [_1196100] : [_1196100 = hAPP(c_Nat_OSuc, _1196100)], (21989 ^ _782464) ^ [_1196135] : [hAPP(c_Nat_OSuc, _1196135) = _1196135], (21991 ^ _782464) ^ [_1196176, _1196178] : [hAPP(c_Nat_OSuc, _1196176) = hAPP(c_Nat_OSuc, _1196178), -(_1196176 = _1196178)], (21997 ^ _782464) ^ [_1196261, _1196263] : [_1196261 = _1196263, -(hAPP(c_Nat_OSuc, _1196261) = hAPP(c_Nat_OSuc, _1196263))], (22003 ^ _782464) ^ [_1196352, _1196354] : [hAPP(c_Nat_OSuc, _1196352) = hAPP(c_Nat_OSuc, _1196354), -(_1196352 = _1196354)], (22009 ^ _782464) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (22011 ^ _782464) ^ [_1196459] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1196459) = 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)), _1196459)))], (22013 ^ _782464) ^ [_1196491, _1196493] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1196491, _1196493)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196493)), _1196491))], (22015 ^ _782464) ^ [_1196532, _1196534] : [class_Orderings_Oorder(_1196532), 22018 ^ _782464 : [(22019 ^ _782464) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1196532, _1196534), 22022 ^ _782464 : [(22023 ^ _782464) ^ [_1196666] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196532), hAPP(_1196534, _1196666)), hAPP(_1196534, hAPP(c_Nat_OSuc, _1196666)))))]]], (22025 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196532), hAPP(_1196534, 22026 ^ [_1196532, _1196534])), hAPP(_1196534, hAPP(c_Nat_OSuc, 22026 ^ [_1196532, _1196534])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1196532, _1196534))]]], (22032 ^ _782464) ^ [] : [-(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))], (22034 ^ _782464) ^ [_1196866] : [hAPP(c_Nat_OSuc, _1196866) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22036 ^ _782464) ^ [_1196901] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1196901)], (22038 ^ _782464) ^ [_1196936] : [hAPP(c_Nat_OSuc, _1196936) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22040 ^ _782464) ^ [_1196971] : [hAPP(c_Nat_OSuc, _1196971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22042 ^ _782464) ^ [_1197006] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1197006)], (22044 ^ _782464) ^ [_1197041] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1197041)], (22046 ^ _782464) ^ [_1197076, _1197078] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197076), _1197078))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197078), hAPP(c_Nat_OSuc, _1197076))))], (22052 ^ _782464) ^ [_1197121, _1197123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197123), hAPP(c_Nat_OSuc, _1197121))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197121), _1197123))], (22068 ^ _782464) ^ [_1197354, _1197356] : [22069 ^ _782464 : [(22070 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197354), _1197356))], (22072 ^ _782464) ^ [] : [_1197354 = _1197356]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197354), hAPP(c_Nat_OSuc, _1197356))))], (22058 ^ _782464) ^ [_1197242, _1197244] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197242), hAPP(c_Nat_OSuc, _1197244))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197242), _1197244))), -(_1197242 = _1197244)], (22076 ^ _782464) ^ [_1197512, _1197514] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197512)), hAPP(c_Nat_OSuc, _1197514))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197512), _1197514)))], (22082 ^ _782464) ^ [_1197617, _1197619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197617), _1197619)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197617)), hAPP(c_Nat_OSuc, _1197619))))], (22088 ^ _782464) ^ [_1197727, _1197729] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197727), _1197729))), 22091 ^ _782464 : [(22092 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197727), hAPP(c_Nat_OSuc, _1197729))), -(_1197727 = _1197729)], (22098 ^ _782464) ^ [] : [_1197727 = _1197729, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197727), hAPP(c_Nat_OSuc, _1197729))))]]], (22104 ^ _782464) ^ [_1197960, _1197962] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197960), _1197962))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197960), hAPP(c_Nat_OSuc, _1197962))), -(_1197962 = _1197960)], (22114 ^ _782464) ^ [_1198108, _1198110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198108), _1198110)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198108), hAPP(c_Nat_OSuc, _1198110))))], (22120 ^ _782464) ^ [_1198211, _1198213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198211), _1198213)), -(hAPP(c_Nat_OSuc, _1198211) = _1198213), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198211)), _1198213)))], (22130 ^ _782464) ^ [_1198335, _1198337, _1198339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198335), _1198337)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198337), _1198339)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198335)), _1198339)))], (22140 ^ _782464) ^ [_1198504, _1198506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198504), hAPP(c_Nat_OSuc, _1198506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198504), _1198506))), -(_1198504 = _1198506)], (22150 ^ _782464) ^ [_1198622, _1198624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198622)), _1198624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198622), _1198624)))], (22156 ^ _782464) ^ [_1198725, _1198727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198725)), hAPP(c_Nat_OSuc, _1198727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198725), _1198727)))], (22162 ^ _782464) ^ [_1198834, _1198836] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198834)), _1198836) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198834), hAPP(c_Nat_OSuc, _1198836)))], (22164 ^ _782464) ^ [_1198877, _1198879] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198877)), _1198879) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198877), _1198879)))], (22166 ^ _782464) ^ [_1198920, _1198922] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198920), hAPP(c_Nat_OSuc, _1198922)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198920), _1198922)))], (22168 ^ _782464) ^ [_1198972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198972)), _1198972))], (22170 ^ _782464) ^ [_1199012, _1199014] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199012), _1199014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199014)), _1199012)))], (22176 ^ _782464) ^ [_1199057, _1199059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199059)), _1199057)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199057), _1199059))], (22192 ^ _782464) ^ [_1199296, _1199298] : [22193 ^ _782464 : [(22194 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199296), _1199298))], (22196 ^ _782464) ^ [] : [_1199296 = hAPP(c_Nat_OSuc, _1199298)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199296), hAPP(c_Nat_OSuc, _1199298))))], (22182 ^ _782464) ^ [_1199178, _1199180] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199178), hAPP(c_Nat_OSuc, _1199180))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199178), _1199180))), -(_1199178 = hAPP(c_Nat_OSuc, _1199180))], (22200 ^ _782464) ^ [_1199460, _1199462] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199460)), hAPP(c_Nat_OSuc, _1199462))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199460), _1199462)))], (22206 ^ _782464) ^ [_1199565, _1199567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199565), _1199567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199565)), hAPP(c_Nat_OSuc, _1199567))))], (22212 ^ _782464) ^ [_1199676, _1199678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199676), _1199678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199676), hAPP(c_Nat_OSuc, _1199678))))], (22218 ^ _782464) ^ [_1199779, _1199781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199779), hAPP(c_Nat_OSuc, _1199781))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199779), _1199781))), -(_1199779 = hAPP(c_Nat_OSuc, _1199781))], (22228 ^ _782464) ^ [_1199903, _1199905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199903)), _1199905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199903), _1199905)))], (22234 ^ _782464) ^ [_1200006, _1200008, _1200010, _1200012, _1200014] : [c_Fun_Obij__betw(_1200006, _1200008, _1200010, _1200012, _1200014), -(hAPP(c_Finite__Set_Ocard(_1200006), _1200012) = hAPP(c_Finite__Set_Ocard(_1200008), _1200014))], (22240 ^ _782464) ^ [_1200115, _1200117] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200115)), hAPP(c_Nat_OSuc, _1200117)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200115), _1200117))], (22242 ^ _782464) ^ [_1200158, _1200160, _1200162] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200158)), _1200160)), hAPP(c_Nat_OSuc, _1200162)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200158), _1200160)), _1200162))], (22244 ^ _782464) ^ [_1200233, _1200235, _1200237] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200233)), _1200235) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200233)), _1200237), -(_1200235 = _1200237)], (22250 ^ _782464) ^ [_1200344, _1200346, _1200348] : [_1200346 = _1200348, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200344)), _1200346) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200344)), _1200348))], (22256 ^ _782464) ^ [_1200461, _1200463] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1200461, _1200463)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200463), hAPP(c_Nat_OSuc, _1200461)))], (22258 ^ _782464) ^ [_1200502] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1200502)) = _1200502)], (22260 ^ _782464) ^ [_1200531, _1200533, _1200535] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200531), _1200533)), 22263 ^ _782464 : [(22264 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1200531), _1200535), _1200533)), -(hAPP(c_Finite__Set_Ocard(_1200531), hAPP(hAPP(c_Set_Oinsert(_1200531), _1200535), _1200533)) = hAPP(c_Finite__Set_Ocard(_1200531), _1200533))], (22270 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200531), _1200535), _1200533))), -(hAPP(c_Finite__Set_Ocard(_1200531), hAPP(hAPP(c_Set_Oinsert(_1200531), _1200535), _1200533)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1200531), _1200533)))]]], (22276 ^ _782464) ^ [_1200825, _1200827, _1200829] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200825), _1200827)), -(hBOOL(hAPP(hAPP(c_member(_1200825), _1200829), _1200827))), -(hAPP(c_Finite__Set_Ocard(_1200825), hAPP(hAPP(c_Set_Oinsert(_1200825), _1200829), _1200827)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1200825), _1200827)))], (22286 ^ _782464) ^ [_1200983, _1200985] : [hBOOL(hAPP(_1200983, _1200985)), -(hBOOL(hAPP(_1200983, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1200983) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_Nat_Onat), _1200983), c_Nat_OSuc))))], (22296 ^ _782464) ^ [_1201113, _1201115, _1201117, _1201119] : [class_Rings_Osemiring__1(_1201113), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1201113, _1201115, hAPP(c_Nat_OSuc, _1201117), _1201119) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1201113, _1201115, _1201117, hAPP(_1201115, _1201119)))], (22302 ^ _782464) ^ [_1201224, _1201226, _1201228] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201224), _1201226)), -(hAPP(c_Finite__Set_Ocard(_1201224), hAPP(hAPP(c_Set_Oinsert(_1201224), _1201228), _1201226)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1201224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201224, tc_HOL_Obool)), _1201226), hAPP(hAPP(c_Set_Oinsert(_1201224), _1201228), c_Orderings_Obot__class_Obot(tc_fun(_1201224, tc_HOL_Obool)))))))], (22308 ^ _782464) ^ [_1201401] : [-(hAPP(c_Finite__Set_Ocard(_1201401), c_Orderings_Obot__class_Obot(tc_fun(_1201401, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22310 ^ _782464) ^ [_1201430, _1201432] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1201430), _1201432))), -(hAPP(c_Finite__Set_Ocard(_1201430), _1201432) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22316 ^ _782464) ^ [_1201475] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1201475))], (22318 ^ _782464) ^ [_1201500, _1201502] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201500), c_Orderings_Otop__class_Otop(tc_fun(_1201500, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1201500), _1201502) = hAPP(c_Finite__Set_Ocard(_1201500), c_Orderings_Otop__class_Otop(tc_fun(_1201500, tc_HOL_Obool))), -(_1201502 = c_Orderings_Otop__class_Otop(tc_fun(_1201500, tc_HOL_Obool)))], (22328 ^ _782464) ^ [_1201687, _1201689, _1201691, _1201693] : [c_Fun_Oinj__on(_1201687, _1201689, _1201691, _1201693), -(hAPP(c_Finite__Set_Ocard(_1201689), hAPP(c_Set_Oimage(_1201687, _1201689, _1201691), _1201693)) = hAPP(c_Finite__Set_Ocard(_1201687), _1201693))], (22334 ^ _782464) ^ [_1201806, _1201808, _1201810, _1201812] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201806), _1201808)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201810), _1201812)), 22341 ^ _782464 : [(22342 ^ _782464) ^ [] : [22343 ^ _782464 : [(22344 ^ _782464) ^ [_1201995] : [c_Fun_Obij__betw(_1201806, _1201810, _1201995, _1201808, _1201812)]], -(hAPP(c_Finite__Set_Ocard(_1201806), _1201808) = hAPP(c_Finite__Set_Ocard(_1201810), _1201812))], (22348 ^ _782464) ^ [] : [hAPP(c_Finite__Set_Ocard(_1201806), _1201808) = hAPP(c_Finite__Set_Ocard(_1201810), _1201812), -(c_Fun_Obij__betw(_1201806, _1201810, 22351 ^ [_1201806, _1201808, _1201810, _1201812], _1201808, _1201812))]]], (22355 ^ _782464) ^ [_1202175, _1202177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202175), hAPP(c_Nat_OSuc, _1202177))), -(_1202175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22363 ^ _782464 : [(22364 ^ _782464) ^ [] : [-(_1202175 = hAPP(c_Nat_OSuc, 22362 ^ [_1202175, _1202177]))], (22366 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22362 ^ [_1202175, _1202177]), _1202177)))]]], (22368 ^ _782464) ^ [_1202355, _1202357] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202355), hAPP(c_Nat_OSuc, _1202357)))), 22369 ^ _782464 : [(22370 ^ _782464) ^ [] : [_1202355 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22372 ^ _782464) ^ [_1202443] : [_1202355 = hAPP(c_Nat_OSuc, _1202443), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202443), _1202357))]]], (22380 ^ _782464) ^ [_1202589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202589), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1202589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22386 ^ _782464) ^ [_1202670] : [_1202670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202670), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (22392 ^ _782464) ^ [_1202769] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202769)), -(_1202769 = hAPP(c_Nat_OSuc, 22395 ^ [_1202769]))], (22399 ^ _782464) ^ [_1202860] : [22400 ^ _782464 : [(22401 ^ _782464) ^ [_1202902] : [_1202860 = hAPP(c_Nat_OSuc, _1202902)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202860)))], (22405 ^ _782464) ^ [_1202975, _1202977] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1202975), _1202977), 22410 ^ _782464 : [(22411 ^ _782464) ^ [] : [-(_1202975 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22413 ^ _782464) ^ [] : [-(_1202977 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22414 ^ _782464 : [(22415 ^ _782464) ^ [] : [-(_1202975 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22417 ^ _782464) ^ [] : [-(_1202977 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (22419 ^ _782464) ^ [_1203159, _1203161] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203159), _1203161)), 22420 ^ _782464 : [(22421 ^ _782464) ^ [] : [_1203159 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203161 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22427 ^ _782464) ^ [] : [_1203159 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1203161 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22435 ^ _782464) ^ [_1203400, _1203402] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203400), _1203402) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22440 ^ _782464 : [(22441 ^ _782464) ^ [] : [-(_1203400 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22443 ^ _782464) ^ [] : [-(_1203402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22444 ^ _782464 : [(22445 ^ _782464) ^ [] : [-(_1203400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22447 ^ _782464) ^ [] : [-(_1203402 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (22449 ^ _782464) ^ [_1203584, _1203586] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203584), _1203586) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 22450 ^ _782464 : [(22451 ^ _782464) ^ [] : [_1203584 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203586 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22457 ^ _782464) ^ [] : [_1203584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1203586 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22465 ^ _782464) ^ [_1203810, _1203812] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203810), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203810), _1203812)))))], (22467 ^ _782464) ^ [_1203849, _1203851] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203849), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203851), _1203849)))))], (22469 ^ _782464) ^ [_1203903, _1203905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203903), _1203905)), -(_1203905 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203903), 22472 ^ [_1203903, _1203905])))], (22476 ^ _782464) ^ [_1204016, _1204018] : [22477 ^ _782464 : [(22478 ^ _782464) ^ [_1204069] : [_1204018 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1204016), _1204069))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204016), _1204018)))], (22482 ^ _782464) ^ [_1204151, _1204153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204151), _1204153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204151)), _1204153)))], (22488 ^ _782464) ^ [_1204250, _1204252] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204250)), _1204252)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204250), _1204252)))], (22494 ^ _782464) ^ [_1204370, _1204372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204370), hAPP(c_Nat_OSuc, _1204372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204370), _1204372)))], (22500 ^ _782464) ^ [_1204469, _1204471] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204469), _1204471)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204469), hAPP(c_Nat_OSuc, _1204471))))], (22506 ^ _782464) ^ [_1204589, _1204591] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204589)), _1204591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204589), _1204591)))], (22512 ^ _782464) ^ [_1204688, _1204690] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204688), _1204690)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204688)), _1204690)))], (22518 ^ _782464) ^ [_1204793, _1204795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204793), _1204795)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204793), hAPP(c_Nat_OSuc, _1204795))))], (22524 ^ _782464) ^ [_1204896, _1204898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204896), _1204898)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204896)), _1204898)))], (22530 ^ _782464) ^ [_1204999, _1205001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204999), _1205001)), 22533 ^ _782464 : [(22534 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205001), hAPP(c_Nat_OSuc, _1204999))), -(_1205001 = _1204999)], (22540 ^ _782464) ^ [] : [_1205001 = _1204999, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205001), hAPP(c_Nat_OSuc, _1204999))))]]], (22546 ^ _782464) ^ [_1205240, _1205242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205240)), _1205242)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205240), _1205242)))], (22552 ^ _782464) ^ [_1205358, _1205360] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205358), _1205360) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22555 ^ _782464 : [(22556 ^ _782464) ^ [] : [-(_1205358 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22558 ^ _782464) ^ [] : [-(_1205360 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (22560 ^ _782464) ^ [_1205469, _1205471] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205469), _1205471) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1205469 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205471 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22570 ^ _782464) ^ [_1205612, _1205614] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1205612), _1205614)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205614), _1205612))], (22572 ^ _782464) ^ [_1205652, _1205654] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205652), _1205654)), hAPP(c_Nat_OSuc, _1205652))))], (22574 ^ _782464) ^ [_1205709, _1205711, _1205713] : [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, _1205709)), _1205711)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205709)), _1205713))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205711), _1205713)))], (22580 ^ _782464) ^ [_1205840, _1205842, _1205844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205842), _1205844)), -(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, _1205840)), _1205842)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205840)), _1205844))))], (22586 ^ _782464) ^ [_1205977, _1205979] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205977)), _1205979) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1205979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205977), _1205979)))], (22588 ^ _782464) ^ [_1206023, _1206025] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206023), hAPP(c_Nat_OSuc, _1206025)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206023), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1206023), _1206025)))], (22590 ^ _782464) ^ [_1206069, _1206071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206069), _1206071)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206071)), _1206069) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206071), _1206069)))], (22596 ^ _782464) ^ [_1206210, _1206212, _1206214] : [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, _1206210)), _1206212)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206210)), _1206214))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206212), _1206214)))], (22602 ^ _782464) ^ [_1206341, _1206343, _1206345] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206343), _1206345)), -(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, _1206341)), _1206343)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206341)), _1206345))))], (22608 ^ _782464) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22610 ^ _782464) ^ [_1206496] : [-(hAPP(c_Nat_OSuc, _1206496) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206496), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (22612 ^ _782464) ^ [_1206528] : [-(hAPP(c_Nat_OSuc, _1206528) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1206528))], (22614 ^ _782464) ^ [_1206557] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206557)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1206557)], (22616 ^ _782464) ^ [_1206589, _1206591] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206589), hAPP(c_Nat_OSuc, _1206591)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206589), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1206591))], (22618 ^ _782464) ^ [_1206635, _1206637] : [hAPP(_1206635, 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), _1206635), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206637)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1206635), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1206637)))], (22624 ^ _782464) ^ [_1206758, _1206760, _1206762] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1206758), _1206760)), hBOOL(hAPP(hAPP(c_member(_1206758), _1206762), _1206760)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1206758), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206758, tc_HOL_Obool)), _1206760), hAPP(hAPP(c_Set_Oinsert(_1206758), _1206762), c_Orderings_Obot__class_Obot(tc_fun(_1206758, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1206758), _1206760))], (22634 ^ _782464) ^ [_1206987, _1206989] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206987), hAPP(c_Nat_OSuc, _1206989)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1206987, _1206989))], (22636 ^ _782464) ^ [_1207025] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1207025) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207025)))], (22638 ^ _782464) ^ [_1207057, _1207059] : [-(hAPP(c_Finite__Set_Ocard(_1207057), _1207059) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1207057, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1207057), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1207059))], (22640 ^ _782464) ^ [_1207102, _1207104] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1207102, _1207104)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1207104), _1207102))], (22642 ^ _782464) ^ [_1207140] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207140)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1207140))], (22644 ^ _782464) ^ [_1207172] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207172)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1207172), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1207172)))], (22646 ^ _782464) ^ [_1207210, _1207212] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207210), _1207212)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207210)), hAPP(c_Nat_OSuc, _1207212)))], (22648 ^ _782464) ^ [_1207256] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207256)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207256)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1207256)))], (22650 ^ _782464) ^ [_1207297, _1207299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1207297, _1207299)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1207297, _1207299), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1207299), c_Orderings_Otop__class_Otop(tc_fun(_1207299, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1207297), c_Orderings_Otop__class_Otop(tc_fun(_1207297, tc_HOL_Obool)))))], (22660 ^ _782464) ^ [_1207457, _1207459, _1207461, _1207463] : [class_Groups_Ocomm__monoid__add(_1207457), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207457), _1207459), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207461)), hAPP(c_Nat_OSuc, _1207463))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207457), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207457, tc_Nat_Onat), _1207459), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207461), _1207463)))], (22666 ^ _782464) ^ [_1207628, _1207630] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1207628, _1207630)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207628), hAPP(c_Nat_OSuc, _1207630)))], (22668 ^ _782464) ^ [_1207670, _1207672, _1207674, _1207676] : [class_Groups_Ocomm__monoid__add(_1207670), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207670), _1207672), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207674), hAPP(c_Nat_OSuc, _1207676))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207670), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207670, tc_Nat_Onat), _1207672), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1207674, _1207676)))], (22684 ^ _782464) ^ [_1208003, _1208005] : [22685 ^ _782464 : [(22686 ^ _782464) ^ [] : [_1208005 = c_Orderings_Obot__class_Obot(tc_fun(_1208003, tc_HOL_Obool))], (22688 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208003), _1208005)))]], -(hAPP(c_Finite__Set_Ocard(_1208003), _1208005) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22674 ^ _782464) ^ [_1207848, _1207850] : [hAPP(c_Finite__Set_Ocard(_1207848), _1207850) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1207850 = c_Orderings_Obot__class_Obot(tc_fun(_1207848, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207848), _1207850))], (22692 ^ _782464) ^ [_1208147, _1208149] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208147), _1208149) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1208147, _1208149))], (22694 ^ _782464) ^ [_1208183, _1208185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1208183), _1208185))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208183), _1208185)))], (22700 ^ _782464) ^ [_1208282, _1208284, _1208286] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208282), _1208284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208282), _1208284)), hAPP(c_Finite__Set_Ocard(_1208282), hAPP(hAPP(c_Set_Oinsert(_1208282), _1208286), _1208284)))))], (22706 ^ _782464) ^ [_1208415, _1208417, _1208419] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208415), _1208417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208415, tc_HOL_Obool)), _1208419), _1208417)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208415), _1208419)), hAPP(c_Finite__Set_Ocard(_1208415), _1208417))))], (22716 ^ _782464) ^ [_1208606, _1208608, _1208610] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208606), _1208608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208606, tc_HOL_Obool)), _1208610), _1208608)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208606), _1208608)), hAPP(c_Finite__Set_Ocard(_1208606), _1208610))), -(_1208610 = _1208608)], (22730 ^ _782464) ^ [_1208851, _1208853, _1208855, _1208857] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208851), _1208853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208855), hAPP(c_Set_Oimage(_1208851, _1208855, _1208857), _1208853))), hAPP(c_Finite__Set_Ocard(_1208851), _1208853))))], (22736 ^ _782464) ^ [_1208984, _1208986] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208984)), _1208986) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1208984, _1208986))], (22738 ^ _782464) ^ [_1209022] : [class_Rings_Oring__1(_1209022), -(hBOOL(hAPP(hAPP(c_member(_1209022), c_Groups_Ozero__class_Ozero(_1209022)), c_Int_Oring__1__class_OInts(_1209022))))], (22744 ^ _782464) ^ [_1209117, _1209119, _1209121, _1209123] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209117), _1209119)), hAPP(c_Finite__Set_Ocard(_1209121), hAPP(c_Set_Oimage(_1209117, _1209121, _1209123), _1209119)) = hAPP(c_Finite__Set_Ocard(_1209117), _1209119), -(c_Fun_Oinj__on(_1209117, _1209121, _1209123, _1209119))], (22754 ^ _782464) ^ [_1209300, _1209302, _1209304, _1209306] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209300), _1209302)), 22757 ^ _782464 : [(22758 ^ _782464) ^ [] : [c_Fun_Oinj__on(_1209300, _1209304, _1209306, _1209302), -(hAPP(c_Finite__Set_Ocard(_1209304), hAPP(c_Set_Oimage(_1209300, _1209304, _1209306), _1209302)) = hAPP(c_Finite__Set_Ocard(_1209300), _1209302))], (22764 ^ _782464) ^ [] : [hAPP(c_Finite__Set_Ocard(_1209304), hAPP(c_Set_Oimage(_1209300, _1209304, _1209306), _1209302)) = hAPP(c_Finite__Set_Ocard(_1209300), _1209302), -(c_Fun_Oinj__on(_1209300, _1209304, _1209306, _1209302))]]], (22770 ^ _782464) ^ [_1209584, _1209586, _1209588, _1209590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1209584), hAPP(c_Set_Oimage(_1209586, _1209584, _1209588), _1209590))), hAPP(c_Finite__Set_Ocard(_1209586), _1209590))), c_Fun_Oinj__on(_1209586, _1209584, _1209588, _1209590)], (22776 ^ _782464) ^ [_1209714, _1209716, _1209718] : [class_Rings_Oring__1(_1209714), hBOOL(hAPP(hAPP(c_member(_1209714), _1209716), c_Int_Oring__1__class_OInts(_1209714))), hBOOL(hAPP(hAPP(c_member(_1209714), _1209718), c_Int_Oring__1__class_OInts(_1209714))), -(hBOOL(hAPP(hAPP(c_member(_1209714), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209714), _1209716), _1209718)), c_Int_Oring__1__class_OInts(_1209714))))], (22790 ^ _782464) ^ [_1209969, _1209971, _1209973] : [class_Rings_Oring__1(_1209969), hBOOL(hAPP(hAPP(c_member(_1209969), _1209971), c_Int_Oring__1__class_OInts(_1209969))), hBOOL(hAPP(hAPP(c_member(_1209969), _1209973), c_Int_Oring__1__class_OInts(_1209969))), -(hBOOL(hAPP(hAPP(c_member(_1209969), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209969), _1209971), _1209973)), c_Int_Oring__1__class_OInts(_1209969))))], (22804 ^ _782464) ^ [_1210224, _1210226, _1210228] : [class_Rings_Oring__1(_1210224), hBOOL(hAPP(hAPP(c_member(_1210224), _1210226), c_Int_Oring__1__class_OInts(_1210224))), hBOOL(hAPP(hAPP(c_member(_1210224), _1210228), c_Int_Oring__1__class_OInts(_1210224))), -(hBOOL(hAPP(hAPP(c_member(_1210224), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1210224), _1210226), _1210228)), c_Int_Oring__1__class_OInts(_1210224))))], (22818 ^ _782464) ^ [_1210479] : [class_Rings_Oring__1(_1210479), -(hBOOL(hAPP(hAPP(c_member(_1210479), c_Groups_Oone__class_Oone(_1210479)), c_Int_Oring__1__class_OInts(_1210479))))], (22824 ^ _782464) ^ [_1210574, _1210576] : [class_Rings_Oring__1(_1210574), hBOOL(hAPP(hAPP(c_member(_1210574), _1210576), c_Int_Oring__1__class_OInts(_1210574))), -(hBOOL(hAPP(hAPP(c_member(_1210574), hAPP(c_Groups_Ouminus__class_Ouminus(_1210574), _1210576)), c_Int_Oring__1__class_OInts(_1210574))))], (22834 ^ _782464) ^ [_1210747, _1210749] : [class_Rings_Oring__1(_1210747), -(hBOOL(hAPP(hAPP(c_member(_1210747), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210747), _1210749)), c_Int_Oring__1__class_OInts(_1210747))))], (22840 ^ _782464) ^ [_1210850, _1210852, _1210854] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1210850), _1210852)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1210850, tc_HOL_Obool)), _1210854), _1210852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1210850), _1210854)), hAPP(c_Finite__Set_Ocard(_1210850), _1210852))))], (22850 ^ _782464) ^ [_1211041, _1211043] : [class_Rings_Osemiring__1(_1211041), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211041), hAPP(c_Nat_OSuc, _1211043)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211041), c_Groups_Oone__class_Oone(_1211041)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211041), _1211043)))], (22856 ^ _782464) ^ [_1211162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211162)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211162), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1211162)], (22862 ^ _782464) ^ [_1211259, _1211261] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211259), hAPP(c_Nat_OSuc, _1211261))), _1211259)))], (22868 ^ _782464) ^ [_1211368, _1211370] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211368)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211370)), -(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), _1211370), _1211368))))], (22878 ^ _782464) ^ [_1211521, _1211523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211521)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211523)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211521), _1211523))))], (22888 ^ _782464) ^ [_1211680, _1211682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211682)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211680), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211682), _1211680))))], (22898 ^ _782464) ^ [_1211854, _1211856] : [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), _1211854), _1211856))), 22901 ^ _782464 : [(22902 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211854)))], (22904 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211856)))]]], (22906 ^ _782464) ^ [_1211977, _1211979] : [-(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), _1211977), _1211979)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211977)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211979))], (22916 ^ _782464) ^ [_1212132, _1212134, _1212136] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212132), _1212134)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212134), _1212132))), _1212136) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1212134)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212132), _1212136)))], (22922 ^ _782464) ^ [_1212281, _1212283, _1212285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212281), _1212283)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212285), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212283), _1212281))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212285), _1212281)), hAPP(c_Nat_OSuc, _1212283)))], (22928 ^ _782464) ^ [] : [-(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))], (22930 ^ _782464) ^ [_1212463, _1212465] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212463), _1212465)), -(_1212465 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212463), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22933 ^ [_1212463, _1212465]))))], (22937 ^ _782464) ^ [_1212582, _1212584] : [22938 ^ _782464 : [(22939 ^ _782464) ^ [_1212638] : [_1212584 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212582), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1212638)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212582), _1212584)))], (22943 ^ _782464) ^ [_1212708] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1212708)) = 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), _1212708)))], (22945 ^ _782464) ^ [_1212743, _1212745, _1212747] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1212743), _1212745)), 22948 ^ _782464 : [(22949 ^ _782464) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212743, tc_Nat_Onat), _1212747), _1212745) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22953 ^ _782464 : [(22954 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212743), 22952 ^ [_1212743, _1212745, _1212747]), _1212745)))], (22956 ^ _782464) ^ [] : [-(hAPP(_1212747, 22952 ^ [_1212743, _1212745, _1212747]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22958 ^ _782464) ^ [_1213063] : [hBOOL(hAPP(hAPP(c_member(_1212743), _1213063), _1212745)), -(22952 ^ [_1212743, _1212745, _1212747] = _1213063), -(hAPP(_1212747, _1213063) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22968 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212743, tc_Nat_Onat), _1212747), _1212745) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 22969 ^ _782464 : [(22970 ^ _782464) ^ [_1213224] : [hBOOL(hAPP(hAPP(c_member(_1212743), _1213224), _1212745)), hAPP(_1212747, _1213224) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22978 ^ _782464 : [(22979 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212743), 22977 ^ [_1212743, _1212745, _1212747, _1213224]), _1212745)))], (22981 ^ _782464) ^ [] : [_1213224 = 22977 ^ [_1212743, _1212745, _1212747, _1213224]], (22983 ^ _782464) ^ [] : [hAPP(_1212747, 22977 ^ [_1212743, _1212745, _1212747, _1213224]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (22987 ^ _782464) ^ [_1213577, _1213579, _1213581, _1213583] : [class_Rings_Osemiring__1(_1213577), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1213579, _1213577), hAPP(c_COMBK(_1213577, _1213579), _1213581)), _1213583) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213577), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1213577), hAPP(c_Finite__Set_Ocard(_1213579), _1213583))), _1213581))], (22993 ^ _782464) ^ [_1213722] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213722)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1213722))], (22995 ^ _782464) ^ [_1213754, _1213756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213754), hAPP(c_Nat_OSuc, _1213756))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1213754, hAPP(c_Nat_OSuc, _1213756)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213756)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1213754, _1213756)))], (23001 ^ _782464) ^ [_1213887, _1213889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213887), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1213889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213889), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1213887))))), -(_1213887 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1213889), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213889), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1213887))))], (23007 ^ _782464) ^ [_1214034] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1214034), hAPP(c_Nat_OSuc, _1214034)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1214034), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (23009 ^ _782464) ^ [_1214087, _1214089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1214087), _1214089))), 23012 ^ _782464 : [(23013 ^ _782464) ^ [] : [_1214089 = c_Orderings_Obot__class_Obot(tc_fun(_1214087, tc_HOL_Obool))], (23015 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1214087), _1214089)))]]], (23017 ^ _782464) ^ [_1214228, _1214230] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1214228), _1214230)))), -(_1214230 = c_Orderings_Obot__class_Obot(tc_fun(_1214228, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214228), _1214230))], (23027 ^ _782464) ^ [_1214394] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214394), c_Orderings_Otop__class_Otop(tc_fun(_1214394, 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(_1214394), c_Orderings_Otop__class_Otop(tc_fun(_1214394, tc_HOL_Obool))))))], (23033 ^ _782464) ^ [_1214511, _1214513, _1214515] : [class_Groups_Ocomm__monoid__add(_1214511), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214511), _1214513), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214515))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214511), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214511), _1214513), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214515))), hAPP(_1214513, _1214515)))], (23039 ^ _782464) ^ [_1214664, _1214666, _1214668] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214664), _1214666)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214664), _1214668)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214664), _1214666)), hAPP(c_Finite__Set_Ocard(_1214664), _1214668)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214664), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214664, tc_HOL_Obool)), _1214666), _1214668))), hAPP(c_Finite__Set_Ocard(_1214664), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1214664, tc_HOL_Obool)), _1214666), _1214668))))], (23049 ^ _782464) ^ [_1214921, _1214923, _1214925] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214921), _1214923)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214921), _1214925)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214921), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214921, tc_HOL_Obool)), _1214923), _1214925))), hAPP(c_Finite__Set_Ocard(_1214921), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1214921, tc_HOL_Obool)), _1214923), _1214925))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214921), _1214923)), hAPP(c_Finite__Set_Ocard(_1214921), _1214925)))], (23059 ^ _782464) ^ [_1215178, _1215180, _1215182, _1215184, _1215186, _1215188] : [c_Fun_Oinj__on(_1215178, _1215180, _1215182, _1215184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215180, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215178, _1215180, _1215182), _1215184)), _1215186)), c_Fun_Oinj__on(_1215180, _1215178, _1215188, _1215186), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215178, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215180, _1215178, _1215188), _1215186)), _1215184)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1215178), _1215184)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1215180), _1215186)), -(hAPP(c_Finite__Set_Ocard(_1215178), _1215184) = hAPP(c_Finite__Set_Ocard(_1215180), _1215186))], (23085 ^ _782464) ^ [_1215675, _1215677, _1215679] : [class_Groups_Ocomm__monoid__add(_1215675), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215675), _1215677), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1215679))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215675), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215675), _1215677), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1215679))), hAPP(_1215677, hAPP(c_Nat_OSuc, _1215679))))], (23091 ^ _782464) ^ [_1215834, _1215836, _1215838] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1215834), _1215836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215834, tc_HOL_Obool)), _1215836), _1215838)), -(hAPP(c_Finite__Set_Ocard(_1215834), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1215834, tc_HOL_Obool)), _1215838), _1215836)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1215834), _1215838)), hAPP(c_Finite__Set_Ocard(_1215834), _1215836)))], (23101 ^ _782464) ^ [_1216059, _1216061, _1216063] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216059), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216059, tc_HOL_Obool)), _1216061), _1216063))), -(hAPP(c_Finite__Set_Ocard(_1216059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216059, tc_HOL_Obool)), _1216061), _1216063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1216059), _1216061)), hAPP(c_Finite__Set_Ocard(_1216059), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216059, tc_HOL_Obool)), _1216061), _1216063))))], (23107 ^ _782464) ^ [_1216254, _1216256, _1216258] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216254), _1216256)), -(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(_1216254), _1216258)), hAPP(c_Finite__Set_Ocard(_1216254), _1216256))), hAPP(c_Finite__Set_Ocard(_1216254), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216254, tc_HOL_Obool)), _1216258), _1216256)))))], (23113 ^ _782464) ^ [_1216415, _1216417, _1216419] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216415), _1216417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1216415, tc_HOL_Obool)), _1216419), _1216417)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1216415), _1216419)), hAPP(c_Finite__Set_Ocard(_1216415), _1216417))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1216415, tc_HOL_Obool)), _1216419), _1216417)))], (23127 ^ _782464) ^ [_1216680] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216680)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216680), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1216680)], (23133 ^ _782464) ^ [_1216777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216777)), -(_1216777 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216777), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (23139 ^ _782464) ^ [_1216883, _1216885] : [_1216883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216883), _1216885) = _1216885)], (23145 ^ _782464) ^ [_1216966, _1216968] : [-(_1216966 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216966), _1216968) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216966), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1216968)))], (23151 ^ _782464) ^ [_1217025] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217025)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1217025)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1217025), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23153 ^ _782464) ^ [_1217069] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217069)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1217069)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217069)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23155 ^ _782464) ^ [_1217125] : [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, _1217125)))))], (23157 ^ _782464) ^ [_1217159] : [-(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, _1217159)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23159 ^ _782464) ^ [_1217196, _1217198] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1217196), _1217198)), -(hAPP(c_Finite__Set_Ocard(_1217196), _1217198) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1217196, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1217196), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217198))], (23165 ^ _782464) ^ [_1217338, _1217340] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1217338), _1217340)), -(hAPP(c_Finite__Set_Ocard(_1217338), _1217340) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1217338, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1217338), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217340))], (23171 ^ _782464) ^ [_1217465, _1217467] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1217465), _1217467))), -(hAPP(c_Finite__Set_Ocard(_1217465), _1217467) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23177 ^ _782464) ^ [_1217512, _1217514] : [class_Int_Oring__char__0(_1217512), hBOOL(hAPP(hAPP(c_member(_1217512), _1217514), c_Int_Oring__1__class_OInts(_1217512))), 23184 ^ _782464 : [(23185 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217512), _1217514), _1217514) = c_Groups_Ozero__class_Ozero(_1217512), -(_1217514 = c_Groups_Ozero__class_Ozero(_1217512))], (23191 ^ _782464) ^ [] : [_1217514 = c_Groups_Ozero__class_Ozero(_1217512), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217512), _1217514), _1217514) = c_Groups_Ozero__class_Ozero(_1217512))]]], (23197 ^ _782464) ^ [_1217823, _1217825, _1217827] : [class_Groups_Ocomm__monoid__add(_1217823), hAPP(_1217825, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1217823), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217823), _1217825), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1217827)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217823), _1217825), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217827)))], (23207 ^ _782464) ^ [_1218012, _1218014, _1218016, _1218018] : [class_Groups_Ocomm__monoid__add(_1218012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1218014), _1218016)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218012), _1218018), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218014), _1218016)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218012), hAPP(_1218018, _1218014)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218012), _1218018), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218014)), _1218016))))], (23217 ^ _782464) ^ [_1218245, _1218247, _1218249, _1218251] : [class_Groups_Ocomm__monoid__add(_1218245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218247), _1218249)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218245), _1218251), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1218247, _1218249)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218245), hAPP(_1218251, _1218247)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218245), _1218251), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218247), _1218249))))], (23227 ^ _782464) ^ [_1218479, _1218481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218479), _1218481)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218479), hAPP(c_Nat_OSuc, _1218481)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1218481), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218479), _1218481)))], (23233 ^ _782464) ^ [_1218602, _1218604] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218602), _1218604))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218602), hAPP(c_Nat_OSuc, _1218604)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23239 ^ _782464) ^ [_1218654, _1218656, _1218658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218654), _1218656)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218654), _1218658)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1218654, tc_HOL_Obool)), _1218656), _1218658) = c_Orderings_Obot__class_Obot(tc_fun(_1218654, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1218654), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218654, tc_HOL_Obool)), _1218656), _1218658)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1218654), _1218656)), hAPP(c_Finite__Set_Ocard(_1218654), _1218658)))], (23253 ^ _782464) ^ [_1218953, _1218955, _1218957] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218953), _1218955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1218953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1218953, tc_HOL_Obool)), _1218955), hAPP(hAPP(c_Set_Oinsert(_1218953), _1218957), c_Orderings_Obot__class_Obot(tc_fun(_1218953, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1218953), _1218955))))], (23259 ^ _782464) ^ [_1219118, _1219120, _1219122] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219118), _1219120)), -(hBOOL(hAPP(hAPP(c_member(_1219118), _1219122), _1219120))), -(hAPP(c_Finite__Set_Ocard(_1219118), hAPP(hAPP(c_Set_Oinsert(_1219118), _1219122), _1219120)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1219118), _1219120)))], (23269 ^ _782464) ^ [_1219276, _1219278, _1219280, _1219282, _1219284] : [c_Fun_Oinj__on(_1219276, _1219278, _1219280, _1219282), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219278, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219276, _1219278, _1219280), _1219282)), _1219284)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219278), _1219284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219276), _1219282)), hAPP(c_Finite__Set_Ocard(_1219278), _1219284))))], (23283 ^ _782464) ^ [_1219551, _1219553, _1219555, _1219557] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219551), _1219553)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219555), _1219557)), 23290 ^ _782464 : [(23301 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219551), _1219553)), hAPP(c_Finite__Set_Ocard(_1219555), _1219557))), 23305 ^ _782464 : [(23306 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1219551, _1219555, 23304 ^ [_1219551, _1219553, _1219555, _1219557], _1219553))], (23308 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219555, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219551, _1219555, 23304 ^ [_1219551, _1219553, _1219555, _1219557]), _1219553)), _1219557)))]]], (23291 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219551), _1219553)), hAPP(c_Finite__Set_Ocard(_1219555), _1219557)))), 23292 ^ _782464 : [(23293 ^ _782464) ^ [_1219762] : [c_Fun_Oinj__on(_1219551, _1219555, _1219762, _1219553), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219555, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219551, _1219555, _1219762), _1219553)), _1219557))]]]]], (23310 ^ _782464) ^ [_1220078, _1220080] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220080)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1220078, _1220080))))], (23320 ^ _782464) ^ [_1220225, _1220227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220225), _1220227)), -(c_Nat__Transfer_Otsub(_1220227, _1220225) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220227), _1220225))], (23326 ^ _782464) ^ [_1220330, _1220332] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220330), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220332)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220330), _1220332)))], (23328 ^ _782464) ^ [_1220373] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220373)) = 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), _1220373))))], (23330 ^ _782464) ^ [_1220411, _1220413, _1220415, _1220417] : [class_Groups_Ocomm__monoid__add(_1220411), 23333 ^ _782464 : [(23334 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220413), _1220415)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220411), _1220417), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220415), hAPP(c_Nat_OSuc, _1220413))) = c_Groups_Ozero__class_Ozero(_1220411))], (23340 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220413), _1220415))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220411), _1220417), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220415), hAPP(c_Nat_OSuc, _1220413))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220411), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220411), _1220417), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220415), _1220413))), hAPP(_1220417, _1220413)))]]], (23346 ^ _782464) ^ [_1220741, _1220743, _1220745, _1220747] : [class_Groups_Ocomm__monoid__add(_1220741), 23349 ^ _782464 : [(23350 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220743)), _1220745)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220741), _1220747), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220745, hAPP(c_Nat_OSuc, _1220743))) = c_Groups_Ozero__class_Ozero(_1220741))], (23356 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220743)), _1220745))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220741), _1220747), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220745, hAPP(c_Nat_OSuc, _1220743))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220741), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220741), _1220747), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220745, _1220743))), hAPP(_1220747, hAPP(c_Nat_OSuc, _1220743))))]]], (23362 ^ _782464) ^ [] : [-(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))))], (23364 ^ _782464) ^ [_1221095, _1221097, _1221099] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221095), _1221097)), hBOOL(hAPP(hAPP(c_member(_1221095), _1221099), _1221097)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221095), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221095, tc_HOL_Obool)), _1221097), hAPP(hAPP(c_Set_Oinsert(_1221095), _1221099), c_Orderings_Obot__class_Obot(tc_fun(_1221095, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1221095), _1221097))))], (23374 ^ _782464) ^ [_1221328, _1221330, _1221332, _1221334] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221328), _1221330)), hBOOL(hAPP(hAPP(c_member(_1221328), _1221332), _1221330)), hBOOL(hAPP(hAPP(c_member(_1221328), _1221334), _1221330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221328), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221328, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221328, tc_HOL_Obool)), _1221330), hAPP(hAPP(c_Set_Oinsert(_1221328), _1221332), c_Orderings_Obot__class_Obot(tc_fun(_1221328, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1221328), _1221334), c_Orderings_Obot__class_Obot(tc_fun(_1221328, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1221328), _1221330))))], (23388 ^ _782464) ^ [_1221683, _1221685] : [class_Int_Oring__char__0(_1221683), hBOOL(hAPP(hAPP(c_member(_1221683), _1221685), c_Int_Oring__1__class_OInts(_1221683))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221683), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221683), c_Groups_Oone__class_Oone(_1221683)), _1221685)), _1221685) = c_Groups_Ozero__class_Ozero(_1221683)], (23398 ^ _782464) ^ [_1221869, _1221871, _1221873, _1221875] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221869), _1221871)), hBOOL(hAPP(hAPP(c_member(_1221869), _1221873), _1221871)), -(hBOOL(hAPP(hAPP(c_member(_1221869), _1221873), _1221875))), -(hAPP(c_Finite__Set_Ocard(_1221869), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221869, tc_HOL_Obool)), _1221871), hAPP(hAPP(c_Set_Oinsert(_1221869), _1221873), _1221875))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221869), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221869, tc_HOL_Obool)), _1221871), _1221875))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23412 ^ _782464) ^ [_1222149, _1222151, _1222153] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222149), _1222151)), -(hAPP(c_Finite__Set_Ocard(_1222149), hAPP(hAPP(c_Set_Oinsert(_1222149), _1222153), _1222151)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1222149), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222149, tc_HOL_Obool)), _1222151), hAPP(hAPP(c_Set_Oinsert(_1222149), _1222153), c_Orderings_Obot__class_Obot(tc_fun(_1222149, tc_HOL_Obool)))))))], (23418 ^ _782464) ^ [_1222326, _1222328, _1222330] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222326), _1222328)), hBOOL(hAPP(hAPP(c_member(_1222326), _1222330), _1222328)), -(hAPP(c_Finite__Set_Ocard(_1222326), _1222328) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1222326), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222326, tc_HOL_Obool)), _1222328), hAPP(hAPP(c_Set_Oinsert(_1222326), _1222330), c_Orderings_Obot__class_Obot(tc_fun(_1222326, tc_HOL_Obool)))))))], (23428 ^ _782464) ^ [_1222555, _1222557, _1222559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222555), _1222557)), 23431 ^ _782464 : [(23432 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1222555), _1222559), _1222557)), -(hAPP(c_Finite__Set_Ocard(_1222555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222555, tc_HOL_Obool)), _1222557), hAPP(hAPP(c_Set_Oinsert(_1222555), _1222559), c_Orderings_Obot__class_Obot(tc_fun(_1222555, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1222555), _1222557)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23438 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222555), _1222559), _1222557))), -(hAPP(c_Finite__Set_Ocard(_1222555), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222555, tc_HOL_Obool)), _1222557), hAPP(hAPP(c_Set_Oinsert(_1222555), _1222559), c_Orderings_Obot__class_Obot(tc_fun(_1222555, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1222555), _1222557))]]], (23444 ^ _782464) ^ [_1222919, _1222921, _1222923] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222919), _1222921)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222919), _1222923)), 23454 ^ _782464 : [(23455 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222919), 23453 ^ [_1222919, _1222921, _1222923]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222919, tc_HOL_Obool)), _1222921), _1222923))))], (23457 ^ _782464) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1222919), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222919, tc_HOL_Obool)), _1222921), _1222923)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1222919), _1222921)), hAPP(c_Finite__Set_Ocard(_1222919), _1222923)))], (23461 ^ _782464) ^ [_1223263, _1223265, _1223267, _1223269, _1223271] : [class_Groups_Oordered__ab__semigroup__add(_1223263), class_Rings_Osemiring__1(_1223263), 23471 ^ _782464 : [(23472 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1223265), 23470 ^ [_1223263, _1223265, _1223267, _1223269, _1223271]), _1223267)))], (23474 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223263), hAPP(_1223269, 23470 ^ [_1223263, _1223265, _1223267, _1223269, _1223271])), _1223271))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223263), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223265, _1223263), _1223269), _1223267)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223263), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223263), hAPP(c_Finite__Set_Ocard(_1223265), _1223267))), _1223271))))], (23478 ^ _782464) ^ [_1223671, _1223673, _1223675] : [hAPP(c_Finite__Set_Ocard(_1223671), _1223673) = hAPP(c_Nat_OSuc, _1223675), 23483 ^ _782464 : [(23484 ^ _782464) ^ [] : [-(_1223673 = hAPP(hAPP(c_Set_Oinsert(_1223671), 23481 ^ [_1223671, _1223673, _1223675]), 23482 ^ [_1223671, _1223673, _1223675]))], (23486 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1223671), 23481 ^ [_1223671, _1223673, _1223675]), 23482 ^ [_1223671, _1223673, _1223675]))], (23488 ^ _782464) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1223671), 23482 ^ [_1223671, _1223673, _1223675]) = _1223675)], (23490 ^ _782464) ^ [] : [_1223675 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(23482 ^ [_1223671, _1223673, _1223675] = c_Orderings_Obot__class_Obot(tc_fun(_1223671, tc_HOL_Obool)))]]], (23496 ^ _782464) ^ [_1224089, _1224091, _1224093] : [-(hAPP(c_Finite__Set_Ocard(_1224089), _1224091) = hAPP(c_Nat_OSuc, _1224093)), 23497 ^ _782464 : [(23498 ^ _782464) ^ [_1224189, _1224191] : [_1224091 = hAPP(hAPP(c_Set_Oinsert(_1224089), _1224191), _1224189), -(hBOOL(hAPP(hAPP(c_member(_1224089), _1224191), _1224189))), hAPP(c_Finite__Set_Ocard(_1224089), _1224189) = _1224093, 23509 ^ _782464 : [(23510 ^ _782464) ^ [] : [-(_1224093 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23512 ^ _782464) ^ [] : [_1224189 = c_Orderings_Obot__class_Obot(tc_fun(_1224089, tc_HOL_Obool))]]]]], (23526 ^ _782464) ^ [_1224731, _1224733, _1224735, _1224737] : [23527 ^ _782464 : [(23528 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1224731), _1224733)))], (23530 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1224735), _1224737)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1224731, _1224735)), c_Sum__Type_OPlus(_1224731, _1224735, _1224733, _1224737)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23516 ^ _782464) ^ [_1224526, _1224528, _1224530, _1224532] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1224526, _1224530)), c_Sum__Type_OPlus(_1224526, _1224530, _1224528, _1224532)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1224526), _1224528)), hAPP(c_Finite__Set_Ocard(_1224530), _1224532))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224526), _1224528)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224530), _1224532))], (23534 ^ _782464) ^ [_1224831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224831)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224831) = 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, _1224831))))], (23540 ^ _782464) ^ [_1224934, _1224936, _1224938, _1224940, _1224942] : [class_Groups_Oordered__ab__group__add(_1224934), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224936), _1224938)), 23550 ^ _782464 : [(23551 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1224936), 23549 ^ [_1224934, _1224936, _1224938, _1224940, _1224942]), _1224938)))], (23553 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224934), c_Groups_Ozero__class_Ozero(_1224934)), hAPP(_1224940, 23549 ^ [_1224934, _1224936, _1224938, _1224940, _1224942])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224936, _1224934), _1224940), _1224938) = c_Groups_Ozero__class_Ozero(_1224934), hBOOL(hAPP(hAPP(c_member(_1224936), _1224942), _1224938)), -(hAPP(_1224940, _1224942) = c_Groups_Ozero__class_Ozero(_1224934))], (23565 ^ _782464) ^ [_1225432] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225432)) = _1225432)], (23567 ^ _782464) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23569 ^ _782464) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23571 ^ _782464) ^ [_1225497, _1225499] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225497)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225499)), 23578 ^ _782464 : [(23579 ^ _782464) ^ [] : [hAPP(c_Int_Onat, _1225497) = hAPP(c_Int_Onat, _1225499), -(_1225497 = _1225499)], (23585 ^ _782464) ^ [] : [_1225497 = _1225499, -(hAPP(c_Int_Onat, _1225497) = hAPP(c_Int_Onat, _1225499))]]], (23591 ^ _782464) ^ [_1225782, _1225784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225782)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225784)), 23598 ^ _782464 : [(23599 ^ _782464) ^ [] : [hAPP(c_Int_Onat, _1225782) = hAPP(c_Int_Onat, _1225784), -(_1225782 = _1225784)], (23605 ^ _782464) ^ [] : [_1225782 = _1225784, -(hAPP(c_Int_Onat, _1225782) = hAPP(c_Int_Onat, _1225784))]]], (23622 ^ _782464) ^ [_1226264] : [23624 ^ _782464 : [(23625 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23623 ^ [_1226264])))], (23627 ^ _782464) ^ [] : [hBOOL(hAPP(_1226264, hAPP(c_Int_Onat, 23623 ^ [_1226264])))]], 23628 ^ _782464 : [(23629 ^ _782464) ^ [_1226397] : [-(hBOOL(hAPP(_1226264, _1226397)))]]], (23611 ^ _782464) ^ [_1226079] : [hBOOL(hAPP(_1226079, 23612 ^ [_1226079])), 23615 ^ _782464 : [(23616 ^ _782464) ^ [_1226173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226173)), -(hBOOL(hAPP(_1226079, hAPP(c_Int_Onat, _1226173))))]]], (23631 ^ _782464) ^ [_1226442] : [23632 ^ _782464 : [(23633 ^ _782464) ^ [_1226499] : [hBOOL(hAPP(_1226442, _1226499))]], 23635 ^ _782464 : [(23636 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23634 ^ [_1226442])))], (23638 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1226442, hAPP(c_Int_Onat, 23634 ^ [_1226442]))))]]], (23640 ^ _782464) ^ [_1226585] : [-(hBOOL(hAPP(_1226585, 23647 ^ [_1226585]))), 23641 ^ _782464 : [(23642 ^ _782464) ^ [_1226637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226637)), hBOOL(hAPP(_1226585, hAPP(c_Int_Onat, _1226637)))]]], (23651 ^ _782464) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23653 ^ _782464) ^ [_1226782] : [-(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)), _1226782)) = _1226782)], (23655 ^ _782464) ^ [_1226811, _1226813] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1226811), _1226813) = 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)), _1226811)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1226813))))], (23657 ^ _782464) ^ [_1226857] : [-(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)), _1226857)) = hAPP(c_Int_Onat, _1226857))], (23659 ^ _782464) ^ [_1226889, _1226891] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1226889), _1226891)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226891), _1226889)))], (23661 ^ _782464) ^ [_1226932, _1226934] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1226932, _1226934)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226934), _1226932)))], (23663 ^ _782464) ^ [] : [-(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))))], (23665 ^ _782464) ^ [_1227003] : [hAPP(c_Int_Onat, _1227003) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227003), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23671 ^ _782464) ^ [_1227090] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227090), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1227090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23677 ^ _782464) ^ [_1227183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227183), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1227183) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23683 ^ _782464) ^ [_1227289, _1227291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227289)), hAPP(c_Int_Onat, _1227291))), 23686 ^ _782464 : [(23687 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227291)))], (23689 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227289), _1227291)))]]], (23691 ^ _782464) ^ [_1227424, _1227426] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227424)), hAPP(c_Int_Onat, _1227426)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227426)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227424), _1227426))], (23701 ^ _782464) ^ [_1227591, _1227593] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227591)), 23704 ^ _782464 : [(23705 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227593)), hAPP(c_Int_Onat, _1227591))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227593), _1227591)))], (23711 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227593), _1227591)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227593)), hAPP(c_Int_Onat, _1227591))))]]], (23717 ^ _782464) ^ [_1227850, _1227852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227852)), 23724 ^ _782464 : [(23725 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1227850)), hAPP(c_Int_Onat, _1227852))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227850), _1227852)))], (23731 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227850), _1227852)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1227850)), hAPP(c_Int_Onat, _1227852))))]]], (23737 ^ _782464) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (23739 ^ _782464) ^ [_1228183] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228183)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228183)) = _1228183)], (23745 ^ _782464) ^ [_1228289, _1228291] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228289) = _1228291, 23748 ^ _782464 : [(23749 ^ _782464) ^ [] : [-(_1228289 = hAPP(c_Int_Onat, _1228291))], (23751 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228291)))]]], (23753 ^ _782464) ^ [_1228404, _1228406] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228404) = _1228406), _1228404 = hAPP(c_Int_Onat, _1228406), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228406))], (23763 ^ _782464) ^ [_1228557] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228557)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228557)) = _1228557)], (23769 ^ _782464) ^ [_1228642] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228642))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228642)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23775 ^ _782464) ^ [_1228701, _1228703] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228701), hAPP(c_Int_Onat, _1228703))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228701)), _1228703)))], (23781 ^ _782464) ^ [_1228806, _1228808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228806)), _1228808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228806), hAPP(c_Int_Onat, _1228808))))], (23787 ^ _782464) ^ [_1228917] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228917))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23789 ^ _782464) ^ [_1228949, _1228951] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228949, _1228951) = 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), _1228949), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228951))))], (23791 ^ _782464) ^ [_1228991, _1228993, _1228995] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228991), _1228993), _1228995) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1228991), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1228991, tc_Int_Oint), _1228993), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1228995))), class_Groups_Ocomm__monoid__add(_1228991), class_Groups_Ocomm__monoid__mult(_1228991)], (23801 ^ _782464) ^ [_1229194] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1229194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229194)))], (23807 ^ _782464) ^ [_1229279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1229279))))], (23813 ^ _782464) ^ [_1229370, _1229372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229370)), 23816 ^ _782464 : [(23817 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229370)), hAPP(c_Int_Onat, _1229372))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229370), _1229372)))], (23823 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229370), _1229372)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229370)), hAPP(c_Int_Onat, _1229372))))]]], (23829 ^ _782464) ^ [_1229629, _1229631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229631)), 23836 ^ _782464 : [(23837 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229629)), hAPP(c_Int_Onat, _1229631))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229629), _1229631)))], (23843 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229629), _1229631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229629)), hAPP(c_Int_Onat, _1229631))))]]], (23865 ^ _782464) ^ [_1230151, _1230153] : [-(_1230151 = hAPP(c_Int_Onat, _1230153)), 23868 ^ _782464 : [(23869 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230153)))], (23871 ^ _782464) ^ [] : [_1230153 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230151)]], 23872 ^ _782464 : [(23873 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230153))], (23875 ^ _782464) ^ [] : [_1230151 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23849 ^ _782464) ^ [_1229959, _1229961] : [_1229959 = hAPP(c_Int_Onat, _1229961), 23852 ^ _782464 : [(23853 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229961)), -(_1229961 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229959))], (23859 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229961))), -(_1229959 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23895 ^ _782464) ^ [_1230582, _1230584] : [-(hAPP(c_Int_Onat, _1230582) = _1230584), 23898 ^ _782464 : [(23899 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230582)))], (23901 ^ _782464) ^ [] : [_1230582 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230584)]], 23902 ^ _782464 : [(23903 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230582))], (23905 ^ _782464) ^ [] : [_1230584 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23879 ^ _782464) ^ [_1230390, _1230392] : [hAPP(c_Int_Onat, _1230390) = _1230392, 23882 ^ _782464 : [(23883 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230390)), -(_1230390 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230392))], (23889 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230390))), -(_1230392 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23909 ^ _782464) ^ [_1230806, _1230808] : [23910 ^ _782464 : [(23911 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230806))], (23913 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230808))]], 23914 ^ _782464 : [(23915 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230806)), hAPP(c_Int_Onat, _1230808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230806), _1230808)))], (23921 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230806), _1230808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230806)), hAPP(c_Int_Onat, _1230808))))]]], (23943 ^ _782464) ^ [_1231385, _1231387] : [-(hBOOL(hAPP(_1231385, hAPP(c_Int_Onat, _1231387)))), 23947 ^ _782464 : [(23948 ^ _782464) ^ [] : [-(_1231387 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23946 ^ [_1231385, _1231387]))], (23950 ^ _782464) ^ [] : [hBOOL(hAPP(_1231385, 23946 ^ [_1231385, _1231387]))]], 23951 ^ _782464 : [(23952 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231387), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23954 ^ _782464) ^ [] : [hBOOL(hAPP(_1231385, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (23927 ^ _782464) ^ [_1231122, _1231124] : [hBOOL(hAPP(_1231122, hAPP(c_Int_Onat, _1231124))), 23930 ^ _782464 : [(23931 ^ _782464) ^ [_1231222] : [_1231124 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231222), -(hBOOL(hAPP(_1231122, _1231222)))], (23937 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231124), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1231122, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (23958 ^ _782464) ^ [_1231648, _1231650] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231648)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231650)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231648), _1231650)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231648)), hAPP(c_Int_Onat, _1231650)))], (23968 ^ _782464) ^ [_1231827, _1231829] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231829)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231827)), hAPP(c_Int_Onat, _1231829)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231827), _1231829)))], (23978 ^ _782464) ^ [_1232006, _1232008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232006)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232006), _1232008)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232006)), hAPP(c_Int_Onat, _1232008)))], (23984 ^ _782464) ^ [_1232129, _1232131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232131)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232129)), hAPP(c_Int_Onat, _1232131)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232129), _1232131)))], (23994 ^ _782464) ^ [_1232308, _1232310] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1232308), _1232310) = 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)), _1232308)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232310))))], (23996 ^ _782464) ^ [_1232354, _1232356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1232354), _1232356)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232356), _1232354)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1232356)), hAPP(c_Int_Onat, _1232354)))], (24006 ^ _782464) ^ [_1232539, _1232541, _1232543] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232539, tc_Nat_Onat), _1232541), _1232543) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1232539, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1232539), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1232541)), _1232543)))], (24008 ^ _782464) ^ [_1232597, _1232599] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1232597, _1232599)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1232599), _1232597)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (24010 ^ _782464) ^ [_1232644] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1232644) = 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), _1232644))))], (24012 ^ _782464) ^ [_1232680, _1232682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232680)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232682)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1232680)), hAPP(c_Int_Onat, _1232682)) = hAPP(c_Int_Onat, c_Nat__Transfer_Otsub(_1232680, _1232682)))], (24022 ^ _782464) ^ [_1232853, _1232855, _1232857, _1232859] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1232853, _1232855)), c_Sum__Type_OPlus(_1232853, _1232855, _1232857, _1232859))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1232855), _1232859)))], (24028 ^ _782464) ^ [_1232966, _1232968, _1232970, _1232972] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1232966, _1232968)), c_Sum__Type_OPlus(_1232966, _1232968, _1232970, _1232972))), 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tc_Nat_Onat, c_Int_Onat), _1238333))))], (24370 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238333))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), _1238333)))]]], (24376 ^ _782464) ^ [_1238553] : [c_Nat__Transfer_Onat__set(_1238553), -(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), _1238553) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238553)))], (24382 ^ _782464) ^ [_1238644, _1238646] : [c_Nat__Transfer_Ois__nat(_1238644), c_Nat__Transfer_Onat__set(_1238646), 24389 ^ _782464 : [(24390 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1238644), _1238646)), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1238644)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1238646))))], (24396 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Int_Onat, _1238644)), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), 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hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1240036))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1240032), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1240036))) = 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)), _1240034)), _1240032)), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1240036)))], (24470 ^ _782464) ^ [_1240265, _1240267, _1240269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1240265)), 24476 ^ _782464 : [(24477 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1240267, 24475 ^ [_1240265, _1240267, _1240269])))], (24479 ^ _782464) ^ [] : [hBOOL(hAPP(_1240267, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 24475 ^ [_1240265, 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(24508 ^ _782464) ^ [] : [_1240792 = _1240794, -(hAPP(c_Int_Oring__1__class_Oof__int(_1240790), _1240792) = hAPP(c_Int_Oring__1__class_Oof__int(_1240790), _1240794))]]], (24514 ^ _782464) ^ [_1241031] : [-(hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241031)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1241031))], (24516 ^ _782464) ^ [_1241063] : [class_Rings_Oring__1(_1241063), -(hAPP(c_Int_Oring__1__class_Oof__int(_1241063), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(_1241063))], (24522 ^ _782464) ^ [_1241150, _1241152] : [class_Int_Oring__char__0(_1241150), 24525 ^ _782464 : [(24526 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(_1241150) = hAPP(c_Int_Oring__1__class_Oof__int(_1241150), _1241152), -(_1241152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24532 ^ _782464) ^ [] : [_1241152 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Ozero__class_Ozero(_1241150) = hAPP(c_Int_Oring__1__class_Oof__int(_1241150), _1241152))]]], (24538 ^ _782464) ^ [_1241376, _1241378] : [class_Int_Oring__char__0(_1241376), 24541 ^ _782464 : [(24542 ^ _782464) ^ [] : [hAPP(c_Int_Oring__1__class_Oof__int(_1241376), _1241378) = c_Groups_Ozero__class_Ozero(_1241376), -(_1241378 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (24548 ^ _782464) ^ [] : [_1241378 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1241376), _1241378) = c_Groups_Ozero__class_Ozero(_1241376))]]], (24554 ^ _782464) ^ [_1241602, _1241604, _1241606] : [class_Rings_Olinordered__idom(_1241602), 24557 ^ _782464 : [(24558 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241602), hAPP(c_Int_Oring__1__class_Oof__int(_1241602), _1241604)), hAPP(c_Int_Oring__1__class_Oof__int(_1241602), _1241606))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1241604), _1241606)))], (24564 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1241604), _1241606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1241602), hAPP(c_Int_Oring__1__class_Oof__int(_1241602), _1241604)), hAPP(c_Int_Oring__1__class_Oof__int(_1241602), _1241606))))]]], (24570 ^ _782464) ^ [_1241879, _1241881, _1241883] : [class_Rings_Olinordered__idom(_1241879), 24573 ^ _782464 : [(24574 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241879), hAPP(c_Int_Oring__1__class_Oof__int(_1241879), _1241881)), hAPP(c_Int_Oring__1__class_Oof__int(_1241879), _1241883))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241881), _1241883)))], (24580 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1241881), _1241883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1241879), hAPP(c_Int_Oring__1__class_Oof__int(_1241879), _1241881)), hAPP(c_Int_Oring__1__class_Oof__int(_1241879), _1241883))))]]], (24586 ^ _782464) ^ [_1242156, 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c_Groups_Ozero__class_Ozero(_1243365))))]]], (24666 ^ _782464) ^ [_1243627, _1243629] : [class_Rings_Olinordered__idom(_1243627), 24669 ^ _782464 : [(24670 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243627), c_Groups_Ozero__class_Ozero(_1243627)), hAPP(c_Int_Oring__1__class_Oof__int(_1243627), _1243629))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243629)))], (24676 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243629)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243627), c_Groups_Ozero__class_Ozero(_1243627)), hAPP(c_Int_Oring__1__class_Oof__int(_1243627), _1243629))))]]], (24682 ^ _782464) ^ [_1243880, _1243882] : [class_Rings_Olinordered__idom(_1243880), 24685 ^ _782464 : [(24686 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243880), hAPP(c_Int_Oring__1__class_Oof__int(_1243880), _1243882)), c_Groups_Ozero__class_Ozero(_1243880))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243882), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24692 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243882), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243880), hAPP(c_Int_Oring__1__class_Oof__int(_1243880), _1243882)), c_Groups_Ozero__class_Ozero(_1243880))))]]], (24698 ^ _782464) ^ [_1244142, _1244144] : [class_Rings_Oring__1(_1244142), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244144)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244142), hAPP(c_Int_Onat, _1244144)) = hAPP(c_Int_Oring__1__class_Oof__int(_1244142), _1244144))], (24708 ^ _782464) ^ [_1244299, _1244301, _1244303] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244299)), 24714 ^ _782464 : [(24715 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1244301, 24713 ^ [_1244299, _1244301, _1244303])))], (24717 ^ _782464) ^ [] : [hBOOL(hAPP(_1244301, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24713 ^ [_1244299, _1244301, _1244303]), _1244299)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244303)), 24722 ^ _782464 : [(24723 ^ _782464) ^ [_1244588] : [hBOOL(hAPP(_1244301, _1244588)), -(hBOOL(hAPP(_1244301, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244588), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244303), _1244299)))))]]], (24729 ^ _782464) ^ [_1244710, _1244712] : [-(hBOOL(hAPP(_1244710, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1244710, _1244712)), 24737 ^ _782464 : [(24738 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24736 ^ [_1244710, _1244712]), _1244712)))], (24746 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1244710, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 24736 ^ [_1244710, _1244712]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (24740 ^ _782464) ^ [_1244948] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244948), 24736 ^ [_1244710, _1244712])), hBOOL(hAPP(_1244710, _1244948))]]], (24748 ^ _782464) ^ [_1245100] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245100)), 24752 ^ _782464 : [(24753 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24751 ^ [_1245100])))], (24755 ^ _782464) ^ [] : [-(_1245100 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24751 ^ [_1245100]))]]], (24757 ^ _782464) ^ [_1245230, _1245232, _1245234, _1245236, _1245238] : [class_Groups_Ocomm__monoid__add(_1245230), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245232), _1245234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245232, tc_HOL_Obool)), _1245236), _1245234)), 24771 ^ _782464 : [(24772 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245232), 24770 ^ [_1245230, _1245232, _1245234, _1245236, _1245238]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1245232, tc_HOL_Obool)), _1245234), _1245236))))], (24774 ^ _782464) ^ [] : [hAPP(_1245238, 24770 ^ [_1245230, _1245232, _1245234, _1245236, _1245238]) = c_Groups_Ozero__class_Ozero(_1245230)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245232, _1245230), _1245238), _1245236) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245232, _1245230), _1245238), _1245234))], (24778 ^ _782464) ^ [_1245681, _1245683, _1245685, _1245687, _1245689] : [class_Groups_Ocomm__monoid__add(_1245681), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245683), _1245685)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245683, tc_HOL_Obool)), _1245687), _1245685)), 24792 ^ _782464 : [(24793 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245683), 24791 ^ [_1245681, _1245683, _1245685, _1245687, _1245689]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1245683, tc_HOL_Obool)), _1245685), _1245687))))], (24795 ^ _782464) ^ [] : [hAPP(_1245689, 24791 ^ [_1245681, _1245683, _1245685, _1245687, _1245689]) = c_Groups_Ozero__class_Ozero(_1245681)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245683, _1245681), _1245689), _1245685) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245683, _1245681), _1245689), _1245687))], (24799 ^ _782464) ^ [_1246132, _1246134] : [class_Groups_Osgn__if(_1246132), 24802 ^ _782464 : [(24803 ^ _782464) ^ [] : [_1246134 = c_Groups_Ozero__class_Ozero(_1246132), -(c_Groups_Osgn__class_Osgn(_1246132, _1246134) = c_Groups_Ozero__class_Ozero(_1246132))], (24809 ^ _782464) ^ [] : [-(_1246134 = c_Groups_Ozero__class_Ozero(_1246132)), 24812 ^ _782464 : [(24813 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246132), c_Groups_Ozero__class_Ozero(_1246132)), _1246134)), -(c_Groups_Osgn__class_Osgn(_1246132, _1246134) = c_Groups_Oone__class_Oone(_1246132))], (24819 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246132), c_Groups_Ozero__class_Ozero(_1246132)), _1246134))), -(c_Groups_Osgn__class_Osgn(_1246132, _1246134) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246132), c_Groups_Oone__class_Oone(_1246132)))]]]]], (24825 ^ _782464) ^ [_1246529, _1246531] : [class_Rings_Olinordered__idom(_1246529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246529), _1246531), c_Groups_Ozero__class_Ozero(_1246529))), -(c_Groups_Osgn__class_Osgn(_1246529, _1246531) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246529), c_Groups_Oone__class_Oone(_1246529)))], (24835 ^ _782464) ^ [_1246694, _1246696] : [class_Rings_Olinordered__idom(_1246694), 24838 ^ _782464 : [(24839 ^ _782464) ^ [] : [c_Groups_Osgn__class_Osgn(_1246694, _1246696) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246694), c_Groups_Oone__class_Oone(_1246694)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246694), _1246696), c_Groups_Ozero__class_Ozero(_1246694))))], (24845 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246694), _1246696), c_Groups_Ozero__class_Ozero(_1246694))), -(c_Groups_Osgn__class_Osgn(_1246694, _1246696) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246694), c_Groups_Oone__class_Oone(_1246694)))]]], (24851 ^ _782464) ^ [_1246956, _1246958, _1246960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246956)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246958), 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), _1246958), _1246960))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1246956))), _1246960)))], (24857 ^ _782464) ^ [_1247103, _1247105, _1247107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247105), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247107), 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), _1247107), _1247105))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1247103)))))], (24863 ^ _782464) ^ [_1247250, _1247252, _1247254, _1247256] : [class_Groups_Oordered__ab__group__add__abs(_1247250), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247250), hAPP(c_Groups_Oabs__class_Oabs(_1247250), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247252, _1247250), _1247254), _1247256))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247252, _1247250), hAPP(hAPP(c_COMBB(_1247250, _1247250, _1247252), c_Groups_Oabs__class_Oabs(_1247250)), _1247254)), _1247256))))], (24869 ^ _782464) ^ [_1247413, _1247415, _1247417, _1247419] : [class_Groups_Oordered__ab__group__add__abs(_1247413), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247413), c_Groups_Ozero__class_Ozero(_1247413)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247415, _1247413), hAPP(hAPP(c_COMBB(_1247413, _1247413, _1247415), c_Groups_Oabs__class_Oabs(_1247413)), _1247417)), _1247419))))], (24875 ^ _782464) ^ [_1247552, _1247554, _1247556] : [class_Groups_Oordered__ab__group__add__abs(_1247552), -(hAPP(c_Groups_Oabs__class_Oabs(_1247552), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247552), hAPP(c_Groups_Oabs__class_Oabs(_1247552), _1247554)), hAPP(c_Groups_Oabs__class_Oabs(_1247552), _1247556))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247552), hAPP(c_Groups_Oabs__class_Oabs(_1247552), _1247554)), hAPP(c_Groups_Oabs__class_Oabs(_1247552), _1247556)))], (24881 ^ _782464) ^ [_1247711, _1247713] : [class_Rings_Olinordered__idom(_1247711), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247711), hAPP(c_Groups_Oabs__class_Oabs(_1247711), _1247713)), hAPP(c_Groups_Oabs__class_Oabs(_1247711), _1247713)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247711), _1247713), _1247713))], (24887 ^ _782464) ^ [_1247838, _1247840, _1247842] : [class_Rings_Olinordered__idom(_1247838), -(hAPP(c_Groups_Oabs__class_Oabs(_1247838), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247838), _1247840), _1247842)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247838), hAPP(c_Groups_Oabs__class_Oabs(_1247838), _1247840)), hAPP(c_Groups_Oabs__class_Oabs(_1247838), _1247842)))], (24893 ^ _782464) ^ [_1247977, _1247979, _1247981] : [class_Groups_Oordered__ab__group__add__abs(_1247977), -(hAPP(c_Groups_Oabs__class_Oabs(_1247977), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1247977), _1247979), _1247981)) = hAPP(c_Groups_Oabs__class_Oabs(_1247977), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1247977), _1247981), _1247979)))], (24899 ^ _782464) ^ [_1248106] : [class_Rings_Olinordered__idom(_1248106), -(hAPP(c_Groups_Oabs__class_Oabs(_1248106), c_Groups_Oone__class_Oone(_1248106)) = c_Groups_Oone__class_Oone(_1248106))], (24905 ^ _782464) ^ [_1248197, _1248199] : [class_Groups_Oordered__ab__group__add__abs(_1248197), -(hAPP(c_Groups_Oabs__class_Oabs(_1248197), hAPP(c_Groups_Ouminus__class_Ouminus(_1248197), _1248199)) = hAPP(c_Groups_Oabs__class_Oabs(_1248197), _1248199))], (24911 ^ _782464) ^ [_1248302, _1248304] : [class_Rings_Olinordered__idom(_1248302), -(hAPP(c_Groups_Oabs__class_Oabs(_1248302), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248302), _1248304)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248302), _1248304))], (24917 ^ _782464) ^ [_1248407, _1248409, _1248411] : [class_Groups_Oordered__ab__group__add__abs(_1248407), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248407), hAPP(c_Groups_Oabs__class_Oabs(_1248407), _1248409)), _1248411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248407), _1248409), _1248411)))], (24927 ^ _782464) ^ [_1248576, _1248578] : [class_Groups_Oordered__ab__group__add__abs(_1248576), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248576), _1248578), hAPP(c_Groups_Oabs__class_Oabs(_1248576), _1248578))))], (24933 ^ _782464) ^ [_1248675, _1248677] : [class_Rings_Olinordered__idom(_1248675), -(c_Groups_Osgn__class_Osgn(_1248675, c_Groups_Osgn__class_Osgn(_1248675, _1248677)) = c_Groups_Osgn__class_Osgn(_1248675, _1248677))], (24939 ^ _782464) ^ [_1248768, _1248770] : [class_Groups_Oordered__ab__group__add__abs(_1248768), -(hAPP(c_Groups_Oabs__class_Oabs(_1248768), hAPP(c_Groups_Oabs__class_Oabs(_1248768), _1248770)) = hAPP(c_Groups_Oabs__class_Oabs(_1248768), _1248770))], (24945 ^ _782464) ^ [_1248873, _1248875] : [class_Rings_Olinordered__idom(_1248873), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248873), c_Groups_Osgn__class_Osgn(_1248873, _1248875)), hAPP(c_Groups_Oabs__class_Oabs(_1248873), _1248875)) = _1248875)], (24951 ^ _782464) ^ [_1248980, _1248982] : [class_Rings_Olinordered__idom(_1248980), -(hAPP(c_Groups_Oabs__class_Oabs(_1248980), _1248982) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248980), _1248982), c_Groups_Osgn__class_Osgn(_1248980, _1248982)))], (24957 ^ _782464) ^ [_1249087, _1249089] : [class_Groups_Oordered__ab__group__add__abs(_1249087), 24960 ^ _782464 : [(24961 ^ _782464) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1249087), _1249089) = c_Groups_Ozero__class_Ozero(_1249087), -(_1249089 = c_Groups_Ozero__class_Ozero(_1249087))], (24967 ^ _782464) ^ [] : [_1249089 = c_Groups_Ozero__class_Ozero(_1249087), -(hAPP(c_Groups_Oabs__class_Oabs(_1249087), _1249089) = c_Groups_Ozero__class_Ozero(_1249087))]]], (24973 ^ _782464) ^ [_1249319] : [class_Groups_Oordered__ab__group__add__abs(_1249319), -(hAPP(c_Groups_Oabs__class_Oabs(_1249319), c_Groups_Ozero__class_Ozero(_1249319)) = c_Groups_Ozero__class_Ozero(_1249319))], (24979 ^ _782464) ^ [_1249410] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249410)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249410))], (24981 ^ _782464) ^ [_1249442, _1249444, _1249446, _1249448] : [class_Groups_Oordered__ab__group__add__abs(_1249442), -(hAPP(c_Groups_Oabs__class_Oabs(_1249442), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249444, _1249442), hAPP(hAPP(c_COMBB(_1249442, _1249442, _1249444), c_Groups_Oabs__class_Oabs(_1249442)), _1249446)), _1249448)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249444, _1249442), hAPP(hAPP(c_COMBB(_1249442, _1249442, _1249444), c_Groups_Oabs__class_Oabs(_1249442)), _1249446)), _1249448))], (24987 ^ _782464) ^ [_1249615, _1249617] : [class_Rings_Olinordered__idom(_1249615), 24990 ^ _782464 : [(24991 ^ _782464) ^ [] : [c_Groups_Osgn__class_Osgn(_1249615, _1249617) = c_Groups_Ozero__class_Ozero(_1249615), -(_1249617 = c_Groups_Ozero__class_Ozero(_1249615))], (24997 ^ _782464) ^ [] : [_1249617 = c_Groups_Ozero__class_Ozero(_1249615), -(c_Groups_Osgn__class_Osgn(_1249615, _1249617) = c_Groups_Ozero__class_Ozero(_1249615))]]], (25003 ^ _782464) ^ [_1249841] : [class_Groups_Osgn__if(_1249841), -(c_Groups_Osgn__class_Osgn(_1249841, c_Groups_Ozero__class_Ozero(_1249841)) = c_Groups_Ozero__class_Ozero(_1249841))], (25009 ^ _782464) ^ [_1249928, _1249930, _1249932] : [class_Rings_Olinordered__idom(_1249928), -(c_Groups_Osgn__class_Osgn(_1249928, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249928), _1249930), _1249932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249928), c_Groups_Osgn__class_Osgn(_1249928, _1249930)), c_Groups_Osgn__class_Osgn(_1249928, _1249932)))], (25015 ^ _782464) ^ [_1250055, _1250057] : [class_Groups_Oordered__ab__group__add__abs(_1250055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250055), c_Groups_Ozero__class_Ozero(_1250055)), _1250057)), -(hAPP(c_Groups_Oabs__class_Oabs(_1250055), _1250057) = _1250057)], (25025 ^ _782464) ^ [_1250210, _1250212] : [class_Groups_Oordered__ab__group__add__abs(_1250210), 25028 ^ _782464 : [(25029 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250210), hAPP(c_Groups_Oabs__class_Oabs(_1250210), _1250212)), c_Groups_Ozero__class_Ozero(_1250210))), -(_1250212 = c_Groups_Ozero__class_Ozero(_1250210))], (25035 ^ _782464) ^ [] : [_1250212 = c_Groups_Ozero__class_Ozero(_1250210), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250210), hAPP(c_Groups_Oabs__class_Oabs(_1250210), _1250212)), c_Groups_Ozero__class_Ozero(_1250210))))]]], (25041 ^ _782464) ^ [_1250463, _1250465] : [class_Groups_Oordered__ab__group__add__abs(_1250463), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250463), c_Groups_Ozero__class_Ozero(_1250463)), hAPP(c_Groups_Oabs__class_Oabs(_1250463), _1250465))))], (25047 ^ _782464) ^ [_1250566, _1250568] : [class_Groups_Oordered__ab__group__add__abs(_1250566), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250566), c_Groups_Ozero__class_Ozero(_1250566)), _1250568)), -(hAPP(c_Groups_Oabs__class_Oabs(_1250566), _1250568) = _1250568)], (25057 ^ _782464) ^ [_1250721, _1250723] : [class_Groups_Oordered__ab__group__add__abs(_1250721), 25060 ^ _782464 : [(25061 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250721), c_Groups_Ozero__class_Ozero(_1250721)), hAPP(c_Groups_Oabs__class_Oabs(_1250721), _1250723))), _1250723 = c_Groups_Ozero__class_Ozero(_1250721)], (25067 ^ _782464) ^ [] : [-(_1250723 = c_Groups_Ozero__class_Ozero(_1250721)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250721), c_Groups_Ozero__class_Ozero(_1250721)), hAPP(c_Groups_Oabs__class_Oabs(_1250721), _1250723))))]]], (25073 ^ _782464) ^ [_1250936, _1250938] : [class_Groups_Oordered__ab__group__add__abs(_1250936), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250936), hAPP(c_Groups_Oabs__class_Oabs(_1250936), _1250938)), c_Groups_Ozero__class_Ozero(_1250936)))], (25079 ^ _782464) ^ [_1251040, _1251042, _1251044] : [class_Groups_Oordered__ab__group__add__abs(_1251040), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251040), hAPP(c_Groups_Oabs__class_Oabs(_1251040), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251040), _1251042), _1251044))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251040), hAPP(c_Groups_Oabs__class_Oabs(_1251040), _1251042)), hAPP(c_Groups_Oabs__class_Oabs(_1251040), _1251044)))))], (25085 ^ _782464) ^ [_1251193, _1251195, _1251197, _1251199, _1251201] : [class_Rings_Olinordered__idom(_1251193), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251193), hAPP(c_Groups_Oabs__class_Oabs(_1251193), _1251195)), _1251197)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251193), hAPP(c_Groups_Oabs__class_Oabs(_1251193), _1251199)), _1251201)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251193), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251193), hAPP(c_Groups_Oabs__class_Oabs(_1251193), _1251195)), hAPP(c_Groups_Oabs__class_Oabs(_1251193), _1251199))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251193), _1251197), _1251201))))], (25099 ^ _782464) ^ [_1251504, _1251506, _1251508] : [class_Groups_Oordered__ab__group__add__abs(_1251504), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251504), hAPP(c_Groups_Oabs__class_Oabs(_1251504), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251504), hAPP(c_Groups_Oabs__class_Oabs(_1251504), _1251506)), hAPP(c_Groups_Oabs__class_Oabs(_1251504), _1251508)))), hAPP(c_Groups_Oabs__class_Oabs(_1251504), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251504), _1251506), _1251508)))))], (25105 ^ _782464) ^ [_1251667, _1251669, _1251671] : [class_Groups_Oordered__ab__group__add__abs(_1251667), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251667), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251667), hAPP(c_Groups_Oabs__class_Oabs(_1251667), _1251669)), hAPP(c_Groups_Oabs__class_Oabs(_1251667), _1251671))), hAPP(c_Groups_Oabs__class_Oabs(_1251667), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251667), _1251669), _1251671)))))], (25111 ^ _782464) ^ [_1251820, _1251822, _1251824] : [class_Groups_Oordered__ab__group__add__abs(_1251820), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251820), hAPP(c_Groups_Oabs__class_Oabs(_1251820), _1251822)), hAPP(c_Groups_Oabs__class_Oabs(_1251820), _1251824))), hAPP(c_Groups_Oabs__class_Oabs(_1251820), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251820), _1251824), _1251822)))))], (25117 ^ _782464) ^ [_1251973, _1251975, _1251977] : [class_Groups_Oordered__ab__group__add__abs(_1251973), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251973), hAPP(c_Groups_Oabs__class_Oabs(_1251973), _1251975)), _1251977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251973), hAPP(c_Groups_Ouminus__class_Ouminus(_1251973), _1251975)), _1251977)))], (25127 ^ _782464) ^ [_1252152, _1252154, _1252156] : [class_Groups_Oordered__ab__group__add__abs(_1252152), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252152), _1252154), _1252156)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252152), hAPP(c_Groups_Ouminus__class_Ouminus(_1252152), _1252154)), _1252156)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252152), hAPP(c_Groups_Oabs__class_Oabs(_1252152), _1252154)), _1252156)))], (25141 ^ _782464) ^ [_1252399, _1252401, _1252403] : [class_Groups_Oordered__ab__group__add__abs(_1252399), 25144 ^ _782464 : [(25145 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252399), hAPP(c_Groups_Oabs__class_Oabs(_1252399), _1252401)), _1252403)), 25148 ^ _782464 : [(25149 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252399), _1252401), _1252403)))], (25151 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252399), hAPP(c_Groups_Ouminus__class_Ouminus(_1252399), _1252401)), _1252403)))]]], (25153 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252399), hAPP(c_Groups_Oabs__class_Oabs(_1252399), _1252401)), _1252403))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252399), _1252401), _1252403)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252399), hAPP(c_Groups_Ouminus__class_Ouminus(_1252399), _1252401)), _1252403))]]], (25163 ^ _782464) ^ [_1252777, _1252779] : [class_Groups_Oordered__ab__group__add__abs(_1252777), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252777), hAPP(c_Groups_Ouminus__class_Ouminus(_1252777), _1252779)), hAPP(c_Groups_Oabs__class_Oabs(_1252777), _1252779))))], (25169 ^ _782464) ^ [_1252886, _1252888, _1252890] : [class_Rings_Olinordered__idom(_1252886), 25172 ^ _782464 : [(25173 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252886), hAPP(c_Groups_Oabs__class_Oabs(_1252886), _1252888)), _1252890)), 25176 ^ _782464 : [(25177 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252886), _1252888), _1252890)))], (25179 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252886), hAPP(c_Groups_Ouminus__class_Ouminus(_1252886), _1252888)), _1252890)))]]], (25181 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252886), hAPP(c_Groups_Oabs__class_Oabs(_1252886), _1252888)), _1252890))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252886), _1252888), _1252890)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252886), hAPP(c_Groups_Ouminus__class_Ouminus(_1252886), _1252888)), _1252890))]]], (25191 ^ _782464) ^ [_1253264, _1253266] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1253264), _1253266)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253264) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25197 ^ _782464) ^ [_1253365, _1253367, _1253369] : [class_Rings_Olinordered__idom(_1253365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253365), c_Groups_Ozero__class_Ozero(_1253365)), _1253367)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253365), hAPP(c_Groups_Oabs__class_Oabs(_1253365), _1253369)), _1253367) = hAPP(c_Groups_Oabs__class_Oabs(_1253365), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253365), _1253369), _1253367)))], (25207 ^ _782464) ^ [_1253566, _1253568, _1253570] : [class_Rings_Oordered__ring__abs(_1253566), -(hAPP(c_Groups_Oabs__class_Oabs(_1253566), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253566), _1253568), _1253570)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253566), hAPP(c_Groups_Oabs__class_Oabs(_1253566), _1253568)), hAPP(c_Groups_Oabs__class_Oabs(_1253566), _1253570))), 25214 ^ _782464 : [(25215 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253566), c_Groups_Ozero__class_Ozero(_1253566)), _1253568))], (25217 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253566), _1253568), c_Groups_Ozero__class_Ozero(_1253566)))]], 25218 ^ _782464 : [(25219 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253566), c_Groups_Ozero__class_Ozero(_1253566)), _1253570))], (25221 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253566), _1253570), c_Groups_Ozero__class_Ozero(_1253566)))]]], (25225 ^ _782464) ^ [_1253961, _1253963, _1253965] : [class_Groups_Oordered__ab__group__add__abs(_1253961), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253961), hAPP(c_Groups_Oabs__class_Oabs(_1253961), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1253961), _1253963), _1253965))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253961), hAPP(c_Groups_Oabs__class_Oabs(_1253961), _1253963)), hAPP(c_Groups_Oabs__class_Oabs(_1253961), _1253965)))))], (25231 ^ _782464) ^ [_1254114, _1254116, _1254118, _1254120, _1254122] : [class_Groups_Oordered__ab__group__add__abs(_1254114), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254114), hAPP(c_Groups_Oabs__class_Oabs(_1254114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254114), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254114), _1254116), _1254118)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254114), _1254120), _1254122)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254114), hAPP(c_Groups_Oabs__class_Oabs(_1254114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254114), _1254116), _1254120))), hAPP(c_Groups_Oabs__class_Oabs(_1254114), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254114), _1254118), _1254122))))))], (25237 ^ _782464) ^ [_1254335, _1254337] : [class_Groups_Oordered__ab__group__add__abs(_1254335), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254335), _1254337), c_Groups_Ozero__class_Ozero(_1254335))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254335), _1254337) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254335), _1254337))], (25247 ^ _782464) ^ [_1254500, _1254502] : [class_Groups_Oordered__ab__group__add__abs(_1254500), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254500), hAPP(c_Groups_Ouminus__class_Ouminus(_1254500), hAPP(c_Groups_Oabs__class_Oabs(_1254500), _1254502))), c_Groups_Ozero__class_Ozero(_1254500))))], (25253 ^ _782464) ^ [_1254613, _1254615] : [class_Groups_Oordered__ab__group__add__abs(_1254613), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254613), _1254615), c_Groups_Ozero__class_Ozero(_1254613))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254613), _1254615) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254613), _1254615))], (25263 ^ _782464) ^ [_1254778, _1254780] : [class_Groups_Oabs__if(_1254778), 25266 ^ _782464 : [(25267 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254778), _1254780), c_Groups_Ozero__class_Ozero(_1254778))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254778), _1254780) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254778), _1254780))], (25273 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254778), _1254780), c_Groups_Ozero__class_Ozero(_1254778)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254778), _1254780) = _1254780)]]], (25279 ^ _782464) ^ [_1255030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255030)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1255030 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25285 ^ _782464) ^ [_1255117] : [_1255117 = 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), _1255117)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (25291 ^ _782464) ^ [_1255216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255216), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255216) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1255216))], (25297 ^ _782464) ^ [_1255307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255307), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255307) = _1255307)], (25303 ^ _782464) ^ [_1255351, _1255353] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255351), _1255353))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255351))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255353))))], (25305 ^ _782464) ^ [_1255406, _1255408] : [class_Rings_Olinordered__idom(_1255406), 25308 ^ _782464 : [(25309 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255406), c_Groups_Osgn__class_Osgn(_1255406, _1255408)), c_Groups_Ozero__class_Ozero(_1255406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255406), _1255408), c_Groups_Ozero__class_Ozero(_1255406))))], (25315 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255406), _1255408), c_Groups_Ozero__class_Ozero(_1255406))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255406), c_Groups_Osgn__class_Osgn(_1255406, _1255408)), c_Groups_Ozero__class_Ozero(_1255406))))]]], (25321 ^ _782464) ^ [_1255674, _1255676] : [class_Rings_Olinordered__idom(_1255674), 25324 ^ _782464 : [(25325 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255674), c_Groups_Ozero__class_Ozero(_1255674)), c_Groups_Osgn__class_Osgn(_1255674, _1255676))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255674), c_Groups_Ozero__class_Ozero(_1255674)), _1255676)))], (25331 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255674), c_Groups_Ozero__class_Ozero(_1255674)), _1255676)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255674), c_Groups_Ozero__class_Ozero(_1255674)), c_Groups_Osgn__class_Osgn(_1255674, _1255676))))]]], (25337 ^ _782464) ^ [_1255942, _1255944] : [class_Rings_Olinordered__idom(_1255942), 25340 ^ _782464 : [(25341 ^ _782464) ^ [] : [c_Groups_Osgn__class_Osgn(_1255942, _1255944) = c_Groups_Oone__class_Oone(_1255942), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255942), c_Groups_Ozero__class_Ozero(_1255942)), _1255944)))], (25347 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255942), c_Groups_Ozero__class_Ozero(_1255942)), _1255944)), -(c_Groups_Osgn__class_Osgn(_1255942, _1255944) = c_Groups_Oone__class_Oone(_1255942))]]], (25353 ^ _782464) ^ [_1256189, _1256191] : [class_Rings_Olinordered__idom(_1256189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256189), c_Groups_Ozero__class_Ozero(_1256189)), _1256191)), -(c_Groups_Osgn__class_Osgn(_1256189, _1256191) = c_Groups_Oone__class_Oone(_1256189))], (25363 ^ _782464) ^ [_1256350] : [_1256350 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256350) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25369 ^ _782464) ^ [_1256426] : [-(_1256426 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25372 ^ _782464 : [(25373 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256426)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256426) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25379 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256426))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256426) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (25385 ^ _782464) ^ [_1256618, _1256620] : [-(c_Nitpick_Oint__lcm(_1256618, _1256620) = 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), _1256618)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256620)))))], (25387 ^ _782464) ^ [_1256664, _1256666, _1256668, _1256670, _1256672] : [class_Groups_Ocomm__monoid__add(_1256664), class_Groups_Ocomm__monoid__mult(_1256664), _1256666 = _1256668, c_Nat__Transfer_Onat__set(_1256668), 25405 ^ _782464 : [(25406 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25404 ^ [_1256664, _1256666, _1256668, _1256670, _1256672])))], (25408 ^ _782464) ^ [] : [hAPP(_1256670, 25404 ^ [_1256664, _1256666, _1256668, _1256670, _1256672]) = hAPP(_1256672, 25404 ^ [_1256664, _1256666, _1256668, _1256670, _1256672])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256664), _1256670), _1256666) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256664), _1256672), _1256668))], (25412 ^ _782464) ^ [_1257127, _1257129] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1257127), hAPP(c_Nat_OSuc, _1257129)) = 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), _1257127), _1257129)))], (25414 ^ _782464) ^ [_1257172, _1257174, _1257176] : [25416 ^ _782464 : [(25417 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25415 ^ [_1257172, _1257174, _1257176]), _1257172)))], (25419 ^ _782464) ^ [] : [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(_1257174, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25415 ^ [_1257172, _1257174, _1257176]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1257174, 25415 ^ [_1257172, _1257174, _1257176])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1257174, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257176)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257176), hAPP(_1257174, _1257172))), 25429 ^ _782464 : [(25430 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25428 ^ [_1257172, _1257174, _1257176]), _1257172)))], (25432 ^ _782464) ^ [] : [-(hAPP(_1257174, 25428 ^ [_1257172, _1257174, _1257176]) = _1257176)]]], (25434 ^ _782464) ^ [_1257622, _1257624, _1257626] : [25436 ^ _782464 : [(25437 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25435 ^ [_1257622, _1257624, _1257626]), _1257622)))], (25439 ^ _782464) ^ [] : [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(_1257624, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25435 ^ [_1257622, _1257624, _1257626]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1257624, 25435 ^ [_1257622, _1257624, _1257626])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1257624, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257626), hAPP(_1257624, _1257622))), 25449 ^ _782464 : [(25450 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25448 ^ [_1257622, _1257624, _1257626]), _1257622)))], (25452 ^ _782464) ^ [] : [-(hAPP(_1257624, 25448 ^ [_1257622, _1257624, _1257626]) = _1257626)]]], (25454 ^ _782464) ^ [_1258072, _1258074, _1258076] : [-(c_Nat_Onat_Onat__case(_1258072, _1258074, _1258076, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1258074)], (25456 ^ _782464) ^ [_1258104, _1258106, _1258108, _1258110] : [-(c_Nat_Onat_Onat__case(_1258104, _1258106, _1258108, hAPP(c_Nat_OSuc, _1258110)) = hAPP(_1258108, _1258110))], (25458 ^ _782464) ^ [_1258144, _1258146] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258144)), -(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)), _1258144))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1258146))))) = 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)), _1258144))), 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, _1258146))))))], (25464 ^ _782464) ^ [_1258321, _1258323] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258321)), 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)), _1258321))), 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, _1258323))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25470 ^ _782464) ^ [_1258447, _1258449] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258447))), -(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)), _1258447))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1258449)))) = 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)), _1258447))), 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, _1258449))))))], (25476 ^ _782464) ^ [_1258530, _1258532] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258530), _1258532)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1258530, 25479 ^ [_1258530, _1258532], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1258530), _1258532)), _1258532))], (25483 ^ _782464) ^ [_1258651, _1258653] : [25485 ^ _782464 : [(25486 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25484 ^ [_1258651, _1258653]), _1258651)))], (25488 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1258653), 25484 ^ [_1258651, _1258653]))]], -(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)), _1258653), _1258651))], (25492 ^ _782464) ^ [_1258826, _1258828, _1258830] : [hBOOL(hAPP(_1258826, _1258828)), -(hBOOL(hAPP(hAPP(c_member(_1258830), _1258828), hAPP(c_Set_OCollect(_1258830), _1258826))))], (25498 ^ _782464) ^ [_1258933, _1258935, _1258937] : [25499 ^ _782464 : [(25500 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258933), hAPP(c_Set_OCollect(_1258933), _1258935)))], (25502 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258933), hAPP(c_Set_OCollect(_1258933), _1258937)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1258933), hAPP(c_Set_OCollect(_1258933), hAPP(hAPP(c_COMBS(_1258933, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1258933), c_fconj), _1258935)), _1258937)))))], (25506 ^ _782464) ^ [_1259144] : [-(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)), _1259144)))))], (25508 ^ _782464) ^ [_1259175] : [-(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)), _1259175)))))], (25510 ^ _782464) ^ [_1259206, _1259208] : [-(hAPP(c_Set_OCollect(_1259206), _1259208) = _1259208)], (25512 ^ _782464) ^ [_1259251, _1259253] : [c_Orderings_Obot__class_Obot(tc_fun(_1259251, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1259251), _1259253), 25515 ^ _782464 : [(25516 ^ _782464) ^ [_1259336] : [hBOOL(hAPP(_1259253, _1259336))]]], (25518 ^ _782464) ^ [_1259359, _1259361] : [-(hBOOL(hAPP(_1259361, 25519 ^ [_1259359, _1259361]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1259359, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1259359), _1259361))], (25525 ^ _782464) ^ [_1259431, _1259433] : [hAPP(c_Set_OCollect(_1259431), _1259433) = c_Orderings_Obot__class_Obot(tc_fun(_1259431, tc_HOL_Obool)), 25528 ^ _782464 : [(25529 ^ _782464) ^ [_1259516] : [hBOOL(hAPP(_1259433, _1259516))]]], (25531 ^ _782464) ^ [_1259539, _1259541] : [-(hBOOL(hAPP(_1259541, 25532 ^ [_1259539, _1259541]))), -(hAPP(c_Set_OCollect(_1259539), _1259541) = c_Orderings_Obot__class_Obot(tc_fun(_1259539, tc_HOL_Obool)))], (25538 ^ _782464) ^ [_1259596, _1259598] : [-(hAPP(c_Set_OCollect(_1259596), hAPP(hAPP(c_COMBC(_1259596, tc_fun(_1259596, tc_HOL_Obool), tc_HOL_Obool), c_member(_1259596)), _1259598)) = _1259598)], (25540 ^ _782464) ^ [_1259659, _1259661, _1259663] : [hBOOL(hAPP(hAPP(c_member(_1259659), _1259661), hAPP(c_Set_OCollect(_1259659), _1259663))), -(hBOOL(hAPP(_1259663, _1259661)))], (25546 ^ _782464) ^ [_1259762, _1259764, _1259766] : [hBOOL(hAPP(_1259766, _1259764)), -(hBOOL(hAPP(hAPP(c_member(_1259762), _1259764), hAPP(c_Set_OCollect(_1259762), _1259766))))], (25552 ^ _782464) ^ [_1259871, _1259873, _1259875] : [hBOOL(hAPP(hAPP(c_member(_1259871), _1259873), hAPP(c_Set_OCollect(_1259871), _1259875))), -(hBOOL(hAPP(_1259875, _1259873)))], (25558 ^ _782464) ^ [_1259978, _1259980, _1259982] : [hBOOL(hAPP(hAPP(c_member(_1259978), _1259980), hAPP(c_Set_OCollect(_1259978), _1259982))), -(hBOOL(hAPP(_1259982, _1259980)))], (25564 ^ _782464) ^ [_1260085] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1260085, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1260085), hAPP(c_COMBK(tc_HOL_Obool, _1260085), c_fFalse)))], (25566 ^ _782464) ^ [_1260142, _1260144, _1260146] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1260142), hAPP(c_Set_OCollect(_1260142), hAPP(hAPP(c_COMBS(_1260142, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260142), c_fdisj), _1260144)), _1260146)))), 25569 ^ _782464 : [(25570 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260142), hAPP(c_Set_OCollect(_1260142), _1260144))))], (25572 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260142), hAPP(c_Set_OCollect(_1260142), _1260146))))]]], (25574 ^ _782464) ^ [_1260337, _1260339, _1260341] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260337), hAPP(c_Set_OCollect(_1260337), hAPP(hAPP(c_COMBS(_1260337, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260337), c_fdisj), _1260339)), _1260341))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260337), hAPP(c_Set_OCollect(_1260337), _1260339))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260337), hAPP(c_Set_OCollect(_1260337), _1260341)))], (25584 ^ _782464) ^ [_1260566, _1260568, _1260570] : [-(hAPP(hAPP(c_Set_Oinsert(_1260566), _1260568), hAPP(c_Set_OCollect(_1260566), _1260570)) = hAPP(c_Set_OCollect(_1260566), hAPP(hAPP(c_COMBS(_1260566, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260566), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1260566), c_fNot), hAPP(hAPP(c_COMBC(_1260566, _1260566, tc_HOL_Obool), c_fequal), _1260568)))), _1260570)))], (25586 ^ _782464) ^ [_1260651] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1260651, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1260651), hAPP(c_COMBK(tc_HOL_Obool, _1260651), c_fTrue)))], (25588 ^ _782464) ^ [_1260690, _1260692, _1260694] : [-(hAPP(c_Set_OCollect(_1260690), hAPP(hAPP(c_COMBS(_1260690, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260690), c_fdisj), _1260692)), _1260694)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260690, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260690), _1260692)), hAPP(c_Set_OCollect(_1260690), _1260694)))], (25590 ^ _782464) ^ [_1260763, _1260765, _1260767] : [-(hAPP(c_Set_OCollect(_1260763), hAPP(hAPP(c_COMBS(_1260763, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260763), c_fconj), _1260765)), _1260767)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1260763, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260763), _1260765)), hAPP(c_Set_OCollect(_1260763), _1260767)))], (25592 ^ _782464) ^ [_1260836, _1260838] : [-(hAPP(c_Set_OCollect(_1260836), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1260836), c_fNot), _1260838)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1260836, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260836), _1260838)))], (25594 ^ _782464) ^ [_1260889, _1260891, _1260893, _1260895] : [-(hAPP(c_Set_Ovimage(_1260889, _1260891, _1260893), hAPP(c_Set_OCollect(_1260891), _1260895)) = hAPP(c_Set_OCollect(_1260889), hAPP(hAPP(c_COMBB(_1260891, tc_HOL_Obool, _1260889), _1260895), _1260893)))], (25596 ^ _782464) ^ [_1260945, _1260947, _1260949] : [-(hAPP(hAPP(c_Set_Oinsert(_1260945), _1260947), _1260949) = hAPP(c_Set_OCollect(_1260945), hAPP(hAPP(c_COMBS(_1260945, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260945), c_fdisj), hAPP(hAPP(c_COMBC(_1260945, _1260945, tc_HOL_Obool), c_fequal), _1260947))), hAPP(hAPP(c_COMBC(_1260945, tc_fun(_1260945, tc_HOL_Obool), tc_HOL_Obool), c_member(_1260945)), _1260949))))], (25598 ^ _782464) ^ [_1261030, _1261032, _1261034] : [-(hAPP(hAPP(c_Set_Oinsert(_1261030), _1261032), _1261034) = hAPP(c_Set_OCollect(_1261030), hAPP(hAPP(c_COMBS(_1261030, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261030), c_fdisj), hAPP(hAPP(c_COMBC(_1261030, _1261030, tc_HOL_Obool), c_fequal), _1261032))), hAPP(hAPP(c_COMBC(_1261030, tc_fun(_1261030, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261030)), _1261034))))], (25600 ^ _782464) ^ [_1261115, _1261117, _1261119] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261115, tc_HOL_Obool)), _1261117), _1261119) = hAPP(c_Set_OCollect(_1261115), hAPP(hAPP(c_COMBS(_1261115, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261115), c_fdisj), hAPP(hAPP(c_COMBC(_1261115, tc_fun(_1261115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261115)), _1261117))), hAPP(hAPP(c_COMBC(_1261115, tc_fun(_1261115, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261115)), _1261119))))], (25602 ^ _782464) ^ [_1261208, _1261210, _1261212] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261208, tc_HOL_Obool)), _1261210), _1261212) = hAPP(c_Set_OCollect(_1261208), hAPP(hAPP(c_COMBS(_1261208, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261208), c_fconj), hAPP(hAPP(c_COMBC(_1261208, tc_fun(_1261208, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261208)), _1261210))), hAPP(hAPP(c_COMBC(_1261208, tc_fun(_1261208, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261208)), _1261212))))], (25604 ^ _782464) ^ [_1261322, _1261324, _1261326, _1261328] : [hBOOL(hAPP(hAPP(c_member(_1261322), _1261324), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261322, tc_HOL_Obool)), _1261326), hAPP(c_Set_OCollect(_1261322), _1261328)))), 25607 ^ _782464 : [(25608 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261322), _1261324), _1261326)))], (25610 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1261328, _1261324)))]]], (25612 ^ _782464) ^ [_1261489, _1261491, _1261493, _1261495] : [-(hBOOL(hAPP(hAPP(c_member(_1261489), _1261491), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261489, tc_HOL_Obool)), _1261493), hAPP(c_Set_OCollect(_1261489), _1261495))))), hBOOL(hAPP(hAPP(c_member(_1261489), _1261491), _1261493)), hBOOL(hAPP(_1261495, _1261491))], (25622 ^ _782464) ^ [_1261692, _1261694] : [-(hAPP(c_Set_OCollect(_1261692), hAPP(c_fequal, _1261694)) = hAPP(hAPP(c_Set_Oinsert(_1261692), _1261694), c_Orderings_Obot__class_Obot(tc_fun(_1261692, tc_HOL_Obool))))], (25624 ^ _782464) ^ [_1261738, _1261740] : [-(hAPP(c_Set_OCollect(_1261738), hAPP(hAPP(c_COMBC(_1261738, _1261738, tc_HOL_Obool), c_fequal), _1261740)) = hAPP(hAPP(c_Set_Oinsert(_1261738), _1261740), c_Orderings_Obot__class_Obot(tc_fun(_1261738, tc_HOL_Obool))))], (25626 ^ _782464) ^ [_1261803, _1261805, _1261807] : [hBOOL(hAPP(_1261803, _1261805)), -(hAPP(c_Set_OCollect(_1261807), hAPP(hAPP(c_COMBS(_1261807, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261807), c_fconj), hAPP(c_fequal, _1261805))), _1261803)) = hAPP(hAPP(c_Set_Oinsert(_1261807), _1261805), c_Orderings_Obot__class_Obot(tc_fun(_1261807, tc_HOL_Obool))))], (25632 ^ _782464) ^ [_1261962, _1261964, _1261966] : [-(hBOOL(hAPP(_1261962, _1261964))), -(hAPP(c_Set_OCollect(_1261966), hAPP(hAPP(c_COMBS(_1261966, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261966), c_fconj), hAPP(c_fequal, _1261964))), _1261962)) = c_Orderings_Obot__class_Obot(tc_fun(_1261966, tc_HOL_Obool)))], (25638 ^ _782464) ^ [_1262049, _1262051, _1262053] : [hBOOL(hAPP(_1262049, _1262051)), -(hAPP(c_Set_OCollect(_1262053), hAPP(hAPP(c_COMBS(_1262053, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262053), c_fconj), hAPP(hAPP(c_COMBC(_1262053, _1262053, tc_HOL_Obool), c_fequal), _1262051))), _1262049)) = hAPP(hAPP(c_Set_Oinsert(_1262053), _1262051), c_Orderings_Obot__class_Obot(tc_fun(_1262053, tc_HOL_Obool))))], (25644 ^ _782464) ^ [_1262222, _1262224, _1262226] : [-(hBOOL(hAPP(_1262222, _1262224))), -(hAPP(c_Set_OCollect(_1262226), hAPP(hAPP(c_COMBS(_1262226, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262226), c_fconj), hAPP(hAPP(c_COMBC(_1262226, _1262226, tc_HOL_Obool), c_fequal), _1262224))), _1262222)) = c_Orderings_Obot__class_Obot(tc_fun(_1262226, tc_HOL_Obool)))], (25650 ^ _782464) ^ [_1262304, _1262306, _1262308] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262304, tc_HOL_Obool)), _1262306), _1262308) = hAPP(c_Set_OCollect(_1262304), hAPP(hAPP(c_COMBS(_1262304, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262304), c_fconj), hAPP(hAPP(c_COMBC(_1262304, tc_fun(_1262304, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262304)), _1262306))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262304), c_fNot), hAPP(hAPP(c_COMBC(_1262304, tc_fun(_1262304, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262304)), _1262308)))))], (25652 ^ _782464) ^ [_1262407, _1262409] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262407), hAPP(c_Set_OCollect(_1262407), _1262409))), 25655 ^ _782464 : [(25656 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262407), hAPP(c_Set_OCollect(_1262407), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262407), c_fNot), _1262409)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1262407), c_Orderings_Otop__class_Otop(tc_fun(_1262407, tc_HOL_Obool)))))], (25662 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262407), c_Orderings_Otop__class_Otop(tc_fun(_1262407, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1262407), hAPP(c_Set_OCollect(_1262407), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262407), c_fNot), _1262409)))))]]], (25668 ^ _782464) ^ [_1262716, _1262718, _1262720] : [-(hAPP(hAPP(c_Set_Oinsert(_1262716), _1262718), _1262720) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262716, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1262716), hAPP(hAPP(c_COMBC(_1262716, _1262716, tc_HOL_Obool), c_fequal), _1262718))), _1262720))], (25670 ^ _782464) ^ [_1262777, _1262779] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262777, tc_HOL_Obool)), _1262779) = hAPP(c_Set_OCollect(_1262777), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262777), c_fNot), hAPP(hAPP(c_COMBC(_1262777, tc_fun(_1262777, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262777)), _1262779))))], (25672 ^ _782464) ^ [_1262840, _1262842, _1262844, _1262846] : [-(hAPP(c_Set_Ovimage(_1262840, _1262842, _1262844), _1262846) = hAPP(c_Set_OCollect(_1262840), hAPP(hAPP(c_COMBC(_1262840, tc_fun(_1262842, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1262842, tc_fun(tc_fun(_1262842, tc_HOL_Obool), tc_HOL_Obool), _1262840), c_member(_1262842)), _1262844)), _1262846)))], (25674 ^ _782464) ^ [_1262912, _1262914, _1262916] : [-(hAPP(c_Set_OCollect(_1262912), hAPP(hAPP(c_COMBS(_1262912, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262912), c_fimplies), _1262914)), _1262916)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262912, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262912, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1262912), _1262914))), hAPP(c_Set_OCollect(_1262912), _1262916)))], (25676 ^ _782464) ^ [_1262993, _1262995] : [-(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), _1262993)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1262995))))))], (25678 ^ _782464) ^ [_1263035, _1263037, _1263039, _1263041, _1263043, _1263045, _1263047] : [class_Groups_Ocomm__monoid__add(_1263035), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263037), _1263039)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263041), _1263043)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263037, _1263035), hAPP(hAPP(c_COMBS(_1263037, tc_fun(_1263041, tc_HOL_Obool), _1263035), hAPP(hAPP(c_COMBB(tc_fun(_1263041, _1263035), tc_fun(tc_fun(_1263041, tc_HOL_Obool), _1263035), _1263037), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263041, _1263035)), _1263045)), hAPP(hAPP(c_COMBB(tc_fun(_1263041, tc_HOL_Obool), tc_fun(_1263041, tc_HOL_Obool), _1263037), c_Set_OCollect(_1263041)), hAPP(hAPP(c_COMBB(tc_fun(_1263041, tc_HOL_Obool), tc_fun(_1263041, tc_HOL_Obool), _1263037), hAPP(c_COMBS(_1263041, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263041), c_fconj), hAPP(hAPP(c_COMBC(_1263041, tc_fun(_1263041, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263041)), _1263043)))), _1263047)))), _1263039) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263041, _1263035), hAPP(hAPP(c_COMBS(_1263041, tc_fun(_1263037, tc_HOL_Obool), _1263035), hAPP(hAPP(c_COMBB(tc_fun(_1263037, _1263035), tc_fun(tc_fun(_1263037, tc_HOL_Obool), _1263035), _1263041), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263037, _1263035)), hAPP(c_COMBC(_1263037, _1263041, _1263035), _1263045))), hAPP(hAPP(c_COMBB(tc_fun(_1263037, tc_HOL_Obool), tc_fun(_1263037, tc_HOL_Obool), _1263041), c_Set_OCollect(_1263037)), hAPP(hAPP(c_COMBB(tc_fun(_1263037, tc_HOL_Obool), tc_fun(_1263037, tc_HOL_Obool), _1263041), hAPP(c_COMBS(_1263037, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263037), c_fconj), hAPP(hAPP(c_COMBC(_1263037, tc_fun(_1263037, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263037)), _1263039)))), hAPP(c_COMBC(_1263037, _1263041, tc_HOL_Obool), _1263047))))), _1263043))], (25692 ^ _782464) ^ [_1263728, _1263730, _1263732, _1263734, _1263736, _1263738] : [-(hAPP(c_Set_Oimage(_1263728, _1263730, hAPP(hAPP(c_COMBS(_1263728, _1263730, _1263730), hAPP(hAPP(c_COMBS(_1263728, _1263730, tc_fun(_1263730, _1263730)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1263730, tc_fun(_1263730, _1263730)), _1263728), c_If(_1263730)), _1263732)), _1263734)), _1263736)), _1263738) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263730, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1263728, _1263730, _1263734), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1263728, tc_HOL_Obool)), _1263738), hAPP(c_Set_OCollect(_1263728), _1263732)))), hAPP(c_Set_Oimage(_1263728, _1263730, _1263736), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1263728, tc_HOL_Obool)), _1263738), hAPP(c_Set_OCollect(_1263728), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1263728), c_fNot), _1263732))))))], (25694 ^ _782464) ^ [_1263876, _1263878, _1263880, _1263882] : [_1263876 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1263878, _1263880), 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)), _1263882))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263878), _1263876)))], (25700 ^ _782464) ^ [_1263991, _1263993, _1263995, _1263997, _1263999] : [class_Groups_Ocomm__monoid__add(_1263991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263993), _1263995)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263993, _1263991), _1263997), hAPP(c_Set_OCollect(_1263993), hAPP(hAPP(c_COMBS(_1263993, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263993), c_fconj), hAPP(hAPP(c_COMBC(_1263993, tc_fun(_1263993, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263993)), _1263995))), hAPP(hAPP(c_COMBC(_1263993, tc_fun(_1263993, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263993)), _1263999)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263993, _1263991), hAPP(hAPP(c_COMBC(_1263993, _1263991, _1263991), hAPP(hAPP(c_COMBS(_1263993, _1263991, tc_fun(_1263991, _1263991)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1263991, tc_fun(_1263991, _1263991)), _1263993), c_If(_1263991)), hAPP(hAPP(c_COMBC(_1263993, tc_fun(_1263993, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263993)), _1263999))), _1263997)), c_Groups_Ozero__class_Ozero(_1263991))), _1263995))], (25710 ^ _782464) ^ [_1264400, _1264402, _1264404, _1264406, _1264408, _1264410] : [class_Groups_Ocomm__monoid__add(_1264400), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264402), _1264404)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264402, _1264400), _1264406), _1264404) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264408, _1264400), hAPP(hAPP(c_COMBB(tc_fun(_1264402, tc_HOL_Obool), _1264400, _1264408), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264402, _1264400), _1264406)), hAPP(hAPP(c_COMBB(tc_fun(_1264402, tc_HOL_Obool), tc_fun(_1264402, tc_HOL_Obool), _1264408), c_Set_OCollect(_1264402)), hAPP(hAPP(c_COMBB(tc_fun(_1264402, tc_HOL_Obool), tc_fun(_1264402, tc_HOL_Obool), _1264408), hAPP(c_COMBS(_1264402, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1264402), c_fconj), hAPP(hAPP(c_COMBC(_1264402, tc_fun(_1264402, tc_HOL_Obool), tc_HOL_Obool), c_member(_1264402)), _1264404)))), hAPP(c_COMBC(_1264402, _1264408, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1264408, tc_fun(_1264408, tc_HOL_Obool), _1264402), c_fequal), _1264410)))))), hAPP(c_Set_Oimage(_1264402, _1264408, _1264410), _1264404)))], (25720 ^ _782464) ^ [_1264811, _1264813, _1264815, _1264817, _1264819, _1264821] : [class_Groups_Ocomm__monoid__add(_1264811), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264813), _1264815)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264813, _1264811), hAPP(hAPP(c_COMBS(_1264813, _1264811, _1264811), hAPP(hAPP(c_COMBS(_1264813, _1264811, tc_fun(_1264811, _1264811)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1264811, tc_fun(_1264811, _1264811)), _1264813), c_If(_1264811)), _1264817)), _1264819)), _1264821)), _1264815) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264811), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264813, _1264811), _1264819), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264813, tc_HOL_Obool)), _1264815), hAPP(c_Set_OCollect(_1264813), _1264817)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264813, _1264811), _1264821), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264813, tc_HOL_Obool)), _1264815), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264813, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1264813), _1264817))))))], (25730 ^ _782464) ^ [_1265209, _1265211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1265209)), _1265211)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265209), _1265211)))], (25736 ^ _782464) ^ [_1265312, _1265314] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265312), _1265314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1265312)), _1265314)))], (25742 ^ _782464) ^ [_1265421, _1265423, _1265425, _1265427, _1265429, _1265431] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265421), _1265423)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265425), _1265427)), 25752 ^ _782464 : [(25753 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1265425), 25751 ^ [_1265421, _1265423, _1265425, _1265427, _1265429, _1265431]), _1265427)))], (25755 ^ _782464) ^ [] : [hAPP(c_Finite__Set_Ocard(_1265421), hAPP(c_Set_OCollect(_1265421), hAPP(hAPP(c_COMBS(_1265421, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1265421), c_fconj), hAPP(hAPP(c_COMBC(_1265421, tc_fun(_1265421, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265421)), _1265423))), hAPP(hAPP(c_COMBC(_1265421, _1265425, tc_HOL_Obool), _1265429), 25751 ^ [_1265421, _1265423, _1265425, _1265427, _1265429, _1265431])))) = _1265431]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1265421, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1265425, tc_HOL_Obool), tc_Nat_Onat, _1265421), c_Finite__Set_Ocard(_1265425)), hAPP(hAPP(c_COMBB(tc_fun(_1265425, tc_HOL_Obool), tc_fun(_1265425, tc_HOL_Obool), _1265421), c_Set_OCollect(_1265425)), hAPP(hAPP(c_COMBB(tc_fun(_1265425, tc_HOL_Obool), tc_fun(_1265425, tc_HOL_Obool), _1265421), hAPP(c_COMBS(_1265425, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1265425), c_fconj), hAPP(hAPP(c_COMBC(_1265425, tc_fun(_1265425, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265425)), _1265427)))), _1265429)))), _1265423) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1265431), hAPP(c_Finite__Set_Ocard(_1265425), _1265427)))], (25759 ^ _782464) ^ [_1266111, _1266113] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266111), _1266113)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1266111, 25762 ^ [_1266111, _1266113], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1266111), _1266113)), _1266113))], (25766 ^ _782464) ^ [_1266230, _1266232, _1266234, _1266236] : [hBOOL(hAPP(hAPP(c_member(_1266230), _1266232), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266230, tc_HOL_Obool), _1266234))), c_Orderings_Oorder__class_Omono(tc_fun(_1266230, tc_HOL_Obool), tc_fun(_1266230, tc_HOL_Obool), _1266234), 25776 ^ _782464 : [(25777 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266230), 25775 ^ [_1266230, _1266232, _1266234, _1266236]), hAPP(_1266234, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266230, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266230, tc_HOL_Obool), _1266234)), hAPP(c_Set_OCollect(_1266230), _1266236))))))], (25779 ^ _782464) ^ [] : [hBOOL(hAPP(_1266236, 25775 ^ [_1266230, _1266232, _1266234, _1266236]))]], -(hBOOL(hAPP(_1266236, _1266232)))], (25783 ^ _782464) ^ [_1266613, _1266615, _1266617, _1266619, _1266621] : [_1266613 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266615, tc_HOL_Obool), _1266617), c_Orderings_Oorder__class_Omono(tc_fun(_1266615, tc_HOL_Obool), tc_fun(_1266615, tc_HOL_Obool), _1266617), hBOOL(hAPP(hAPP(c_member(_1266615), _1266619), _1266613)), 25797 ^ _782464 : [(25798 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266615), 25796 ^ [_1266613, _1266615, _1266617, _1266619, _1266621]), hAPP(_1266617, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266615, tc_HOL_Obool)), _1266613), hAPP(c_Set_OCollect(_1266615), _1266621))))))], (25800 ^ _782464) ^ [] : [hBOOL(hAPP(_1266621, 25796 ^ [_1266613, _1266615, _1266617, _1266619, _1266621]))]], -(hBOOL(hAPP(_1266621, _1266619)))], (25804 ^ _782464) ^ [_1267054, _1267056, _1267058, _1267060, _1267062] : [_1267054 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1267056, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1267056, tc_HOL_Obool), tc_fun(_1267056, tc_HOL_Obool), tc_fun(_1267056, tc_HOL_Obool)), c_Set_OCollect(_1267056)), _1267058)), c_Orderings_Oorder__class_Omono(tc_fun(_1267056, tc_HOL_Obool), tc_fun(_1267056, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1267056, tc_HOL_Obool), tc_fun(_1267056, tc_HOL_Obool), tc_fun(_1267056, tc_HOL_Obool)), c_Set_OCollect(_1267056)), _1267058)), hBOOL(hAPP(hAPP(c_member(_1267056), _1267060), _1267062)), 25818 ^ _782464 : [(25819 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267056), 25817 ^ [_1267054, _1267056, _1267058, _1267060, _1267062]), _1267062)))], (25821 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1267058, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267056, tc_HOL_Obool)), _1267062), _1267054)), 25817 ^ [_1267054, _1267056, _1267058, _1267060, _1267062]))]], -(hBOOL(hAPP(hAPP(c_member(_1267056), _1267060), _1267054)))], (25825 ^ _782464) ^ [_1267594, _1267596] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267594), _1267596)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1267594, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1267594, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1267594, tc_HOL_Obool), tc_fun(_1267594, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1267594, tc_HOL_Obool))), _1267596)))))], (25831 ^ _782464) ^ [_1267751, _1267753] : [-(hAPP(c_Set_OPow(_1267751), _1267753) = hAPP(c_Set_OCollect(tc_fun(_1267751, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1267751, tc_HOL_Obool), tc_fun(_1267751, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1267751, tc_HOL_Obool))), _1267753)))], (25833 ^ _782464) ^ [_1267810] : [-(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)))), _1267810))))], (25835 ^ _782464) ^ [_1267838] : [-(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)))), _1267838)) = 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), _1267838), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (25837 ^ _782464) ^ [_1267879] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1267879) = 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), _1267879), c_Int_Onat)))))], (25839 ^ _782464) ^ [_1267920, _1267922, _1267924, _1267926, _1267928, _1267930] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267920), _1267922)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267924), _1267926)), 25849 ^ _782464 : [(25850 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267924), 25848 ^ [_1267920, _1267922, _1267924, _1267926, _1267928, _1267930]), _1267926)))], (25852 ^ _782464) ^ [] : [hAPP(c_Finite__Set_Ocard(_1267920), hAPP(c_Set_OCollect(_1267920), hAPP(hAPP(c_COMBS(_1267920, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1267920), c_fconj), hAPP(hAPP(c_COMBC(_1267920, tc_fun(_1267920, tc_HOL_Obool), tc_HOL_Obool), c_member(_1267920)), _1267922))), hAPP(hAPP(c_COMBC(_1267920, _1267924, tc_HOL_Obool), _1267928), 25848 ^ [_1267920, _1267922, _1267924, _1267926, _1267928, _1267930])))) = hAPP(_1267930, 25848 ^ [_1267920, _1267922, _1267924, _1267926, _1267928, _1267930])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267920, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1267924, tc_HOL_Obool), tc_Nat_Onat, _1267920), c_Finite__Set_Ocard(_1267924)), hAPP(hAPP(c_COMBB(tc_fun(_1267924, tc_HOL_Obool), tc_fun(_1267924, tc_HOL_Obool), _1267920), c_Set_OCollect(_1267924)), hAPP(hAPP(c_COMBB(tc_fun(_1267924, tc_HOL_Obool), tc_fun(_1267924, tc_HOL_Obool), _1267920), hAPP(c_COMBS(_1267924, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1267924), c_fconj), hAPP(hAPP(c_COMBC(_1267924, tc_fun(_1267924, tc_HOL_Obool), tc_HOL_Obool), c_member(_1267924)), _1267926)))), _1267928)))), _1267922) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267924, tc_Nat_Onat), _1267930), _1267926))], (25856 ^ _782464) ^ [_1268630, _1268632, _1268634] : [class_Lattices_Odistrib__lattice(_1268630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268630), _1268632)), -(_1268632 = c_Orderings_Obot__class_Obot(tc_fun(_1268630, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268630), _1268634)), -(_1268634 = c_Orderings_Obot__class_Obot(tc_fun(_1268630, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1268630), c_Big__Operators_Olattice__class_OSup__fin(_1268630, _1268632)), c_Big__Operators_Olattice__class_OSup__fin(_1268630, _1268634)) = c_Big__Operators_Olattice__class_OSup__fin(_1268630, hAPP(c_Set_OCollect(_1268630), hAPP(hAPP(c_COMBB(tc_fun(_1268630, tc_HOL_Obool), tc_HOL_Obool, _1268630), c_HOL_OEx(_1268630)), hAPP(hAPP(c_COMBB(tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool)), tc_fun(_1268630, tc_HOL_Obool), _1268630), hAPP(c_COMBB(tc_fun(_1268630, tc_HOL_Obool), tc_HOL_Obool, _1268630), c_HOL_OEx(_1268630))), hAPP(hAPP(c_COMBC(_1268630, tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool)), tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268630, tc_fun(tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_HOL_Obool))), tc_fun(tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool)), tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool))), _1268630), c_COMBS(_1268630, tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268630, tc_fun(_1268630, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1268630, tc_fun(tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_HOL_Obool))), _1268630), hAPP(c_COMBB(tc_fun(_1268630, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_HOL_Obool)), _1268630), c_COMBS(_1268630, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool)), tc_fun(_1268630, tc_fun(_1268630, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1268630), hAPP(c_COMBB(tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1268630), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268630), c_fconj))), hAPP(hAPP(c_COMBC(_1268630, tc_fun(_1268630, tc_fun(_1268630, _1268630)), tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268630, _1268630), tc_fun(_1268630, tc_HOL_Obool)), tc_fun(tc_fun(_1268630, tc_fun(_1268630, _1268630)), tc_fun(_1268630, tc_fun(_1268630, tc_HOL_Obool))), _1268630), c_COMBB(tc_fun(_1268630, _1268630), tc_fun(_1268630, tc_HOL_Obool), _1268630)), hAPP(hAPP(c_COMBB(tc_fun(_1268630, tc_HOL_Obool), tc_fun(tc_fun(_1268630, _1268630), tc_fun(_1268630, tc_HOL_Obool)), _1268630), c_COMBB(_1268630, tc_HOL_Obool, _1268630)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1268630)))))), hAPP(hAPP(c_COMBC(_1268630, tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1268630, tc_HOL_Obool), tc_fun(_1268630, tc_HOL_Obool)), _1268630), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1268630)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268630), c_fconj), hAPP(hAPP(c_COMBC(_1268630, tc_fun(_1268630, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268630)), _1268632)))), hAPP(hAPP(c_COMBC(_1268630, tc_fun(_1268630, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268630)), _1268634))))))))], (25878 ^ _782464) ^ [_1269729, _1269731, _1269733] : [class_Lattices_Odistrib__lattice(_1269729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269729), _1269731)), -(_1269731 = c_Orderings_Obot__class_Obot(tc_fun(_1269729, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1269729), _1269733), c_Big__Operators_Olattice__class_OSup__fin(_1269729, _1269731)) = c_Big__Operators_Olattice__class_OSup__fin(_1269729, hAPP(c_Set_OCollect(_1269729), hAPP(hAPP(c_COMBB(tc_fun(_1269729, tc_HOL_Obool), tc_HOL_Obool, _1269729), c_HOL_OEx(_1269729)), hAPP(hAPP(c_COMBC(_1269729, tc_fun(_1269729, tc_HOL_Obool), tc_fun(_1269729, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269729, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1269729, tc_HOL_Obool), tc_fun(_1269729, tc_HOL_Obool)), _1269729), c_COMBS(_1269729, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269729, tc_HOL_Obool), tc_fun(_1269729, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1269729), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269729), c_fconj)), hAPP(hAPP(c_COMBC(_1269729, tc_fun(_1269729, _1269729), tc_fun(_1269729, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269729, tc_HOL_Obool), tc_fun(tc_fun(_1269729, _1269729), tc_fun(_1269729, tc_HOL_Obool)), _1269729), c_COMBB(_1269729, tc_HOL_Obool, _1269729)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1269729), _1269733))))), hAPP(hAPP(c_COMBC(_1269729, tc_fun(_1269729, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269729)), _1269731))))))], (25892 ^ _782464) ^ [_1270215, _1270217, _1270219] : [class_Lattices_Odistrib__lattice(_1270215), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270215), _1270217)), -(_1270217 = c_Orderings_Obot__class_Obot(tc_fun(_1270215, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270215), _1270219)), -(_1270219 = c_Orderings_Obot__class_Obot(tc_fun(_1270215, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270215), c_Big__Operators_Olattice__class_OInf__fin(_1270215, _1270217)), c_Big__Operators_Olattice__class_OInf__fin(_1270215, _1270219)) = c_Big__Operators_Olattice__class_OInf__fin(_1270215, hAPP(c_Set_OCollect(_1270215), hAPP(hAPP(c_COMBB(tc_fun(_1270215, tc_HOL_Obool), tc_HOL_Obool, _1270215), c_HOL_OEx(_1270215)), hAPP(hAPP(c_COMBB(tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool)), tc_fun(_1270215, tc_HOL_Obool), _1270215), hAPP(c_COMBB(tc_fun(_1270215, tc_HOL_Obool), tc_HOL_Obool, _1270215), c_HOL_OEx(_1270215))), hAPP(hAPP(c_COMBC(_1270215, tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool)), tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270215, tc_fun(tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_HOL_Obool))), tc_fun(tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool)), tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool))), _1270215), c_COMBS(_1270215, tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270215, tc_fun(_1270215, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1270215, tc_fun(tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_HOL_Obool))), _1270215), hAPP(c_COMBB(tc_fun(_1270215, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_HOL_Obool)), _1270215), c_COMBS(_1270215, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool)), tc_fun(_1270215, tc_fun(_1270215, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1270215), hAPP(c_COMBB(tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1270215), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270215), c_fconj))), hAPP(hAPP(c_COMBC(_1270215, tc_fun(_1270215, tc_fun(_1270215, _1270215)), tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1270215, _1270215), tc_fun(_1270215, tc_HOL_Obool)), tc_fun(tc_fun(_1270215, tc_fun(_1270215, _1270215)), tc_fun(_1270215, tc_fun(_1270215, tc_HOL_Obool))), _1270215), c_COMBB(tc_fun(_1270215, _1270215), tc_fun(_1270215, tc_HOL_Obool), _1270215)), hAPP(hAPP(c_COMBB(tc_fun(_1270215, tc_HOL_Obool), tc_fun(tc_fun(_1270215, _1270215), tc_fun(_1270215, tc_HOL_Obool)), _1270215), c_COMBB(_1270215, tc_HOL_Obool, _1270215)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1270215)))))), hAPP(hAPP(c_COMBC(_1270215, tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1270215, tc_HOL_Obool), tc_fun(_1270215, tc_HOL_Obool)), _1270215), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1270215)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270215), c_fconj), hAPP(hAPP(c_COMBC(_1270215, tc_fun(_1270215, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270215)), _1270217)))), hAPP(hAPP(c_COMBC(_1270215, tc_fun(_1270215, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270215)), _1270219))))))))], (25914 ^ _782464) ^ [_1271314, _1271316, _1271318] : [class_Lattices_Odistrib__lattice(_1271314), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271314), _1271316)), -(_1271316 = c_Orderings_Obot__class_Obot(tc_fun(_1271314, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271314), _1271318), c_Big__Operators_Olattice__class_OInf__fin(_1271314, _1271316)) = c_Big__Operators_Olattice__class_OInf__fin(_1271314, hAPP(c_Set_OCollect(_1271314), hAPP(hAPP(c_COMBB(tc_fun(_1271314, tc_HOL_Obool), tc_HOL_Obool, _1271314), c_HOL_OEx(_1271314)), hAPP(hAPP(c_COMBC(_1271314, tc_fun(_1271314, tc_HOL_Obool), tc_fun(_1271314, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271314, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1271314, tc_HOL_Obool), tc_fun(_1271314, tc_HOL_Obool)), _1271314), c_COMBS(_1271314, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271314, tc_HOL_Obool), tc_fun(_1271314, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1271314), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1271314), c_fconj)), hAPP(hAPP(c_COMBC(_1271314, tc_fun(_1271314, _1271314), tc_fun(_1271314, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271314, tc_HOL_Obool), tc_fun(tc_fun(_1271314, _1271314), tc_fun(_1271314, tc_HOL_Obool)), _1271314), c_COMBB(_1271314, tc_HOL_Obool, _1271314)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271314), _1271318))))), hAPP(hAPP(c_COMBC(_1271314, tc_fun(_1271314, tc_HOL_Obool), tc_HOL_Obool), c_member(_1271314)), _1271316))))))], (25928 ^ _782464) ^ [_1271800, _1271802, _1271804, _1271806] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1271800), hAPP(c_Set_OCollect(_1271800), _1271802))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1271804), hAPP(c_Set_OCollect(_1271804), hAPP(hAPP(c_COMBB(tc_fun(_1271800, tc_HOL_Obool), tc_HOL_Obool, _1271804), c_HOL_OEx(_1271800)), hAPP(hAPP(c_COMBC(_1271804, tc_fun(_1271800, tc_HOL_Obool), tc_fun(_1271800, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271800, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1271800, tc_HOL_Obool), tc_fun(_1271800, tc_HOL_Obool)), _1271804), c_COMBS(_1271800, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271800, tc_HOL_Obool), tc_fun(_1271800, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1271804), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1271800), c_fconj)), hAPP(hAPP(c_COMBC(_1271804, tc_fun(_1271800, _1271804), tc_fun(_1271800, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271804, tc_HOL_Obool), tc_fun(tc_fun(_1271800, _1271804), tc_fun(_1271800, tc_HOL_Obool)), _1271804), c_COMBB(_1271804, tc_HOL_Obool, _1271800)), c_fequal)), _1271806)))), _1271802))))))], (25934 ^ _782464) ^ [_1272161, _1272163, _1272165, _1272167] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272161), hAPP(c_Set_OCollect(_1272161), _1272163))), 25937 ^ _782464 : [(25948 ^ _782464) ^ [] : [25950 ^ _782464 : [(25951 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1272163, 25949 ^ [_1272161, _1272163, _1272165, _1272167])))], (25953 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272165), hAPP(c_Set_OCollect(_1272165), hAPP(hAPP(c_COMBC(_1272165, _1272161, tc_HOL_Obool), _1272167), 25949 ^ [_1272161, _1272163, _1272165, _1272167]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272165), hAPP(c_Set_OCollect(_1272165), hAPP(hAPP(c_COMBB(tc_fun(_1272161, tc_HOL_Obool), tc_HOL_Obool, _1272165), c_HOL_OEx(_1272161)), hAPP(hAPP(c_COMBB(tc_fun(_1272161, tc_HOL_Obool), tc_fun(_1272161, tc_HOL_Obool), _1272165), hAPP(c_COMBS(_1272161, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272161), c_fconj), _1272163))), _1272167))))))], (25938 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272165), hAPP(c_Set_OCollect(_1272165), hAPP(hAPP(c_COMBB(tc_fun(_1272161, tc_HOL_Obool), tc_HOL_Obool, _1272165), c_HOL_OEx(_1272161)), hAPP(hAPP(c_COMBB(tc_fun(_1272161, tc_HOL_Obool), tc_fun(_1272161, tc_HOL_Obool), _1272165), hAPP(c_COMBS(_1272161, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272161), c_fconj), _1272163))), _1272167))))), 25941 ^ _782464 : [(25942 ^ _782464) ^ [_1272444] : [hBOOL(hAPP(_1272163, _1272444)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272165), hAPP(c_Set_OCollect(_1272165), hAPP(hAPP(c_COMBC(_1272165, _1272161, tc_HOL_Obool), _1272167), _1272444)))))]]]]], (25957 ^ _782464) ^ [_1272809, _1272811] : [-(hAPP(c_Set_OPow(_1272809), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272809, tc_HOL_Obool)), _1272811)) = hAPP(c_Set_OCollect(tc_fun(_1272809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272809, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1272809, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1272809, tc_HOL_Obool), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1272809, tc_HOL_Obool)), c_COMBS(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1272809, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1272809, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1272809, tc_HOL_Obool), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_fun(_1272809, tc_HOL_Obool)), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_fun(_1272809, tc_HOL_Obool)), tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1272809, tc_HOL_Obool)), c_COMBB(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272809, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1272809, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272809, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272809, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1272809, tc_HOL_Obool)), _1272811)), c_Set_OPow(_1272809))))))], (25959 ^ _782464) ^ [_1273089, _1273091, _1273093] : [class_Groups_Olinordered__ab__semigroup__add(_1273089), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273089), _1273091)), -(_1273091 = c_Orderings_Obot__class_Obot(tc_fun(_1273089, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273089), _1273093), c_Big__Operators_Olinorder__class_OMin(_1273089, _1273091)) = c_Big__Operators_Olinorder__class_OMin(_1273089, hAPP(c_Set_OCollect(_1273089), hAPP(hAPP(c_COMBB(tc_fun(_1273089, tc_HOL_Obool), tc_HOL_Obool, _1273089), c_HOL_OEx(_1273089)), hAPP(hAPP(c_COMBC(_1273089, tc_fun(_1273089, tc_HOL_Obool), tc_fun(_1273089, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273089, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1273089, tc_HOL_Obool), tc_fun(_1273089, tc_HOL_Obool)), _1273089), c_COMBS(_1273089, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273089, tc_HOL_Obool), tc_fun(_1273089, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1273089), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1273089), c_fconj)), hAPP(hAPP(c_COMBC(_1273089, tc_fun(_1273089, _1273089), tc_fun(_1273089, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273089, tc_HOL_Obool), tc_fun(tc_fun(_1273089, _1273089), tc_fun(_1273089, tc_HOL_Obool)), _1273089), c_COMBB(_1273089, tc_HOL_Obool, _1273089)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1273089), _1273093))))), hAPP(hAPP(c_COMBC(_1273089, tc_fun(_1273089, tc_HOL_Obool), tc_HOL_Obool), c_member(_1273089)), _1273091))))))], (25973 ^ _782464) ^ [_1273575, _1273577, _1273579] : [class_Groups_Olinordered__ab__semigroup__add(_1273575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273575), _1273577)), -(_1273577 = c_Orderings_Obot__class_Obot(tc_fun(_1273575, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273575), _1273579), c_Big__Operators_Olinorder__class_OMax(_1273575, _1273577)) = c_Big__Operators_Olinorder__class_OMax(_1273575, hAPP(c_Set_OCollect(_1273575), hAPP(hAPP(c_COMBB(tc_fun(_1273575, tc_HOL_Obool), tc_HOL_Obool, _1273575), c_HOL_OEx(_1273575)), hAPP(hAPP(c_COMBC(_1273575, tc_fun(_1273575, tc_HOL_Obool), tc_fun(_1273575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273575, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1273575, tc_HOL_Obool), tc_fun(_1273575, tc_HOL_Obool)), _1273575), c_COMBS(_1273575, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273575, tc_HOL_Obool), tc_fun(_1273575, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1273575), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1273575), c_fconj)), hAPP(hAPP(c_COMBC(_1273575, tc_fun(_1273575, _1273575), tc_fun(_1273575, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273575, tc_HOL_Obool), tc_fun(tc_fun(_1273575, _1273575), tc_fun(_1273575, tc_HOL_Obool)), _1273575), c_COMBB(_1273575, tc_HOL_Obool, _1273575)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1273575), _1273579))))), hAPP(hAPP(c_COMBC(_1273575, tc_fun(_1273575, tc_HOL_Obool), tc_HOL_Obool), c_member(_1273575)), _1273577))))))], (25987 ^ _782464) ^ [_1274076, _1274078] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274076), _1274078)), -(_1274078 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1274076, 25991 ^ [_1274076, _1274078]), 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)), 25990 ^ [_1274076, _1274078]))))], (25995 ^ _782464) ^ [_1274207, _1274209] : [25996 ^ _782464 : [(25997 ^ _782464) ^ [_1274271, _1274273] : [_1274209 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1274207, _1274271), 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)), _1274273)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274207), _1274209)))], (26001 ^ _782464) ^ [_1274342, _1274344, _1274346, _1274348] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274342), _1274344))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274346), hAPP(c_Set_Oimage(_1274342, _1274346, _1274348), _1274344))), 26009 ^ _782464 : [(26010 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1274342), 26008 ^ [_1274342, _1274344, _1274346, _1274348]), _1274344)))], (26012 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274342), hAPP(c_Set_OCollect(_1274342), hAPP(hAPP(c_COMBS(_1274342, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1274342), c_fconj), hAPP(hAPP(c_COMBC(_1274342, tc_fun(_1274342, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274342)), _1274344))), hAPP(hAPP(c_COMBC(_1274342, _1274346, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1274346, tc_fun(_1274346, tc_HOL_Obool), _1274342), c_fequal), _1274348)), hAPP(_1274348, 26008 ^ [_1274342, _1274344, _1274346, _1274348]))))))]]], (26014 ^ _782464) ^ [_1274816, _1274818] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1274816)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1274818)), hAPP(c_Int_Onat, _1274816)) = hAPP(c_Int_Onat, _1274818))], (26020 ^ _782464) ^ [_1274921, _1274923] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1274921))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1274923)), hAPP(c_Int_Onat, _1274921)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1274923), _1274921)), 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)))], (26026 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26028 ^ _782464) ^ [_1275018] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1275018)))], (26030 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26032 ^ _782464) ^ [_1275070, _1275072] : [class_Groups_Olinordered__ab__group__add(_1275070), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275070), _1275072)), -(_1275072 = c_Orderings_Obot__class_Obot(tc_fun(_1275070, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275070), c_Big__Operators_Olinorder__class_OMin(_1275070, _1275072)) = c_Big__Operators_Olinorder__class_OMax(_1275070, hAPP(c_Set_Oimage(_1275070, _1275070, c_Groups_Ouminus__class_Ouminus(_1275070)), _1275072)))], (26046 ^ _782464) ^ [_1275270, _1275272] : [class_Groups_Olinordered__ab__group__add(_1275270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275270), _1275272)), -(_1275272 = c_Orderings_Obot__class_Obot(tc_fun(_1275270, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275270), c_Big__Operators_Olinorder__class_OMax(_1275270, _1275272)) = c_Big__Operators_Olinorder__class_OMin(_1275270, hAPP(c_Set_Oimage(_1275270, _1275270, c_Groups_Ouminus__class_Ouminus(_1275270)), _1275272)))], (26060 ^ _782464) ^ [_1275470, _1275472] : [class_Orderings_Olinorder(_1275470), -(c_Big__Operators_Olinorder__class_OMin(_1275470, hAPP(hAPP(c_Set_Oinsert(_1275470), _1275472), c_Orderings_Obot__class_Obot(tc_fun(_1275470, tc_HOL_Obool)))) = _1275472)], (26066 ^ _782464) ^ [_1275577, _1275579] : [class_Orderings_Olinorder(_1275577), -(c_Big__Operators_Olinorder__class_OMax(_1275577, hAPP(hAPP(c_Set_Oinsert(_1275577), _1275579), c_Orderings_Obot__class_Obot(tc_fun(_1275577, tc_HOL_Obool)))) = _1275579)], (26072 ^ _782464) ^ [_1275690] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275690))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275690)))], (26078 ^ _782464) ^ [_1275724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275724)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275724))], (26084 ^ _782464) ^ [_1275822] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275822)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275822), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26090 ^ _782464) ^ [_1275907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275907), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275907)))], (26096 ^ _782464) ^ [_1275998] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275998)), -(hAPP(c_Int_Onat, _1275998) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26102 ^ _782464) ^ [_1276079] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1276079))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1276079)) = _1276079)], (26108 ^ _782464) ^ [_1276121, _1276123, _1276125] : [class_Orderings_Olinorder(_1276121), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276121), _1276123)), hBOOL(hAPP(hAPP(c_member(_1276121), _1276125), _1276123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276121), _1276125), c_Big__Operators_Olinorder__class_OMax(_1276121, _1276123))))], (26122 ^ _782464) ^ [_1276348, _1276350, _1276352] : [class_Orderings_Olinorder(_1276348), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276348), _1276350)), hBOOL(hAPP(hAPP(c_member(_1276348), _1276352), _1276350)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276348), c_Big__Operators_Olinorder__class_OMin(_1276348, _1276350)), _1276352)))], (26136 ^ _782464) ^ [_1276575, _1276577] : [class_Orderings_Olinorder(_1276575), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276575), _1276577)), -(_1276577 = c_Orderings_Obot__class_Obot(tc_fun(_1276575, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1276575), c_Big__Operators_Olinorder__class_OMin(_1276575, _1276577)), _1276577)))], (26150 ^ _782464) ^ [_1276755, _1276757] : [class_Orderings_Olinorder(_1276755), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276755), _1276757)), -(_1276757 = c_Orderings_Obot__class_Obot(tc_fun(_1276755, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1276755), c_Big__Operators_Olinorder__class_OMax(_1276755, _1276757)), _1276757)))], (26164 ^ _782464) ^ [_1276935] : [-(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, _1276935))))))], (26166 ^ _782464) ^ [_1276969, _1276971, _1276973] : [class_Orderings_Olinorder(_1276969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276969, tc_HOL_Obool)), _1276971), _1276973)), -(_1276971 = c_Orderings_Obot__class_Obot(tc_fun(_1276969, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276969), _1276973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276969), c_Big__Operators_Olinorder__class_OMax(_1276969, _1276971)), c_Big__Operators_Olinorder__class_OMax(_1276969, _1276973))))], (26184 ^ _782464) ^ [_1277275, _1277277, _1277279] : [class_Orderings_Olinorder(_1277275), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277275, tc_HOL_Obool)), _1277277), _1277279)), -(_1277277 = c_Orderings_Obot__class_Obot(tc_fun(_1277275, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277275), _1277279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277275), c_Big__Operators_Olinorder__class_OMin(_1277275, _1277279)), c_Big__Operators_Olinorder__class_OMin(_1277275, _1277277))))], (26202 ^ _782464) ^ [_1277581, _1277583, _1277585] : [class_Orderings_Olinorder(_1277581), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277581), _1277583)), hBOOL(hAPP(hAPP(c_member(_1277581), _1277585), _1277583)), 26213 ^ _782464 : [(26214 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277581, tc_HOL_Obool)), _1277583), hAPP(hAPP(c_Set_Oinsert(_1277581), _1277585), c_Orderings_Obot__class_Obot(tc_fun(_1277581, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1277581, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1277581, _1277583) = _1277585)], (26220 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277581, tc_HOL_Obool)), _1277583), hAPP(hAPP(c_Set_Oinsert(_1277581), _1277585), c_Orderings_Obot__class_Obot(tc_fun(_1277581, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1277581, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1277581, _1277583) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277581), _1277585), c_Big__Operators_Olinorder__class_OMin(_1277581, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277581, tc_HOL_Obool)), _1277583), hAPP(hAPP(c_Set_Oinsert(_1277581), _1277585), c_Orderings_Obot__class_Obot(tc_fun(_1277581, tc_HOL_Obool)))))))]]], (26226 ^ _782464) ^ [_1278087, _1278089, _1278091] : [class_Orderings_Olinorder(_1278087), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278087), _1278089)), hBOOL(hAPP(hAPP(c_member(_1278087), _1278091), _1278089)), 26237 ^ _782464 : [(26238 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278087, tc_HOL_Obool)), _1278089), hAPP(hAPP(c_Set_Oinsert(_1278087), _1278091), c_Orderings_Obot__class_Obot(tc_fun(_1278087, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278087, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1278087, _1278089) = _1278091)], (26244 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278087, tc_HOL_Obool)), _1278089), hAPP(hAPP(c_Set_Oinsert(_1278087), _1278091), c_Orderings_Obot__class_Obot(tc_fun(_1278087, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278087, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1278087, _1278089) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1278087), _1278091), c_Big__Operators_Olinorder__class_OMax(_1278087, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278087, tc_HOL_Obool)), _1278089), hAPP(hAPP(c_Set_Oinsert(_1278087), _1278091), c_Orderings_Obot__class_Obot(tc_fun(_1278087, tc_HOL_Obool)))))))]]], (26250 ^ _782464) ^ [_1278593, _1278595, _1278597, _1278599] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1278593, tc_Nat_Onat), _1278595), _1278597) = hAPP(c_Nat_OSuc, _1278599), 26254 ^ _782464 : [(26255 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1278593), 26253 ^ [_1278593, _1278595, _1278597, _1278599]), _1278597)))], (26257 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1278595, 26253 ^ [_1278593, _1278595, _1278597, _1278599]))))]]], (26259 ^ _782464) ^ [_1278775, _1278777, _1278779, _1278781, _1278783, _1278785] : [c_Fun_Oinj__on(_1278775, _1278777, _1278779, _1278781), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278777, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278775, _1278777, _1278779), _1278781)), _1278783)), c_Fun_Oinj__on(_1278777, _1278775, _1278785, _1278783), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278775, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278777, _1278775, _1278785), _1278783)), _1278781)), -(c_Fun_Obij__betw(_1278775, _1278777, 26274 ^ [_1278775, _1278777, _1278779, _1278781, _1278783, _1278785], _1278781, _1278783))], (26278 ^ _782464) ^ [_1279142, _1279144, _1279146, _1279148, _1279150] : [class_Groups_Ocomm__monoid__mult(_1279142), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279144), _1279146)), hBOOL(hAPP(hAPP(c_member(_1279144), _1279148), _1279146)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279144, _1279142), _1279150), _1279146) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279142), hAPP(_1279150, _1279148)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279144, _1279142), _1279150), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279144, tc_HOL_Obool)), _1279146), hAPP(hAPP(c_Set_Oinsert(_1279144), _1279148), c_Orderings_Obot__class_Obot(tc_fun(_1279144, tc_HOL_Obool)))))))], (26292 ^ _782464) ^ [_1279467, _1279469, _1279471, _1279473, _1279475] : [class_Orderings_Olinorder(_1279467), class_Orderings_Olinorder(_1279469), c_Orderings_Oorder__class_Omono(_1279469, _1279467, _1279471), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279467), hAPP(_1279471, _1279473)), hAPP(_1279471, _1279475)) = hAPP(_1279471, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279469), _1279473), _1279475)))], (26306 ^ _782464) ^ [_1279716, _1279718, _1279720, _1279722, _1279724] : [class_Orderings_Olinorder(_1279716), class_Orderings_Olinorder(_1279718), c_Orderings_Oorder__class_Omono(_1279718, _1279716, _1279720), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279716), hAPP(_1279720, _1279722)), hAPP(_1279720, _1279724)) = hAPP(_1279720, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279718), _1279722), _1279724)))], (26320 ^ _782464) ^ [_1279965, _1279967, _1279969, _1279971] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1279965), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279967, tc_Int_Oint), _1279969), _1279971)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279967, _1279965), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1279965, _1279967), c_Int_Oring__1__class_Oof__int(_1279965)), _1279969)), _1279971)), class_Groups_Ocomm__monoid__mult(_1279965), class_Rings_Oring__1(_1279965)], (26330 ^ _782464) ^ [_1280168, _1280170, _1280172] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280168, tc_Nat_Onat), _1280170), _1280172) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280168, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1280168), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1280170)), _1280172)))], (26332 ^ _782464) ^ [_1280226, _1280228, _1280230, _1280232] : [class_Orderings_Olinorder(_1280226), 26335 ^ _782464 : [(26346 ^ _782464) ^ [] : [26347 ^ _782464 : [(26348 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280226), _1280228), _1280230))], (26350 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280226), _1280228), _1280232))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280226), _1280228), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280226), _1280230), _1280232))))], (26336 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280226), _1280228), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280226), _1280230), _1280232))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280226), _1280228), _1280230))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280226), _1280228), _1280232)))]]], (26354 ^ _782464) ^ [_1280575, _1280577, _1280579, _1280581] : [class_Orderings_Olinorder(_1280575), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280575), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280575), _1280577), _1280579)), _1280581)), 26361 ^ _782464 : [(26362 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280575), _1280577), _1280581)))], (26364 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280575), _1280579), _1280581)))]]], (26366 ^ _782464) ^ [_1280798, _1280800, _1280802, _1280804, _1280806] : [class_Orderings_Olinorder(_1280798), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280798), _1280800), _1280802)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280798), _1280804), _1280806)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280798), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280798), _1280800), _1280804)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280798), _1280802), _1280806))))], (26380 ^ _782464) ^ [_1281069, _1281071, _1281073, _1281075] : [class_Orderings_Olinorder(_1281069), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281069), _1281071), _1281073)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281069), _1281075), _1281073)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281069), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281069), _1281071), _1281075)), _1281073)))], (26394 ^ _782464) ^ [_1281318, _1281320, _1281322, _1281324] : [class_Orderings_Olinorder(_1281318), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281318), _1281320), _1281322)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281318), _1281324), _1281322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281318), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281318), _1281320), _1281324)), _1281322)))], (26408 ^ _782464) ^ [_1281567, _1281569, _1281571] : [class_Orderings_Olinorder(_1281567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281567), _1281569), _1281571)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281567), _1281571), _1281569) = _1281571)], (26418 ^ _782464) ^ [_1281728, _1281730, _1281732] : [class_Orderings_Olinorder(_1281728), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281728), _1281730), _1281732)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281728), _1281730), _1281732) = _1281732)], (26428 ^ _782464) ^ [_1281889, _1281891, _1281893, _1281895] : [class_Orderings_Olinorder(_1281889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281889), _1281891), _1281893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281889), _1281891), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281889), _1281895), _1281893))))], (26438 ^ _782464) ^ [_1282068, _1282070, _1282072, _1282074] : [class_Orderings_Olinorder(_1282068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282068), _1282070), _1282072)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282068), _1282070), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282068), _1282072), _1282074))))], (26448 ^ _782464) ^ [_1282247, _1282249, _1282251, _1282253] : [class_Orderings_Olinorder(_1282247), 26451 ^ _782464 : [(26452 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282247), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282247), _1282249), _1282251)), _1282253)), 26455 ^ _782464 : [(26456 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282247), _1282249), _1282253)))], (26458 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282247), _1282251), _1282253)))]]], (26460 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282247), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282247), _1282249), _1282251)), _1282253))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282247), _1282249), _1282253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282247), _1282251), _1282253))]]], (26470 ^ _782464) ^ [_1282627, _1282629, _1282631] : [class_Orderings_Olinorder(_1282627), 26473 ^ _782464 : [(26474 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282627), _1282629), _1282631)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282627), _1282629), _1282631) = _1282631)], (26480 ^ _782464) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282627), _1282629), _1282631) = _1282631, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282627), _1282629), _1282631)))]]], (26486 ^ _782464) ^ [_1282883, _1282885, _1282887] : [class_Orderings_Olinorder(_1282883), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282883), _1282885), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282883), _1282887), _1282885))))], (26492 ^ _782464) ^ [_1282990, _1282992, _1282994] : [class_Orderings_Olinorder(_1282990), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282990), _1282992), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282990), _1282992), _1282994))))], (26498 ^ _782464) ^ [_1283097, _1283099, _1283101, _1283103] : [class_Orderings_Olinorder(_1283097), 26501 ^ _782464 : [(26512 ^ _782464) ^ [] : [26513 ^ _782464 : [(26514 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283097), _1283099), _1283103))], (26516 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283097), _1283101), _1283103))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283097), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283097), _1283099), _1283101)), _1283103)))], (26502 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283097), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283097), _1283099), _1283101)), _1283103)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283097), _1283099), _1283103))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283097), _1283101), _1283103)))]]], (26520 ^ _782464) ^ [_1283446, _1283448, _1283450, _1283452] : [class_Orderings_Olinorder(_1283446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283446), _1283448), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283446), _1283450), _1283452))), 26527 ^ _782464 : [(26528 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283446), _1283448), _1283450)))], (26530 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283446), _1283448), _1283452)))]]], (26532 ^ _782464) ^ [_1283669, _1283671, _1283673, _1283675, _1283677] : [class_Orderings_Olinorder(_1283669), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283669), _1283671), _1283673)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283669), _1283675), _1283677)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283669), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283669), _1283671), _1283675)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283669), _1283673), _1283677))))], (26546 ^ _782464) ^ [_1283940, _1283942, _1283944, _1283946] : [class_Orderings_Olinorder(_1283940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283940), _1283942), _1283944)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283940), _1283942), _1283946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283940), _1283942), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283940), _1283944), _1283946))))], (26560 ^ _782464) ^ [_1284189, _1284191, _1284193, _1284195] : [class_Orderings_Olinorder(_1284189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284189), _1284191), _1284193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284189), _1284191), _1284195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284189), _1284191), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284189), _1284193), _1284195))))], (26574 ^ _782464) ^ [_1284438, _1284440, _1284442] : [class_Orderings_Olinorder(_1284438), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284438), _1284440), _1284442)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284438), _1284442), _1284440) = _1284440)], (26584 ^ _782464) ^ [_1284599, _1284601, _1284603] : [class_Orderings_Olinorder(_1284599), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284599), _1284601), _1284603)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284599), _1284601), _1284603) = _1284601)], (26594 ^ _782464) ^ [_1284760, _1284762, _1284764, _1284766] : [class_Orderings_Olinorder(_1284760), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284760), _1284762), _1284764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284760), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284760), _1284766), _1284762)), _1284764)))], (26604 ^ _782464) ^ [_1284939, _1284941, _1284943, _1284945] : [class_Orderings_Olinorder(_1284939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284939), _1284941), _1284943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284939), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284939), _1284941), _1284945)), _1284943)))], (26614 ^ _782464) ^ [_1285118, _1285120, _1285122, _1285124] : [class_Orderings_Olinorder(_1285118), 26617 ^ _782464 : [(26618 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285118), _1285120), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285118), _1285122), _1285124))), 26621 ^ _782464 : [(26622 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285118), _1285120), _1285122)))], (26624 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285118), _1285120), _1285124)))]]], (26626 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285118), _1285120), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285118), _1285122), _1285124)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285118), _1285120), _1285122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285118), _1285120), _1285124))]]], (26636 ^ _782464) ^ [_1285498, _1285500, _1285502] : [class_Orderings_Olinorder(_1285498), 26639 ^ _782464 : [(26640 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285498), _1285500), _1285502)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285498), _1285500), _1285502) = _1285500)], (26646 ^ _782464) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285498), _1285500), _1285502) = _1285500, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285498), _1285500), _1285502)))]]], (26652 ^ _782464) ^ [_1285754, _1285756, _1285758] : [class_Orderings_Olinorder(_1285754), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285754), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285754), _1285756), _1285758)), _1285758)))], (26658 ^ _782464) ^ [_1285861, _1285863, _1285865] : [class_Orderings_Olinorder(_1285861), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285861), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285861), _1285863), _1285865)), _1285863)))], (26664 ^ _782464) ^ [_1285968, _1285970, _1285972, _1285974] : [class_Orderings_Olinorder(_1285968), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285968), _1285970), _1285972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285968), _1285970), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285968), _1285974), _1285972))))], (26674 ^ _782464) ^ [_1286147, _1286149, _1286151, _1286153] : [class_Orderings_Olinorder(_1286147), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286147), _1286149), _1286151)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286147), _1286149), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286147), _1286151), _1286153))))], (26684 ^ _782464) ^ [_1286326, _1286328, _1286330, _1286332] : [class_Orderings_Olinorder(_1286326), 26687 ^ _782464 : [(26688 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286326), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286326), _1286328), _1286330)), _1286332)), 26691 ^ _782464 : [(26692 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286326), _1286328), _1286332)))], (26694 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286326), _1286330), _1286332)))]]], (26696 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286326), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286326), _1286328), _1286330)), _1286332))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286326), _1286328), _1286332)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286326), _1286330), _1286332))]]], (26706 ^ _782464) ^ [_1286706, _1286708, _1286710, _1286712] : [class_Orderings_Olinorder(_1286706), 26709 ^ _782464 : [(26720 ^ _782464) ^ [] : [26721 ^ _782464 : [(26722 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286706), _1286708), _1286710))], (26724 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286706), _1286708), _1286712))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286706), _1286708), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286706), _1286710), _1286712))))], (26710 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286706), _1286708), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286706), _1286710), _1286712))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286706), _1286708), _1286710))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286706), _1286708), _1286712)))]]], (26728 ^ _782464) ^ [_1287055, _1287057, _1287059, _1287061] : [class_Orderings_Olinorder(_1287055), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287055), _1287057), _1287059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287055), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287055), _1287061), _1287057)), _1287059)))], (26738 ^ _782464) ^ [_1287234, _1287236, _1287238, _1287240] : [class_Orderings_Olinorder(_1287234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287234), _1287236), _1287238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287234), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287234), _1287236), _1287240)), _1287238)))], (26748 ^ _782464) ^ [_1287413, _1287415, _1287417, _1287419] : [class_Orderings_Olinorder(_1287413), 26751 ^ _782464 : [(26762 ^ _782464) ^ [] : [26763 ^ _782464 : [(26764 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287413), _1287415), _1287419))], (26766 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287413), _1287417), _1287419))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287413), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287413), _1287415), _1287417)), _1287419)))], (26752 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287413), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287413), _1287415), _1287417)), _1287419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287413), _1287415), _1287419))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287413), _1287417), _1287419)))]]], (26770 ^ _782464) ^ [_1287762, _1287764, _1287766, _1287768] : [class_Orderings_Olinorder(_1287762), 26773 ^ _782464 : [(26774 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287762), _1287764), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287762), _1287766), _1287768))), 26777 ^ _782464 : [(26778 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287762), _1287764), _1287766)))], (26780 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287762), _1287764), _1287768)))]]], (26782 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287762), _1287764), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287762), _1287766), _1287768)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287762), _1287764), _1287766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287762), _1287764), _1287768))]]], (26792 ^ _782464) ^ [_1288142, _1288144, _1288146, _1288148] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1288142), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288142), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288142), _1288144), _1288146)), _1288148) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288142), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288142), _1288144), _1288148)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288142), _1288146), _1288148)))], (26798 ^ _782464) ^ [_1288301, _1288303, _1288305, _1288307] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1288301), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288301), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288301), _1288303), _1288305)), _1288307) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288301), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288301), _1288303), _1288307)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288301), _1288305), _1288307)))], (26804 ^ _782464) ^ [_1288460, _1288462, _1288464, _1288466] : [class_Groups_Oordered__ab__group__add(_1288460), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288460), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288460), _1288462), _1288464)), _1288466) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288460), _1288462), _1288466)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288460), _1288464), _1288466)))], (26810 ^ _782464) ^ [_1288619, _1288621, _1288623, _1288625] : [class_Groups_Oordered__ab__group__add(_1288619), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288619), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288619), _1288621), _1288623)), _1288625) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288619), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288619), _1288621), _1288625)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288619), _1288623), _1288625)))], (26816 ^ _782464) ^ [_1288778] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288778) = _1288778)], (26818 ^ _782464) ^ [_1288804] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1288804), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1288804)], (26820 ^ _782464) ^ [_1288833] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288833) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26822 ^ _782464) ^ [_1288859] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1288859), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26824 ^ _782464) ^ [_1288888, _1288890] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288888)), hAPP(c_Nat_OSuc, _1288890)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1288888), _1288890)))], (26826 ^ _782464) ^ [_1288934, _1288936] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288934)), hAPP(c_Nat_OSuc, _1288936)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1288934), _1288936)))], (26828 ^ _782464) ^ [_1288980, _1288982, _1288984, _1288986] : [class_Orderings_Olinorder(_1288980), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288980), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288980), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288980), _1288982), _1288984)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288980), _1288982), _1288986))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288980), _1288982), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288980), _1288984), _1288986)))))], (26834 ^ _782464) ^ [_1289153, _1289155, _1289157, _1289159] : [class_Orderings_Olinorder(_1289153), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289153), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289153), _1289155), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289153), _1289157), _1289159))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289153), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289153), _1289155), _1289157)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289153), _1289155), _1289159)))))], (26840 ^ _782464) ^ [_1289326, _1289328] : [class_Orderings_Olinorder(_1289326), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289326), _1289328), _1289328) = _1289328)], (26846 ^ _782464) ^ [_1289417, _1289419] : [class_Orderings_Olinorder(_1289417), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289417), _1289419), _1289419) = _1289419)], (26852 ^ _782464) ^ [_1289508, _1289510] : [class_Orderings_Olinorder(_1289508), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289508), _1289510), _1289510) = _1289510)], (26858 ^ _782464) ^ [_1289599, _1289601] : [class_Orderings_Olinorder(_1289599), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289599), _1289601), _1289601) = _1289601)], (26864 ^ _782464) ^ [_1289690, _1289692, _1289694] : [class_Orderings_Olinorder(_1289690), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289690), _1289692), _1289694) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289690), _1289694), _1289692))], (26870 ^ _782464) ^ [_1289799, _1289801, _1289803] : [class_Orderings_Olinorder(_1289799), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289799), _1289801), _1289803) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289799), _1289803), _1289801))], (26876 ^ _782464) ^ [_1289908, _1289910, _1289912] : [class_Orderings_Olinorder(_1289908), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289908), _1289910), _1289912) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289908), _1289912), _1289910))], (26882 ^ _782464) ^ [_1290017, _1290019, _1290021] : [class_Orderings_Olinorder(_1290017), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290017), _1290019), _1290021) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290017), _1290021), _1290019))], (26888 ^ _782464) ^ [_1290126, _1290128, _1290130] : [class_Orderings_Olinorder(_1290126), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290126), _1290128), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290126), _1290128), _1290130)) = _1290128)], (26894 ^ _782464) ^ [_1290235, _1290237, _1290239] : [class_Orderings_Olinorder(_1290235), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290235), _1290237), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290235), _1290237), _1290239)) = _1290237)], (26900 ^ _782464) ^ [_1290344, _1290346, _1290348] : [class_Orderings_Olinorder(_1290344), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290344), _1290346), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290344), _1290346), _1290348)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290344), _1290346), _1290348))], (26906 ^ _782464) ^ [_1290469, _1290471, _1290473] : [class_Orderings_Olinorder(_1290469), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290469), _1290471), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290469), _1290471), _1290473)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290469), _1290471), _1290473))], (26912 ^ _782464) ^ [_1290594, _1290596, _1290598] : [class_Orderings_Olinorder(_1290594), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290594), _1290596), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290594), _1290596), _1290598)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290594), _1290596), _1290598))], (26918 ^ _782464) ^ [_1290719, _1290721, _1290723] : [class_Orderings_Olinorder(_1290719), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290719), _1290721), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290719), _1290721), _1290723)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290719), _1290721), _1290723))], (26924 ^ _782464) ^ [_1290844, _1290846, _1290848, _1290850] : [class_Orderings_Olinorder(_1290844), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290844), _1290846), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290844), _1290848), _1290850)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290844), _1290848), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290844), _1290846), _1290850)))], (26930 ^ _782464) ^ [_1290987, _1290989, _1290991, _1290993] : [class_Orderings_Olinorder(_1290987), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290987), _1290989), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290987), _1290991), _1290993)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290987), _1290991), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290987), _1290989), _1290993)))], (26936 ^ _782464) ^ [_1291130, _1291132, _1291134, _1291136] : [class_Orderings_Olinorder(_1291130), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291130), _1291132), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291130), _1291134), _1291136)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291130), _1291134), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291130), _1291132), _1291136)))], (26942 ^ _782464) ^ [_1291273, _1291275, _1291277, _1291279] : [class_Orderings_Olinorder(_1291273), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291273), _1291275), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291273), _1291277), _1291279)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291273), _1291277), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291273), _1291275), _1291279)))], (26948 ^ _782464) ^ [_1291416, _1291418, _1291420, _1291422] : [class_Orderings_Olinorder(_1291416), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291416), _1291418), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291416), _1291420), _1291422)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291416), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291416), _1291418), _1291420)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291416), _1291418), _1291422)))], (26954 ^ _782464) ^ [_1291575, _1291577, _1291579, _1291581] : [class_Orderings_Olinorder(_1291575), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291575), _1291577), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291575), _1291579), _1291581)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291575), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291575), _1291577), _1291579)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291575), _1291577), _1291581)))], (26960 ^ _782464) ^ [_1291734, _1291736, _1291738, _1291740] : [class_Orderings_Olinorder(_1291734), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291734), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291734), _1291736), _1291738)), _1291740) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291734), _1291736), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291734), _1291738), _1291740)))], (26966 ^ _782464) ^ [_1291877, _1291879, _1291881, _1291883] : [class_Orderings_Olinorder(_1291877), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291877), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291877), _1291879), _1291881)), _1291883) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291877), _1291879), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291877), _1291881), _1291883)))], (26972 ^ _782464) ^ [_1292020, _1292022, _1292024, _1292026] : [class_Orderings_Olinorder(_1292020), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292020), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292020), _1292022), _1292024)), _1292026) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292020), _1292022), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292020), _1292024), _1292026)))], (26978 ^ _782464) ^ [_1292163, _1292165, _1292167, _1292169] : [class_Orderings_Olinorder(_1292163), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292163), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292163), _1292165), _1292167)), _1292169) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292163), _1292165), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292163), _1292167), _1292169)))], (26984 ^ _782464) ^ [_1292306, _1292308, _1292310, _1292312] : [class_Orderings_Olinorder(_1292306), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292306), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292306), _1292308), _1292310)), _1292312) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292306), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292306), _1292308), _1292312)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292306), _1292310), _1292312)))], (26990 ^ _782464) ^ [_1292465, _1292467, _1292469, _1292471] : [class_Orderings_Olinorder(_1292465), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292465), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292465), _1292467), _1292469)), _1292471) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292465), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292465), _1292467), _1292471)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292465), _1292469), _1292471)))], (26996 ^ _782464) ^ [_1292624, _1292626, _1292628] : [class_Groups_Olinordered__ab__group__add(_1292624), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292624), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292624), _1292626), _1292628)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292624), hAPP(c_Groups_Ouminus__class_Ouminus(_1292624), _1292626)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292624), _1292628)))], (27002 ^ _782464) ^ [_1292763, _1292765, _1292767] : [class_Groups_Olinordered__ab__group__add(_1292763), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292763), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292763), _1292765), _1292767)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292763), hAPP(c_Groups_Ouminus__class_Ouminus(_1292763), _1292765)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292763), _1292767)))], (27008 ^ _782464) ^ [_1292902, _1292904, _1292906, _1292908] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1292902), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292904, tc_Nat_Onat), _1292906), _1292908)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292904, _1292902), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1292902, _1292904), c_Nat_Osemiring__1__class_Oof__nat(_1292902)), _1292906)), _1292908)), class_Groups_Ocomm__monoid__mult(_1292902), class_Rings_Osemiring__1(_1292902)], (27018 ^ _782464) ^ [_1293105, _1293107, _1293109] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293105, tc_Nat_Onat), _1293107), _1293109)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293105, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1293105), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1293107)), _1293109))], (27020 ^ _782464) ^ [_1293163, _1293165, _1293167] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1293163), _1293165)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1293167), _1293165)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1293163), _1293167)), _1293165))], (27022 ^ _782464) ^ [_1293220, _1293222, _1293224, _1293226, _1293228] : [class_Orderings_Olinorder(_1293220), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293220, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293220, _1293222), _1293224)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293220, _1293226), _1293228)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293220, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293220), _1293222), _1293226)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293220), _1293224), _1293228)))], (27028 ^ _782464) ^ [_1293391, _1293393, _1293395, _1293397, _1293399] : [class_Orderings_Olinorder(_1293391), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293391, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1293391, _1293393, _1293395)), c_SetInterval_Oord__class_OatLeastAtMost(_1293391, _1293397, _1293399)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293391, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293391), _1293393), _1293397), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293391), _1293395), _1293399)))], (27034 ^ _782464) ^ [_1293550, _1293552, _1293554, _1293556, _1293558] : [class_Orderings_Olinorder(_1293550), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293550, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293550, _1293552, _1293554)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293550, _1293556, _1293558)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1293550, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293550), _1293552), _1293556), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293550), _1293554), _1293558)))], (27040 ^ _782464) ^ [_1293709] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1293709) = c_Orderings_Oord__class_Omin(_1293709)), class_Lattices_Osemilattice__inf(_1293709), class_Orderings_Olinorder(_1293709)], (27050 ^ _782464) ^ [_1293838] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1293838) = c_Orderings_Oord__class_Omax(_1293838)), class_Lattices_Osemilattice__sup(_1293838), class_Orderings_Olinorder(_1293838)], (27060 ^ _782464) ^ [_1293967, _1293969, _1293971, _1293973, _1293975] : [class_Orderings_Olinorder(_1293967), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293967, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1293967, _1293969, _1293971)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1293967, _1293973, _1293975)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1293967, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293967), _1293969), _1293973), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293967), _1293971), _1293975)))], (27066 ^ _782464) ^ [_1294126, _1294128, _1294130, _1294132, _1294134] : [class_Groups_Ocomm__monoid__mult(_1294126), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294128, _1294126), hAPP(hAPP(c_COMBS(_1294128, _1294126, _1294126), hAPP(hAPP(c_COMBB(_1294126, tc_fun(_1294126, _1294126), _1294128), c_Groups_Otimes__class_Otimes(_1294126)), _1294130)), _1294132)), _1294134) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294126), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294128, _1294126), _1294130), _1294134)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294128, _1294126), _1294132), _1294134)))], (27072 ^ _782464) ^ [_1294327, _1294329, _1294331] : [class_Groups_Ocomm__monoid__mult(_1294327), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294329, _1294327), hAPP(c_COMBK(_1294327, _1294329), c_Groups_Oone__class_Oone(_1294327))), _1294331) = c_Groups_Oone__class_Oone(_1294327))], (27078 ^ _782464) ^ [_1294442, _1294444, _1294446, _1294448] : [class_Fields_Olinordered__field(_1294442), -(hAPP(c_Groups_Oabs__class_Oabs(_1294442), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294444, _1294442), _1294446), _1294448)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294444, _1294442), hAPP(hAPP(c_COMBB(_1294442, _1294442, _1294444), c_Groups_Oabs__class_Oabs(_1294442)), _1294446)), _1294448))], (27084 ^ _782464) ^ [_1294591] : [class_Orderings_Olinorder(_1294591), -(c_Finite__Set_Ofun__left__comm__idem(_1294591, _1294591, c_Orderings_Oord__class_Omax(_1294591)))], (27090 ^ _782464) ^ [_1294670] : [class_Orderings_Olinorder(_1294670), -(c_Finite__Set_Ofun__left__comm__idem(_1294670, _1294670, c_Orderings_Oord__class_Omin(_1294670)))], (27096 ^ _782464) ^ [_1294749, _1294751, _1294753] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1294749), _1294751), _1294753) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1294749), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1294749, tc_Int_Oint), _1294751), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1294753))), class_Groups_Ocomm__monoid__add(_1294749), class_Groups_Ocomm__monoid__mult(_1294749)], (27106 ^ _782464) ^ [_1294940, _1294942, _1294944, _1294946] : [class_Rings_Ocomm__semiring__1(_1294940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294942), _1294944)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294942, _1294940), _1294946), _1294944) = c_Groups_Ozero__class_Ozero(_1294940)), 27115 ^ _782464 : [(27116 ^ _782464) ^ [_1295121] : [hBOOL(hAPP(hAPP(c_member(_1294942), _1295121), _1294944)), hAPP(_1294946, _1295121) = c_Groups_Ozero__class_Ozero(_1294940)]]], (27124 ^ _782464) ^ [_1295270, _1295272, _1295274, _1295276] : [class_Rings_Ocomm__semiring__1(_1295270), class_Rings_Ono__zero__divisors(_1295270), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295272), _1295274)), 27135 ^ _782464 : [(27136 ^ _782464) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295272, _1295270), _1295276), _1295274) = c_Groups_Ozero__class_Ozero(_1295270), 27140 ^ _782464 : [(27141 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295272), 27139 ^ [_1295270, _1295272, _1295274, _1295276]), _1295274)))], (27143 ^ _782464) ^ [] : [-(hAPP(_1295276, 27139 ^ [_1295270, _1295272, _1295274, _1295276]) = c_Groups_Ozero__class_Ozero(_1295270))]]], (27145 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295272, _1295270), _1295276), _1295274) = c_Groups_Ozero__class_Ozero(_1295270)), 27146 ^ _782464 : [(27147 ^ _782464) ^ [_1295648] : [hBOOL(hAPP(hAPP(c_member(_1295272), _1295648), _1295274)), hAPP(_1295276, _1295648) = c_Groups_Ozero__class_Ozero(_1295270)]]]]], (27155 ^ _782464) ^ [_1295803, _1295805, _1295807] : [class_Groups_Ocomm__monoid__mult(_1295803), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295805, _1295803), _1295807), c_Orderings_Obot__class_Obot(tc_fun(_1295805, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1295803))], (27161 ^ _782464) ^ [_1295912, _1295914, _1295916] : [class_Groups_Ocomm__monoid__mult(_1295912), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295914, _1295912), _1295916), c_Orderings_Obot__class_Obot(tc_fun(_1295914, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1295912))], (27167 ^ _782464) ^ [_1296021, _1296023, _1296025, _1296027] : [class_Groups_Ocomm__monoid__mult(_1296021), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1296023), _1296025))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296023, _1296021), _1296027), _1296025) = c_Groups_Oone__class_Oone(_1296021))], (27177 ^ _782464) ^ [_1296145, _1296147, _1296149, _1296151] : [class_Groups_Ocomm__monoid__mult(_1296145), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1296147), _1296149))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296147, _1296145), _1296151), _1296149) = c_Groups_Oone__class_Oone(_1296145))], (27187 ^ _782464) ^ [_1296269, _1296271, _1296273] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1296269), _1296271)), 27190 ^ _782464 : [(27201 ^ _782464) ^ [] : [27203 ^ _782464 : [(27204 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1296269), 27202 ^ [_1296269, _1296271, _1296273]), _1296271)))], (27206 ^ _782464) ^ [] : [hAPP(_1296273, 27202 ^ [_1296269, _1296271, _1296273]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296269, tc_Nat_Onat), _1296273), _1296271) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27191 ^ _782464) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296269, tc_Nat_Onat), _1296273), _1296271) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 27194 ^ _782464 : [(27195 ^ _782464) ^ [_1296431] : [hBOOL(hAPP(hAPP(c_member(_1296269), _1296431), _1296271)), -(hAPP(_1296273, _1296431) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (27210 ^ _782464) ^ [_1296689, _1296691, _1296693] : [class_Groups_Ocomm__monoid__add(_1296689), class_Groups_Ocomm__monoid__mult(_1296689), c_Nat__Transfer_Onat__set(_1296691), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1296689), _1296693), _1296691) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1296689), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1296689, tc_Nat_Onat), _1296693), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1296691)))], (27224 ^ _782464) ^ [_1296934, _1296936] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1296934), _1296936)), _1296936) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1296934), _1296936))], (27226 ^ _782464) ^ [_1296977, _1296979, _1296981, _1296983, _1296985] : [class_Groups_Ocomm__monoid__mult(_1296977), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296979), _1296981)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296979, _1296977), hAPP(hAPP(c_COMBS(_1296979, _1296977, _1296977), hAPP(hAPP(c_COMBB(_1296977, tc_fun(_1296977, _1296977), _1296979), c_Groups_Otimes__class_Otimes(_1296977)), _1296983)), _1296985)), _1296981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296977), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296979, _1296977), _1296983), _1296981)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296979, _1296977), _1296985), _1296981)))], (27236 ^ _782464) ^ [_1297244, _1297246, _1297248] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297244), _1297246)), 27239 ^ _782464 : [(27250 ^ _782464) ^ [] : [27252 ^ _782464 : [(27253 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1297244), 27251 ^ [_1297244, _1297246, _1297248]), _1297246)))], (27255 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1297248, 27251 ^ [_1297244, _1297246, _1297248])))]], -(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(_1297244, tc_Nat_Onat), _1297248), _1297246))))], (27240 ^ _782464) ^ [] : [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(_1297244, tc_Nat_Onat), _1297248), _1297246))), 27243 ^ _782464 : [(27244 ^ _782464) ^ [_1297412] : [hBOOL(hAPP(hAPP(c_member(_1297244), _1297412), _1297246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1297248, _1297412))))]]]]], (27259 ^ _782464) ^ [_1297680, _1297682, _1297684, _1297686, _1297688, _1297690, _1297692, _1297694] : [class_Groups_Ocomm__monoid__mult(_1297680), c_Fun_Oinj__on(_1297682, _1297684, _1297686, _1297688), _1297690 = hAPP(c_Set_Oimage(_1297682, _1297684, _1297686), _1297688), _1297692 = hAPP(c_Fun_Ocomp(_1297684, _1297680, _1297682, _1297694), _1297686), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297684, _1297680), _1297694), _1297690) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297682, _1297680), _1297692), _1297688))], (27277 ^ _782464) ^ [_1298029, _1298031, _1298033, _1298035, _1298037, _1298039] : [class_Groups_Ocomm__monoid__mult(_1298029), c_Fun_Oinj__on(_1298031, _1298033, _1298035, _1298037), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298033, _1298029), _1298039), hAPP(c_Set_Oimage(_1298031, _1298033, _1298035), _1298037)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298031, _1298029), hAPP(c_Fun_Ocomp(_1298033, _1298029, _1298031, _1298039), _1298035)), _1298037))], (27287 ^ _782464) ^ [_1298242, _1298244] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298242)), _1298244) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298242), 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), _1298242)), _1298244))], (27289 ^ _782464) ^ [_1298290, _1298292] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1298290), hAPP(c_Nat_OSuc, _1298292)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298292), 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)), _1298292)), _1298290))], (27291 ^ _782464) ^ [_1298338, _1298340, _1298342, _1298344, _1298346] : [class_Groups_Ocomm__monoid__mult(_1298338), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298340), _1298342)), 27298 ^ _782464 : [(27299 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298340), _1298344), _1298342)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298340, _1298338), hAPP(hAPP(c_COMBC(_1298340, _1298338, _1298338), hAPP(hAPP(c_COMBS(_1298340, _1298338, tc_fun(_1298338, _1298338)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298338, tc_fun(_1298338, _1298338)), _1298340), c_If(_1298338)), hAPP(c_fequal, _1298344))), _1298346)), c_Groups_Oone__class_Oone(_1298338))), _1298342) = hAPP(_1298346, _1298344))], (27305 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298340), _1298344), _1298342))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298340, _1298338), hAPP(hAPP(c_COMBC(_1298340, _1298338, _1298338), hAPP(hAPP(c_COMBS(_1298340, _1298338, tc_fun(_1298338, _1298338)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298338, tc_fun(_1298338, _1298338)), _1298340), c_If(_1298338)), hAPP(c_fequal, _1298344))), _1298346)), c_Groups_Oone__class_Oone(_1298338))), _1298342) = c_Groups_Oone__class_Oone(_1298338))]]], (27311 ^ _782464) ^ [_1298848, _1298850, _1298852, _1298854, _1298856] : [class_Groups_Ocomm__monoid__mult(_1298848), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298850), _1298852)), 27318 ^ _782464 : [(27319 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298850), _1298854), _1298852)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298850, _1298848), hAPP(hAPP(c_COMBC(_1298850, _1298848, _1298848), hAPP(hAPP(c_COMBS(_1298850, _1298848, tc_fun(_1298848, _1298848)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298848, tc_fun(_1298848, _1298848)), _1298850), c_If(_1298848)), hAPP(hAPP(c_COMBC(_1298850, _1298850, tc_HOL_Obool), c_fequal), _1298854))), _1298856)), c_Groups_Oone__class_Oone(_1298848))), _1298852) = hAPP(_1298856, _1298854))], (27325 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298850), _1298854), _1298852))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298850, _1298848), hAPP(hAPP(c_COMBC(_1298850, _1298848, _1298848), hAPP(hAPP(c_COMBS(_1298850, _1298848, tc_fun(_1298848, _1298848)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298848, tc_fun(_1298848, _1298848)), _1298850), c_If(_1298848)), hAPP(hAPP(c_COMBC(_1298850, _1298850, tc_HOL_Obool), c_fequal), _1298854))), _1298856)), c_Groups_Oone__class_Oone(_1298848))), _1298852) = c_Groups_Oone__class_Oone(_1298848))]]], (27331 ^ _782464) ^ [_1299386, _1299388, _1299390] : [class_Orderings_Olinorder(_1299386), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299386), _1299388)), hBOOL(hAPP(hAPP(c_member(_1299386), _1299390), _1299388)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299386), _1299390), c_Big__Operators_Olinorder__class_OMax(_1299386, _1299388)) = c_Big__Operators_Olinorder__class_OMax(_1299386, _1299388))], (27345 ^ _782464) ^ [_1299621, _1299623, _1299625] : [class_Orderings_Olinorder(_1299621), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299621), _1299623)), hBOOL(hAPP(hAPP(c_member(_1299621), _1299625), _1299623)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299621), _1299625), c_Big__Operators_Olinorder__class_OMin(_1299621, _1299623)) = c_Big__Operators_Olinorder__class_OMin(_1299621, _1299623))], (27359 ^ _782464) ^ [_1299856, _1299858, _1299860, _1299862, _1299864] : [class_Lattices_Osemilattice__sup(_1299856), class_Orderings_Olinorder(_1299858), c_Orderings_Oorder__class_Omono(_1299858, _1299856, _1299860), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299856), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299856), hAPP(_1299860, _1299862)), hAPP(_1299860, _1299864))), hAPP(_1299860, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299858), _1299862), _1299864)))))], (27373 ^ _782464) ^ [_1300119, _1300121, _1300123, _1300125, _1300127] : [class_Lattices_Osemilattice__inf(_1300119), class_Orderings_Olinorder(_1300121), c_Orderings_Oorder__class_Omono(_1300121, _1300119, _1300123), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300119), hAPP(_1300123, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300121), _1300125), _1300127))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300119), hAPP(_1300123, _1300125)), hAPP(_1300123, _1300127)))))], (27387 ^ _782464) ^ [_1300382, _1300384, _1300386, _1300388] : [class_Orderings_Olinorder(_1300382), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300382, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1300382), _1300384)), c_SetInterval_Oord__class_OatLeastAtMost(_1300382, _1300386, _1300388)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300382, _1300386, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300382), _1300384), _1300388)))], (27393 ^ _782464) ^ [_1300525, _1300527, _1300529, _1300531] : [class_Orderings_Olinorder(_1300525), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300525, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300525, _1300527, _1300529)), hAPP(c_SetInterval_Oord__class_OatMost(_1300525), _1300531)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300525, _1300527, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300525), _1300529), _1300531)))], (27399 ^ _782464) ^ [_1300668, _1300670, _1300672, _1300674] : [class_Orderings_Olinorder(_1300668), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300668, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1300668), _1300670)), c_SetInterval_Oord__class_OatLeastAtMost(_1300668, _1300672, _1300674)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300668, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300668), _1300670), _1300672), _1300674))], (27405 ^ _782464) ^ [_1300811, _1300813, _1300815, _1300817] : [class_Orderings_Olinorder(_1300811), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300811, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300811, _1300813, _1300815)), hAPP(c_SetInterval_Oord__class_OatLeast(_1300811), _1300817)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300811, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300811), _1300813), _1300817), _1300815))], (27411 ^ _782464) ^ [_1300954, _1300956] : [class_Orderings_Olinorder(_1300954), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300954), _1300956)), -(c_Big__Operators_Olinorder__class_OMax(_1300954, _1300956) = hAPP(c_Finite__Set_Ofold1(_1300954, c_Orderings_Oord__class_Omax(_1300954)), _1300956))], (27421 ^ _782464) ^ [_1301111, _1301113] : [class_Orderings_Olinorder(_1301111), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301111), _1301113)), -(c_Big__Operators_Olinorder__class_OMin(_1301111, _1301113) = hAPP(c_Finite__Set_Ofold1(_1301111, c_Orderings_Oord__class_Omin(_1301111)), _1301113))], (27431 ^ _782464) ^ [_1301268, _1301270, _1301272, _1301274, _1301276] : [class_Groups_Ocomm__monoid__mult(_1301268), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301270), _1301272)), -(hBOOL(hAPP(hAPP(c_member(_1301270), _1301274), _1301272))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301270, _1301268), _1301276), hAPP(hAPP(c_Set_Oinsert(_1301270), _1301274), _1301272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301268), hAPP(_1301276, _1301274)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301270, _1301268), _1301276), _1301272)))], (27445 ^ _782464) ^ [_1301518, _1301520, _1301522, _1301524, _1301526] : [class_Groups_Ocomm__monoid__mult(_1301518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301520), _1301522)), -(hBOOL(hAPP(hAPP(c_member(_1301520), _1301524), _1301522))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301520, _1301518), _1301526), hAPP(hAPP(c_Set_Oinsert(_1301520), _1301524), _1301522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301518), hAPP(_1301526, _1301524)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301520, _1301518), _1301526), _1301522)))], (27459 ^ _782464) ^ [_1301768, _1301770, _1301772, _1301774, _1301776] : [class_Groups_Ocomm__monoid__mult(_1301768), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301770), _1301772)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301770), _1301774)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301768), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301770, _1301768), _1301776), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301770, tc_HOL_Obool)), _1301772), _1301774))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301770, _1301768), _1301776), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301770, tc_HOL_Obool)), _1301772), _1301774))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301768), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301770, _1301768), _1301776), _1301772)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301770, _1301768), _1301776), _1301774)))], (27473 ^ _782464) ^ [_1302129, _1302131, _1302133, _1302135, _1302137] : [class_Groups_Ocomm__monoid__mult(_1302129), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302131), _1302133)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302131), _1302135)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302129), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302131, _1302129), _1302137), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302131, tc_HOL_Obool)), _1302133), _1302135))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302131, _1302129), _1302137), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302131, tc_HOL_Obool)), _1302133), _1302135))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302129), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302131, _1302129), _1302137), _1302133)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302131, _1302129), _1302137), _1302135)))], (27487 ^ _782464) ^ [_1302490, _1302492, _1302494, _1302496, _1302498] : [class_Groups_Ocomm__monoid__mult(_1302490), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302492), _1302494)), c_Fun_Oinj__on(_1302492, _1302492, _1302496, _1302494), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302492, _1302490), _1302498), hAPP(c_Set_Oimage(_1302492, _1302492, _1302496), _1302494)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302492, _1302490), hAPP(c_Fun_Ocomp(_1302492, _1302490, _1302492, _1302498), _1302496)), _1302494))], (27501 ^ _782464) ^ [_1302765, _1302767, _1302769, _1302771] : [class_Groups_Ocomm__monoid__mult(_1302765), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302767), _1302769)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302767, _1302765), _1302771), _1302769) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1302765, _1302767, c_Groups_Otimes__class_Otimes(_1302765)), _1302771), c_Groups_Oone__class_Oone(_1302765)), _1302769))], (27511 ^ _782464) ^ [_1302960, _1302962, _1302964, _1302966] : [class_Groups_Ocomm__monoid__mult(_1302960), 27514 ^ _782464 : [(27515 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302962), _1302964)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302962, _1302960), _1302966), _1302964) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1302960, _1302962, c_Groups_Otimes__class_Otimes(_1302960)), _1302966), c_Groups_Oone__class_Oone(_1302960)), _1302964))], (27521 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1302962), _1302964))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302962, _1302960), _1302966), _1302964) = c_Groups_Oone__class_Oone(_1302960))]]], (27527 ^ _782464) ^ [_1303232, _1303234] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303232)), _1303234) = 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), _1303232)), _1303234))], (27529 ^ _782464) ^ [_1303277, _1303279] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1303277), hAPP(c_Nat_OSuc, _1303279)) = 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)), _1303279)), _1303277))], (27531 ^ _782464) ^ [_1303322, _1303324, _1303326] : [class_Orderings_Olinorder(_1303322), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303322), _1303324)), hBOOL(hAPP(hAPP(c_member(_1303322), _1303326), _1303324)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303322), hAPP(c_Finite__Set_Ofold1(_1303322, c_Orderings_Oord__class_Omin(_1303322)), _1303324)), _1303326)))], (27545 ^ _782464) ^ [_1303559, _1303561, _1303563] : [class_Orderings_Olinorder(_1303559), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303559), _1303561)), -(_1303561 = c_Orderings_Obot__class_Obot(tc_fun(_1303559, tc_HOL_Obool))), 27556 ^ _782464 : [(27557 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303559), hAPP(c_Finite__Set_Ofold1(_1303559, c_Orderings_Oord__class_Omin(_1303559)), _1303561)), _1303563)), 27561 ^ _782464 : [(27562 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303559), 27560 ^ [_1303559, _1303561, _1303563]), _1303561)))], (27564 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303559), 27560 ^ [_1303559, _1303561, _1303563]), _1303563)))]]], (27566 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303559), hAPP(c_Finite__Set_Ofold1(_1303559, c_Orderings_Oord__class_Omin(_1303559)), _1303561)), _1303563))), 27567 ^ _782464 : [(27568 ^ _782464) ^ [_1303948] : [hBOOL(hAPP(hAPP(c_member(_1303559), _1303948), _1303561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303559), _1303948), _1303563))]]]]], (27576 ^ _782464) ^ [_1304109, _1304111, _1304113] : [class_Orderings_Olinorder(_1304109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304109), _1304111)), -(_1304111 = c_Orderings_Obot__class_Obot(tc_fun(_1304109, tc_HOL_Obool))), 27587 ^ _782464 : [(27598 ^ _782464) ^ [] : [27600 ^ _782464 : [(27601 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304109), 27599 ^ [_1304109, _1304111, _1304113]), _1304111)))], (27603 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304109), _1304113), 27599 ^ [_1304109, _1304111, _1304113]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304109), _1304113), hAPP(c_Finite__Set_Ofold1(_1304109, c_Orderings_Oord__class_Omin(_1304109)), _1304111))))], (27588 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304109), _1304113), hAPP(c_Finite__Set_Ofold1(_1304109, c_Orderings_Oord__class_Omin(_1304109)), _1304111))), 27591 ^ _782464 : [(27592 ^ _782464) ^ [_1304402] : [hBOOL(hAPP(hAPP(c_member(_1304109), _1304402), _1304111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304109), _1304113), _1304402)))]]]]], (27607 ^ _782464) ^ [_1304687, _1304689, _1304691] : [class_Orderings_Olinorder(_1304687), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304687), _1304689)), -(_1304689 = c_Orderings_Obot__class_Obot(tc_fun(_1304687, tc_HOL_Obool))), 27618 ^ _782464 : [(27619 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304687), hAPP(c_Finite__Set_Ofold1(_1304687, c_Orderings_Oord__class_Omin(_1304687)), _1304689)), _1304691)), 27623 ^ _782464 : [(27624 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304687), 27622 ^ [_1304687, _1304689, _1304691]), _1304689)))], (27626 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304687), 27622 ^ [_1304687, _1304689, _1304691]), _1304691)))]]], (27628 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304687), hAPP(c_Finite__Set_Ofold1(_1304687, c_Orderings_Oord__class_Omin(_1304687)), _1304689)), _1304691))), 27629 ^ _782464 : [(27630 ^ _782464) ^ [_1305076] : [hBOOL(hAPP(hAPP(c_member(_1304687), _1305076), _1304689)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304687), _1305076), _1304691))]]]]], (27638 ^ _782464) ^ [_1305237, _1305239, _1305241] : [class_Orderings_Olinorder(_1305237), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305237), _1305239)), -(_1305239 = c_Orderings_Obot__class_Obot(tc_fun(_1305237, tc_HOL_Obool))), 27649 ^ _782464 : [(27660 ^ _782464) ^ [] : [27662 ^ _782464 : [(27663 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305237), 27661 ^ [_1305237, _1305239, _1305241]), _1305239)))], (27665 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305237), _1305241), 27661 ^ [_1305237, _1305239, _1305241]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305237), _1305241), hAPP(c_Finite__Set_Ofold1(_1305237, c_Orderings_Oord__class_Omin(_1305237)), _1305239))))], (27650 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305237), _1305241), hAPP(c_Finite__Set_Ofold1(_1305237, c_Orderings_Oord__class_Omin(_1305237)), _1305239))), 27653 ^ _782464 : [(27654 ^ _782464) ^ [_1305530] : [hBOOL(hAPP(hAPP(c_member(_1305237), _1305530), _1305239)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305237), _1305241), _1305530)))]]]]], (27669 ^ _782464) ^ [_1305815, _1305817, _1305819] : [class_Orderings_Olinorder(_1305815), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305815), _1305817)), -(_1305817 = c_Orderings_Obot__class_Obot(tc_fun(_1305815, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1305815, hAPP(hAPP(c_Set_Oinsert(_1305815), _1305819), _1305817)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305815), _1305819), c_Big__Operators_Olinorder__class_OMax(_1305815, _1305817)))], (27683 ^ _782464) ^ [_1306023, _1306025, _1306027] : [class_Orderings_Olinorder(_1306023), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306023), _1306025)), -(_1306025 = c_Orderings_Obot__class_Obot(tc_fun(_1306023, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1306023, hAPP(hAPP(c_Set_Oinsert(_1306023), _1306027), _1306025)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306023), _1306027), c_Big__Operators_Olinorder__class_OMin(_1306023, _1306025)))], (27697 ^ _782464) ^ [_1306231, _1306233, _1306235] : [class_Orderings_Olinorder(_1306231), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306231), _1306233)), -(_1306235 = c_Orderings_Obot__class_Obot(tc_fun(_1306231, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306231, tc_HOL_Obool)), _1306235), _1306233)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306231), c_Big__Operators_Olinorder__class_OMax(_1306231, _1306235)), c_Big__Operators_Olinorder__class_OMax(_1306231, _1306233)) = c_Big__Operators_Olinorder__class_OMax(_1306231, _1306233))], (27715 ^ _782464) ^ [_1306545, _1306547, _1306549] : [class_Orderings_Olinorder(_1306545), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306545), _1306547)), -(_1306549 = c_Orderings_Obot__class_Obot(tc_fun(_1306545, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306545, tc_HOL_Obool)), _1306549), _1306547)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306545), c_Big__Operators_Olinorder__class_OMin(_1306545, _1306549)), c_Big__Operators_Olinorder__class_OMin(_1306545, _1306547)) = c_Big__Operators_Olinorder__class_OMin(_1306545, _1306547))], (27733 ^ _782464) ^ [_1306859, _1306861, _1306863] : [class_Orderings_Olinorder(_1306859), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306859), _1306861)), -(_1306861 = c_Orderings_Obot__class_Obot(tc_fun(_1306859, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306859), _1306863)), -(_1306863 = c_Orderings_Obot__class_Obot(tc_fun(_1306859, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306859, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306859, tc_HOL_Obool)), _1306861), _1306863)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306859), c_Big__Operators_Olinorder__class_OMax(_1306859, _1306861)), c_Big__Operators_Olinorder__class_OMax(_1306859, _1306863)))], (27755 ^ _782464) ^ [_1307208, _1307210, _1307212] : [class_Orderings_Olinorder(_1307208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307208), _1307210)), -(_1307210 = c_Orderings_Obot__class_Obot(tc_fun(_1307208, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307208), _1307212)), -(_1307212 = c_Orderings_Obot__class_Obot(tc_fun(_1307208, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1307208, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307208, tc_HOL_Obool)), _1307210), _1307212)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307208), c_Big__Operators_Olinorder__class_OMin(_1307208, _1307210)), c_Big__Operators_Olinorder__class_OMin(_1307208, _1307212)))], (27777 ^ _782464) ^ [_1307557, _1307559, _1307561, _1307563, _1307565] : [class_Groups_Ocomm__monoid__mult(_1307557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307559), _1307561)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307559, _1307557), _1307563), hAPP(hAPP(c_Set_Oinsert(_1307559), _1307565), _1307561)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307557), hAPP(_1307563, _1307565)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307559, _1307557), _1307563), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307559, tc_HOL_Obool)), _1307561), hAPP(hAPP(c_Set_Oinsert(_1307559), _1307565), c_Orderings_Obot__class_Obot(tc_fun(_1307559, tc_HOL_Obool)))))))], (27787 ^ _782464) ^ [_1307826, _1307828, _1307830, _1307832, _1307834] : [class_Groups_Ocomm__monoid__mult(_1307826), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307828), _1307830)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307828), _1307832)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307828, tc_HOL_Obool)), _1307830), _1307832) = c_Orderings_Obot__class_Obot(tc_fun(_1307828, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307828, _1307826), _1307834), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307828, tc_HOL_Obool)), _1307830), _1307832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307826), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307828, _1307826), _1307834), _1307830)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307828, _1307826), _1307834), _1307832)))], (27805 ^ _782464) ^ [_1308221, _1308223, _1308225, _1308227, _1308229] : [class_Groups_Ocomm__monoid__mult(_1308221), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308223), _1308225)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308223), _1308227)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308223, tc_HOL_Obool)), _1308225), _1308227) = c_Orderings_Obot__class_Obot(tc_fun(_1308223, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308223, _1308221), _1308229), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308223, tc_HOL_Obool)), _1308225), _1308227)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308221), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308223, _1308221), _1308229), _1308225)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308223, _1308221), _1308229), _1308227)))], (27823 ^ _782464) ^ [_1308616, _1308618, _1308620] : [class_Orderings_Olinorder(_1308616), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308616), _1308618)), -(hBOOL(hAPP(hAPP(c_member(_1308616), _1308620), _1308618))), -(_1308618 = c_Orderings_Obot__class_Obot(tc_fun(_1308616, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1308616, hAPP(hAPP(c_Set_Oinsert(_1308616), _1308620), _1308618)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308616), _1308620), c_Big__Operators_Olinorder__class_OMax(_1308616, _1308618)))], (27841 ^ _782464) ^ [_1308853, _1308855, _1308857] : [class_Orderings_Olinorder(_1308853), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308853), _1308855)), -(hBOOL(hAPP(hAPP(c_member(_1308853), _1308857), _1308855))), -(_1308855 = c_Orderings_Obot__class_Obot(tc_fun(_1308853, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1308853, hAPP(hAPP(c_Set_Oinsert(_1308853), _1308857), _1308855)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1308853), _1308857), c_Big__Operators_Olinorder__class_OMin(_1308853, _1308855)))], (27859 ^ _782464) ^ [_1309090, _1309092, _1309094] : [class_Orderings_Olinorder(_1309090), -(_1309092 = c_Orderings_Obot__class_Obot(tc_fun(_1309090, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309090, tc_HOL_Obool)), _1309092), _1309094)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309090), _1309094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309090), hAPP(c_Finite__Set_Ofold1(_1309090, c_Orderings_Oord__class_Omin(_1309090)), _1309094)), hAPP(c_Finite__Set_Ofold1(_1309090, c_Orderings_Oord__class_Omin(_1309090)), _1309092))))], (27877 ^ _782464) ^ [_1309416, _1309418, _1309420] : [class_Orderings_Olinorder(_1309416), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309416), _1309418)), 27884 ^ _782464 : [(27885 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309416, tc_HOL_Obool)), _1309418), hAPP(hAPP(c_Set_Oinsert(_1309416), _1309420), c_Orderings_Obot__class_Obot(tc_fun(_1309416, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309416, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1309416, hAPP(hAPP(c_Set_Oinsert(_1309416), _1309420), _1309418)) = _1309420)], (27891 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309416, tc_HOL_Obool)), _1309418), hAPP(hAPP(c_Set_Oinsert(_1309416), _1309420), c_Orderings_Obot__class_Obot(tc_fun(_1309416, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309416, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1309416, hAPP(hAPP(c_Set_Oinsert(_1309416), _1309420), _1309418)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309416), _1309420), c_Big__Operators_Olinorder__class_OMax(_1309416, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309416, tc_HOL_Obool)), _1309418), hAPP(hAPP(c_Set_Oinsert(_1309416), _1309420), c_Orderings_Obot__class_Obot(tc_fun(_1309416, tc_HOL_Obool)))))))]]], (27897 ^ _782464) ^ [_1309886, _1309888, _1309890] : [class_Orderings_Olinorder(_1309886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309886), _1309888)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309886), _1309890)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309886, tc_HOL_Obool)), _1309888), _1309890) = c_Orderings_Obot__class_Obot(tc_fun(_1309886, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309886), c_Big__Operators_Olinorder__class_OMax(_1309886, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309886, tc_HOL_Obool)), _1309888), _1309890))), c_Big__Operators_Olinorder__class_OMax(_1309886, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309886, tc_HOL_Obool)), _1309888), _1309890))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309886), c_Big__Operators_Olinorder__class_OMax(_1309886, _1309888)), c_Big__Operators_Olinorder__class_OMax(_1309886, _1309890)))], (27915 ^ _782464) ^ [_1310234, _1310236, _1310238] : [class_Orderings_Olinorder(_1310234), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310234), _1310236)), -(_1310236 = c_Orderings_Obot__class_Obot(tc_fun(_1310234, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310234), _1310238)), -(_1310238 = c_Orderings_Obot__class_Obot(tc_fun(_1310234, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310234, tc_HOL_Obool)), _1310236), _1310238) = c_Orderings_Obot__class_Obot(tc_fun(_1310234, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1310234, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310234, tc_HOL_Obool)), _1310236), _1310238)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310234), c_Big__Operators_Olinorder__class_OMax(_1310234, _1310236)), c_Big__Operators_Olinorder__class_OMax(_1310234, _1310238)))], (27941 ^ _782464) ^ [_1310711, _1310713, _1310715] : [class_Orderings_Olinorder(_1310711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310711), _1310713)), 27948 ^ _782464 : [(27949 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310711, tc_HOL_Obool)), _1310713), hAPP(hAPP(c_Set_Oinsert(_1310711), _1310715), c_Orderings_Obot__class_Obot(tc_fun(_1310711, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310711, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1310711, hAPP(hAPP(c_Set_Oinsert(_1310711), _1310715), _1310713)) = _1310715)], (27955 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310711, tc_HOL_Obool)), _1310713), hAPP(hAPP(c_Set_Oinsert(_1310711), _1310715), c_Orderings_Obot__class_Obot(tc_fun(_1310711, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310711, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1310711, hAPP(hAPP(c_Set_Oinsert(_1310711), _1310715), _1310713)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310711), _1310715), c_Big__Operators_Olinorder__class_OMin(_1310711, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310711, tc_HOL_Obool)), _1310713), hAPP(hAPP(c_Set_Oinsert(_1310711), _1310715), c_Orderings_Obot__class_Obot(tc_fun(_1310711, tc_HOL_Obool)))))))]]], (27961 ^ _782464) ^ [_1311181, _1311183, _1311185] : [class_Orderings_Olinorder(_1311181), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311181), _1311183)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311181), _1311185)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311181, tc_HOL_Obool)), _1311183), _1311185) = c_Orderings_Obot__class_Obot(tc_fun(_1311181, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311181), c_Big__Operators_Olinorder__class_OMin(_1311181, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311181, tc_HOL_Obool)), _1311183), _1311185))), c_Big__Operators_Olinorder__class_OMin(_1311181, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311181, tc_HOL_Obool)), _1311183), _1311185))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311181), c_Big__Operators_Olinorder__class_OMin(_1311181, _1311183)), c_Big__Operators_Olinorder__class_OMin(_1311181, _1311185)))], (27979 ^ _782464) ^ [_1311529, _1311531, _1311533] : [class_Orderings_Olinorder(_1311529), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311529), _1311531)), -(_1311531 = c_Orderings_Obot__class_Obot(tc_fun(_1311529, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311529), _1311533)), -(_1311533 = c_Orderings_Obot__class_Obot(tc_fun(_1311529, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311529, tc_HOL_Obool)), _1311531), _1311533) = c_Orderings_Obot__class_Obot(tc_fun(_1311529, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1311529, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311529, tc_HOL_Obool)), _1311531), _1311533)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311529), c_Big__Operators_Olinorder__class_OMin(_1311529, _1311531)), c_Big__Operators_Olinorder__class_OMin(_1311529, _1311533)))], (28005 ^ _782464) ^ [_1312006] : [class_Orderings_Olinorder(_1312006), -(c_Orderings_Oord_Omin(_1312006, hAPP(c_COMBC(_1312006, _1312006, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1312006))) = c_Orderings_Oord__class_Omax(_1312006))], (28011 ^ _782464) ^ [_1312107] : [class_Orderings_Olinorder(_1312107), -(c_Orderings_Oord_Omax(_1312107, hAPP(c_COMBC(_1312107, _1312107, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1312107))) = c_Orderings_Oord__class_Omin(_1312107))], (28017 ^ _782464) ^ [_1312208] : [class_Orderings_Oord(_1312208), -(c_Orderings_Oord__class_Omax(_1312208) = c_Orderings_Oord_Omax(_1312208, c_Orderings_Oord__class_Oless__eq(_1312208)))], (28023 ^ _782464) ^ [_1312295] : [class_Orderings_Oord(_1312295), -(c_Orderings_Oord__class_Omin(_1312295) = c_Orderings_Oord_Omin(_1312295, c_Orderings_Oord__class_Oless__eq(_1312295)))], (28029 ^ _782464) ^ [_1312382, _1312384, _1312386] : [class_Orderings_Olinorder(_1312382), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312382), _1312384)), -(_1312384 = c_Orderings_Obot__class_Obot(tc_fun(_1312382, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312382), _1312386), c_Big__Operators_Olattice_OInf__fin(_1312382, c_Orderings_Oord__class_Omin(_1312382), _1312384)) = c_Big__Operators_Olattice_OInf__fin(_1312382, c_Orderings_Oord__class_Omin(_1312382), hAPP(c_Set_OCollect(_1312382), hAPP(hAPP(c_COMBB(tc_fun(_1312382, tc_HOL_Obool), tc_HOL_Obool, _1312382), c_HOL_OEx(_1312382)), hAPP(hAPP(c_COMBC(_1312382, tc_fun(_1312382, tc_HOL_Obool), tc_fun(_1312382, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312382, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1312382, tc_HOL_Obool), tc_fun(_1312382, tc_HOL_Obool)), _1312382), c_COMBS(_1312382, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312382, tc_HOL_Obool), tc_fun(_1312382, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1312382), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1312382), c_fconj)), hAPP(hAPP(c_COMBC(_1312382, tc_fun(_1312382, _1312382), tc_fun(_1312382, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312382, tc_HOL_Obool), tc_fun(tc_fun(_1312382, _1312382), tc_fun(_1312382, tc_HOL_Obool)), _1312382), c_COMBB(_1312382, tc_HOL_Obool, _1312382)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1312382), _1312386))))), hAPP(hAPP(c_COMBC(_1312382, tc_fun(_1312382, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312382)), _1312384))))))], (28043 ^ _782464) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (28045 ^ _782464) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (28047 ^ _782464) ^ [_1312916, _1312918, _1312920] : [class_Orderings_Olinorder(_1312916), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312916), _1312918)), hBOOL(hAPP(hAPP(c_member(_1312916), _1312920), _1312918)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312916), _1312920), c_Big__Operators_Olattice_OInf__fin(_1312916, c_Orderings_Oord__class_Omin(_1312916), _1312918)) = c_Big__Operators_Olattice_OInf__fin(_1312916, c_Orderings_Oord__class_Omin(_1312916), _1312918))], (28061 ^ _782464) ^ [_1313163, _1313165] : [class_Orderings_Olinorder(_1313163), -(c_Big__Operators_Olattice_OInf__fin(_1313163, c_Orderings_Oord__class_Omin(_1313163), hAPP(hAPP(c_Set_Oinsert(_1313163), _1313165), c_Orderings_Obot__class_Obot(tc_fun(_1313163, tc_HOL_Obool)))) = _1313165)], (28067 ^ _782464) ^ [_1313276, _1313278] : [class_Orderings_Olinorder(_1313276), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313276), _1313278)), -(c_Big__Operators_Olattice_OInf__fin(_1313276, c_Orderings_Oord__class_Omin(_1313276), _1313278) = hAPP(c_Finite__Set_Ofold1(_1313276, c_Orderings_Oord__class_Omin(_1313276)), _1313278))], (28077 ^ _782464) ^ [_1313439, _1313441, _1313443] : [class_Orderings_Olinorder(_1313439), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313439), _1313441)), -(_1313441 = c_Orderings_Obot__class_Obot(tc_fun(_1313439, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1313439, c_Orderings_Oord__class_Omin(_1313439), hAPP(hAPP(c_Set_Oinsert(_1313439), _1313443), _1313441)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313439), _1313443), c_Big__Operators_Olattice_OInf__fin(_1313439, c_Orderings_Oord__class_Omin(_1313439), _1313441)))], (28091 ^ _782464) ^ [_1313659, _1313661, _1313663] : [class_Orderings_Olinorder(_1313659), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313659), _1313661)), -(_1313663 = c_Orderings_Obot__class_Obot(tc_fun(_1313659, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313659, tc_HOL_Obool)), _1313663), _1313661)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313659), c_Big__Operators_Olattice_OInf__fin(_1313659, c_Orderings_Oord__class_Omin(_1313659), _1313663)), c_Big__Operators_Olattice_OInf__fin(_1313659, c_Orderings_Oord__class_Omin(_1313659), _1313661)) = c_Big__Operators_Olattice_OInf__fin(_1313659, c_Orderings_Oord__class_Omin(_1313659), _1313661))], (28109 ^ _782464) ^ [_1313991, _1313993, _1313995] : [class_Orderings_Olinorder(_1313991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313991), _1313993)), hBOOL(hAPP(hAPP(c_member(_1313991), _1313995), _1313993)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1313991), _1313995), c_Big__Operators_Olattice_OInf__fin(_1313991, c_Orderings_Oord__class_Omin(_1313991), _1313993)) = _1313995)], (28123 ^ _782464) ^ [_1314226, _1314228, _1314230] : [class_Orderings_Olinorder(_1314226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314226), _1314228)), -(_1314228 = c_Orderings_Obot__class_Obot(tc_fun(_1314226, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314226), _1314230)), -(_1314230 = c_Orderings_Obot__class_Obot(tc_fun(_1314226, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314226, c_Orderings_Oord__class_Omin(_1314226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314226, tc_HOL_Obool)), _1314228), _1314230)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314226), c_Big__Operators_Olattice_OInf__fin(_1314226, c_Orderings_Oord__class_Omin(_1314226), _1314228)), c_Big__Operators_Olattice_OInf__fin(_1314226, c_Orderings_Oord__class_Omin(_1314226), _1314230)))], (28145 ^ _782464) ^ [_1314593, _1314595, _1314597] : [class_Orderings_Olinorder(_1314593), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314593), _1314595)), -(hBOOL(hAPP(hAPP(c_member(_1314593), _1314597), _1314595))), -(_1314595 = c_Orderings_Obot__class_Obot(tc_fun(_1314593, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314593, c_Orderings_Oord__class_Omin(_1314593), hAPP(hAPP(c_Set_Oinsert(_1314593), _1314597), _1314595)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314593), _1314597), c_Big__Operators_Olattice_OInf__fin(_1314593, c_Orderings_Oord__class_Omin(_1314593), _1314595)))], (28163 ^ _782464) ^ [_1314842, _1314844, _1314846] : [class_Orderings_Olinorder(_1314842), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314842), _1314844)), 28170 ^ _782464 : [(28171 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314842, tc_HOL_Obool)), _1314844), hAPP(hAPP(c_Set_Oinsert(_1314842), _1314846), c_Orderings_Obot__class_Obot(tc_fun(_1314842, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314842, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1314842, c_Orderings_Oord__class_Omin(_1314842), hAPP(hAPP(c_Set_Oinsert(_1314842), _1314846), _1314844)) = _1314846)], (28177 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314842, tc_HOL_Obool)), _1314844), hAPP(hAPP(c_Set_Oinsert(_1314842), _1314846), c_Orderings_Obot__class_Obot(tc_fun(_1314842, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314842, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314842, c_Orderings_Oord__class_Omin(_1314842), hAPP(hAPP(c_Set_Oinsert(_1314842), _1314846), _1314844)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314842), _1314846), c_Big__Operators_Olattice_OInf__fin(_1314842, c_Orderings_Oord__class_Omin(_1314842), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314842, tc_HOL_Obool)), _1314844), hAPP(hAPP(c_Set_Oinsert(_1314842), _1314846), c_Orderings_Obot__class_Obot(tc_fun(_1314842, tc_HOL_Obool)))))))]]], (28183 ^ _782464) ^ [_1315330, _1315332, _1315334] : [class_Orderings_Olinorder(_1315330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315330), _1315332)), -(_1315332 = c_Orderings_Obot__class_Obot(tc_fun(_1315330, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315330), _1315334)), -(_1315334 = c_Orderings_Obot__class_Obot(tc_fun(_1315330, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315330, tc_HOL_Obool)), _1315332), _1315334) = c_Orderings_Obot__class_Obot(tc_fun(_1315330, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1315330, c_Orderings_Oord__class_Omin(_1315330), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315330, tc_HOL_Obool)), _1315332), _1315334)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315330), c_Big__Operators_Olattice_OInf__fin(_1315330, c_Orderings_Oord__class_Omin(_1315330), _1315332)), c_Big__Operators_Olattice_OInf__fin(_1315330, c_Orderings_Oord__class_Omin(_1315330), _1315334)))], (28209 ^ _782464) ^ [_1315825, _1315827, _1315829] : [class_Orderings_Olinorder(_1315825), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315825), _1315827)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315825), _1315829)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315825, tc_HOL_Obool)), _1315827), _1315829) = c_Orderings_Obot__class_Obot(tc_fun(_1315825, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315825), c_Big__Operators_Olattice_OInf__fin(_1315825, c_Orderings_Oord__class_Omin(_1315825), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315825, tc_HOL_Obool)), _1315827), _1315829))), c_Big__Operators_Olattice_OInf__fin(_1315825, c_Orderings_Oord__class_Omin(_1315825), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315825, tc_HOL_Obool)), _1315827), _1315829))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315825), c_Big__Operators_Olattice_OInf__fin(_1315825, c_Orderings_Oord__class_Omin(_1315825), _1315827)), c_Big__Operators_Olattice_OInf__fin(_1315825, c_Orderings_Oord__class_Omin(_1315825), _1315829)))], (28227 ^ _782464) ^ [_1316197, _1316199, _1316201] : [class_Orderings_Olinorder(_1316197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316197), _1316199)), hBOOL(hAPP(hAPP(c_member(_1316197), _1316201), _1316199)), 28238 ^ _782464 : [(28239 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316197, tc_HOL_Obool)), _1316199), hAPP(hAPP(c_Set_Oinsert(_1316197), _1316201), c_Orderings_Obot__class_Obot(tc_fun(_1316197, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1316197, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1316197, c_Orderings_Oord__class_Omin(_1316197), _1316199) = _1316201)], (28245 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316197, tc_HOL_Obool)), _1316199), hAPP(hAPP(c_Set_Oinsert(_1316197), _1316201), c_Orderings_Obot__class_Obot(tc_fun(_1316197, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1316197, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1316197, c_Orderings_Oord__class_Omin(_1316197), _1316199) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316197), _1316201), c_Big__Operators_Olattice_OInf__fin(_1316197, c_Orderings_Oord__class_Omin(_1316197), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316197, tc_HOL_Obool)), _1316199), hAPP(hAPP(c_Set_Oinsert(_1316197), _1316201), c_Orderings_Obot__class_Obot(tc_fun(_1316197, tc_HOL_Obool)))))))]]], (28251 ^ _782464) ^ [_1316721, _1316723, _1316725] : [class_Orderings_Olinorder(_1316721), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316721), _1316723)), -(_1316723 = c_Orderings_Obot__class_Obot(tc_fun(_1316721, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316721), _1316725)), -(_1316725 = c_Orderings_Obot__class_Obot(tc_fun(_1316721, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316721), c_Big__Operators_Olattice_OInf__fin(_1316721, c_Orderings_Oord__class_Omin(_1316721), _1316723)), c_Big__Operators_Olattice_OInf__fin(_1316721, c_Orderings_Oord__class_Omin(_1316721), _1316725)) = c_Big__Operators_Olattice_OInf__fin(_1316721, c_Orderings_Oord__class_Omin(_1316721), hAPP(c_Set_OCollect(_1316721), hAPP(hAPP(c_COMBB(tc_fun(_1316721, tc_HOL_Obool), tc_HOL_Obool, _1316721), c_HOL_OEx(_1316721)), hAPP(hAPP(c_COMBB(tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool)), tc_fun(_1316721, tc_HOL_Obool), _1316721), hAPP(c_COMBB(tc_fun(_1316721, tc_HOL_Obool), tc_HOL_Obool, _1316721), c_HOL_OEx(_1316721))), hAPP(hAPP(c_COMBC(_1316721, tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool)), tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316721, tc_fun(tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_HOL_Obool))), tc_fun(tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool)), tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool))), _1316721), c_COMBS(_1316721, tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316721, tc_fun(_1316721, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1316721, tc_fun(tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_HOL_Obool))), _1316721), hAPP(c_COMBB(tc_fun(_1316721, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_HOL_Obool)), _1316721), c_COMBS(_1316721, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool)), tc_fun(_1316721, tc_fun(_1316721, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1316721), hAPP(c_COMBB(tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1316721), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1316721), c_fconj))), hAPP(hAPP(c_COMBC(_1316721, tc_fun(_1316721, tc_fun(_1316721, _1316721)), tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1316721, _1316721), tc_fun(_1316721, tc_HOL_Obool)), tc_fun(tc_fun(_1316721, tc_fun(_1316721, _1316721)), tc_fun(_1316721, tc_fun(_1316721, tc_HOL_Obool))), _1316721), c_COMBB(tc_fun(_1316721, _1316721), tc_fun(_1316721, tc_HOL_Obool), _1316721)), hAPP(hAPP(c_COMBB(tc_fun(_1316721, tc_HOL_Obool), tc_fun(tc_fun(_1316721, _1316721), tc_fun(_1316721, tc_HOL_Obool)), _1316721), c_COMBB(_1316721, tc_HOL_Obool, _1316721)), c_fequal))), c_Orderings_Oord__class_Omax(_1316721)))))), hAPP(hAPP(c_COMBC(_1316721, tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1316721, tc_HOL_Obool), tc_fun(_1316721, tc_HOL_Obool)), _1316721), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1316721)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1316721), c_fconj), hAPP(hAPP(c_COMBC(_1316721, tc_fun(_1316721, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316721)), _1316723)))), hAPP(hAPP(c_COMBC(_1316721, tc_fun(_1316721, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316721)), _1316725))))))))], (28273 ^ _782464) ^ [_1317838, _1317840, _1317842] : [28275 ^ _782464 : [(28276 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317838), 28274 ^ [_1317838, _1317840, _1317842]), _1317840)))], (28278 ^ _782464) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1317842, 28274 ^ [_1317838, _1317840, _1317842]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317838, tc_Int_Oint), _1317842), _1317840) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317838, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1317838), c_Int_Onat), _1317842)), _1317840)))], (28282 ^ _782464) ^ [_1318068, _1318070, _1318072] : [class_Orderings_Olinorder(_1318068), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318068), _1318070)), -(_1318070 = c_Orderings_Obot__class_Obot(tc_fun(_1318068, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318068), _1318072)), -(_1318072 = c_Orderings_Obot__class_Obot(tc_fun(_1318068, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318068), c_Big__Operators_Olattice_OSup__fin(_1318068, c_Orderings_Oord__class_Omax(_1318068), _1318070)), c_Big__Operators_Olattice_OSup__fin(_1318068, c_Orderings_Oord__class_Omax(_1318068), _1318072)) = c_Big__Operators_Olattice_OSup__fin(_1318068, c_Orderings_Oord__class_Omax(_1318068), hAPP(c_Set_OCollect(_1318068), hAPP(hAPP(c_COMBB(tc_fun(_1318068, tc_HOL_Obool), tc_HOL_Obool, _1318068), c_HOL_OEx(_1318068)), hAPP(hAPP(c_COMBB(tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool)), tc_fun(_1318068, tc_HOL_Obool), _1318068), hAPP(c_COMBB(tc_fun(_1318068, tc_HOL_Obool), tc_HOL_Obool, _1318068), c_HOL_OEx(_1318068))), hAPP(hAPP(c_COMBC(_1318068, tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool)), tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318068, tc_fun(tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_HOL_Obool))), tc_fun(tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool)), tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool))), _1318068), c_COMBS(_1318068, tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318068, tc_fun(_1318068, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1318068, tc_fun(tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_HOL_Obool))), _1318068), hAPP(c_COMBB(tc_fun(_1318068, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_HOL_Obool)), _1318068), c_COMBS(_1318068, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool)), tc_fun(_1318068, tc_fun(_1318068, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1318068), hAPP(c_COMBB(tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1318068), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1318068), c_fconj))), hAPP(hAPP(c_COMBC(_1318068, tc_fun(_1318068, tc_fun(_1318068, _1318068)), tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1318068, _1318068), tc_fun(_1318068, tc_HOL_Obool)), tc_fun(tc_fun(_1318068, tc_fun(_1318068, _1318068)), tc_fun(_1318068, tc_fun(_1318068, tc_HOL_Obool))), _1318068), c_COMBB(tc_fun(_1318068, _1318068), tc_fun(_1318068, tc_HOL_Obool), _1318068)), hAPP(hAPP(c_COMBB(tc_fun(_1318068, tc_HOL_Obool), tc_fun(tc_fun(_1318068, _1318068), tc_fun(_1318068, tc_HOL_Obool)), _1318068), c_COMBB(_1318068, tc_HOL_Obool, _1318068)), c_fequal))), c_Orderings_Oord__class_Omin(_1318068)))))), hAPP(hAPP(c_COMBC(_1318068, tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1318068, tc_HOL_Obool), tc_fun(_1318068, tc_HOL_Obool)), _1318068), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1318068)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1318068), c_fconj), hAPP(hAPP(c_COMBC(_1318068, tc_fun(_1318068, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318068)), _1318070)))), hAPP(hAPP(c_COMBC(_1318068, tc_fun(_1318068, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318068)), _1318072))))))))], (28304 ^ _782464) ^ [_1319185, _1319187, _1319189] : [class_Orderings_Olinorder(_1319185), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319185), _1319187)), -(_1319187 = c_Orderings_Obot__class_Obot(tc_fun(_1319185, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319185), _1319189), c_Big__Operators_Olattice_OSup__fin(_1319185, c_Orderings_Oord__class_Omax(_1319185), _1319187)) = c_Big__Operators_Olattice_OSup__fin(_1319185, c_Orderings_Oord__class_Omax(_1319185), hAPP(c_Set_OCollect(_1319185), hAPP(hAPP(c_COMBB(tc_fun(_1319185, tc_HOL_Obool), tc_HOL_Obool, _1319185), c_HOL_OEx(_1319185)), hAPP(hAPP(c_COMBC(_1319185, tc_fun(_1319185, tc_HOL_Obool), tc_fun(_1319185, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319185, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1319185, tc_HOL_Obool), tc_fun(_1319185, tc_HOL_Obool)), _1319185), c_COMBS(_1319185, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319185, tc_HOL_Obool), tc_fun(_1319185, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1319185), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1319185), c_fconj)), hAPP(hAPP(c_COMBC(_1319185, tc_fun(_1319185, _1319185), tc_fun(_1319185, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319185, tc_HOL_Obool), tc_fun(tc_fun(_1319185, _1319185), tc_fun(_1319185, tc_HOL_Obool)), _1319185), c_COMBB(_1319185, tc_HOL_Obool, _1319185)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1319185), _1319189))))), hAPP(hAPP(c_COMBC(_1319185, tc_fun(_1319185, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319185)), _1319187))))))], (28318 ^ _782464) ^ [_1319683, _1319685] : [class_Orderings_Olinorder(_1319683), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319683), _1319685)), -(_1319685 = c_Orderings_Obot__class_Obot(tc_fun(_1319683, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1319683), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319683), 28331 ^ [_1319683, _1319685]), 28332 ^ [_1319683, _1319685])), hAPP(hAPP(c_Set_Oinsert(_1319683), 28331 ^ [_1319683, _1319685]), hAPP(hAPP(c_Set_Oinsert(_1319683), 28332 ^ [_1319683, _1319685]), c_Orderings_Obot__class_Obot(tc_fun(_1319683, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1319683), c_Big__Operators_Olattice_OInf__fin(_1319683, c_Orderings_Oord__class_Omin(_1319683), _1319685)), _1319685)))], (28338 ^ _782464) ^ [_1320133, _1320135, _1320137] : [class_Orderings_Olinorder(_1320133), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320133), _1320135)), hBOOL(hAPP(hAPP(c_member(_1320133), _1320137), _1320135)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320133), _1320137), c_Big__Operators_Olattice_OSup__fin(_1320133, c_Orderings_Oord__class_Omax(_1320133), _1320135)) = c_Big__Operators_Olattice_OSup__fin(_1320133, c_Orderings_Oord__class_Omax(_1320133), _1320135))], (28352 ^ _782464) ^ [_1320380, _1320382] : [class_Orderings_Olinorder(_1320380), -(c_Big__Operators_Olattice_OSup__fin(_1320380, c_Orderings_Oord__class_Omax(_1320380), hAPP(hAPP(c_Set_Oinsert(_1320380), _1320382), c_Orderings_Obot__class_Obot(tc_fun(_1320380, tc_HOL_Obool)))) = _1320382)], (28358 ^ _782464) ^ [_1320493, _1320495] : [class_Orderings_Olinorder(_1320493), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320493), _1320495)), -(c_Big__Operators_Olattice_OSup__fin(_1320493, c_Orderings_Oord__class_Omax(_1320493), _1320495) = hAPP(c_Finite__Set_Ofold1(_1320493, c_Orderings_Oord__class_Omax(_1320493)), _1320495))], (28368 ^ _782464) ^ [_1320656, _1320658, _1320660] : [class_Orderings_Olinorder(_1320656), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320656), _1320658)), -(_1320658 = c_Orderings_Obot__class_Obot(tc_fun(_1320656, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1320656, c_Orderings_Oord__class_Omax(_1320656), hAPP(hAPP(c_Set_Oinsert(_1320656), _1320660), _1320658)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320656), _1320660), c_Big__Operators_Olattice_OSup__fin(_1320656, c_Orderings_Oord__class_Omax(_1320656), _1320658)))], (28382 ^ _782464) ^ [_1320876, _1320878, _1320880] : [class_Orderings_Olinorder(_1320876), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320876), _1320878)), -(_1320880 = c_Orderings_Obot__class_Obot(tc_fun(_1320876, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320876, tc_HOL_Obool)), _1320880), _1320878)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320876), c_Big__Operators_Olattice_OSup__fin(_1320876, c_Orderings_Oord__class_Omax(_1320876), _1320880)), c_Big__Operators_Olattice_OSup__fin(_1320876, c_Orderings_Oord__class_Omax(_1320876), _1320878)) = c_Big__Operators_Olattice_OSup__fin(_1320876, c_Orderings_Oord__class_Omax(_1320876), _1320878))], (28400 ^ _782464) ^ [_1321208, _1321210, _1321212] : [class_Orderings_Olinorder(_1321208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321208), _1321210)), hBOOL(hAPP(hAPP(c_member(_1321208), _1321212), _1321210)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321208), _1321212), c_Big__Operators_Olattice_OSup__fin(_1321208, c_Orderings_Oord__class_Omax(_1321208), _1321210)) = _1321212)], (28414 ^ _782464) ^ [_1321443, _1321445, _1321447] : [class_Orderings_Olinorder(_1321443), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321443), _1321445)), -(_1321445 = c_Orderings_Obot__class_Obot(tc_fun(_1321443, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321443), _1321447)), -(_1321447 = c_Orderings_Obot__class_Obot(tc_fun(_1321443, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321443, c_Orderings_Oord__class_Omax(_1321443), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321443, tc_HOL_Obool)), _1321445), _1321447)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321443), c_Big__Operators_Olattice_OSup__fin(_1321443, c_Orderings_Oord__class_Omax(_1321443), _1321445)), c_Big__Operators_Olattice_OSup__fin(_1321443, c_Orderings_Oord__class_Omax(_1321443), _1321447)))], (28436 ^ _782464) ^ [_1321810, _1321812, _1321814] : [class_Orderings_Olinorder(_1321810), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321810), _1321812)), -(hBOOL(hAPP(hAPP(c_member(_1321810), _1321814), _1321812))), -(_1321812 = c_Orderings_Obot__class_Obot(tc_fun(_1321810, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321810, c_Orderings_Oord__class_Omax(_1321810), hAPP(hAPP(c_Set_Oinsert(_1321810), _1321814), _1321812)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321810), _1321814), c_Big__Operators_Olattice_OSup__fin(_1321810, c_Orderings_Oord__class_Omax(_1321810), _1321812)))], (28454 ^ _782464) ^ [_1322059, _1322061, _1322063] : [class_Orderings_Olinorder(_1322059), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322059), _1322061)), 28461 ^ _782464 : [(28462 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322059, tc_HOL_Obool)), _1322061), hAPP(hAPP(c_Set_Oinsert(_1322059), _1322063), c_Orderings_Obot__class_Obot(tc_fun(_1322059, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322059, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1322059, c_Orderings_Oord__class_Omax(_1322059), hAPP(hAPP(c_Set_Oinsert(_1322059), _1322063), _1322061)) = _1322063)], (28468 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322059, tc_HOL_Obool)), _1322061), hAPP(hAPP(c_Set_Oinsert(_1322059), _1322063), c_Orderings_Obot__class_Obot(tc_fun(_1322059, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322059, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1322059, c_Orderings_Oord__class_Omax(_1322059), hAPP(hAPP(c_Set_Oinsert(_1322059), _1322063), _1322061)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322059), _1322063), c_Big__Operators_Olattice_OSup__fin(_1322059, c_Orderings_Oord__class_Omax(_1322059), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322059, tc_HOL_Obool)), _1322061), hAPP(hAPP(c_Set_Oinsert(_1322059), _1322063), c_Orderings_Obot__class_Obot(tc_fun(_1322059, tc_HOL_Obool)))))))]]], (28474 ^ _782464) ^ [_1322547, _1322549, _1322551] : [class_Orderings_Olinorder(_1322547), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322547), _1322549)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322547), _1322551)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322547, tc_HOL_Obool)), _1322549), _1322551) = c_Orderings_Obot__class_Obot(tc_fun(_1322547, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322547), c_Big__Operators_Olattice_OSup__fin(_1322547, c_Orderings_Oord__class_Omax(_1322547), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322547, tc_HOL_Obool)), _1322549), _1322551))), c_Big__Operators_Olattice_OSup__fin(_1322547, c_Orderings_Oord__class_Omax(_1322547), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322547, tc_HOL_Obool)), _1322549), _1322551))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322547), c_Big__Operators_Olattice_OSup__fin(_1322547, c_Orderings_Oord__class_Omax(_1322547), _1322549)), c_Big__Operators_Olattice_OSup__fin(_1322547, c_Orderings_Oord__class_Omax(_1322547), _1322551)))], (28492 ^ _782464) ^ [_1322919, _1322921, _1322923] : [class_Orderings_Olinorder(_1322919), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322919), _1322921)), -(_1322921 = c_Orderings_Obot__class_Obot(tc_fun(_1322919, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322919), _1322923)), -(_1322923 = c_Orderings_Obot__class_Obot(tc_fun(_1322919, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322919, tc_HOL_Obool)), _1322921), _1322923) = c_Orderings_Obot__class_Obot(tc_fun(_1322919, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1322919, c_Orderings_Oord__class_Omax(_1322919), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322919, tc_HOL_Obool)), _1322921), _1322923)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322919), c_Big__Operators_Olattice_OSup__fin(_1322919, c_Orderings_Oord__class_Omax(_1322919), _1322921)), c_Big__Operators_Olattice_OSup__fin(_1322919, c_Orderings_Oord__class_Omax(_1322919), _1322923)))], (28518 ^ _782464) ^ [_1323414, _1323416, _1323418] : [class_Orderings_Olinorder(_1323414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323414), _1323416)), hBOOL(hAPP(hAPP(c_member(_1323414), _1323418), _1323416)), 28529 ^ _782464 : [(28530 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323414, tc_HOL_Obool)), _1323416), hAPP(hAPP(c_Set_Oinsert(_1323414), _1323418), c_Orderings_Obot__class_Obot(tc_fun(_1323414, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323414, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1323414, c_Orderings_Oord__class_Omax(_1323414), _1323416) = _1323418)], (28536 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323414, tc_HOL_Obool)), _1323416), hAPP(hAPP(c_Set_Oinsert(_1323414), _1323418), c_Orderings_Obot__class_Obot(tc_fun(_1323414, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323414, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1323414, c_Orderings_Oord__class_Omax(_1323414), _1323416) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323414), _1323418), c_Big__Operators_Olattice_OSup__fin(_1323414, c_Orderings_Oord__class_Omax(_1323414), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323414, tc_HOL_Obool)), _1323416), hAPP(hAPP(c_Set_Oinsert(_1323414), _1323418), c_Orderings_Obot__class_Obot(tc_fun(_1323414, tc_HOL_Obool)))))))]]], (28542 ^ _782464) ^ [_1323938, _1323940] : [class_Orderings_Olinorder(_1323938), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323938), _1323940)), -(_1323940 = c_Orderings_Obot__class_Obot(tc_fun(_1323938, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323938), c_Big__Operators_Olattice_OInf__fin(_1323938, c_Orderings_Oord__class_Omin(_1323938), _1323940)), c_Big__Operators_Olattice_OSup__fin(_1323938, c_Orderings_Oord__class_Omax(_1323938), _1323940))))], (28556 ^ _782464) ^ [_1324136, _1324138] : [class_Orderings_Olinorder(_1324136), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324136), _1324138)), -(_1324138 = c_Orderings_Obot__class_Obot(tc_fun(_1324136, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324136), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324136), 28569 ^ [_1324136, _1324138]), 28570 ^ [_1324136, _1324138])), hAPP(hAPP(c_Set_Oinsert(_1324136), 28569 ^ [_1324136, _1324138]), hAPP(hAPP(c_Set_Oinsert(_1324136), 28570 ^ [_1324136, _1324138]), c_Orderings_Obot__class_Obot(tc_fun(_1324136, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324136), c_Big__Operators_Olattice_OSup__fin(_1324136, c_Orderings_Oord__class_Omax(_1324136), _1324138)), _1324138)))], (28576 ^ _782464) ^ [_1324586, _1324588] : [class_Orderings_Olinorder(_1324586), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324586), _1324588)), -(_1324588 = c_Orderings_Obot__class_Obot(tc_fun(_1324586, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324586), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324586), 28589 ^ [_1324586, _1324588]), 28590 ^ [_1324586, _1324588])), hAPP(hAPP(c_Set_Oinsert(_1324586), 28589 ^ [_1324586, _1324588]), hAPP(hAPP(c_Set_Oinsert(_1324586), 28590 ^ [_1324586, _1324588]), c_Orderings_Obot__class_Obot(tc_fun(_1324586, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324586), c_Big__Operators_Olinorder__class_OMax(_1324586, _1324588)), _1324588)))], (28596 ^ _782464) ^ [_1325030, _1325032] : [class_Orderings_Olinorder(_1325030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325030), _1325032)), -(_1325032 = c_Orderings_Obot__class_Obot(tc_fun(_1325030, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1325030), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325030), 28609 ^ [_1325030, _1325032]), 28610 ^ [_1325030, _1325032])), hAPP(hAPP(c_Set_Oinsert(_1325030), 28609 ^ [_1325030, _1325032]), hAPP(hAPP(c_Set_Oinsert(_1325030), 28610 ^ [_1325030, _1325032]), c_Orderings_Obot__class_Obot(tc_fun(_1325030, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1325030), c_Big__Operators_Olinorder__class_OMin(_1325030, _1325032)), _1325032)))], (28616 ^ _782464) ^ [_1325474, _1325476, _1325478, _1325480, _1325482] : [class_Groups_Ocomm__monoid__mult(_1325474), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325476), _1325478)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325476), _1325480)), 28630 ^ _782464 : [(28631 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325476), 28629 ^ [_1325474, _1325476, _1325478, _1325480, _1325482]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325476, tc_HOL_Obool)), _1325478), _1325480))))], (28633 ^ _782464) ^ [] : [hAPP(_1325482, 28629 ^ [_1325474, _1325476, _1325478, _1325480, _1325482]) = c_Groups_Oone__class_Oone(_1325474)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325476, _1325474), _1325482), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325476, tc_HOL_Obool)), _1325478), _1325480)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325474), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325476, _1325474), _1325482), _1325478)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325476, _1325474), _1325482), _1325480)))], (28637 ^ _782464) ^ [_1325969, _1325971, _1325973, _1325975, _1325977] : [class_Groups_Ocomm__monoid__mult(_1325969), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325971), _1325973)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325971), _1325975)), 28651 ^ _782464 : [(28652 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325971), 28650 ^ [_1325969, _1325971, _1325973, _1325975, _1325977]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325971, tc_HOL_Obool)), _1325973), _1325975))))], (28654 ^ _782464) ^ [] : [hAPP(_1325977, 28650 ^ [_1325969, _1325971, _1325973, _1325975, _1325977]) = c_Groups_Oone__class_Oone(_1325969)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325971, _1325969), _1325977), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325971, tc_HOL_Obool)), _1325973), _1325975)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325969), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325971, _1325969), _1325977), _1325973)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325971, _1325969), _1325977), _1325975)))], (28658 ^ _782464) ^ [_1326464, _1326466, _1326468, _1326470, _1326472, _1326474] : [class_Groups_Ocomm__monoid__mult(_1326464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326466), _1326468)), 28665 ^ _782464 : [(28666 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1326466), _1326470), _1326468)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1326466, _1326464), hAPP(hAPP(c_COMBC(_1326466, _1326464, _1326464), hAPP(hAPP(c_COMBS(_1326466, _1326464, tc_fun(_1326464, _1326464)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1326464, tc_fun(_1326464, _1326464)), _1326466), c_If(_1326464)), hAPP(hAPP(c_COMBC(_1326466, _1326466, tc_HOL_Obool), c_fequal), _1326470))), _1326472)), _1326474)), _1326468) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326464), hAPP(_1326472, _1326470)), hAPP(hAPP(c_Power_Opower__class_Opower(_1326464), _1326474), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1326466), _1326468)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (28672 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326466), _1326470), _1326468))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1326466, _1326464), hAPP(hAPP(c_COMBC(_1326466, _1326464, _1326464), hAPP(hAPP(c_COMBS(_1326466, _1326464, tc_fun(_1326464, _1326464)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1326464, tc_fun(_1326464, _1326464)), _1326466), c_If(_1326464)), hAPP(hAPP(c_COMBC(_1326466, _1326466, tc_HOL_Obool), c_fequal), _1326470))), _1326472)), _1326474)), _1326468) = hAPP(hAPP(c_Power_Opower__class_Opower(_1326464), _1326474), hAPP(c_Finite__Set_Ocard(_1326466), _1326468)))]]], (28678 ^ _782464) ^ [_1327076, _1327078, _1327080, _1327082, _1327084] : [class_Fields_Ofield(_1327076), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327078), _1327080)), -(hAPP(_1327082, _1327084) = c_Groups_Ozero__class_Ozero(_1327076)), 28689 ^ _782464 : [(28690 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327078), _1327084), _1327080)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327078, _1327076), _1327082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327078, tc_HOL_Obool)), _1327080), hAPP(hAPP(c_Set_Oinsert(_1327078), _1327084), c_Orderings_Obot__class_Obot(tc_fun(_1327078, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327076), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327078, _1327076), _1327082), _1327080)), hAPP(_1327082, _1327084)))], (28696 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327078), _1327084), _1327080))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327078, _1327076), _1327082), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327078, tc_HOL_Obool)), _1327080), hAPP(hAPP(c_Set_Oinsert(_1327078), _1327084), c_Orderings_Obot__class_Obot(tc_fun(_1327078, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327078, _1327076), _1327082), _1327080))]]], (28702 ^ _782464) ^ [_1327617, _1327619, _1327621] : [class_Orderings_Olinorder(_1327617), hAPP(_1327619, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327617), 28707 ^ [_1327617, _1327619, _1327621]), 28708 ^ [_1327617, _1327619, _1327621])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327617), hAPP(_1327619, 28707 ^ [_1327617, _1327619, _1327621])), hAPP(_1327619, 28708 ^ [_1327617, _1327619, _1327621])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327617), _1327621)), -(_1327621 = c_Orderings_Obot__class_Obot(tc_fun(_1327617, tc_HOL_Obool))), -(hAPP(_1327619, c_Big__Operators_Olattice_OSup__fin(_1327617, c_Orderings_Oord__class_Omax(_1327617), _1327621)) = c_Big__Operators_Olattice_OSup__fin(_1327617, c_Orderings_Oord__class_Omax(_1327617), hAPP(c_Set_Oimage(_1327617, _1327617, _1327619), _1327621)))], (28722 ^ _782464) ^ [_1328032, _1328034] : [c_Nat__Transfer_Ois__nat(_1328032), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328032), _1328034)))], (28728 ^ _782464) ^ [_1328117, _1328119, _1328121] : [class_Rings_Oring__1(_1328117), -(hAPP(c_Int_Oring__1__class_Oof__int(_1328117), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328119), _1328121)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1328117), hAPP(c_Int_Oring__1__class_Oof__int(_1328117), _1328119)), _1328121))], (28734 ^ _782464) ^ [_1328242, _1328244] : [class_Rings_Ocomm__semiring__1(_1328242), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1328242), _1328244), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1328244)], (28740 ^ _782464) ^ [_1328333, _1328335, _1328337] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328333), _1328335)), _1328337) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328333), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328335), _1328337)))], (28742 ^ _782464) ^ [_1328384, _1328386] : [class_Rings_Odivision__ring__inverse__zero(_1328384), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328384), _1328386), c_Groups_Ozero__class_Ozero(_1328384)) = c_Groups_Ozero__class_Ozero(_1328384))], (28748 ^ _782464) ^ [_1328483, _1328485] : [class_Rings_Odivision__ring(_1328483), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328483), c_Groups_Ozero__class_Ozero(_1328483)), _1328485) = c_Groups_Ozero__class_Ozero(_1328483))], (28754 ^ _782464) ^ [_1328582, _1328584, _1328586, _1328588] : [class_Rings_Odivision__ring(_1328582), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328582), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328582), _1328584), _1328586)), _1328588) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328582), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328582), _1328584), _1328588)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328582), _1328586), _1328588)))], (28760 ^ _782464) ^ [_1328741, _1328743, _1328745, _1328747] : [class_Rings_Odivision__ring(_1328741), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328741), _1328743), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328741), _1328745), _1328747)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328741), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328741), _1328743), _1328745)), _1328747))], (28766 ^ _782464) ^ [_1328884, _1328886, _1328888, _1328890] : [class_Rings_Odivision__ring(_1328884), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328884), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1328884), _1328886), _1328888)), _1328890) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1328884), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328884), _1328886), _1328890)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328884), _1328888), _1328890)))], (28772 ^ _782464) ^ [_1329043, _1329045, _1329047, _1329049] : [class_Rings_Ocomm__semiring__1(_1329043), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1329043), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329043), _1329045), _1329047)), _1329049) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329043), hAPP(hAPP(c_Power_Opower__class_Opower(_1329043), _1329045), _1329049)), hAPP(hAPP(c_Power_Opower__class_Opower(_1329043), _1329047), _1329049)))], (28778 ^ _782464) ^ [_1329202, _1329204] : [class_Rings_Odivision__ring(_1329202), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329202), _1329204), c_Groups_Oone__class_Oone(_1329202)) = _1329204)], (28784 ^ _782464) ^ [_1329297, _1329299, _1329301] : [class_Rings_Odivision__ring(_1329297), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1329297), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329297), _1329299), _1329301)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329297), hAPP(c_Groups_Ouminus__class_Ouminus(_1329297), _1329299)), _1329301))], (28790 ^ _782464) ^ [_1329426, _1329428] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329426), _1329428)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329426)), _1329428))], (28792 ^ _782464) ^ [_1329469, _1329471] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329469)), _1329471) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329469), _1329471)))], (28794 ^ _782464) ^ [_1329512, _1329514] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329512)), _1329514) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329512), _1329514)))], (28796 ^ _782464) ^ [_1329555, _1329557, _1329559, _1329561] : [class_Rings_Ocomm__semiring__1(_1329555), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1329555), hAPP(hAPP(c_Power_Opower__class_Opower(_1329555), _1329557), _1329559)), _1329561) = hAPP(hAPP(c_Power_Opower__class_Opower(_1329555), _1329557), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1329559), _1329561)))], (28802 ^ _782464) ^ [_1329694, _1329696] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329694)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1329694)), _1329696) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1329694), _1329696)))], (28808 ^ _782464) ^ [_1329811, _1329813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329811)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1329811), _1329813)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1329811)), _1329813))], (28814 ^ _782464) ^ [_1329928, _1329930, _1329932, _1329934, _1329936] : [class_Fields_Ofield(_1329928), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329928), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329930, _1329928), _1329932), _1329934)), _1329936) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329930, _1329928), hAPP(hAPP(c_COMBC(_1329930, _1329928, _1329928), hAPP(hAPP(c_COMBB(_1329928, tc_fun(_1329928, _1329928), _1329930), c_Rings_Oinverse__class_Odivide(_1329928)), _1329932)), _1329936)), _1329934))], (28820 ^ _782464) ^ [_1330111, _1330113, _1330115, _1330117] : [class_Rings_Odivision__ring(_1330111), -(_1330113 = c_Groups_Ozero__class_Ozero(_1330111)), 28827 ^ _782464 : [(28828 ^ _782464) ^ [] : [_1330115 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330111), _1330117), _1330113), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330111), _1330115), _1330113) = _1330117)], (28834 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330111), _1330115), _1330113) = _1330117, -(_1330115 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330111), _1330117), _1330113))]]], (28840 ^ _782464) ^ [_1330439, _1330441, _1330443, _1330445] : [class_Rings_Odivision__ring(_1330439), -(_1330441 = c_Groups_Ozero__class_Ozero(_1330439)), 28847 ^ _782464 : [(28848 ^ _782464) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330439), _1330443), _1330441) = _1330445, -(_1330443 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330439), _1330445), _1330441))], (28854 ^ _782464) ^ [] : [_1330443 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330439), _1330445), _1330441), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330439), _1330443), _1330441) = _1330445)]]], (28860 ^ _782464) ^ [_1330767, _1330769, _1330771, _1330773] : [class_Rings_Odivision__ring(_1330767), -(_1330769 = c_Groups_Ozero__class_Ozero(_1330767)), _1330771 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330767), _1330773), _1330769), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330767), _1330771), _1330769) = _1330773)], (28874 ^ _782464) ^ [_1330997, _1330999, _1331001, _1331003] : [class_Rings_Odivision__ring(_1330997), -(_1330999 = c_Groups_Ozero__class_Ozero(_1330997)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330997), _1331001), _1330999) = _1331003, -(_1331001 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330997), _1331003), _1330999))], (28888 ^ _782464) ^ [_1331227, _1331229] : [class_Rings_Odivision__ring__inverse__zero(_1331227), 28891 ^ _782464 : [(28892 ^ _782464) ^ [] : [_1331229 = c_Groups_Ozero__class_Ozero(_1331227), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331227), _1331229), _1331229) = c_Groups_Ozero__class_Ozero(_1331227))], (28898 ^ _782464) ^ [] : [-(_1331229 = c_Groups_Ozero__class_Ozero(_1331227)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331227), _1331229), _1331229) = c_Groups_Oone__class_Oone(_1331227))]]], (28904 ^ _782464) ^ [_1331449, _1331451] : [class_Rings_Odivision__ring(_1331449), -(_1331451 = c_Groups_Ozero__class_Ozero(_1331449)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331449), _1331451), _1331451) = c_Groups_Oone__class_Oone(_1331449))], (28914 ^ _782464) ^ [_1331563, _1331565, _1331567] : [class_Rings_Odivision__ring(_1331563), -(_1331565 = c_Groups_Ozero__class_Ozero(_1331563)), 28921 ^ _782464 : [(28922 ^ _782464) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331563), _1331567), _1331565) = c_Groups_Oone__class_Oone(_1331563), -(_1331567 = _1331565)], (28928 ^ _782464) ^ [] : [_1331567 = _1331565, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331563), _1331567), _1331565) = c_Groups_Oone__class_Oone(_1331563))]]], (28934 ^ _782464) ^ [_1331865, _1331867, _1331869] : [class_Rings_Odivision__ring(_1331865), -(_1331867 = c_Groups_Ozero__class_Ozero(_1331865)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1331865), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331865), _1331869), _1331867)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331865), _1331869), hAPP(c_Groups_Ouminus__class_Ouminus(_1331865), _1331867)))], (28944 ^ _782464) ^ [_1332013, _1332015, _1332017] : [class_Rings_Odivision__ring(_1332013), -(_1332015 = c_Groups_Ozero__class_Ozero(_1332013)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332013), hAPP(c_Groups_Ouminus__class_Ouminus(_1332013), _1332017)), hAPP(c_Groups_Ouminus__class_Ouminus(_1332013), _1332015)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1332013), _1332017), _1332015))], (28954 ^ _782464) ^ [_1332161, _1332163, _1332165] : [class_Rings_Ocomm__semiring__1(_1332161), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332161), hAPP(hAPP(c_Power_Opower__class_Opower(_1332161), _1332163), _1332165)), _1332163) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332161), _1332163), hAPP(c_Nat_OSuc, _1332165)))], (28960 ^ _782464) ^ [_1332292, _1332294, _1332296] : [class_Rings_Ocomm__semiring__1(_1332292), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332292), _1332294), hAPP(hAPP(c_Power_Opower__class_Opower(_1332292), _1332294), _1332296)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332292), _1332294), hAPP(c_Nat_OSuc, _1332296)))], (28966 ^ _782464) ^ [_1332423, _1332425, _1332427] : [class_Rings_Ocomm__semiring__1(_1332423), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1332423), _1332425), hAPP(c_Nat_OSuc, _1332427)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332423), _1332425), hAPP(hAPP(c_Power_Opower__class_Opower(_1332423), _1332425), _1332427)))], (28972 ^ _782464) ^ [_1332554, _1332556] : [class_Rings_Ocomm__semiring__1(_1332554), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1332554), _1332556), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1332554))], (28978 ^ _782464) ^ [_1332649, _1332651, _1332653, _1332655] : [class_Rings_Ocomm__semiring__1(_1332649), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332649), hAPP(hAPP(c_Power_Opower__class_Opower(_1332649), _1332651), _1332653)), hAPP(hAPP(c_Power_Opower__class_Opower(_1332649), _1332651), _1332655)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332649), _1332651), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332653), _1332655)))], (28984 ^ _782464) ^ [_1332804, _1332806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332804)), -(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), _1332804), _1332806))))], (28990 ^ _782464) ^ [_1332901, _1332903, _1332905] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332901), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332903), _1332905)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332901), _1332903)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332901), _1332905)))], (28992 ^ _782464) ^ [_1332958, _1332960, _1332962] : [class_Rings_Oring__1(_1332958), hBOOL(hAPP(hAPP(c_member(_1332958), _1332960), c_Int_Oring__1__class_OInts(_1332958))), -(hBOOL(hAPP(hAPP(c_member(_1332958), hAPP(hAPP(c_Power_Opower__class_Opower(_1332958), _1332960), _1332962)), c_Int_Oring__1__class_OInts(_1332958))))], (29002 ^ _782464) ^ [_1333141, _1333143, _1333145, _1333147, _1333149] : [class_Fields_Ofield__inverse__zero(_1333141), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333143), _1333145)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333143, _1333141), hAPP(hAPP(c_COMBS(_1333143, _1333141, _1333141), hAPP(hAPP(c_COMBB(_1333141, tc_fun(_1333141, _1333141), _1333143), c_Rings_Oinverse__class_Odivide(_1333141)), _1333147)), _1333149)), _1333145) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333141), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333143, _1333141), _1333147), _1333145)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333143, _1333141), _1333149), _1333145)))], (29012 ^ _782464) ^ [_1333408, _1333410, _1333412] : [class_Fields_Ofield(_1333408), -(_1333410 = c_Groups_Oone__class_Oone(_1333408)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1333408), hAPP(c_Power_Opower__class_Opower(_1333408), _1333410)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1333412)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333408), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1333408), hAPP(hAPP(c_Power_Opower__class_Opower(_1333408), _1333410), _1333412)), c_Groups_Oone__class_Oone(_1333408))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1333408), _1333410), c_Groups_Oone__class_Oone(_1333408))))], (29022 ^ _782464) ^ [_1333610, _1333612] : [-(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), _1333610)), _1333612))))], (29024 ^ _782464) ^ [_1333646, _1333648, _1333650, _1333652] : [class_Groups_Ocomm__monoid__mult(_1333646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333648), _1333650)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333648, _1333646), hAPP(c_COMBK(_1333646, _1333648), _1333652)), _1333650) = hAPP(hAPP(c_Power_Opower__class_Opower(_1333646), _1333652), hAPP(c_Finite__Set_Ocard(_1333648), _1333650)))], (29034 ^ _782464) ^ [_1333854, _1333856] : [_1333854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333856), _1333854) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29040 ^ _782464) ^ [_1333937, _1333939] : [-(_1333937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333939), _1333937) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1333939), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333939), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1333937), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (29056 ^ _782464) ^ [_1334163, _1334165] : [29057 ^ _782464 : [(29058 ^ _782464) ^ [] : [-(_1334163 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29060 ^ _782464) ^ [] : [_1334165 = 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), _1334163)), _1334165))))], (29046 ^ _782464) ^ [_1334014, _1334016] : [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), _1334014)), _1334016))), _1334014 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1334016 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29064 ^ _782464) ^ [_1334299, _1334301] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334299), _1334301)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1334299, tc_HOL_Obool)), hAPP(c_Set_OPow(_1334299), _1334301)) = 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(_1334299), _1334301)))], (29070 ^ _782464) ^ [_1334426, _1334428, _1334430, _1334432] : [class_Rings_Olinordered__semidom(_1334426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334426), _1334428), _1334430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334426), c_Groups_Ozero__class_Ozero(_1334426)), _1334428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1334432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334426), hAPP(hAPP(c_Power_Opower__class_Opower(_1334426), _1334428), _1334432)), hAPP(hAPP(c_Power_Opower__class_Opower(_1334426), _1334430), _1334432))))], (29088 ^ _782464) ^ [_1334755, _1334757, _1334759, _1334761] : [class_Fields_Ofield(_1334755), -(_1334757 = c_Groups_Ozero__class_Ozero(_1334755)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1334759), _1334761)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1334755), _1334757), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1334761), _1334759)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334755), hAPP(hAPP(c_Power_Opower__class_Opower(_1334755), _1334757), _1334761)), hAPP(hAPP(c_Power_Opower__class_Opower(_1334755), _1334757), _1334759)))], (29102 ^ _782464) ^ [_1335039, _1335041, _1335043] : [class_Rings_Olinordered__semidom(_1335039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335039), c_Groups_Oone__class_Oone(_1335039)), _1335041)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1335043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335039), c_Groups_Oone__class_Oone(_1335039)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335039), _1335041), _1335043))))], (29116 ^ _782464) ^ [_1335280, _1335282, _1335284, _1335286] : [class_Rings_Olinordered__semidom(_1335280), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335280), c_Groups_Oone__class_Oone(_1335280)), _1335282)), 29123 ^ _782464 : [(29124 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335280), hAPP(hAPP(c_Power_Opower__class_Opower(_1335280), _1335282), _1335284)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335280), _1335282), _1335286))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335284), _1335286)))], (29130 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335284), _1335286)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335280), hAPP(hAPP(c_Power_Opower__class_Opower(_1335280), _1335282), _1335284)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335280), _1335282), _1335286))))]]], (29136 ^ _782464) ^ [_1335655, _1335657, _1335659] : [class_Rings_Oring__1__no__zero__divisors(_1335655), -(_1335657 = c_Groups_Ozero__class_Ozero(_1335655)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335655), _1335657), _1335659) = c_Groups_Ozero__class_Ozero(_1335655)], (29146 ^ _782464) ^ [_1335814] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1335814) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29158 ^ _782464) ^ [_1335953, _1335955] : [29159 ^ _782464 : [(29160 ^ _782464) ^ [] : [_1335955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29162 ^ _782464) ^ [] : [_1335953 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1335953), _1335955) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29148 ^ _782464) ^ [_1335855, _1335857] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1335855), _1335857) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1335857 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1335855 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29166 ^ _782464) ^ [_1336082, _1336084, _1336086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336082)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336082), _1336084)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336082), _1336086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336084), _1336086)))], (29186 ^ _782464) ^ [_1336384, _1336386] : [29187 ^ _782464 : [(29188 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336384))], (29190 ^ _782464) ^ [] : [_1336386 = 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), _1336384), _1336386))))], (29176 ^ _782464) ^ [_1336278, _1336280] : [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), _1336278), _1336280))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336278))), -(_1336280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29194 ^ _782464) ^ [_1336521, _1336523, _1336525, _1336527] : [class_Groups_Ocomm__monoid__mult(_1336521), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1336521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336521), _1336523), _1336525)), _1336527) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336521), hAPP(hAPP(c_Power_Opower__class_Opower(_1336521), _1336523), _1336527)), hAPP(hAPP(c_Power_Opower__class_Opower(_1336521), _1336525), _1336527)))], (29200 ^ _782464) ^ [_1336680, _1336682, _1336684] : [class_Groups_Omonoid__mult(_1336680), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336680), hAPP(hAPP(c_Power_Opower__class_Opower(_1336680), _1336682), _1336684)), _1336682) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336680), _1336682), hAPP(hAPP(c_Power_Opower__class_Opower(_1336680), _1336682), _1336684)))], (29206 ^ _782464) ^ [_1336821, _1336823] : [class_Groups_Omonoid__mult(_1336821), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1336821), c_Groups_Oone__class_Oone(_1336821)), _1336823) = c_Groups_Oone__class_Oone(_1336821))], (29212 ^ _782464) ^ [_1336920, _1336922, _1336924] : [class_Rings_Osemiring__1(_1336920), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336920), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336922), _1336924)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1336920), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336920), _1336922)), _1336924))], (29218 ^ _782464) ^ [_1337045, _1337047, _1337049, _1337051] : [class_Groups_Omonoid__mult(_1337045), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337045), _1337047), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337049), _1337051)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337045), hAPP(hAPP(c_Power_Opower__class_Opower(_1337045), _1337047), _1337049)), _1337051))], (29224 ^ _782464) ^ [_1337184, _1337186, _1337188, _1337190] : [class_Fields_Ofield__inverse__zero(_1337184), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337184), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337184), _1337186), _1337188)), _1337190) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337184), hAPP(hAPP(c_Power_Opower__class_Opower(_1337184), _1337186), _1337190)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337184), _1337188), _1337190)))], (29230 ^ _782464) ^ [_1337343, _1337345, _1337347] : [class_Rings_Olinordered__idom(_1337343), -(hAPP(c_Groups_Oabs__class_Oabs(_1337343), hAPP(hAPP(c_Power_Opower__class_Opower(_1337343), _1337345), _1337347)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337343), hAPP(c_Groups_Oabs__class_Oabs(_1337343), _1337345)), _1337347))], (29236 ^ _782464) ^ [_1337472, _1337474] : [class_Groups_Omonoid__mult(_1337472), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337472), _1337474), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1337474)], (29242 ^ _782464) ^ [_1337563, _1337565, _1337567] : [class_Rings_Olinordered__semidom(_1337563), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337563), c_Groups_Ozero__class_Ozero(_1337563)), _1337565)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337563), c_Groups_Ozero__class_Ozero(_1337563)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337563), _1337565), _1337567))))], (29252 ^ _782464) ^ [_1337746, _1337748, _1337750, _1337752] : [class_Rings_Olinordered__semidom(_1337746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337746), _1337748), _1337750)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337746), c_Groups_Ozero__class_Ozero(_1337746)), _1337748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337746), hAPP(hAPP(c_Power_Opower__class_Opower(_1337746), _1337748), _1337752)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337746), _1337750), _1337752))))], (29266 ^ _782464) ^ [_1338015, _1338017, _1338019] : [class_Rings_Olinordered__semidom(_1338015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338015), c_Groups_Ozero__class_Ozero(_1338015)), _1338017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338015), c_Groups_Ozero__class_Ozero(_1338015)), hAPP(hAPP(c_Power_Opower__class_Opower(_1338015), _1338017), _1338019))))], (29276 ^ _782464) ^ [_1338198, _1338200, _1338202] : [class_Power_Opower(_1338198), class_Rings_Omult__zero(_1338198), class_Rings_Ono__zero__divisors(_1338198), class_Rings_Ozero__neq__one(_1338198), 29291 ^ _782464 : [(29292 ^ _782464) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1338198), _1338200), _1338202) = c_Groups_Ozero__class_Ozero(_1338198), 29295 ^ _782464 : [(29296 ^ _782464) ^ [] : [-(_1338200 = c_Groups_Ozero__class_Ozero(_1338198))], (29298 ^ _782464) ^ [] : [_1338202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29300 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1338198), _1338200), _1338202) = c_Groups_Ozero__class_Ozero(_1338198)), _1338200 = c_Groups_Ozero__class_Ozero(_1338198), -(_1338202 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29310 ^ _782464) ^ [_1338690, _1338692, _1338694] : [class_Rings_Olinordered__semidom(_1338690), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338690), c_Groups_Oone__class_Oone(_1338690)), _1338692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338690), c_Groups_Oone__class_Oone(_1338690)), hAPP(hAPP(c_Power_Opower__class_Opower(_1338690), _1338692), _1338694))))], (29320 ^ _782464) ^ [_1338873, _1338875] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1338873), c_Groups_Ozero__class_Ozero(_1338873)), hAPP(c_Nat_OSuc, _1338875)) = c_Groups_Ozero__class_Ozero(_1338873)), class_Power_Opower(_1338873), class_Rings_Osemiring__0(_1338873)], (29330 ^ _782464) ^ [_1339028, _1339030, _1339032, _1339034] : [class_Rings_Olinordered__semidom(_1339028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1339028), c_Groups_Oone__class_Oone(_1339028)), _1339030)), 29337 ^ _782464 : [(29338 ^ _782464) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1339028), _1339030), _1339032) = hAPP(hAPP(c_Power_Opower__class_Opower(_1339028), _1339030), _1339034), -(_1339032 = _1339034)], (29344 ^ _782464) ^ [] : [_1339032 = _1339034, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339028), _1339030), _1339032) = hAPP(hAPP(c_Power_Opower__class_Opower(_1339028), _1339030), _1339034))]]], (29350 ^ _782464) ^ [_1339367, _1339369, _1339371] : [class_Power_Opower(_1339367), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339367), _1339369), hAPP(c_Nat_OSuc, _1339371)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339367), _1339369), hAPP(hAPP(c_Power_Opower__class_Opower(_1339367), _1339369), _1339371)))], (29356 ^ _782464) ^ [_1339498, _1339500, _1339502] : [class_Groups_Omonoid__mult(_1339498), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339498), _1339500), hAPP(c_Nat_OSuc, _1339502)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339498), hAPP(hAPP(c_Power_Opower__class_Opower(_1339498), _1339500), _1339502)), _1339500))], (29362 ^ _782464) ^ [_1339629, _1339631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1339629)), -(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), _1339629), _1339631))))], (29368 ^ _782464) ^ [_1339726, _1339728] : [class_Power_Opower(_1339726), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339726), _1339728), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1339726))], (29374 ^ _782464) ^ [_1339821, _1339823, _1339825, _1339827] : [class_Groups_Omonoid__mult(_1339821), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339821), _1339823), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1339825), _1339827)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339821), hAPP(hAPP(c_Power_Opower__class_Opower(_1339821), _1339823), _1339825)), hAPP(hAPP(c_Power_Opower__class_Opower(_1339821), _1339823), _1339827)))], (29380 ^ _782464) ^ [_1339976, _1339978, _1339980, _1339982] : [class_Fields_Ofield(_1339976), -(_1339978 = c_Groups_Ozero__class_Ozero(_1339976)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339976), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339976), _1339980), _1339978)), _1339982) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339976), hAPP(hAPP(c_Power_Opower__class_Opower(_1339976), _1339980), _1339982)), hAPP(hAPP(c_Power_Opower__class_Opower(_1339976), _1339978), _1339982)))], (29390 ^ _782464) ^ [_1340154, _1340156, _1340158] : [class_Fields_Ofield__inverse__zero(_1340154), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340154), c_Groups_Oone__class_Oone(_1340154)), hAPP(hAPP(c_Power_Opower__class_Opower(_1340154), _1340156), _1340158)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340154), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340154), c_Groups_Oone__class_Oone(_1340154)), _1340156)), _1340158))], (29396 ^ _782464) ^ [_1340303, _1340305, _1340307] : [class_Rings_Olinordered__idom(_1340303), -(hAPP(c_Groups_Oabs__class_Oabs(_1340303), hAPP(hAPP(c_Power_Opower__class_Opower(_1340303), hAPP(c_Groups_Ouminus__class_Ouminus(_1340303), _1340305)), _1340307)) = hAPP(c_Groups_Oabs__class_Oabs(_1340303), hAPP(hAPP(c_Power_Opower__class_Opower(_1340303), _1340305), _1340307)))], (29402 ^ _782464) ^ [_1340442, _1340444, _1340446, _1340448] : [class_Rings_Olinordered__semidom(_1340442), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340442), hAPP(hAPP(c_Power_Opower__class_Opower(_1340442), _1340444), _1340446)), hAPP(hAPP(c_Power_Opower__class_Opower(_1340442), _1340448), _1340446))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340442), c_Groups_Ozero__class_Ozero(_1340442)), _1340448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340442), _1340444), _1340448)))], (29416 ^ _782464) ^ [_1340711, _1340713, _1340715, _1340717] : [class_Rings_Olinordered__semidom(_1340711), hAPP(hAPP(c_Power_Opower__class_Opower(_1340711), _1340713), hAPP(c_Nat_OSuc, _1340715)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340711), _1340717), hAPP(c_Nat_OSuc, _1340715)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340711), c_Groups_Ozero__class_Ozero(_1340711)), _1340713)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340711), c_Groups_Ozero__class_Ozero(_1340711)), _1340717)), -(_1340713 = _1340717)], (29434 ^ _782464) ^ [_1341038, _1341040, _1341042, _1341044] : [class_Rings_Olinordered__semidom(_1341038), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341038), hAPP(hAPP(c_Power_Opower__class_Opower(_1341038), _1341040), hAPP(c_Nat_OSuc, _1341042))), hAPP(hAPP(c_Power_Opower__class_Opower(_1341038), _1341044), hAPP(c_Nat_OSuc, _1341042)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341038), c_Groups_Ozero__class_Ozero(_1341038)), _1341044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341038), _1341040), _1341044)))], (29448 ^ _782464) ^ [_1341319, _1341321, _1341323] : [class_Rings_Olinordered__semidom(_1341319), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341319), c_Groups_Oone__class_Oone(_1341319)), _1341321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341319), hAPP(hAPP(c_Power_Opower__class_Opower(_1341319), _1341321), _1341323)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341319), _1341321), hAPP(hAPP(c_Power_Opower__class_Opower(_1341319), _1341321), _1341323)))))], (29458 ^ _782464) ^ [_1341530, _1341532, _1341534] : [class_Rings_Olinordered__semidom(_1341530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341530), c_Groups_Oone__class_Oone(_1341530)), _1341532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341530), c_Groups_Oone__class_Oone(_1341530)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341530), _1341532), hAPP(hAPP(c_Power_Opower__class_Opower(_1341530), _1341532), _1341534)))))], (29468 ^ _782464) ^ [_1341729, _1341731] : [class_Power_Opower(_1341729), class_Rings_Osemiring__0(_1341729), 29475 ^ _782464 : [(29476 ^ _782464) ^ [] : [_1341731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341729), c_Groups_Ozero__class_Ozero(_1341729)), _1341731) = c_Groups_Oone__class_Oone(_1341729))], (29482 ^ _782464) ^ [] : [-(_1341731 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341729), c_Groups_Ozero__class_Ozero(_1341729)), _1341731) = c_Groups_Ozero__class_Ozero(_1341729))]]], (29488 ^ _782464) ^ [_1342003, _1342005, _1342007] : [class_Rings_Olinordered__semidom(_1342003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342003), c_Groups_Oone__class_Oone(_1342003)), _1342005)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342003), c_Groups_Oone__class_Oone(_1342003)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342003), _1342005), hAPP(c_Nat_OSuc, _1342007)))))], (29498 ^ _782464) ^ [_1342192, _1342194, _1342196, _1342198] : [class_Rings_Olinordered__semidom(_1342192), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342192), c_Groups_Oone__class_Oone(_1342192)), _1342194)), 29505 ^ _782464 : [(29506 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342192), hAPP(hAPP(c_Power_Opower__class_Opower(_1342192), _1342194), _1342196)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342192), _1342194), _1342198))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342196), _1342198)))], (29512 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342196), _1342198)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342192), hAPP(hAPP(c_Power_Opower__class_Opower(_1342192), _1342194), _1342196)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342192), _1342194), _1342198))))]]], (29518 ^ _782464) ^ [_1342567, _1342569, _1342571, _1342573] : [class_Rings_Olinordered__semidom(_1342567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342567), c_Groups_Oone__class_Oone(_1342567)), _1342569)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342567), hAPP(hAPP(c_Power_Opower__class_Opower(_1342567), _1342569), _1342571)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342567), _1342569), _1342573))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342571), _1342573)))], (29532 ^ _782464) ^ [_1342832, _1342834, _1342836, _1342838] : [class_Rings_Olinordered__semidom(_1342832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342834), _1342836)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342832), c_Groups_Oone__class_Oone(_1342832)), _1342838)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342832), hAPP(hAPP(c_Power_Opower__class_Opower(_1342832), _1342838), _1342834)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342832), _1342838), _1342836))))], (29546 ^ _782464) ^ [_1343097, _1343099, _1343101] : [class_Rings_Olinordered__idom(_1343097), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343097), c_Groups_Ozero__class_Ozero(_1343097)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343097), hAPP(c_Groups_Oabs__class_Oabs(_1343097), _1343099)), _1343101))))], (29552 ^ _782464) ^ [_1343218, _1343220, _1343222, _1343224] : [class_Rings_Olinordered__semidom(_1343218), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1343220), _1343222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343218), c_Groups_Oone__class_Oone(_1343218)), _1343224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343218), hAPP(hAPP(c_Power_Opower__class_Opower(_1343218), _1343224), _1343220)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343218), _1343224), _1343222))))], (29566 ^ _782464) ^ [_1343483, _1343485, _1343487] : [class_Rings_Oring__1(_1343483), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1343483), hAPP(c_Groups_Ouminus__class_Ouminus(_1343483), _1343485)), _1343487) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343483), hAPP(hAPP(c_Power_Opower__class_Opower(_1343483), hAPP(c_Groups_Ouminus__class_Ouminus(_1343483), c_Groups_Oone__class_Oone(_1343483))), _1343487)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343483), _1343485), _1343487)))], (29572 ^ _782464) ^ [_1343648, _1343650, _1343652] : [class_Rings_Olinordered__semidom(_1343648), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343648), c_Groups_Ozero__class_Ozero(_1343648)), _1343650)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343648), _1343650), c_Groups_Oone__class_Oone(_1343648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343648), _1343650), hAPP(hAPP(c_Power_Opower__class_Opower(_1343648), _1343650), _1343652))), hAPP(hAPP(c_Power_Opower__class_Opower(_1343648), _1343650), _1343652))))], (29586 ^ _782464) ^ [_1343931, _1343933, _1343935, _1343937] : [class_Rings_Olinordered__semidom(_1343931), hAPP(hAPP(c_Power_Opower__class_Opower(_1343931), _1343933), _1343935) = hAPP(hAPP(c_Power_Opower__class_Opower(_1343931), _1343937), _1343935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343931), c_Groups_Ozero__class_Ozero(_1343931)), _1343933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343931), c_Groups_Ozero__class_Ozero(_1343931)), _1343937)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1343935)), -(_1343933 = _1343937)], (29608 ^ _782464) ^ [_1344306, _1344308, _1344310] : [class_Rings_Olinordered__semidom(_1344306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344306), c_Groups_Ozero__class_Ozero(_1344306)), _1344308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344306), _1344308), c_Groups_Oone__class_Oone(_1344306))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344306), hAPP(hAPP(c_Power_Opower__class_Opower(_1344306), _1344308), hAPP(c_Nat_OSuc, _1344310))), c_Groups_Oone__class_Oone(_1344306))))], (29622 ^ _782464) ^ [_1344567, _1344569, _1344571, _1344573] : [class_Rings_Olinordered__semidom(_1344567), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1344569), _1344571)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344567), c_Groups_Ozero__class_Ozero(_1344567)), _1344573)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344567), _1344573), c_Groups_Oone__class_Oone(_1344567))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344567), hAPP(hAPP(c_Power_Opower__class_Opower(_1344567), _1344573), _1344571)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344567), _1344573), _1344569))))], (29640 ^ _782464) ^ [_1344906, _1344908, _1344910, _1344912] : [class_Rings_Olinordered__semidom(_1344906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1344908), _1344910)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344906), c_Groups_Ozero__class_Ozero(_1344906)), _1344912)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344906), _1344912), c_Groups_Oone__class_Oone(_1344906))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344906), hAPP(hAPP(c_Power_Opower__class_Opower(_1344906), _1344912), _1344910)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344906), _1344912), _1344908))))], (29658 ^ _782464) ^ [_1345245, _1345247, _1345249, _1345251] : [class_Rings_Olinordered__semidom(_1345245), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345245), c_Groups_Oone__class_Oone(_1345245)), _1345247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345245), hAPP(hAPP(c_Power_Opower__class_Opower(_1345245), _1345247), _1345249)), hAPP(hAPP(c_Power_Opower__class_Opower(_1345245), _1345247), _1345251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1345249), _1345251)))], (29672 ^ _782464) ^ [_1345510, _1345512, _1345514, _1345516] : [class_Fields_Olinordered__field__inverse__zero(_1345510), 29675 ^ _782464 : [(29702 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), _1345512), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345510), _1345514), _1345516)))), 29705 ^ _782464 : [(29706 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), c_Groups_Ozero__class_Ozero(_1345510)), _1345516)))], (29708 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345510), _1345512), _1345516)), _1345514))]], 29709 ^ _782464 : [(29710 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), c_Groups_Ozero__class_Ozero(_1345510)), _1345516))], (29712 ^ _782464) ^ [] : [29713 ^ _782464 : [(29714 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), _1345516), c_Groups_Ozero__class_Ozero(_1345510))))], (29716 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), _1345514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345510), _1345512), _1345516)))]], 29717 ^ _782464 : [(29718 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), _1345516), c_Groups_Ozero__class_Ozero(_1345510)))], (29720 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), _1345512), c_Groups_Ozero__class_Ozero(_1345510)))]]]]], (29676 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), _1345512), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345510), _1345514), _1345516))), 29679 ^ _782464 : [(29680 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), c_Groups_Ozero__class_Ozero(_1345510)), _1345516)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345510), _1345512), _1345516)), _1345514)))], (29686 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), c_Groups_Ozero__class_Ozero(_1345510)), _1345516))), 29689 ^ _782464 : [(29690 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), _1345516), c_Groups_Ozero__class_Ozero(_1345510))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), _1345514), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345510), _1345512), _1345516))))], (29696 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345510), _1345516), c_Groups_Ozero__class_Ozero(_1345510)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345510), _1345512), c_Groups_Ozero__class_Ozero(_1345510))))]]]]]]], (29724 ^ _782464) ^ [_1346463, _1346465, _1346467, _1346469] : [class_Fields_Olinordered__field__inverse__zero(_1346463), 29727 ^ _782464 : [(29754 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346463), _1346465), _1346467)), _1346469))), 29757 ^ _782464 : [(29758 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), c_Groups_Ozero__class_Ozero(_1346463)), _1346467)))], (29760 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), _1346465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346463), _1346469), _1346467)))]], 29761 ^ _782464 : [(29762 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), c_Groups_Ozero__class_Ozero(_1346463)), _1346467))], (29764 ^ _782464) ^ [] : [29765 ^ _782464 : [(29766 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), _1346467), c_Groups_Ozero__class_Ozero(_1346463))))], (29768 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346463), _1346469), _1346467)), _1346465))]], 29769 ^ _782464 : [(29770 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), _1346467), c_Groups_Ozero__class_Ozero(_1346463)))], (29772 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), c_Groups_Ozero__class_Ozero(_1346463)), _1346469))]]]]], (29728 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346463), _1346465), _1346467)), _1346469)), 29731 ^ _782464 : [(29732 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), c_Groups_Ozero__class_Ozero(_1346463)), _1346467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), _1346465), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346463), _1346469), _1346467))))], (29738 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), c_Groups_Ozero__class_Ozero(_1346463)), _1346467))), 29741 ^ _782464 : [(29742 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), _1346467), c_Groups_Ozero__class_Ozero(_1346463))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346463), _1346469), _1346467)), _1346465)))], (29748 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346463), _1346467), c_Groups_Ozero__class_Ozero(_1346463)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346463), c_Groups_Ozero__class_Ozero(_1346463)), _1346469)))]]]]]]], (29776 ^ _782464) ^ [_1347416, _1347418, _1347420, _1347422] : [class_Fields_Olinordered__field(_1347416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347416), c_Groups_Ozero__class_Ozero(_1347416)), _1347418)), 29783 ^ _782464 : [(29784 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347416), _1347420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347416), _1347422), _1347418))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347416), _1347420), _1347418)), _1347422)))], (29790 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347416), _1347420), _1347418)), _1347422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347416), _1347420), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347416), _1347422), _1347418))))]]], (29796 ^ _782464) ^ [_1347797, _1347799, _1347801, _1347803] : [class_Fields_Olinordered__field(_1347797), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347797), c_Groups_Ozero__class_Ozero(_1347797)), _1347799)), 29803 ^ _782464 : [(29804 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347797), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347797), _1347801), _1347799)), _1347803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347797), _1347801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347797), _1347803), _1347799))))], (29810 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347797), _1347801), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347797), _1347803), _1347799))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347797), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347797), _1347801), _1347799)), _1347803)))]]], (29816 ^ _782464) ^ [_1348178, _1348180, _1348182, _1348184, _1348186] : [class_Fields_Ofield__inverse__zero(_1348178), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348178), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348178), _1348180), _1348182)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348178), _1348184), _1348186)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348178), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348178), _1348180), _1348184)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348178), _1348182), _1348186)))], (29822 ^ _782464) ^ [_1348355, _1348357, _1348359] : [class_Fields_Ofield__inverse__zero(_1348355), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348355), hAPP(c_Groups_Ouminus__class_Ouminus(_1348355), _1348357)), hAPP(c_Groups_Ouminus__class_Ouminus(_1348355), _1348359)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348355), _1348357), _1348359))], (29828 ^ _782464) ^ [_1348484, _1348486, _1348488] : [class_Fields_Ofield__inverse__zero(_1348484), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348484), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348484), _1348486), _1348488)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348484), _1348486), hAPP(c_Groups_Ouminus__class_Ouminus(_1348484), _1348488)))], (29834 ^ _782464) ^ [_1348613, _1348615, _1348617] : [class_Fields_Olinordered__field__inverse__zero(_1348613), -(hAPP(c_Groups_Oabs__class_Oabs(_1348613), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348613), _1348615), _1348617)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348613), hAPP(c_Groups_Oabs__class_Oabs(_1348613), _1348615)), hAPP(c_Groups_Oabs__class_Oabs(_1348613), _1348617)))], (29840 ^ _782464) ^ [_1348752, _1348754, _1348756, _1348758] : [class_Fields_Olinordered__field__inverse__zero(_1348752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348752), _1348754), _1348756)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348752), _1348758), c_Groups_Ozero__class_Ozero(_1348752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348752), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348752), _1348756), _1348758)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348752), _1348754), _1348758))))], (29854 ^ _782464) ^ [_1349021, _1349023, _1349025, _1349027] : [class_Fields_Olinordered__field__inverse__zero(_1349021), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349021), _1349023), _1349025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349021), c_Groups_Ozero__class_Ozero(_1349021)), _1349027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349021), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349021), _1349023), _1349027)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349021), _1349025), _1349027))))], (29868 ^ _782464) ^ [_1349290, _1349292, _1349294] : [class_Fields_Olinordered__field__inverse__zero(_1349290), 29871 ^ _782464 : [(29872 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349290), _1349292), _1349294)), c_Groups_Ozero__class_Ozero(_1349290))), 29877 ^ _782464 : [(29878 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), c_Groups_Ozero__class_Ozero(_1349290)), _1349292)))], (29880 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), _1349294), c_Groups_Ozero__class_Ozero(_1349290))))]], 29881 ^ _782464 : [(29882 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), _1349292), c_Groups_Ozero__class_Ozero(_1349290))))], (29884 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), c_Groups_Ozero__class_Ozero(_1349290)), _1349294)))]]], (29886 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349290), _1349292), _1349294)), c_Groups_Ozero__class_Ozero(_1349290)))), 29887 ^ _782464 : [(29888 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), c_Groups_Ozero__class_Ozero(_1349290)), _1349292)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), _1349294), c_Groups_Ozero__class_Ozero(_1349290)))], (29894 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), _1349292), c_Groups_Ozero__class_Ozero(_1349290))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349290), c_Groups_Ozero__class_Ozero(_1349290)), _1349294))]]]]], (29902 ^ _782464) ^ [_1349880, _1349882, _1349884] : [class_Fields_Olinordered__field__inverse__zero(_1349880), 29905 ^ _782464 : [(29906 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Groups_Ozero__class_Ozero(_1349880)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349880), _1349882), _1349884))), 29911 ^ _782464 : [(29912 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Groups_Ozero__class_Ozero(_1349880)), _1349882)))], (29914 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Groups_Ozero__class_Ozero(_1349880)), _1349884)))]], 29915 ^ _782464 : [(29916 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), _1349882), c_Groups_Ozero__class_Ozero(_1349880))))], (29918 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), _1349884), c_Groups_Ozero__class_Ozero(_1349880))))]]], (29920 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Groups_Ozero__class_Ozero(_1349880)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349880), _1349882), _1349884)))), 29921 ^ _782464 : [(29922 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Groups_Ozero__class_Ozero(_1349880)), _1349882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), c_Groups_Ozero__class_Ozero(_1349880)), _1349884))], (29928 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), _1349882), c_Groups_Ozero__class_Ozero(_1349880))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349880), _1349884), c_Groups_Ozero__class_Ozero(_1349880)))]]]]], (29936 ^ _782464) ^ [_1350470, _1350472, _1350474, _1350476] : [class_Fields_Olinordered__field(_1350470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350470), _1350472), _1350474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350470), _1350476), c_Groups_Ozero__class_Ozero(_1350470))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350470), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350470), _1350474), _1350476)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350470), _1350472), _1350476))))], (29950 ^ _782464) ^ [_1350739, _1350741, _1350743, _1350745] : [class_Fields_Olinordered__field(_1350739), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350739), _1350741), _1350743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350739), c_Groups_Ozero__class_Ozero(_1350739)), _1350745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350739), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350739), _1350741), _1350745)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350739), _1350743), _1350745))))], (29964 ^ _782464) ^ [_1351008, _1351010, _1351012] : [class_Fields_Olinordered__field(_1351008), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351008), _1351010), c_Groups_Ozero__class_Ozero(_1351008))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351008), _1351012), c_Groups_Ozero__class_Ozero(_1351008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351008), c_Groups_Ozero__class_Ozero(_1351008)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351008), _1351010), _1351012))))], (29978 ^ _782464) ^ [_1351263, _1351265, _1351267] : [class_Fields_Olinordered__field(_1351263), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351263), _1351265), c_Groups_Ozero__class_Ozero(_1351263))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351263), c_Groups_Ozero__class_Ozero(_1351263)), _1351267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351263), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351263), _1351265), _1351267)), c_Groups_Ozero__class_Ozero(_1351263))))], (29992 ^ _782464) ^ [_1351518, _1351520, _1351522] : [class_Fields_Olinordered__field(_1351518), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351518), c_Groups_Ozero__class_Ozero(_1351518)), _1351520)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351518), _1351522), c_Groups_Ozero__class_Ozero(_1351518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351518), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351518), _1351520), _1351522)), c_Groups_Ozero__class_Ozero(_1351518))))], (30006 ^ _782464) ^ [_1351773, _1351775, _1351777] : [class_Fields_Olinordered__field(_1351773), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351773), c_Groups_Ozero__class_Ozero(_1351773)), _1351775)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351773), c_Groups_Ozero__class_Ozero(_1351773)), _1351777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351773), c_Groups_Ozero__class_Ozero(_1351773)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351773), _1351775), _1351777))))], (30020 ^ _782464) ^ [_1352028, _1352030, _1352032] : [class_Fields_Olinordered__field__inverse__zero(_1352028), 30023 ^ _782464 : [(30024 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352028), _1352030), _1352032)), c_Groups_Ozero__class_Ozero(_1352028))), 30029 ^ _782464 : [(30030 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), c_Groups_Ozero__class_Ozero(_1352028)), _1352030)))], (30032 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), _1352032), c_Groups_Ozero__class_Ozero(_1352028))))]], 30033 ^ _782464 : [(30034 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), _1352030), c_Groups_Ozero__class_Ozero(_1352028))))], (30036 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), c_Groups_Ozero__class_Ozero(_1352028)), _1352032)))]]], (30038 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352028), _1352030), _1352032)), c_Groups_Ozero__class_Ozero(_1352028)))), 30039 ^ _782464 : [(30040 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), c_Groups_Ozero__class_Ozero(_1352028)), _1352030)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), _1352032), c_Groups_Ozero__class_Ozero(_1352028)))], (30046 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), _1352030), c_Groups_Ozero__class_Ozero(_1352028))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352028), c_Groups_Ozero__class_Ozero(_1352028)), _1352032))]]]]], (30054 ^ _782464) ^ [_1352618, _1352620, _1352622] : [class_Fields_Olinordered__field__inverse__zero(_1352618), 30057 ^ _782464 : [(30058 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), c_Groups_Ozero__class_Ozero(_1352618)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352618), _1352620), _1352622))), 30063 ^ _782464 : [(30064 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), c_Groups_Ozero__class_Ozero(_1352618)), _1352620)))], (30066 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), c_Groups_Ozero__class_Ozero(_1352618)), _1352622)))]], 30067 ^ _782464 : [(30068 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), _1352620), c_Groups_Ozero__class_Ozero(_1352618))))], (30070 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), _1352622), c_Groups_Ozero__class_Ozero(_1352618))))]]], (30072 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), c_Groups_Ozero__class_Ozero(_1352618)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352618), _1352620), _1352622)))), 30073 ^ _782464 : [(30074 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), c_Groups_Ozero__class_Ozero(_1352618)), _1352620)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), c_Groups_Ozero__class_Ozero(_1352618)), _1352622))], (30080 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), _1352620), c_Groups_Ozero__class_Ozero(_1352618))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352618), _1352622), c_Groups_Ozero__class_Ozero(_1352618)))]]]]], (30088 ^ _782464) ^ [_1353208, _1353210, _1353212, _1353214] : [class_Fields_Ofield__inverse__zero(_1353208), 30091 ^ _782464 : [(30108 ^ _782464) ^ [] : [-(_1353210 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353208), _1353212), _1353214)), 30111 ^ _782464 : [(30112 ^ _782464) ^ [] : [_1353214 = c_Groups_Ozero__class_Ozero(_1353208)], (30114 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353208), _1353210), _1353214) = _1353212]], 30115 ^ _782464 : [(30116 ^ _782464) ^ [] : [-(_1353214 = c_Groups_Ozero__class_Ozero(_1353208))], (30118 ^ _782464) ^ [] : [_1353210 = c_Groups_Ozero__class_Ozero(_1353208)]]], (30092 ^ _782464) ^ [] : [_1353210 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353208), _1353212), _1353214), 30095 ^ _782464 : [(30096 ^ _782464) ^ [] : [-(_1353214 = c_Groups_Ozero__class_Ozero(_1353208)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353208), _1353210), _1353214) = _1353212)], (30102 ^ _782464) ^ [] : [_1353214 = c_Groups_Ozero__class_Ozero(_1353208), -(_1353210 = c_Groups_Ozero__class_Ozero(_1353208))]]]]], (30122 ^ _782464) ^ [_1353702, _1353704, _1353706, _1353708] : [class_Fields_Ofield__inverse__zero(_1353702), 30125 ^ _782464 : [(30142 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353702), _1353704), _1353706) = _1353708), 30145 ^ _782464 : [(30146 ^ _782464) ^ [] : [_1353706 = c_Groups_Ozero__class_Ozero(_1353702)], (30148 ^ _782464) ^ [] : [_1353704 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353702), _1353708), _1353706)]], 30149 ^ _782464 : [(30150 ^ _782464) ^ [] : [-(_1353706 = c_Groups_Ozero__class_Ozero(_1353702))], (30152 ^ _782464) ^ [] : [_1353708 = c_Groups_Ozero__class_Ozero(_1353702)]]], (30126 ^ _782464) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353702), _1353704), _1353706) = _1353708, 30129 ^ _782464 : [(30130 ^ _782464) ^ [] : [-(_1353706 = c_Groups_Ozero__class_Ozero(_1353702)), -(_1353704 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353702), _1353708), _1353706))], (30136 ^ _782464) ^ [] : [_1353706 = c_Groups_Ozero__class_Ozero(_1353702), -(_1353708 = c_Groups_Ozero__class_Ozero(_1353702))]]]]], (30156 ^ _782464) ^ [_1354196, _1354198, _1354200, _1354202] : [class_Fields_Ofield__inverse__zero(_1354196), -(_1354198 = c_Groups_Ozero__class_Ozero(_1354196)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354196), _1354200), _1354198)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354196), _1354202), _1354198)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354196), _1354200), _1354202))], (30166 ^ _782464) ^ [_1354358, _1354360, _1354362, _1354364] : [class_Fields_Ofield__inverse__zero(_1354358), -(_1354360 = c_Groups_Ozero__class_Ozero(_1354358)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354358), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354358), _1354360), _1354362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354358), _1354360), _1354364)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354358), _1354362), _1354364))], (30176 ^ _782464) ^ [_1354520, _1354522, _1354524, _1354526, _1354528] : [class_Fields_Ofield(_1354520), -(_1354522 = c_Groups_Ozero__class_Ozero(_1354520)), -(_1354524 = c_Groups_Ozero__class_Ozero(_1354520)), 30187 ^ _782464 : [(30188 ^ _782464) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354520), _1354526), _1354522) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354520), _1354528), _1354524), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354520), _1354526), _1354524) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354520), _1354528), _1354522))], (30194 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354520), _1354526), _1354524) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354520), _1354528), _1354522), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354520), _1354526), _1354522) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354520), _1354528), _1354524))]]], (30200 ^ _782464) ^ [_1354969, _1354971, _1354973] : [class_Fields_Olinordered__field(_1354969), -(_1354971 = c_Groups_Ozero__class_Ozero(_1354969)), -(hAPP(c_Groups_Oabs__class_Oabs(_1354969), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354969), _1354973), _1354971)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354969), hAPP(c_Groups_Oabs__class_Oabs(_1354969), _1354973)), hAPP(c_Groups_Oabs__class_Oabs(_1354969), _1354971)))], (30210 ^ _782464) ^ [_1355127, _1355129, _1355131] : [class_Fields_Olinordered__field(_1355127), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355127), c_Groups_Ozero__class_Ozero(_1355127)), _1355129)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355127), c_Groups_Ozero__class_Ozero(_1355127)), _1355131)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355127), c_Groups_Ozero__class_Ozero(_1355127)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355127), _1355129), _1355131))))], (30224 ^ _782464) ^ [_1355382, _1355384, _1355386] : [class_Fields_Olinordered__field(_1355382), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355382), c_Groups_Ozero__class_Ozero(_1355382)), _1355384)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355382), _1355386), c_Groups_Ozero__class_Ozero(_1355382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355382), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355382), _1355384), _1355386)), c_Groups_Ozero__class_Ozero(_1355382))))], (30238 ^ _782464) ^ [_1355637, _1355639, _1355641, _1355643, _1355645] : [class_Fields_Olinordered__field(_1355637), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355637), c_Groups_Ozero__class_Ozero(_1355637)), _1355639)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355637), _1355639), _1355641)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355637), c_Groups_Ozero__class_Ozero(_1355637)), _1355643)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355637), _1355643), _1355645)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355637), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355637), _1355639), _1355645)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355637), _1355641), _1355643))))], (30260 ^ _782464) ^ [_1356060, _1356062, _1356064, _1356066, _1356068] : [class_Fields_Olinordered__field(_1356060), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356060), c_Groups_Ozero__class_Ozero(_1356060)), _1356062)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356060), _1356062), _1356064)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356060), c_Groups_Ozero__class_Ozero(_1356060)), _1356066)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356060), _1356066), _1356068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356060), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356060), _1356062), _1356068)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356060), _1356064), _1356066))))], (30282 ^ _782464) ^ [_1356483, _1356485, _1356487, _1356489, _1356491] : [class_Fields_Olinordered__field(_1356483), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356483), c_Groups_Ozero__class_Ozero(_1356483)), _1356485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356483), _1356485), _1356487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356483), c_Groups_Ozero__class_Ozero(_1356483)), _1356489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356483), _1356489), _1356491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356483), _1356485), _1356491)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356483), _1356487), _1356489))))], (30304 ^ _782464) ^ [_1356906, _1356908, _1356910] : [class_Fields_Olinordered__field(_1356906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356906), _1356908), c_Groups_Ozero__class_Ozero(_1356906))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356906), c_Groups_Ozero__class_Ozero(_1356906)), _1356910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356906), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356906), _1356908), _1356910)), c_Groups_Ozero__class_Ozero(_1356906))))], (30318 ^ _782464) ^ [_1357161, _1357163, _1357165] : [class_Fields_Olinordered__field(_1357161), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357161), _1357163), c_Groups_Ozero__class_Ozero(_1357161))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357161), _1357165), c_Groups_Ozero__class_Ozero(_1357161))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357161), c_Groups_Ozero__class_Ozero(_1357161)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357161), _1357163), _1357165))))], (30332 ^ _782464) ^ [_1357416, _1357418, _1357420, _1357422] : [class_Fields_Olinordered__field(_1357416), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357416), _1357418), _1357420)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357416), _1357422), c_Groups_Ozero__class_Ozero(_1357416))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357416), c_Groups_Ozero__class_Ozero(_1357416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357416), _1357418), _1357420))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357416), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357416), _1357422), _1357418)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357416), _1357422), _1357420))))], (30350 ^ _782464) ^ [_1357775, _1357777, _1357779, _1357781] : [class_Fields_Olinordered__field(_1357775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357775), _1357777), _1357779)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357775), c_Groups_Ozero__class_Ozero(_1357775)), _1357781)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357775), c_Groups_Ozero__class_Ozero(_1357775)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357775), _1357779), _1357777))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357775), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357775), _1357781), _1357779)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357775), _1357781), _1357777))))], (30368 ^ _782464) ^ [_1358134, _1358136, _1358138, _1358140] : [class_Fields_Olinordered__field(_1358134), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358134), _1358136), c_Groups_Ozero__class_Ozero(_1358134))), 30375 ^ _782464 : [(30376 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358134), _1358138), _1358136)), _1358140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358134), _1358140), _1358136)), _1358138)))], (30382 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358134), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358134), _1358140), _1358136)), _1358138)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358134), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358134), _1358138), _1358136)), _1358140)))]]], (30388 ^ _782464) ^ [_1358515, _1358517, _1358519, _1358521] : [class_Fields_Olinordered__field(_1358515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358515), _1358517), c_Groups_Ozero__class_Ozero(_1358515))), 30395 ^ _782464 : [(30396 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358515), _1358519), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358515), _1358521), _1358517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358515), _1358521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358515), _1358519), _1358517))))], (30402 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358515), _1358521), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358515), _1358519), _1358517))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358515), _1358519), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358515), _1358521), _1358517))))]]], (30408 ^ _782464) ^ [_1358896, _1358898, _1358900, _1358902] : [class_Fields_Olinordered__field(_1358896), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358896), c_Groups_Ozero__class_Ozero(_1358896)), _1358898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358896), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358896), _1358900), _1358898)), _1358902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358896), _1358900), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358896), _1358902), _1358898))))], (30422 ^ _782464) ^ [_1359165, _1359167, _1359169, _1359171] : [class_Fields_Olinordered__field(_1359165), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359165), c_Groups_Ozero__class_Ozero(_1359165)), _1359167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359165), _1359169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359165), _1359171), _1359167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359165), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359165), _1359169), _1359167)), _1359171)))], (30436 ^ _782464) ^ [_1359434, _1359436, _1359438, _1359440] : [class_Fields_Olinordered__field(_1359434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359434), c_Groups_Ozero__class_Ozero(_1359434)), _1359436)), 30443 ^ _782464 : [(30444 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359434), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359434), _1359438), _1359436)), _1359440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359434), _1359438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359434), _1359440), _1359436))))], (30450 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359434), _1359438), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359434), _1359440), _1359436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359434), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359434), _1359438), _1359436)), _1359440)))]]], (30456 ^ _782464) ^ [_1359815, _1359817, _1359819, _1359821] : [class_Fields_Olinordered__field(_1359815), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359815), c_Groups_Ozero__class_Ozero(_1359815)), _1359817)), 30463 ^ _782464 : [(30464 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359815), _1359819), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359815), _1359821), _1359817))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359815), _1359819), _1359817)), _1359821)))], (30470 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359815), _1359819), _1359817)), _1359821)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359815), _1359819), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359815), _1359821), _1359817))))]]], (30476 ^ _782464) ^ [_1360196, _1360198, _1360200, _1360202] : [class_Fields_Olinordered__field__inverse__zero(_1360196), 30479 ^ _782464 : [(30506 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360196), _1360198), _1360200)), _1360202))), 30509 ^ _782464 : [(30510 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), c_Groups_Ozero__class_Ozero(_1360196)), _1360200)))], (30512 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), _1360198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360196), _1360202), _1360200)))]], 30513 ^ _782464 : [(30514 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), c_Groups_Ozero__class_Ozero(_1360196)), _1360200))], (30516 ^ _782464) ^ [] : [30517 ^ _782464 : [(30518 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), _1360200), c_Groups_Ozero__class_Ozero(_1360196))))], (30520 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360196), _1360202), _1360200)), _1360198))]], 30521 ^ _782464 : [(30522 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), _1360200), c_Groups_Ozero__class_Ozero(_1360196)))], (30524 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), c_Groups_Ozero__class_Ozero(_1360196)), _1360202))]]]]], (30480 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360196), _1360198), _1360200)), _1360202)), 30483 ^ _782464 : [(30484 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), c_Groups_Ozero__class_Ozero(_1360196)), _1360200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), _1360198), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360196), _1360202), _1360200))))], (30490 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), c_Groups_Ozero__class_Ozero(_1360196)), _1360200))), 30493 ^ _782464 : [(30494 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), _1360200), c_Groups_Ozero__class_Ozero(_1360196))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360196), _1360202), _1360200)), _1360198)))], (30500 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), _1360200), c_Groups_Ozero__class_Ozero(_1360196)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360196), c_Groups_Ozero__class_Ozero(_1360196)), _1360202)))]]]]]]], (30528 ^ _782464) ^ [_1361149, _1361151, _1361153, _1361155] : [class_Fields_Olinordered__field__inverse__zero(_1361149), 30531 ^ _782464 : [(30558 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361151), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361149), _1361153), _1361155)))), 30561 ^ _782464 : [(30562 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), c_Groups_Ozero__class_Ozero(_1361149)), _1361155)))], (30564 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361149), _1361151), _1361155)), _1361153))]], 30565 ^ _782464 : [(30566 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), c_Groups_Ozero__class_Ozero(_1361149)), _1361155))], (30568 ^ _782464) ^ [] : [30569 ^ _782464 : [(30570 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361155), c_Groups_Ozero__class_Ozero(_1361149))))], (30572 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361149), _1361151), _1361155)))]], 30573 ^ _782464 : [(30574 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361155), c_Groups_Ozero__class_Ozero(_1361149)))], (30576 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361151), c_Groups_Ozero__class_Ozero(_1361149)))]]]]], (30532 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361151), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361149), _1361153), _1361155))), 30535 ^ _782464 : [(30536 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), c_Groups_Ozero__class_Ozero(_1361149)), _1361155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361149), _1361151), _1361155)), _1361153)))], (30542 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), c_Groups_Ozero__class_Ozero(_1361149)), _1361155))), 30545 ^ _782464 : [(30546 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361155), c_Groups_Ozero__class_Ozero(_1361149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361153), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361149), _1361151), _1361155))))], (30552 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361155), c_Groups_Ozero__class_Ozero(_1361149)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361149), _1361151), c_Groups_Ozero__class_Ozero(_1361149))))]]]]]]], (30580 ^ _782464) ^ [_1362102, _1362104, _1362106, _1362108] : [class_Fields_Ofield__inverse__zero(_1362102), -(_1362104 = c_Groups_Ozero__class_Ozero(_1362102)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362102), _1362106), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362102), _1362108), _1362104)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362102), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362102), _1362108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362102), _1362106), _1362104))), _1362104))], (30590 ^ _782464) ^ [_1362280, _1362282, _1362284, _1362286] : [class_Fields_Ofield(_1362280), -(_1362282 = c_Groups_Ozero__class_Ozero(_1362280)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362280), _1362284), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362280), _1362286), _1362282)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362280), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362280), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362280), _1362282), _1362284)), _1362286)), _1362282))], (30600 ^ _782464) ^ [_1362458, _1362460, _1362462, _1362464] : [class_Fields_Ofield__inverse__zero(_1362458), -(_1362460 = c_Groups_Ozero__class_Ozero(_1362458)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362458), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362458), _1362462), _1362460)), _1362464) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362458), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362458), _1362462), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362458), _1362464), _1362460))), _1362460))], (30610 ^ _782464) ^ [_1362636, _1362638, _1362640, _1362642] : [class_Fields_Ofield(_1362636), -(_1362638 = c_Groups_Ozero__class_Ozero(_1362636)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362636), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362636), _1362640), _1362638)), _1362642) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362636), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362636), _1362640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362636), _1362638), _1362642))), _1362638))], (30620 ^ _782464) ^ [_1362814, _1362816, _1362818, _1362820, _1362822] : [class_Fields_Ofield(_1362814), -(_1362816 = c_Groups_Ozero__class_Ozero(_1362814)), -(_1362818 = c_Groups_Ozero__class_Ozero(_1362814)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362814), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362814), _1362820), _1362816)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362814), _1362822), _1362818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362814), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362814), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362814), _1362820), _1362818)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362814), _1362822), _1362816))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362814), _1362816), _1362818)))], (30634 ^ _782464) ^ [_1363061, _1363063, _1363065, _1363067] : [class_Fields_Ofield(_1363061), -(_1363063 = c_Groups_Ozero__class_Ozero(_1363061)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363061), _1363065), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363061), _1363067), _1363063)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363061), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363061), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363061), _1363063), _1363065)), _1363067)), _1363063))], (30644 ^ _782464) ^ [_1363239, _1363241, _1363243, _1363245] : [class_Fields_Ofield(_1363239), -(_1363241 = c_Groups_Ozero__class_Ozero(_1363239)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363239), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363239), _1363243), _1363241)), _1363245) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363239), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363239), _1363243), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363239), _1363241), _1363245))), _1363241))], (30654 ^ _782464) ^ [_1363417, _1363419, _1363421, _1363423, _1363425] : [class_Fields_Ofield(_1363417), -(_1363419 = c_Groups_Ozero__class_Ozero(_1363417)), -(_1363421 = c_Groups_Ozero__class_Ozero(_1363417)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363417), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363417), _1363423), _1363419)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363417), _1363425), _1363421)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363417), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363417), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363417), _1363423), _1363421)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363417), _1363425), _1363419))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363417), _1363419), _1363421)))], (30668 ^ _782464) ^ [_1363664, _1363666, _1363668] : [class_Fields_Olinordered__field(_1363664), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363664), _1363666), _1363668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363664), _1363666), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363664), _1363666), _1363668)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363664), c_Groups_Oone__class_Oone(_1363664)), c_Groups_Oone__class_Oone(_1363664))))))], (30678 ^ _782464) ^ [_1363879, _1363881, _1363883] : [class_Fields_Olinordered__field(_1363879), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363879), _1363881), _1363883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363879), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363879), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363879), _1363881), _1363883)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363879), c_Groups_Oone__class_Oone(_1363879)), c_Groups_Oone__class_Oone(_1363879)))), _1363883)))], (30688 ^ _782464) ^ [_1364094, _1364096, _1364098] : [class_Fields_Olinordered__field__inverse__zero(_1364094), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364094), c_Groups_Ozero__class_Ozero(_1364094)), _1364096)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364094), hAPP(c_Groups_Oabs__class_Oabs(_1364094), _1364098)), _1364096) = hAPP(c_Groups_Oabs__class_Oabs(_1364094), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364094), _1364098), _1364096)))], (30698 ^ _782464) ^ [_1364295, _1364297, _1364299, _1364301] : [class_Fields_Olinordered__field__inverse__zero(_1364295), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364295), _1364297), _1364299)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364295), _1364301), c_Groups_Ozero__class_Ozero(_1364295))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364295), c_Groups_Ozero__class_Ozero(_1364295)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364295), _1364297), _1364299))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364295), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364295), _1364301), _1364297)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364295), _1364301), _1364299))))], (30716 ^ _782464) ^ [_1364654, _1364656, _1364658, _1364660] : [class_Fields_Olinordered__field(_1364654), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364654), _1364656), _1364658)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364654), c_Groups_Ozero__class_Ozero(_1364654)), _1364660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364654), c_Groups_Ozero__class_Ozero(_1364654)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364654), _1364658), _1364656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364654), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364654), _1364660), _1364658)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364654), _1364660), _1364656))))], (30734 ^ _782464) ^ [_1365013, _1365015, _1365017, _1365019] : [class_Fields_Olinordered__field(_1365013), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365013), _1365015), c_Groups_Ozero__class_Ozero(_1365013))), 30741 ^ _782464 : [(30742 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365013), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365013), _1365017), _1365015)), _1365019)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365013), _1365019), _1365015)), _1365017)))], (30748 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365013), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365013), _1365019), _1365015)), _1365017)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365013), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365013), _1365017), _1365015)), _1365019)))]]], (30754 ^ _782464) ^ [_1365394, _1365396, _1365398, _1365400] : [class_Fields_Olinordered__field(_1365394), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365394), _1365396), c_Groups_Ozero__class_Ozero(_1365394))), 30761 ^ _782464 : [(30762 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365394), _1365398), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365394), _1365400), _1365396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365394), _1365400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365394), _1365398), _1365396))))], (30768 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365394), _1365400), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365394), _1365398), _1365396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365394), _1365398), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365394), _1365400), _1365396))))]]], (30774 ^ _782464) ^ [_1365775, _1365777, _1365779, _1365781] : [class_Fields_Olinordered__field(_1365775), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365775), c_Groups_Ozero__class_Ozero(_1365775)), _1365777)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365775), _1365779), _1365777)), _1365781)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365775), _1365779), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365775), _1365781), _1365777))))], (30788 ^ _782464) ^ [_1366044, _1366046, _1366048, _1366050] : [class_Fields_Olinordered__field(_1366044), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366044), c_Groups_Ozero__class_Ozero(_1366044)), _1366046)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366044), _1366048), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366044), _1366050), _1366046))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366044), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366044), _1366048), _1366046)), _1366050)))], (30802 ^ _782464) ^ [_1366313, _1366315, _1366317, _1366319, _1366321] : [class_Fields_Ofield(_1366313), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366315), _1366317)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366315), _1366319)), 30816 ^ _782464 : [(30817 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366315), 30815 ^ [_1366313, _1366315, _1366317, _1366319, _1366321]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366315, tc_HOL_Obool)), _1366317), _1366319))))], (30819 ^ _782464) ^ [] : [-(hAPP(_1366321, 30815 ^ [_1366313, _1366315, _1366317, _1366319, _1366321]) = c_Groups_Ozero__class_Ozero(_1366313))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366315, _1366313), _1366321), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366315, tc_HOL_Obool)), _1366317), _1366319)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366313), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366313), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366315, _1366313), _1366321), _1366317)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366315, _1366313), _1366321), _1366319))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366315, _1366313), _1366321), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366315, tc_HOL_Obool)), _1366317), _1366319))))], (30823 ^ _782464) ^ [_1366809] : [class_Power_Opower(_1366809), -(c_Power_Opower__class_Opower(_1366809) = c_Power_Opower_Opower(_1366809, c_Groups_Oone__class_Oone(_1366809), c_Groups_Otimes__class_Otimes(_1366809)))], (30829 ^ _782464) ^ [_1366902, _1366904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1366902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366904)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366904), _1366902)), _1366904) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366904), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1366902), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (30839 ^ _782464) ^ [_1367087, _1367089, _1367091] : [class_Orderings_Olinorder(_1367087), hAPP(_1367089, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367087), 30844 ^ [_1367087, _1367089, _1367091]), 30845 ^ [_1367087, _1367089, _1367091])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367087), hAPP(_1367089, 30844 ^ [_1367087, _1367089, _1367091])), hAPP(_1367089, 30845 ^ [_1367087, _1367089, _1367091])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367087), _1367091)), -(_1367091 = c_Orderings_Obot__class_Obot(tc_fun(_1367087, tc_HOL_Obool))), -(hAPP(_1367089, c_Big__Operators_Olattice_OInf__fin(_1367087, c_Orderings_Oord__class_Omin(_1367087), _1367091)) = c_Big__Operators_Olattice_OInf__fin(_1367087, c_Orderings_Oord__class_Omin(_1367087), hAPP(c_Set_Oimage(_1367087, _1367087, _1367089), _1367091)))], (30859 ^ _782464) ^ [_1367502] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367502) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30861 ^ _782464) ^ [_1367528, _1367530] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367528), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367530)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367528)), _1367530))], (30863 ^ _782464) ^ [_1367571, _1367573] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367571)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367573)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367571), _1367573))], (30865 ^ _782464) ^ [_1367614, _1367616] : [class_Divides_Osemiring__div(_1367614), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367614), c_Groups_Ozero__class_Ozero(_1367614)), _1367616) = c_Groups_Ozero__class_Ozero(_1367614))], (30871 ^ _782464) ^ [_1367713, _1367715] : [class_Divides_Osemiring__div(_1367713), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367713), _1367715), c_Groups_Ozero__class_Ozero(_1367713)) = c_Groups_Ozero__class_Ozero(_1367713))], (30877 ^ _782464) ^ [_1367812, _1367814] : [c_Nat__Transfer_Ois__nat(_1367812), c_Nat__Transfer_Ois__nat(_1367814), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367812), _1367814)))], (30887 ^ _782464) ^ [_1367947, _1367949] : [class_Divides_Osemiring__div(_1367947), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367947), _1367949), c_Groups_Oone__class_Oone(_1367947)) = _1367949)], (30893 ^ _782464) ^ [_1368042, _1368044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368042)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368044)), -(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), _1368042), _1368044))))], (30903 ^ _782464) ^ [_1368195, _1368197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368195), 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)), _1368197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368195), _1368197)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30913 ^ _782464) ^ [_1368360, _1368362] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368360), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30916 ^ _782464 : [(30917 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368362), _1368360)), 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)), _1368362)))], (30923 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368362)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368362), _1368360)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30929 ^ _782464) ^ [_1368616, _1368618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368616)), 30932 ^ _782464 : [(30933 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368618), _1368616)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368618), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30939 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368618), 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), _1368618), _1368616)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30945 ^ _782464) ^ [_1368871] : [-(_1368871 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368871), _1368871) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30951 ^ _782464) ^ [_1368911, _1368913, _1368915, _1368917] : [class_Divides_Osemiring__div(_1368911), 30954 ^ _782464 : [(30955 ^ _782464) ^ [] : [_1368913 = c_Groups_Ozero__class_Ozero(_1368911), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368911), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368911), _1368913), _1368915)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368911), _1368913), _1368917)) = c_Groups_Ozero__class_Ozero(_1368911))], (30961 ^ _782464) ^ [] : [-(_1368913 = c_Groups_Ozero__class_Ozero(_1368911)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368911), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368911), _1368913), _1368915)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368911), _1368913), _1368917)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368911), _1368915), _1368917))]]], (30967 ^ _782464) ^ [_1369217, _1369219, _1369221] : [class_Divides_Osemiring__div(_1369217), -(_1369219 = c_Groups_Ozero__class_Ozero(_1369217)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369217), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369217), _1369221), _1369219)), _1369219) = _1369221)], (30977 ^ _782464) ^ [_1369345, _1369347, _1369349] : [class_Divides_Osemiring__div(_1369345), -(_1369347 = c_Groups_Ozero__class_Ozero(_1369345)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369345), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369345), _1369347), _1369349)), _1369347) = _1369349)], (30987 ^ _782464) ^ [_1369473, _1369475, _1369477, _1369479] : [class_Divides_Osemiring__div(_1369473), -(_1369475 = c_Groups_Ozero__class_Ozero(_1369473)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369473), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369473), _1369477), _1369475)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369473), _1369479), _1369475)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369473), _1369477), _1369479))], (30997 ^ _782464) ^ [_1369635, _1369637, _1369639, _1369641] : [class_Divides_Osemiring__div(_1369635), -(_1369637 = c_Groups_Ozero__class_Ozero(_1369635)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369635), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369635), _1369637), _1369639)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369635), _1369637), _1369641)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369635), _1369639), _1369641))], (31007 ^ _782464) ^ [_1369797, _1369799] : [class_Divides_Osemiring__div(_1369797), -(_1369799 = c_Groups_Ozero__class_Ozero(_1369797)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369797), _1369799), _1369799) = c_Groups_Oone__class_Oone(_1369797))], (31017 ^ _782464) ^ [_1369926, _1369928] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369926), _1369928) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1369928 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31026 ^ _782464 : [(31027 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369926)))], (31029 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369926), _1369928)))]], 31030 ^ _782464 : [(31031 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1369926), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31033 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369928), _1369926)))]]], (31035 ^ _782464) ^ [_1370157, _1370159] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1370157), _1370159) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31036 ^ _782464 : [(31037 ^ _782464) ^ [] : [_1370159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (31039 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370157)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370157), _1370159))], (31045 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370157), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370159), _1370157))]]], (31053 ^ _782464) ^ [_1370452, _1370454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370452)), 31056 ^ _782464 : [(31057 ^ _782464) ^ [] : [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), _1370454), _1370452))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370454)))], (31063 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370454)), -(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), _1370454), _1370452))))]]], (31069 ^ _782464) ^ [_1370693, _1370695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370693)), 31072 ^ _782464 : [(31073 ^ _782464) ^ [] : [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), _1370695), _1370693))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370693), _1370695)))], (31079 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370693), _1370695)), -(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), _1370695), _1370693))))]]], (31085 ^ _782464) ^ [_1370943, _1370945] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370943)), 31088 ^ _782464 : [(31089 ^ _782464) ^ [] : [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), _1370943), _1370945))), 31092 ^ _782464 : [(31093 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370945), _1370943)))], (31095 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370945)))]]], (31097 ^ _782464) ^ [] : [-(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), _1370943), _1370945)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370945), _1370943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370945))]]], (31107 ^ _782464) ^ [_1371271, _1371273, _1371275] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371271)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371273)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371273), _1371275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371271), _1371275)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371271), _1371273))))], (31121 ^ _782464) ^ [_1371510, _1371512] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371510)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371512), 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), _1371510), _1371512)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31131 ^ _782464) ^ [_1371675, _1371677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371675)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371675), _1371677)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371675), _1371677) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31141 ^ _782464) ^ [_1371830, _1371832] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371830), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31144 ^ _782464 : [(31145 ^ _782464) ^ [] : [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), _1371832), _1371830))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371832), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31151 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371832), 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), _1371832), _1371830))))]]], (31157 ^ _782464) ^ [_1372086, _1372088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372086), 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)), _1372088)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372086), _1372088)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31167 ^ _782464) ^ [_1372251, _1372253, _1372255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372251), 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)), _1372253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372253), _1372255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372251), _1372253)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372251), _1372255))))], (31181 ^ _782464) ^ [_1372496, _1372498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372496), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372498), _1372496)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372496), _1372498) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31191 ^ _782464) ^ [_1372657, _1372659, _1372661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372657), _1372659)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1372661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372657), _1372661)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372659), _1372661))))], (31201 ^ _782464) ^ [_1372838, _1372840, _1372842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372838), _1372840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372842), 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), _1372840), _1372842)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372838), _1372842))))], (31211 ^ _782464) ^ [_1373025, _1373027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373025)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1373027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373025), _1373027)), _1373025)))], (31221 ^ _782464) ^ [_1373184, _1373186, _1373188] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373184)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373186), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1373188), _1373184)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373186), _1373188)), _1373184))], (31227 ^ _782464) ^ [_1373315, _1373317, _1373319, _1373321] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1373315, _1373317, _1373319), _1373321), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1373317)], (31229 ^ _782464) ^ [_1373354, _1373356, _1373358, _1373360, _1373362] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1373354, _1373356, _1373358), _1373360), hAPP(c_Nat_OSuc, _1373362)) = hAPP(hAPP(_1373358, _1373360), hAPP(hAPP(c_Power_Opower_Opower(_1373354, _1373356, _1373358), _1373360), _1373362)))], (31231 ^ _782464) ^ [_1373414, _1373416, _1373418, _1373420] : [class_Divides_Osemiring__div(_1373414), -(_1373416 = c_Groups_Ozero__class_Ozero(_1373414)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373414), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373414), _1373418), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373414), _1373420), _1373416))), _1373416) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373414), _1373420), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373414), _1373418), _1373416)))], (31241 ^ _782464) ^ [_1373592, _1373594, _1373596, _1373598] : [class_Divides_Osemiring__div(_1373592), -(_1373594 = c_Groups_Ozero__class_Ozero(_1373592)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373592), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373592), _1373596), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373592), _1373594), _1373598))), _1373594) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373592), _1373598), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373592), _1373596), _1373594)))], (31251 ^ _782464) ^ [_1373770, _1373772, _1373774] : [class_Divides_Osemiring__div(_1373770), -(_1373772 = c_Groups_Ozero__class_Ozero(_1373770)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373770), _1373772), _1373774)), _1373772) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373770), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373770), _1373774), _1373772)), c_Groups_Oone__class_Oone(_1373770)))], (31261 ^ _782464) ^ [_1373934, _1373936, _1373938] : [class_Divides_Osemiring__div(_1373934), -(_1373936 = c_Groups_Ozero__class_Ozero(_1373934)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373934), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373934), _1373938), _1373936)), _1373936) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373934), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373934), _1373938), _1373936)), c_Groups_Oone__class_Oone(_1373934)))], (31271 ^ _782464) ^ [_1374098, _1374100, _1374102, _1374104] : [_1374098 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374100), _1374102)), _1374104), -(_1374100 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1374098), _1374100) = _1374102), 31278 ^ _782464 : [(31279 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374100)))], (31281 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374104), _1374100))]], 31286 ^ _782464 : [(31287 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374100))], (31289 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374100), _1374104)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1374104), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (31347 ^ _782464) ^ [_1375545, _1375547, _1375549] : [-(hBOOL(hAPP(_1375545, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1375547), _1375549)))), 31350 ^ _782464 : [(31351 ^ _782464) ^ [] : [-(_1375549 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31353 ^ _782464) ^ [] : [hBOOL(hAPP(_1375545, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 31356 ^ _782464 : [(31357 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375549)))], (31361 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31359 ^ [_1375545, _1375547, _1375549])))], (31363 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 31359 ^ [_1375545, _1375547, _1375549]), _1375549)))], (31365 ^ _782464) ^ [] : [-(_1375547 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1375549), 31358 ^ [_1375545, _1375547, _1375549])), 31359 ^ [_1375545, _1375547, _1375549]))], (31367 ^ _782464) ^ [] : [hBOOL(hAPP(_1375545, 31358 ^ [_1375545, _1375547, _1375549]))]], 31368 ^ _782464 : [(31369 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375549), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31373 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375549), 31371 ^ [_1375545, _1375547, _1375549])))], (31375 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31371 ^ [_1375545, _1375547, _1375549]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31377 ^ _782464) ^ [] : [-(_1375547 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1375549), 31370 ^ [_1375545, _1375547, _1375549])), 31371 ^ [_1375545, _1375547, _1375549]))], (31379 ^ _782464) ^ [] : [hBOOL(hAPP(_1375545, 31370 ^ [_1375545, _1375547, _1375549]))]]], (31301 ^ _782464) ^ [_1374585, _1374587, _1374589] : [hBOOL(hAPP(_1374585, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1374587), _1374589))), 31304 ^ _782464 : [(31305 ^ _782464) ^ [] : [_1374589 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1374585, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31311 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374589)), 31314 ^ _782464 : [(31315 ^ _782464) ^ [_1374919] : [-(hBOOL(hAPP(_1374585, _1374919))), 31316 ^ _782464 : [(31317 ^ _782464) ^ [_1374990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374990)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374990), _1374589)), _1374587 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374589), _1374919)), _1374990)]]]]], (31329 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374589), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31332 ^ _782464 : [(31333 ^ _782464) ^ [_1375249] : [-(hBOOL(hAPP(_1374585, _1375249))), 31334 ^ _782464 : [(31335 ^ _782464) ^ [_1375323] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374589), _1375323)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375323), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1374587 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374589), _1375249)), _1375323)]]]]]]], (31383 ^ _782464) ^ [_1376268, _1376270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376268)), -(c_SMT_Oz3div(_1376270, _1376268) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376270), _1376268))], (31389 ^ _782464) ^ [_1376361, _1376363] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376361))), -(c_SMT_Oz3div(_1376363, _1376361) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376363), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1376361))))], (31395 ^ _782464) ^ [_1376416, _1376418, _1376420] : [class_Orderings_Olinorder(_1376416), hAPP(_1376418, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376416), 31400 ^ [_1376416, _1376418, _1376420]), 31401 ^ [_1376416, _1376418, _1376420])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376416), hAPP(_1376418, 31400 ^ [_1376416, _1376418, _1376420])), hAPP(_1376418, 31401 ^ [_1376416, _1376418, _1376420])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376416), _1376420)), -(_1376420 = c_Orderings_Obot__class_Obot(tc_fun(_1376416, tc_HOL_Obool))), -(hAPP(_1376418, c_Big__Operators_Olinorder__class_OMax(_1376416, _1376420)) = c_Big__Operators_Olinorder__class_OMax(_1376416, hAPP(c_Set_Oimage(_1376416, _1376416, _1376418), _1376420)))], (31415 ^ _782464) ^ [_1376819, _1376821, _1376823] : [class_Orderings_Olinorder(_1376819), hAPP(_1376821, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376819), 31420 ^ [_1376819, _1376821, _1376823]), 31421 ^ [_1376819, _1376821, _1376823])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376819), hAPP(_1376821, 31420 ^ [_1376819, _1376821, _1376823])), hAPP(_1376821, 31421 ^ [_1376819, _1376821, _1376823])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376819), _1376823)), -(_1376823 = c_Orderings_Obot__class_Obot(tc_fun(_1376819, tc_HOL_Obool))), -(hAPP(_1376821, c_Big__Operators_Olinorder__class_OMin(_1376819, _1376823)) = c_Big__Operators_Olinorder__class_OMin(_1376819, hAPP(c_Set_Oimage(_1376819, _1376819, _1376821), _1376823)))], (31435 ^ _782464) ^ [_1377222, _1377224, _1377226, _1377228, _1377230, _1377232, _1377234, _1377236] : [class_Groups_Ocomm__monoid__mult(_1377222), c_Fun_Oinj__on(_1377224, _1377226, _1377228, _1377230), _1377232 = hAPP(c_Set_Oimage(_1377224, _1377226, _1377228), _1377230), 31449 ^ _782464 : [(31450 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377224), 31448 ^ [_1377222, _1377224, _1377226, _1377228, _1377230, _1377232, _1377234, _1377236]), _1377230)))], (31452 ^ _782464) ^ [] : [hAPP(_1377234, 31448 ^ [_1377222, _1377224, _1377226, _1377228, _1377230, _1377232, _1377234, _1377236]) = hAPP(hAPP(c_Fun_Ocomp(_1377226, _1377222, _1377224, _1377236), _1377228), 31448 ^ [_1377222, _1377224, _1377226, _1377228, _1377230, _1377232, _1377234, _1377236])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377226, _1377222), _1377236), _1377232) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377224, _1377222), _1377234), _1377230))], (31456 ^ _782464) ^ [_1377730, _1377732, _1377734] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377730), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1377732), _1377734)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377730), _1377732)), _1377734))], (31458 ^ _782464) ^ [_1377781, _1377783, _1377785] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1377781), _1377783)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377781), _1377785)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377783), _1377785))))], (31464 ^ _782464) ^ [_1377904, _1377906] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377904), _1377906)), _1377904)))], (31466 ^ _782464) ^ [_1377940] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377940), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1377940)], (31468 ^ _782464) ^ [_1377969, _1377971] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1377969), _1377971)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377969), _1377971) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31474 ^ _782464) ^ [_1378080, _1378082, _1378084] : [_1378080 = 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), _1378080), _1378082)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378080), _1378084)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31480 ^ _782464) ^ [_1378189, _1378191, _1378193] : [-(_1378189 = 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), _1378189), _1378191)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378189), _1378193)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378191), _1378193))], (31486 ^ _782464) ^ [_1378253, _1378255] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378253), _1378255)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378253)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378255)))], (31488 ^ _782464) ^ [_1378299, _1378301] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378299)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378301)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378299), _1378301)))], (31490 ^ _782464) ^ [_1378345, _1378347, _1378349] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378345)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1378345), _1378347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378349), _1378347)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378349), _1378345))))], (31500 ^ _782464) ^ [_1378526, _1378528, _1378530] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378526)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378526), _1378528)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378526), _1378530)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378528), _1378530))], (31506 ^ _782464) ^ [_1378657, _1378659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378657)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378657), _1378659)), _1378657) = _1378659)], (31512 ^ _782464) ^ [_1378762, _1378764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378762)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378764), _1378762)), _1378762) = _1378764)], (31518 ^ _782464) ^ [_1378867, _1378869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1378867)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378869), _1378867)), _1378869)))], (31528 ^ _782464) ^ [_1379026, _1379028] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1379026)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379028), _1379026))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379028), _1379026) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1379028), _1379026)), _1379026)))], (31538 ^ _782464) ^ [_1379174, _1379176] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1379174)), 31541 ^ _782464 : [(31542 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379176), _1379174)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379176), _1379174) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31548 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379176), _1379174))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379176), _1379174) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1379176), _1379174)), _1379174)))]]], (31578 ^ _782464) ^ [_1379883, _1379885, _1379887] : [-(hBOOL(hAPP(_1379883, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379885), _1379887)))), 31581 ^ _782464 : [(31582 ^ _782464) ^ [] : [-(_1379887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31584 ^ _782464) ^ [] : [hBOOL(hAPP(_1379883, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 31585 ^ _782464 : [(31586 ^ _782464) ^ [] : [_1379887 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31590 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31588 ^ [_1379883, _1379885, _1379887]), _1379887)))], (31592 ^ _782464) ^ [] : [-(_1379885 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1379887), 31587 ^ [_1379883, _1379885, _1379887])), 31588 ^ [_1379883, _1379885, _1379887]))], (31594 ^ _782464) ^ [] : [hBOOL(hAPP(_1379883, 31587 ^ [_1379883, _1379885, _1379887]))]]], (31554 ^ _782464) ^ [_1379446, _1379448, _1379450] : [hBOOL(hAPP(_1379446, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379448), _1379450))), 31557 ^ _782464 : [(31558 ^ _782464) ^ [] : [_1379450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1379446, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31564 ^ _782464) ^ [] : [-(_1379450 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31567 ^ _782464 : [(31568 ^ _782464) ^ [_1379698, _1379700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379698), _1379450)), _1379448 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1379450), _1379700)), _1379698), -(hBOOL(hAPP(_1379446, _1379700)))]]]]], (31598 ^ _782464) ^ [_1380305, _1380307] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380305)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1380305), _1380307)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1380305)), hAPP(c_Int_Onat, _1380307)))], (31604 ^ _782464) ^ [_1380428, _1380430] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380430)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1380428)), hAPP(c_Int_Onat, _1380430)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1380428), _1380430)))], (31614 ^ _782464) ^ [_1380607, _1380609] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1380607)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380607), _1380609)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1380609), _1380607) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1380609), _1380607)), _1380607)))], (31624 ^ _782464) ^ [_1380810, _1380812, _1380814] : [hBOOL(hAPP(_1380810, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1380812), _1380814))), 31629 ^ _782464 : [(31630 ^ _782464) ^ [] : [-(_1380814 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31632 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1380810, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 31634 ^ _782464 : [(31635 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380814), 31633 ^ [_1380810, _1380812, _1380814])), _1380812)))], (31637 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1380812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380814), hAPP(c_Nat_OSuc, 31633 ^ [_1380810, _1380812, _1380814])))))], (31639 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1380810, 31633 ^ [_1380810, _1380812, _1380814])))]]], (31641 ^ _782464) ^ [_1381114, _1381116, _1381118] : [-(hBOOL(hAPP(_1381114, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381116), _1381118)))), 31642 ^ _782464 : [(31643 ^ _782464) ^ [] : [_1381118 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1381114, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31649 ^ _782464) ^ [_1381282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381118), _1381282)), _1381116)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381116), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381118), hAPP(c_Nat_OSuc, _1381282)))), hBOOL(hAPP(_1381114, _1381282))]]], (31661 ^ _782464) ^ [_1381512, _1381514, _1381516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1381512)), 31664 ^ _782464 : [(31675 ^ _782464) ^ [] : [_1381514 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381516), _1381512), 31678 ^ _782464 : [(31679 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381512), _1381514)), _1381516)))], (31681 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381512), hAPP(c_Nat_OSuc, _1381514)))))]]], (31665 ^ _782464) ^ [] : [-(_1381514 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381516), _1381512)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381512), _1381514)), _1381516)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381516), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381512), hAPP(c_Nat_OSuc, _1381514))))]]], (31683 ^ _782464) ^ [_1381896, _1381898] : [-(c_Nitpick_Onat__lcm(_1381896, _1381898) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381896), _1381898)), c_Nitpick_Onat__gcd(_1381896, _1381898)))], (31685 ^ _782464) ^ [_1381939, _1381941, _1381943, _1381945, _1381947] : [class_Groups_Ocomm__monoid__mult(_1381939), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381941), _1381943)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381941, tc_HOL_Obool)), _1381945), _1381943)), 31699 ^ _782464 : [(31700 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381941), 31698 ^ [_1381939, _1381941, _1381943, _1381945, _1381947]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1381941, tc_HOL_Obool)), _1381943), _1381945))))], (31702 ^ _782464) ^ [] : [hAPP(_1381947, 31698 ^ [_1381939, _1381941, _1381943, _1381945, _1381947]) = c_Groups_Oone__class_Oone(_1381939)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381941, _1381939), _1381947), _1381945) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381941, _1381939), _1381947), _1381943))], (31706 ^ _782464) ^ [_1382390, _1382392, _1382394, _1382396, _1382398] : [class_Groups_Ocomm__monoid__mult(_1382390), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382392), _1382394)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382392, tc_HOL_Obool)), _1382396), _1382394)), 31720 ^ _782464 : [(31721 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382392), 31719 ^ [_1382390, _1382392, _1382394, _1382396, _1382398]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1382392, tc_HOL_Obool)), _1382394), _1382396))))], (31723 ^ _782464) ^ [] : [hAPP(_1382398, 31719 ^ [_1382390, _1382392, _1382394, _1382396, _1382398]) = c_Groups_Oone__class_Oone(_1382390)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382392, _1382390), _1382398), _1382394) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382392, _1382390), _1382398), _1382396))], (31727 ^ _782464) ^ [_1382841, _1382843, _1382845] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1382841, tc_HOL_Obool)), _1382843)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382841), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1382841, tc_HOL_Obool), _1382843))), 31737 ^ _782464 : [(31738 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382841, tc_HOL_Obool)), 31736 ^ [_1382841, _1382843, _1382845]), _1382843)))], (31740 ^ _782464) ^ [] : [hAPP(c_Finite__Set_Ocard(_1382841), 31736 ^ [_1382841, _1382843, _1382845]) = _1382845]], 31744 ^ _782464 : [(31745 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382841, tc_HOL_Obool)), 31743 ^ [_1382841, _1382843, _1382845]), _1382843)))], (31748 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382841, tc_HOL_Obool)), 31746 ^ [_1382841, _1382843, _1382845]), _1382843)))], (31750 ^ _782464) ^ [] : [31743 ^ [_1382841, _1382843, _1382845] = 31746 ^ [_1382841, _1382843, _1382845]], (31752 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382841, tc_HOL_Obool)), 31743 ^ [_1382841, _1382843, _1382845]), 31746 ^ [_1382841, _1382843, _1382845]) = c_Orderings_Obot__class_Obot(tc_fun(_1382841, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1382845), hAPP(c_Finite__Set_Ocard(tc_fun(_1382841, tc_HOL_Obool)), _1382843)) = hAPP(c_Finite__Set_Ocard(_1382841), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1382841, tc_HOL_Obool), _1382843)))], (31756 ^ _782464) ^ [_1383623, _1383625] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1383623), _1383625) = 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), _1383623)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1383625)))))], (31758 ^ _782464) ^ [_1383672, _1383674, _1383676] : [class_Fields_Olinordered__field__inverse__zero(_1383672), 31764 ^ _782464 : [(31765 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383672), c_Groups_Ozero__class_Ozero(_1383672)), 31763 ^ [_1383672, _1383674, _1383676])))], (31767 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383672), 31763 ^ [_1383672, _1383674, _1383676]), c_Groups_Oone__class_Oone(_1383672))))], (31769 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383672), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383672), 31763 ^ [_1383672, _1383674, _1383676]), _1383674)), _1383676))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383672), _1383674), _1383676)))], (31773 ^ _782464) ^ [_1384021, _1384023, _1384025, _1384027, _1384029] : [class_Groups_Ocomm__monoid__add(_1384021), class_Groups_Ocomm__monoid__mult(_1384021), _1384023 = _1384025, c_Nat__Transfer_Onat__set(_1384025), 31791 ^ _782464 : [(31792 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31790 ^ [_1384021, _1384023, _1384025, _1384027, _1384029])))], (31794 ^ _782464) ^ [] : [hAPP(_1384027, 31790 ^ [_1384021, _1384023, _1384025, _1384027, _1384029]) = hAPP(_1384029, 31790 ^ [_1384021, _1384023, _1384025, _1384027, _1384029])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1384021), _1384027), _1384023) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1384021), _1384029), _1384025))], (31798 ^ _782464) ^ [_1384484, _1384486, _1384488] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384484), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31801 ^ _782464 : [(31820 ^ _782464) ^ [] : [31823 ^ _782464 : [(31824 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384484), 31822 ^ [_1384484, _1384486, _1384488])))], (31826 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31822 ^ [_1384484, _1384486, _1384488]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31828 ^ _782464) ^ [] : [-(_1384488 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384484), 31821 ^ [_1384484, _1384486, _1384488])), 31822 ^ [_1384484, _1384486, _1384488]))], (31830 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1384486, 31821 ^ [_1384484, _1384486, _1384488]), 31822 ^ [_1384484, _1384486, _1384488]))]], -(hBOOL(hAPP(hAPP(_1384486, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384488), _1384484)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384488, _1384484))))], (31802 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1384486, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384488), _1384484)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384488, _1384484))), 31805 ^ _782464 : [(31806 ^ _782464) ^ [_1384694, _1384696] : [-(hBOOL(hAPP(hAPP(_1384486, _1384696), _1384694))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384484), _1384694)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1384694), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1384488 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384484), _1384696)), _1384694)]]]]], (31834 ^ _782464) ^ [_1385217, _1385219, _1385221] : [-(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, _1385217, _1385219)), _1385221), _1385219) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1385217), _1385221), _1385219))], (31836 ^ _782464) ^ [_1385268, _1385270] : [c_Nat__Transfer_Ois__nat(_1385268), c_Nat__Transfer_Ois__nat(_1385270), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385268, _1385270)))], (31846 ^ _782464) ^ [_1385399, _1385401, _1385403] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385399), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385401, _1385403)), _1385403) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385399), _1385401), _1385403))], (31848 ^ _782464) ^ [_1385450, _1385452, _1385454] : [-(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, _1385450, _1385452)), _1385454), _1385452) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385450), _1385454), _1385452))], (31850 ^ _782464) ^ [_1385501, _1385503] : [-(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, _1385501, _1385503)), _1385503) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385501), _1385503))], (31852 ^ _782464) ^ [_1385544, _1385546] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385544), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385546)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385544, _1385546)))], (31854 ^ _782464) ^ [_1385586, _1385588] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385586, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385588)) = 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), _1385586), _1385588)))], (31856 ^ _782464) ^ [_1385628, _1385630, _1385632, _1385634, _1385636, _1385638] : [class_Divides_Osemiring__div(_1385628), c_Divides_Odiv__class_Omod(_1385628, _1385630, _1385632) = c_Divides_Odiv__class_Omod(_1385628, _1385634, _1385632), c_Divides_Odiv__class_Omod(_1385628, _1385636, _1385632) = c_Divides_Odiv__class_Omod(_1385628, _1385638, _1385632), -(c_Divides_Odiv__class_Omod(_1385628, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385628), _1385630), _1385636), _1385632) = c_Divides_Odiv__class_Omod(_1385628, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385628), _1385634), _1385638), _1385632))], (31870 ^ _782464) ^ [_1385911, _1385913, _1385915, _1385917] : [class_Divides_Osemiring__div(_1385911), -(c_Divides_Odiv__class_Omod(_1385911, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385911), c_Divides_Odiv__class_Omod(_1385911, _1385913, _1385915)), _1385917), _1385915) = c_Divides_Odiv__class_Omod(_1385911, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385911), _1385913), _1385917), _1385915))], (31876 ^ _782464) ^ [_1386046, _1386048, _1386050, _1386052] : [class_Divides_Osemiring__div(_1386046), -(c_Divides_Odiv__class_Omod(_1386046, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386046), _1386048), c_Divides_Odiv__class_Omod(_1386046, _1386050, _1386052)), _1386052) = c_Divides_Odiv__class_Omod(_1386046, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386046), _1386048), _1386050), _1386052))], (31882 ^ _782464) ^ [_1386181, _1386183, _1386185, _1386187] : [class_Divides_Osemiring__div(_1386181), -(c_Divides_Odiv__class_Omod(_1386181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386181), _1386183), _1386185), _1386187) = c_Divides_Odiv__class_Omod(_1386181, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386181), c_Divides_Odiv__class_Omod(_1386181, _1386183, _1386187)), c_Divides_Odiv__class_Omod(_1386181, _1386185, _1386187)), _1386187))], (31888 ^ _782464) ^ [_1386324, _1386326, _1386328, _1386330] : [class_Divides_Osemiring__div(_1386324), -(c_Divides_Odiv__class_Omod(_1386324, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386324), _1386326), _1386328), _1386330) = c_Divides_Odiv__class_Omod(_1386324, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386324), c_Divides_Odiv__class_Omod(_1386324, _1386326, _1386330)), _1386328), _1386330))], (31894 ^ _782464) ^ [_1386459, _1386461, _1386463, _1386465] : [class_Divides_Osemiring__div(_1386459), -(c_Divides_Odiv__class_Omod(_1386459, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386459), _1386461), _1386463), _1386465) = c_Divides_Odiv__class_Omod(_1386459, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386459), _1386461), c_Divides_Odiv__class_Omod(_1386459, _1386463, _1386465)), _1386465))], (31900 ^ _782464) ^ [_1386594, _1386596, _1386598] : [class_Divides_Osemiring__div(_1386594), -(c_Divides_Odiv__class_Omod(_1386594, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386594), _1386596), _1386598), _1386596) = c_Divides_Odiv__class_Omod(_1386594, _1386598, _1386596))], (31906 ^ _782464) ^ [_1386703, _1386705, _1386707] : [class_Divides_Osemiring__div(_1386703), -(c_Divides_Odiv__class_Omod(_1386703, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386703), _1386705), _1386707), _1386707) = c_Divides_Odiv__class_Omod(_1386703, _1386705, _1386707))], (31912 ^ _782464) ^ [_1386812, _1386814, _1386816, _1386818, _1386820, _1386822] : [class_Divides_Osemiring__div(_1386812), c_Divides_Odiv__class_Omod(_1386812, _1386814, _1386816) = c_Divides_Odiv__class_Omod(_1386812, _1386818, _1386816), c_Divides_Odiv__class_Omod(_1386812, _1386820, _1386816) = c_Divides_Odiv__class_Omod(_1386812, _1386822, _1386816), -(c_Divides_Odiv__class_Omod(_1386812, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386812), _1386814), _1386820), _1386816) = c_Divides_Odiv__class_Omod(_1386812, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386812), _1386818), _1386822), _1386816))], (31926 ^ _782464) ^ [_1387095, _1387097, _1387099, _1387101] : [class_Divides_Osemiring__div(_1387095), -(c_Divides_Odiv__class_Omod(_1387095, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387095), c_Divides_Odiv__class_Omod(_1387095, _1387097, _1387099)), _1387101), _1387099) = c_Divides_Odiv__class_Omod(_1387095, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387095), _1387097), _1387101), _1387099))], (31932 ^ _782464) ^ [_1387230, _1387232, _1387234, _1387236] : [class_Divides_Osemiring__div(_1387230), -(c_Divides_Odiv__class_Omod(_1387230, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387230), _1387232), _1387234), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387230), _1387236), _1387234)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387230), c_Divides_Odiv__class_Omod(_1387230, _1387232, _1387236)), _1387234))], (31938 ^ _782464) ^ [_1387373, _1387375, _1387377, _1387379] : [class_Divides_Osemiring__div(_1387373), -(c_Divides_Odiv__class_Omod(_1387373, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387373), _1387375), _1387377), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387373), _1387375), _1387379)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387373), _1387375), c_Divides_Odiv__class_Omod(_1387373, _1387377, _1387379)))], (31944 ^ _782464) ^ [_1387516, _1387518, _1387520, _1387522] : [class_Divides_Osemiring__div(_1387516), -(c_Divides_Odiv__class_Omod(_1387516, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387516), _1387518), _1387520), _1387522) = c_Divides_Odiv__class_Omod(_1387516, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387516), c_Divides_Odiv__class_Omod(_1387516, _1387518, _1387522)), c_Divides_Odiv__class_Omod(_1387516, _1387520, _1387522)), _1387522))], (31950 ^ _782464) ^ [_1387659, _1387661, _1387663, _1387665] : [class_Divides_Osemiring__div(_1387659), -(c_Divides_Odiv__class_Omod(_1387659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387659), _1387661), _1387663), _1387665) = c_Divides_Odiv__class_Omod(_1387659, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387659), c_Divides_Odiv__class_Omod(_1387659, _1387661, _1387665)), _1387663), _1387665))], (31956 ^ _782464) ^ [_1387794, _1387796, _1387798, _1387800] : [class_Divides_Osemiring__div(_1387794), -(c_Divides_Odiv__class_Omod(_1387794, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387794), _1387796), _1387798), _1387800) = c_Divides_Odiv__class_Omod(_1387794, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387794), _1387796), c_Divides_Odiv__class_Omod(_1387794, _1387798, _1387800)), _1387800))], (31962 ^ _782464) ^ [_1387929, _1387931, _1387933, _1387935] : [class_Divides_Oring__div(_1387929), -(c_Divides_Odiv__class_Omod(_1387929, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387929), _1387931), _1387933), _1387935) = c_Divides_Odiv__class_Omod(_1387929, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387929), _1387931), c_Divides_Odiv__class_Omod(_1387929, _1387933, _1387935)), _1387935))], (31968 ^ _782464) ^ [_1388064, _1388066, _1388068, _1388070] : [class_Divides_Oring__div(_1388064), -(c_Divides_Odiv__class_Omod(_1388064, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388064), _1388066), _1388068), _1388070) = c_Divides_Odiv__class_Omod(_1388064, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388064), c_Divides_Odiv__class_Omod(_1388064, _1388066, _1388070)), _1388068), _1388070))], (31974 ^ _782464) ^ [_1388199, _1388201, _1388203, _1388205] : [class_Divides_Oring__div(_1388199), -(c_Divides_Odiv__class_Omod(_1388199, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388199), _1388201), _1388203), _1388205) = c_Divides_Odiv__class_Omod(_1388199, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388199), c_Divides_Odiv__class_Omod(_1388199, _1388201, _1388205)), c_Divides_Odiv__class_Omod(_1388199, _1388203, _1388205)), _1388205))], (31980 ^ _782464) ^ [_1388342, _1388344, _1388346, _1388348, _1388350, _1388352] : [class_Divides_Oring__div(_1388342), c_Divides_Odiv__class_Omod(_1388342, _1388344, _1388346) = c_Divides_Odiv__class_Omod(_1388342, _1388348, _1388346), c_Divides_Odiv__class_Omod(_1388342, _1388350, _1388346) = c_Divides_Odiv__class_Omod(_1388342, _1388352, _1388346), -(c_Divides_Odiv__class_Omod(_1388342, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388342), _1388344), _1388350), _1388346) = c_Divides_Odiv__class_Omod(_1388342, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388342), _1388348), _1388352), _1388346))], (31994 ^ _782464) ^ [_1388625, _1388627, _1388629] : [class_Divides_Oring__div(_1388625), -(c_Divides_Odiv__class_Omod(_1388625, hAPP(c_Groups_Ouminus__class_Ouminus(_1388625), _1388627), _1388629) = c_Divides_Odiv__class_Omod(_1388625, hAPP(c_Groups_Ouminus__class_Ouminus(_1388625), c_Divides_Odiv__class_Omod(_1388625, _1388627, _1388629)), _1388629))], (32000 ^ _782464) ^ [_1388746, _1388748, _1388750, _1388752] : [class_Divides_Oring__div(_1388746), c_Divides_Odiv__class_Omod(_1388746, _1388748, _1388750) = c_Divides_Odiv__class_Omod(_1388746, _1388752, _1388750), -(c_Divides_Odiv__class_Omod(_1388746, hAPP(c_Groups_Ouminus__class_Ouminus(_1388746), _1388748), _1388750) = c_Divides_Odiv__class_Omod(_1388746, hAPP(c_Groups_Ouminus__class_Ouminus(_1388746), _1388752), _1388750))], (32010 ^ _782464) ^ [_1388933] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1388933, _1388933) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32012 ^ _782464) ^ [_1388960] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1388960) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32014 ^ _782464) ^ [_1388987, _1388989] : [class_Divides_Osemiring__div(_1388987), -(c_Divides_Odiv__class_Omod(_1388987, _1388989, _1388989) = c_Groups_Ozero__class_Ozero(_1388987))], (32020 ^ _782464) ^ [_1389074, _1389076] : [class_Divides_Osemiring__div(_1389074), -(c_Divides_Odiv__class_Omod(_1389074, _1389076, c_Groups_Ozero__class_Ozero(_1389074)) = _1389076)], (32026 ^ _782464) ^ [_1389161, _1389163] : [class_Divides_Osemiring__div(_1389161), -(c_Divides_Odiv__class_Omod(_1389161, c_Groups_Ozero__class_Ozero(_1389161), _1389163) = c_Groups_Ozero__class_Ozero(_1389161))], (32032 ^ _782464) ^ [_1389252, _1389254, _1389256] : [class_Divides_Osemiring__div(_1389252), -(c_Divides_Odiv__class_Omod(_1389252, c_Divides_Odiv__class_Omod(_1389252, _1389254, _1389256), _1389256) = c_Divides_Odiv__class_Omod(_1389252, _1389254, _1389256))], (32038 ^ _782464) ^ [_1389353, _1389355, _1389357] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389353), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1389355, _1389357)), _1389357) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389353), _1389355), _1389357))], (32040 ^ _782464) ^ [_1389404, _1389406, _1389408] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389404), _1389406), _1389408) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389404), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1389406, _1389408)), _1389408))], (32042 ^ _782464) ^ [_1389455, _1389457, _1389459] : [class_Divides_Osemiring__div(_1389455), -(c_Divides_Odiv__class_Omod(_1389455, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389455), _1389457), _1389459), _1389457) = c_Groups_Ozero__class_Ozero(_1389455))], (32048 ^ _782464) ^ [_1389560, _1389562, _1389564] : [class_Divides_Osemiring__div(_1389560), -(c_Divides_Odiv__class_Omod(_1389560, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389560), _1389562), _1389564), _1389564) = c_Groups_Ozero__class_Ozero(_1389560))], (32054 ^ _782464) ^ [_1389665, _1389667, _1389669, _1389671] : [class_Divides_Osemiring__div(_1389665), -(c_Divides_Odiv__class_Omod(_1389665, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389665), _1389667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389665), _1389669), _1389671)), _1389669) = c_Divides_Odiv__class_Omod(_1389665, _1389667, _1389669))], (32060 ^ _782464) ^ [_1389792, _1389794, _1389796, _1389798] : [class_Divides_Osemiring__div(_1389792), -(c_Divides_Odiv__class_Omod(_1389792, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389792), _1389794), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389792), _1389796), _1389798)), _1389798) = c_Divides_Odiv__class_Omod(_1389792, _1389794, _1389798))], (32066 ^ _782464) ^ [_1389919, _1389921] : [class_Divides_Osemiring__div(_1389919), -(c_Divides_Odiv__class_Omod(_1389919, _1389921, c_Groups_Oone__class_Oone(_1389919)) = c_Groups_Ozero__class_Ozero(_1389919))], (32072 ^ _782464) ^ [_1390010, _1390012, _1390014] : [class_Divides_Osemiring__div(_1390010), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1390010), c_Divides_Odiv__class_Omod(_1390010, _1390012, _1390014)), _1390014) = c_Groups_Ozero__class_Ozero(_1390010))], (32078 ^ _782464) ^ [_1390115, _1390117] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390115)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390115, _1390117)), _1390115)))], (32084 ^ _782464) ^ [_1390214, _1390216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390214)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390216)), -(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, _1390214, _1390216))))], (32094 ^ _782464) ^ [_1390363, _1390365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390363)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390365, _1390363)), _1390363)))], (32100 ^ _782464) ^ [_1390462, _1390464] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390462), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390462), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390464, _1390462))))], (32106 ^ _782464) ^ [_1390582, _1390584] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390582, _1390584) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1390582 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390584), 32109 ^ [_1390582, _1390584]))], (32113 ^ _782464) ^ [_1390687, _1390689] : [32114 ^ _782464 : [(32115 ^ _782464) ^ [_1390736] : [_1390687 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390689), _1390736)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390687, _1390689) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32119 ^ _782464) ^ [_1390798, _1390800] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390798), _1390800) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390798, _1390800) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32125 ^ _782464) ^ [_1390888, _1390890] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390888, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390890)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390888, _1390890) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32131 ^ _782464) ^ [_1390979, _1390981] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390979, _1390981)), _1390981) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32133 ^ _782464) ^ [_1391012] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1391012), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32135 ^ _782464) ^ [_1391038] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391038, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1391038)], (32137 ^ _782464) ^ [_1391067, _1391069, _1391071] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1391067), _1391069)), _1391071) = 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), _1391067), _1391071)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1391069), _1391071))), 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, _1391067, _1391071)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391069, _1391071))), _1391071)))], (32139 ^ _782464) ^ [_1391150, _1391152, _1391154] : [class_Divides_Osemiring__div(_1391150), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391150), c_Divides_Odiv__class_Omod(_1391150, _1391152, _1391154)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391150), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391150), _1391152), _1391154)), _1391154)) = _1391152)], (32145 ^ _782464) ^ [_1391283, _1391285, _1391287] : [class_Divides_Osemiring__div(_1391283), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391283), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391283), _1391285), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391283), _1391287), _1391285))), c_Divides_Odiv__class_Omod(_1391283, _1391287, _1391285)) = _1391287)], (32151 ^ _782464) ^ [_1391416, _1391418, _1391420] : [class_Divides_Osemiring__div(_1391416), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391416), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391416), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391416), _1391418), _1391420)), _1391420)), c_Divides_Odiv__class_Omod(_1391416, _1391418, _1391420)) = _1391418)], (32157 ^ _782464) ^ [_1391549, _1391551, _1391553, _1391555] : [class_Divides_Osemiring__div(_1391549), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391549), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391549), _1391551), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391549), _1391553), _1391551))), c_Divides_Odiv__class_Omod(_1391549, _1391553, _1391551))), _1391555) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391549), _1391553), _1391555))], (32163 ^ _782464) ^ [_1391716, _1391718, _1391720, _1391722] : [class_Divides_Osemiring__div(_1391716), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391716), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391716), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391716), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391716), _1391718), _1391720)), _1391720)), c_Divides_Odiv__class_Omod(_1391716, _1391718, _1391720))), _1391722) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391716), _1391718), _1391722))], (32169 ^ _782464) ^ [_1391883, _1391885] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1391883), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391885), _1391883)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391883, _1391885) = _1391883)], (32179 ^ _782464) ^ [_1392040, _1392042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392040), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 32182 ^ _782464 : [(32183 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392042, _1392040)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32185 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392040), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392042, _1392040))))]]], (32187 ^ _782464) ^ [_1392189, _1392191] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392189), 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, _1392191, _1392189)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32193 ^ _782464) ^ [_1392294, _1392296] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392294), _1392296)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392294, _1392296) = _1392294)], (32203 ^ _782464) ^ [_1392445, _1392447] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392445)), 32206 ^ _782464 : [(32207 ^ _782464) ^ [] : [-(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, _1392447, _1392445))))], (32209 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392447, _1392445)), _1392445)))]]], (32211 ^ _782464) ^ [_1392582, _1392584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392582)), -(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, _1392584, _1392582))))], (32217 ^ _782464) ^ [_1392684, _1392686] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392684, _1392686) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392684, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392686)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32223 ^ _782464) ^ [_1392777, _1392779] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392777, _1392779) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392777, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392779)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392777, _1392779)), _1392779))], (32229 ^ _782464) ^ [_1392845, _1392847] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392845, _1392847) = 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), _1392845), _1392847) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32235 ^ _782464) ^ [_1392938, _1392940] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392938, _1392940) = 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), _1392938), _1392940) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1392940), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392938, _1392940)))], (32241 ^ _782464) ^ [_1392997, _1392999] : [-(_1392997 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1392999), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1392997), _1392999))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392997, _1392999)))], (32243 ^ _782464) ^ [_1393044, _1393046, _1393048] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393044), _1393046)), _1393048) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393044), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393046), _1393048))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393044), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393046, _1393048))), _1393048)))], (32245 ^ _782464) ^ [_1393117, _1393119, _1393121] : [-(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), _1393117), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393119), _1393117))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393119, _1393117))), _1393121) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393119), _1393121))], (32247 ^ _782464) ^ [_1393178, _1393180, _1393182] : [-(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), _1393178), _1393180)), _1393180)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393178, _1393180))), _1393182) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393178), _1393182))], (32249 ^ _782464) ^ [_1393239, _1393241] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393239), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393241), _1393239)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1393241), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393241, _1393239)))], (32251 ^ _782464) ^ [_1393286, _1393288] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393286, _1393288) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1393286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393286), _1393288)), _1393288)))], (32253 ^ _782464) ^ [_1393333, _1393335] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393333), _1393335)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393333, _1393335) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393333), _1393335))], (32309 ^ _782464) ^ [_1394403, _1394405, _1394407] : [-(hBOOL(hAPP(_1394403, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1394405, _1394407)))), 32312 ^ _782464 : [(32313 ^ _782464) ^ [] : [-(_1394407 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32315 ^ _782464) ^ [] : [hBOOL(hAPP(_1394403, _1394405))]], 32318 ^ _782464 : [(32319 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394407)))], (32323 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32321 ^ [_1394403, _1394405, _1394407])))], (32325 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32321 ^ [_1394403, _1394405, _1394407]), _1394407)))], (32327 ^ _782464) ^ [] : [-(_1394405 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394407), 32320 ^ [_1394403, _1394405, _1394407])), 32321 ^ [_1394403, _1394405, _1394407]))], (32329 ^ _782464) ^ [] : [hBOOL(hAPP(_1394403, 32321 ^ [_1394403, _1394405, _1394407]))]], 32330 ^ _782464 : [(32331 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394407), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32335 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394407), 32333 ^ [_1394403, _1394405, _1394407])))], (32337 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 32333 ^ [_1394403, _1394405, _1394407]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32339 ^ _782464) ^ [] : [-(_1394405 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394407), 32332 ^ [_1394403, _1394405, _1394407])), 32333 ^ [_1394403, _1394405, _1394407]))], (32341 ^ _782464) ^ [] : [hBOOL(hAPP(_1394403, 32333 ^ [_1394403, _1394405, _1394407]))]]], (32263 ^ _782464) ^ [_1393526, _1393528, _1393530] : [hBOOL(hAPP(_1393526, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393528, _1393530))), 32266 ^ _782464 : [(32267 ^ _782464) ^ [] : [_1393530 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1393526, _1393528)))], (32273 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393530)), 32276 ^ _782464 : [(32277 ^ _782464) ^ [_1393856, _1393858] : [-(hBOOL(hAPP(_1393526, _1393856))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393856)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393856), _1393530)), _1393528 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393530), _1393858)), _1393856)]]], (32291 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393530), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 32294 ^ _782464 : [(32295 ^ _782464) ^ [_1394148, _1394150] : [-(hBOOL(hAPP(_1393526, _1394148))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393530), _1394148)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1394148), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1393528 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393530), _1394150)), _1394148)]]]]], (32345 ^ _782464) ^ [_1395115, _1395117, _1395119, _1395121] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395115)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395117)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395117), _1395119)), -(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), _1395119), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395121, _1395115))), _1395117))))], (32359 ^ _782464) ^ [_1395362, _1395364, _1395366, _1395368] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395362)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395364)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395364), _1395366)), -(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), _1395366), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395368, _1395362))), _1395364)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1395366), _1395362))))], (32373 ^ _782464) ^ [_1395627, _1395629, _1395631, _1395633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395627)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395629), _1395631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395631), 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), _1395629), _1395627)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1395629), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395633, _1395627))), _1395631))))], (32387 ^ _782464) ^ [_1395898, _1395900, _1395902, _1395904] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395900), _1395902)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395902), 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), _1395900), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395904, _1395898))), _1395902)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32401 ^ _782464) ^ [_1396157, _1396159, _1396161, _1396163] : [_1396157 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396159), _1396161)), _1396163), -(_1396159 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396157, _1396159) = _1396163), 32408 ^ _782464 : [(32409 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396159)))], (32411 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396163), _1396159))]], 32416 ^ _782464 : [(32417 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396159))], (32419 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396159), _1396163)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396163), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (32431 ^ _782464) ^ [_1396622, _1396624, _1396626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396622)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396624, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396626), _1396622)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396626), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396624), _1396626), _1396622))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396624, _1396626)))], (32437 ^ _782464) ^ [_1396776, _1396778] : [-(_1396776 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32440 ^ _782464 : [(32441 ^ _782464) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396778, _1396776) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396778), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396776)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396778), _1396776)))], (32447 ^ _782464) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396778, _1396776) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396778), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396776)) = 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), _1396778), _1396776))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (32453 ^ _782464) ^ [_1397049, _1397051] : [-(_1397049 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32456 ^ _782464 : [(32457 ^ _782464) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397051, _1397049) = 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), _1397051)), _1397049) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397051), _1397049)))], (32463 ^ _782464) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397051, _1397049) = 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), _1397051)), _1397049) = 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), _1397051), _1397049))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (32469 ^ _782464) ^ [_1397323, _1397325, _1397327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397323)), 32472 ^ _782464 : [(32491 ^ _782464) ^ [] : [32494 ^ _782464 : [(32495 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32493 ^ [_1397323, _1397325, _1397327])))], (32497 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32493 ^ [_1397323, _1397325, _1397327]), _1397323)))], (32499 ^ _782464) ^ [] : [-(_1397327 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1397323), 32492 ^ [_1397323, _1397325, _1397327])), 32493 ^ [_1397323, _1397325, _1397327]))], (32501 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1397325, 32492 ^ [_1397323, _1397325, _1397327]), 32493 ^ [_1397323, _1397325, _1397327]))]], -(hBOOL(hAPP(hAPP(_1397325, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397327), _1397323)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397327, _1397323))))], (32473 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1397325, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397327), _1397323)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397327, _1397323))), 32476 ^ _782464 : [(32477 ^ _782464) ^ [_1397524, _1397526] : [-(hBOOL(hAPP(hAPP(_1397325, _1397526), _1397524))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397524)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397524), _1397323)), _1397327 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1397323), _1397526)), _1397524)]]]]], (32505 ^ _782464) ^ [_1398047, _1398049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398047)), -(c_SMT_Oz3mod(_1398049, _1398047) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1398049, _1398047))], (32511 ^ _782464) ^ [_1398136, _1398138] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398136))), -(c_SMT_Oz3mod(_1398138, _1398136) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1398138, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1398136)))], (32517 ^ _782464) ^ [_1398186, _1398188, _1398190] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398186), _1398188)), 32523 ^ _782464 : [(32524 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398186), 32522 ^ [_1398186, _1398188, _1398190]), _1398188)))], (32526 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1398190, 32522 ^ [_1398186, _1398188, _1398190])))]], -(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(_1398186, tc_Nat_Onat), _1398190), _1398188))))], (32530 ^ _782464) ^ [_1398447, _1398449, _1398451] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398447), _1398449)), c_Fun_Oinj__on(_1398447, tc_fun(tc_fun(_1398447, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1398447, tc_fun(tc_prod(_1398447, _1398447), tc_HOL_Obool), tc_fun(tc_fun(_1398447, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398447, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1398447, _1398447), tc_HOL_Obool), tc_fun(tc_fun(_1398447, tc_HOL_Obool), tc_HOL_Obool)), _1398447), c_Equiv__Relations_Oquotient(_1398447)), hAPP(hAPP(c_COMBC(_1398447, tc_fun(_1398447, tc_HOL_Obool), tc_fun(_1398447, tc_HOL_Obool)), c_Set_Oinsert(_1398447)), c_Orderings_Obot__class_Obot(tc_fun(_1398447, tc_HOL_Obool))))), _1398451), _1398449), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1398447, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398447), _1398449), _1398451)) = hAPP(c_Finite__Set_Ocard(_1398447), _1398449))], (32540 ^ _782464) ^ [_1398796, _1398798] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398796), _1398798)), -(c_Fun_Obij__betw(_1398796, tc_Nat_Onat, 32543 ^ [_1398796, _1398798], _1398798, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1398796), _1398798))))], (32547 ^ _782464) ^ [_1398915, _1398917] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1398915), _1398917) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1398915, _1398917)), _1398917))], (32549 ^ _782464) ^ [_1398958, _1398960] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1398958), _1398960)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1398958, _1398960) = _1398958)], (32555 ^ _782464) ^ [_1399053, _1399055, _1399057] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399053, _1399055)), _1399057) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399053), _1399057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399055), _1399057)))], (32557 ^ _782464) ^ [_1399106, _1399108, _1399110] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399106), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399108, _1399110)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399106), _1399108), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399106), _1399110)))], (32559 ^ _782464) ^ [_1399159, _1399161] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399159, _1399161)), _1399159)))], (32561 ^ _782464) ^ [_1399193, _1399195] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399193), c_Orderings_Obot__class_Obot(tc_fun(_1399193, tc_HOL_Obool))), _1399195) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399193, tc_HOL_Obool), tc_HOL_Obool)))], (32563 ^ _782464) ^ [_1399257, _1399259, _1399261] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399257, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399257), _1399259), _1399261), -(_1399259 = c_Orderings_Obot__class_Obot(tc_fun(_1399257, tc_HOL_Obool)))], (32569 ^ _782464) ^ [_1399374, _1399376, _1399378] : [_1399376 = c_Orderings_Obot__class_Obot(tc_fun(_1399374, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399374, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399374), _1399376), _1399378))], (32575 ^ _782464) ^ [_1399515, _1399517, _1399519] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399515), _1399517), _1399519) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399515, tc_HOL_Obool), tc_HOL_Obool)), -(_1399517 = c_Orderings_Obot__class_Obot(tc_fun(_1399515, tc_HOL_Obool)))], (32581 ^ _782464) ^ [_1399632, _1399634, _1399636] : [_1399634 = c_Orderings_Obot__class_Obot(tc_fun(_1399632, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399632), _1399634), _1399636) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399632, tc_HOL_Obool), tc_HOL_Obool)))], (32587 ^ _782464) ^ [_1399755] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399755, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32589 ^ _782464) ^ [_1399791, _1399793] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399791, _1399793)) = _1399793, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399791), _1399793) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32595 ^ _782464) ^ [_1399890, _1399892] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399890, _1399892)) = _1399892), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399890), _1399892) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399890, _1399892)))], (32601 ^ _782464) ^ [_1399949, _1399951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1399949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399951, _1399949)), _1399949)))], (32607 ^ _782464) ^ [_1400063, _1400065] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400063, _1400065) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1400063 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1400065), 32610 ^ [_1400063, _1400065]))], (32614 ^ _782464) ^ [_1400168, _1400170] : [32615 ^ _782464 : [(32616 ^ _782464) ^ [_1400217] : [_1400168 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1400170), _1400217)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400168, _1400170) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32620 ^ _782464) ^ [_1400289, _1400291] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400289), _1400291)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400289, _1400291) = _1400289)], (32626 ^ _782464) ^ [_1400378, _1400380] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400378), _1400380))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400378, _1400380) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400378), _1400380), _1400380))], (32632 ^ _782464) ^ [_1400431, _1400433] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400431), _1400433))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400431, _1400433) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400431), _1400433), _1400433))], (32638 ^ _782464) ^ [_1400486, _1400488, _1400490] : [-(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), _1400486), _1400488)), _1400490), _1400488) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400490, _1400488))], (32640 ^ _782464) ^ [_1400533, _1400535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1400533), _1400535)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400535, _1400533) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400535), _1400533), _1400533))], (32646 ^ _782464) ^ [_1400648, _1400650] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400648), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400650)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400648, _1400650)))], (32648 ^ _782464) ^ [_1400690, _1400692] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400690, _1400692)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400690), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400692)))], (32650 ^ _782464) ^ [_1400732, _1400734, _1400736] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1400732), _1400734)), _1400736) = 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), _1400732), _1400736)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1400734), _1400736))), 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, _1400732, _1400736)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400734, _1400736))), _1400736)))], (32652 ^ _782464) ^ [_1400824, _1400826] : [_1400824 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1400826, _1400824) = _1400826)], (32658 ^ _782464) ^ [_1400901, _1400903] : [-(_1400901 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1400903, _1400901) = c_Nitpick_Onat__gcd(_1400901, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400903, _1400901)))], (32664 ^ _782464) ^ [_1400949, _1400951] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1400949)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400951, _1400949)), _1400949)))], (32670 ^ _782464) ^ [_1401048, _1401050, _1401052] : [-(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), _1401048), _1401050)), _1401052)), _1401050) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1401052), _1401050))], (32672 ^ _782464) ^ [_1401101, _1401103, _1401105] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401101, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401103), _1401105)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401103), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401101), _1401103), _1401105))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401101, _1401103)))], (32674 ^ _782464) ^ [_1401164, _1401166, _1401168] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401164), _1401166)), _1401168) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401164), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401166), _1401168))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401164), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401166, _1401168))), _1401168)))], (32676 ^ _782464) ^ [_1401237, _1401239] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401237), _1401239)), _1401239) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401237), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401237, _1401239)))], (32678 ^ _782464) ^ [_1401284, _1401286] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401284), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401286), _1401284)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401286), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401286, _1401284)))], (32680 ^ _782464) ^ [_1401331, _1401333] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401331, _1401333) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401331), _1401333)), _1401333)))], (32682 ^ _782464) ^ [_1401378, _1401380, _1401382, _1401384] : [c_Fun_Oinj__on(_1401378, tc_fun(tc_fun(_1401378, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1401378, tc_fun(tc_prod(_1401378, _1401378), tc_HOL_Obool), tc_fun(tc_fun(_1401378, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401378, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1401378, _1401378), tc_HOL_Obool), tc_fun(tc_fun(_1401378, tc_HOL_Obool), tc_HOL_Obool)), _1401378), c_Equiv__Relations_Oquotient(_1401378)), hAPP(hAPP(c_COMBC(_1401378, tc_fun(_1401378, tc_HOL_Obool), tc_fun(_1401378, tc_HOL_Obool)), c_Set_Oinsert(_1401378)), c_Orderings_Obot__class_Obot(tc_fun(_1401378, tc_HOL_Obool))))), _1401380), _1401382), hBOOL(hAPP(hAPP(c_member(_1401378), _1401384), _1401382)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401378), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401378, tc_HOL_Obool)), _1401382), hAPP(hAPP(c_Set_Oinsert(_1401378), _1401384), c_Orderings_Obot__class_Obot(tc_fun(_1401378, tc_HOL_Obool))))), _1401380) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1401378, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401378), _1401382), _1401380)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401378), hAPP(hAPP(c_Set_Oinsert(_1401378), _1401384), c_Orderings_Obot__class_Obot(tc_fun(_1401378, tc_HOL_Obool)))), _1401380)))], (32716 ^ _782464) ^ [_1402296, _1402298, _1402300] : [-(hBOOL(hAPP(_1402296, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1402298, _1402300)))), 32719 ^ _782464 : [(32720 ^ _782464) ^ [] : [-(_1402300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32722 ^ _782464) ^ [] : [hBOOL(hAPP(_1402296, _1402298))]], 32723 ^ _782464 : [(32724 ^ _782464) ^ [] : [_1402300 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32728 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32726 ^ [_1402296, _1402298, _1402300]), _1402300)))], (32730 ^ _782464) ^ [] : [-(_1402298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402300), 32725 ^ [_1402296, _1402298, _1402300])), 32726 ^ [_1402296, _1402298, _1402300]))], (32732 ^ _782464) ^ [] : [hBOOL(hAPP(_1402296, 32726 ^ [_1402296, _1402298, _1402300]))]]], (32692 ^ _782464) ^ [_1401863, _1401865, _1401867] : [hBOOL(hAPP(_1401863, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401865, _1401867))), 32695 ^ _782464 : [(32696 ^ _782464) ^ [] : [_1401867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1401863, _1401865)))], (32702 ^ _782464) ^ [] : [-(_1401867 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 32705 ^ _782464 : [(32706 ^ _782464) ^ [_1402111, _1402113] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402111), _1401867)), _1401865 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401867), _1402113)), _1402111), -(hBOOL(hAPP(_1401863, _1402111)))]]]]], (32736 ^ _782464) ^ [_1402705, _1402707, _1402709, _1402711] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1402705)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402707), _1402709)), -(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), _1402709), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1402711, _1402705))), _1402707)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402709), _1402705))))], (32746 ^ _782464) ^ [_1402910, _1402912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1402910)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402910), _1402912)), _1402910) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (32752 ^ _782464) ^ [_1403017, _1403019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403019)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1403017), hAPP(c_Int_Onat, _1403019)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1403017, _1403019)))], (32762 ^ _782464) ^ [_1403188, _1403190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403188)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403190)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1403188, _1403190)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1403188), hAPP(c_Int_Onat, _1403190)))], (32772 ^ _782464) ^ [_1403359, _1403361, _1403363] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403359), _1403361), _1403363) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403359, tc_fun(tc_fun(_1403359, tc_HOL_Obool), tc_HOL_Obool)), _1403361), hAPP(hAPP(c_COMBC(_1403359, tc_fun(tc_fun(_1403359, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1403359, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1403359, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1403359, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1403359, tc_HOL_Obool), tc_HOL_Obool)), _1403359), c_Set_Oinsert(tc_fun(_1403359, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1403359, tc_HOL_Obool), tc_fun(_1403359, tc_HOL_Obool), _1403359), c_Relation_OImage(_1403359, _1403359, _1403363)), hAPP(hAPP(c_COMBC(_1403359, tc_fun(_1403359, tc_HOL_Obool), tc_fun(_1403359, tc_HOL_Obool)), c_Set_Oinsert(_1403359)), c_Orderings_Obot__class_Obot(tc_fun(_1403359, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1403359, tc_HOL_Obool), tc_HOL_Obool)))))], (32774 ^ _782464) ^ [_1403515, _1403517, _1403519] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403515), hAPP(hAPP(c_Set_Oinsert(_1403515), _1403517), c_Orderings_Obot__class_Obot(tc_fun(_1403515, tc_HOL_Obool)))), _1403519) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1403515, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403515, _1403515, _1403519), hAPP(hAPP(c_Set_Oinsert(_1403515), _1403517), c_Orderings_Obot__class_Obot(tc_fun(_1403515, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1403515, tc_HOL_Obool), tc_HOL_Obool))))], (32776 ^ _782464) ^ [_1403602, _1403604, _1403606, _1403608] : [hBOOL(hAPP(hAPP(c_member(_1403602), _1403604), _1403606)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1403602, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403602, _1403602, _1403608), hAPP(hAPP(c_Set_Oinsert(_1403602), _1403604), c_Orderings_Obot__class_Obot(tc_fun(_1403602, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403602), _1403606), _1403608))))], (32782 ^ _782464) ^ [_1403773, _1403775, _1403777, _1403779] : [class_Groups_Ocomm__monoid__mult(_1403773), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403775), _1403777)), 32792 ^ _782464 : [(32793 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403775), 32791 ^ [_1403773, _1403775, _1403777, _1403779]), _1403777)))], (32795 ^ _782464) ^ [] : [hAPP(_1403779, 32791 ^ [_1403773, _1403775, _1403777, _1403779]) = c_Groups_Oone__class_Oone(_1403773)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403773, _1403775, c_Groups_Otimes__class_Otimes(_1403773)), _1403779), c_Groups_Oone__class_Oone(_1403773)), _1403777) = c_Groups_Oone__class_Oone(_1403773))], (32799 ^ _782464) ^ [_1404114, _1404116, _1404118, _1404120] : [-(hAPP(c_Relation_OImage(_1404114, _1404116, _1404118), _1404120) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404114, tc_fun(_1404116, tc_HOL_Obool)), _1404120), hAPP(hAPP(c_COMBB(tc_fun(_1404114, tc_HOL_Obool), tc_fun(_1404116, tc_HOL_Obool), _1404114), c_Relation_OImage(_1404114, _1404116, _1404118)), hAPP(hAPP(c_COMBC(_1404114, tc_fun(_1404114, tc_HOL_Obool), tc_fun(_1404114, tc_HOL_Obool)), c_Set_Oinsert(_1404114)), c_Orderings_Obot__class_Obot(tc_fun(_1404114, tc_HOL_Obool))))))], (32801 ^ _782464) ^ [_1404205, _1404207, _1404209, _1404211, _1404213, _1404215] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404205, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404207, _1404205, _1404209), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404211, tc_fun(_1404207, tc_HOL_Obool)), _1404213), _1404215))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404211, tc_fun(_1404205, tc_HOL_Obool)), _1404213), hAPP(hAPP(c_COMBB(tc_fun(_1404207, tc_HOL_Obool), tc_fun(_1404205, tc_HOL_Obool), _1404211), c_Relation_OImage(_1404207, _1404205, _1404209)), _1404215)))))], (32803 ^ _782464) ^ [_1404299, _1404301, _1404303, _1404305, _1404307] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404299, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404301, _1404299, _1404303), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404301, tc_HOL_Obool)), _1404305), _1404307))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404299, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404301, _1404299, _1404303), _1404305)), hAPP(c_Relation_OImage(_1404301, _1404299, _1404303), _1404307)))))], (32805 ^ _782464) ^ [_1404383, _1404385, _1404387, _1404389, _1404391, _1404393] : [-(hAPP(c_Relation_OImage(_1404383, _1404385, _1404387), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404389, tc_fun(_1404383, tc_HOL_Obool)), _1404391), _1404393)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404389, tc_fun(_1404385, tc_HOL_Obool)), _1404391), hAPP(hAPP(c_COMBB(tc_fun(_1404383, tc_HOL_Obool), tc_fun(_1404385, tc_HOL_Obool), _1404389), c_Relation_OImage(_1404383, _1404385, _1404387)), _1404393)))], (32807 ^ _782464) ^ [_1404467, _1404469, _1404471] : [-(hAPP(c_Relation_OImage(_1404467, _1404469, _1404471), c_Orderings_Obot__class_Obot(tc_fun(_1404467, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1404469, tc_HOL_Obool)))], (32809 ^ _782464) ^ [_1404511, _1404513, _1404515, _1404517, _1404519, _1404521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1404511, _1404513), tc_HOL_Obool)), _1404515), _1404517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404511, tc_HOL_Obool)), _1404519), _1404521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404513, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404511, _1404513, _1404515), _1404519)), hAPP(c_Relation_OImage(_1404511, _1404513, _1404517), _1404521))))], (32819 ^ _782464) ^ [_1404750, _1404752, _1404754, _1404756, _1404758] : [-(hAPP(c_Relation_OImage(_1404750, _1404752, _1404754), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404750, tc_HOL_Obool)), _1404756), _1404758)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404752, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404750, _1404752, _1404754), _1404756)), hAPP(c_Relation_OImage(_1404750, _1404752, _1404754), _1404758)))], (32821 ^ _782464) ^ [_1404824, _1404826, _1404828, _1404830, _1404832] : [-(hAPP(c_Relation_OImage(_1404824, _1404826, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1404824, _1404826), tc_HOL_Obool)), _1404828), _1404830)), _1404832) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404826, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404824, _1404826, _1404828), _1404832)), hAPP(c_Relation_OImage(_1404824, _1404826, _1404830), _1404832)))], (32823 ^ _782464) ^ [_1404901, _1404903, _1404905, _1404907] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1404901, tc_HOL_Obool)), _1404903), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1404901), _1404905), _1404907))), 32827 ^ _782464 : [(32828 ^ _782464) ^ [] : [-(_1404903 = hAPP(c_Relation_OImage(_1404901, _1404901, _1404907), hAPP(hAPP(c_Set_Oinsert(_1404901), 32826 ^ [_1404901, _1404903, _1404905, _1404907]), c_Orderings_Obot__class_Obot(tc_fun(_1404901, tc_HOL_Obool)))))], (32830 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404901), 32826 ^ [_1404901, _1404903, _1404905, _1404907]), _1404905)))]]], (32832 ^ _782464) ^ [_1405129, _1405131, _1405133] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1405129, _1405131) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1405133, _1405131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1405133), _1405129)), -(_1405129 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405133), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1405131), 32839 ^ [_1405129, _1405131, _1405133])))], (32843 ^ _782464) ^ [_1405326, _1405328] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1405326), _1405328)), 32849 ^ _782464 : [(32850 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405326), 32848 ^ [_1405326, _1405328]), _1405328)))], (32852 ^ _782464) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1405326), _1405328) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32856 ^ _782464) ^ [_1405526, _1405528, _1405530] : [32858 ^ _782464 : [(32859 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32857 ^ [_1405526, _1405528, _1405530]), _1405526)))], (32861 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1405528, 32857 ^ [_1405526, _1405528, _1405530])))], (32863 ^ _782464) ^ [] : [hBOOL(hAPP(_1405528, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 32857 ^ [_1405526, _1405528, _1405530]), _1405526)))]], hBOOL(hAPP(_1405528, _1405530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405530), _1405526)), -(hBOOL(hAPP(_1405528, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32875 ^ _782464) ^ [_1405888, _1405890, _1405892] : [_1405888 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1405890, _1405890), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1405890, _1405890), tc_HOL_Obool)), _1405888), _1405892)))], (32881 ^ _782464) ^ [_1406009, _1406011, _1406013, _1406015, _1406017, _1406019] : [class_Groups_Oab__semigroup__mult(_1406009), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406011), _1406013)), 32891 ^ _782464 : [(32892 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406011), 32890 ^ [_1406009, _1406011, _1406013, _1406015, _1406017, _1406019]), _1406013)))], (32894 ^ _782464) ^ [] : [hAPP(_1406015, 32890 ^ [_1406009, _1406011, _1406013, _1406015, _1406017, _1406019]) = hAPP(_1406017, 32890 ^ [_1406009, _1406011, _1406013, _1406015, _1406017, _1406019])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406009, _1406011, c_Groups_Otimes__class_Otimes(_1406009)), _1406015), _1406019), _1406013) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1406009, _1406011, c_Groups_Otimes__class_Otimes(_1406009)), _1406017), _1406019), _1406013))], (32898 ^ _782464) ^ [_1406414, _1406416, _1406418] : [class_Orderings_Olinorder(_1406414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406414), _1406416)), 32908 ^ _782464 : [(32909 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406414), 32907 ^ [_1406414, _1406416, _1406418]), _1406416)))], (32911 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406414), 32907 ^ [_1406414, _1406416, _1406418]), _1406418))]], hBOOL(hAPP(hAPP(c_member(_1406414), _1406418), _1406416)), -(c_Big__Operators_Olinorder__class_OMax(_1406414, _1406416) = _1406418)], (32919 ^ _782464) ^ [_1406786, _1406788, _1406790] : [class_Orderings_Olinorder(_1406786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406786), _1406788)), 32929 ^ _782464 : [(32930 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406786), 32928 ^ [_1406786, _1406788, _1406790]), _1406788)))], (32932 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406786), _1406790), 32928 ^ [_1406786, _1406788, _1406790]))]], hBOOL(hAPP(hAPP(c_member(_1406786), _1406790), _1406788)), -(c_Big__Operators_Olinorder__class_OMin(_1406786, _1406788) = _1406790)], (32940 ^ _782464) ^ [_1407158] : [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), _1407158))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407158) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407158)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32946 ^ _782464) ^ [_1407273, _1407275] : [class_Int_Onumber__ring(_1407273), 32949 ^ _782464 : [(32950 ^ _782464) ^ [] : [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), _1407275))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407273), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407275)) = hAPP(c_Int_Onumber__class_Onumber__of(_1407273), _1407275))], (32956 ^ _782464) ^ [] : [-(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), _1407275)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407273), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407275)) = c_Groups_Ozero__class_Ozero(_1407273))]]], (32962 ^ _782464) ^ [_1407513, _1407515] : [class_Int_Onumber__ring(_1407513), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407513), _1407515) = hAPP(c_Int_Oring__1__class_Oof__int(_1407513), _1407515))], (32968 ^ _782464) ^ [_1407608, _1407610, _1407612] : [class_Int_Onumber__ring(_1407608), class_Int_Oring__char__0(_1407608), 32975 ^ _782464 : [(32976 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1407608), _1407610) = hAPP(c_Int_Onumber__class_Onumber__of(_1407608), _1407612), -(_1407610 = _1407612)], (32982 ^ _782464) ^ [] : [_1407610 = _1407612, -(hAPP(c_Int_Onumber__class_Onumber__of(_1407608), _1407610) = hAPP(c_Int_Onumber__class_Onumber__of(_1407608), _1407612))]]], (32988 ^ _782464) ^ [_1407903, _1407905, _1407907] : [class_Int_Onumber(_1407903), 32991 ^ _782464 : [(32992 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1407903), _1407905) = _1407907, -(_1407907 = hAPP(c_Int_Onumber__class_Onumber__of(_1407903), _1407905))], (32998 ^ _782464) ^ [] : [_1407907 = hAPP(c_Int_Onumber__class_Onumber__of(_1407903), _1407905), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407903), _1407905) = _1407907)]]], (33004 ^ _782464) ^ [_1408144, _1408146] : [class_Int_Onumber__ring(_1408144), -(hAPP(c_Int_Oring__1__class_Oof__int(_1408144), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408146)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408144), _1408146))], (33010 ^ _782464) ^ [_1408245, _1408247] : [class_Int_Onumber__ring(_1408245), 33013 ^ _782464 : [(33014 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408247))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408245), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408247)) = c_Groups_Ozero__class_Ozero(_1408245))], (33020 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408247)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408245), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408247)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408245), _1408247))]]], (33026 ^ _782464) ^ [_1408485, _1408487, _1408489] : [class_Int_Onumber(_1408485), class_Orderings_Olinorder(_1408485), 33033 ^ _782464 : [(33034 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408485), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408487)), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408489))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408485), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408489)), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408487)))], (33040 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408485), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408489)), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408487)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408485), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408487)), hAPP(c_Int_Onumber__class_Onumber__of(_1408485), _1408489))))]]], (33046 ^ _782464) ^ [_1408812, _1408814, _1408816, _1408818] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408812), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408812), _1408814), _1408816)), hAPP(c_Int_Onumber__class_Onumber__of(_1408812), _1408818)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408812), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408812), _1408814), hAPP(c_Int_Onumber__class_Onumber__of(_1408812), _1408818))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408812), _1408816), hAPP(c_Int_Onumber__class_Onumber__of(_1408812), _1408818)))), class_Int_Onumber(_1408812), class_Rings_Osemiring(_1408812)], (33056 ^ _782464) ^ [_1409055, _1409057, _1409059, _1409061] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409055), hAPP(c_Int_Onumber__class_Onumber__of(_1409055), _1409057)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409055), _1409059), _1409061)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409055), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409055), hAPP(c_Int_Onumber__class_Onumber__of(_1409055), _1409057)), _1409059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409055), hAPP(c_Int_Onumber__class_Onumber__of(_1409055), _1409057)), _1409061))), class_Int_Onumber(_1409055), class_Rings_Osemiring(_1409055)], (33066 ^ _782464) ^ [_1409298, _1409300, _1409302, _1409304] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409298), hAPP(c_Int_Onumber__class_Onumber__of(_1409298), _1409300)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409298), _1409302), _1409304)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409298), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409298), hAPP(c_Int_Onumber__class_Onumber__of(_1409298), _1409300)), _1409302)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409298), hAPP(c_Int_Onumber__class_Onumber__of(_1409298), _1409300)), _1409304))), class_Int_Onumber(_1409298), class_Rings_Oring(_1409298)], (33076 ^ _782464) ^ [_1409541, _1409543, _1409545, _1409547] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409541), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409541), _1409543), _1409545)), hAPP(c_Int_Onumber__class_Onumber__of(_1409541), _1409547)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409541), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409541), _1409543), hAPP(c_Int_Onumber__class_Onumber__of(_1409541), _1409547))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409541), _1409545), hAPP(c_Int_Onumber__class_Onumber__of(_1409541), _1409547)))), class_Int_Onumber(_1409541), class_Rings_Oring(_1409541)], (33086 ^ _782464) ^ [_1409784, _1409786, _1409788] : [class_Int_Onumber__ring(_1409784), class_Rings_Olinordered__idom(_1409784), 33093 ^ _782464 : [(33094 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409784), hAPP(c_Int_Onumber__class_Onumber__of(_1409784), _1409786)), hAPP(c_Int_Onumber__class_Onumber__of(_1409784), _1409788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409786), _1409788)))], (33100 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409786), _1409788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409784), hAPP(c_Int_Onumber__class_Onumber__of(_1409784), _1409786)), hAPP(c_Int_Onumber__class_Onumber__of(_1409784), _1409788))))]]], (33106 ^ _782464) ^ [_1410115, _1410117, _1410119] : [class_Int_Onumber__ring(_1410115), class_Rings_Olinordered__idom(_1410115), 33113 ^ _782464 : [(33114 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410115), hAPP(c_Int_Onumber__class_Onumber__of(_1410115), _1410117)), hAPP(c_Int_Onumber__class_Onumber__of(_1410115), _1410119))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410117), _1410119)))], (33120 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410117), _1410119)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410115), hAPP(c_Int_Onumber__class_Onumber__of(_1410115), _1410117)), hAPP(c_Int_Onumber__class_Onumber__of(_1410115), _1410119))))]]], (33126 ^ _782464) ^ [_1410446, _1410448, _1410450] : [class_Int_Onumber(_1410446), class_Orderings_Oord(_1410446), 33133 ^ _782464 : [(33134 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410446), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410448)), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410450))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410446), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410448)), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410450)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410448))], (33140 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410446), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410448)), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410450)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410446), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410448)), hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410450)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410446), _1410450))]]], (33146 ^ _782464) ^ [_1410838, _1410840, _1410842] : [class_Int_Onumber(_1410838), class_Orderings_Oord(_1410838), 33153 ^ _782464 : [(33154 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410838), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410840)), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410842))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410838), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410840)), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410842)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410842))], (33160 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410838), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410840)), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410842)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410838), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410840)), hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410842)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410838), _1410840))]]], (33166 ^ _782464) ^ [_1411230, _1411232, _1411234] : [class_Int_Onumber__ring(_1411230), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411230), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411232), _1411234)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411230), hAPP(c_Int_Onumber__class_Onumber__of(_1411230), _1411232)), hAPP(c_Int_Onumber__class_Onumber__of(_1411230), _1411234)))], (33172 ^ _782464) ^ [_1411365, _1411367, _1411369] : [class_Int_Onumber__ring(_1411365), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411365), hAPP(c_Int_Onumber__class_Onumber__of(_1411365), _1411367)), hAPP(c_Int_Onumber__class_Onumber__of(_1411365), _1411369)) = hAPP(c_Int_Onumber__class_Onumber__of(_1411365), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411367), _1411369)))], (33178 ^ _782464) ^ [_1411500, _1411502, _1411504, _1411506] : [class_Int_Onumber__ring(_1411500), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411500), hAPP(c_Int_Onumber__class_Onumber__of(_1411500), _1411502)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411500), hAPP(c_Int_Onumber__class_Onumber__of(_1411500), _1411504)), _1411506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411500), hAPP(c_Int_Onumber__class_Onumber__of(_1411500), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411502), _1411504))), _1411506))], (33184 ^ _782464) ^ [_1411669, _1411671, _1411673] : [class_Int_Onumber__ring(_1411669), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411669), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411671), _1411673)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411669), hAPP(c_Int_Onumber__class_Onumber__of(_1411669), _1411671)), hAPP(c_Int_Onumber__class_Onumber__of(_1411669), _1411673)))], (33190 ^ _782464) ^ [_1411804, _1411806, _1411808] : [class_Int_Onumber__ring(_1411804), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411804), hAPP(c_Int_Onumber__class_Onumber__of(_1411804), _1411806)), hAPP(c_Int_Onumber__class_Onumber__of(_1411804), _1411808)) = hAPP(c_Int_Onumber__class_Onumber__of(_1411804), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411806), _1411808)))], (33196 ^ _782464) ^ [_1411939, _1411941, _1411943, _1411945] : [class_Int_Onumber__ring(_1411939), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411939), hAPP(c_Int_Onumber__class_Onumber__of(_1411939), _1411941)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411939), hAPP(c_Int_Onumber__class_Onumber__of(_1411939), _1411943)), _1411945)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411939), hAPP(c_Int_Onumber__class_Onumber__of(_1411939), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411941), _1411943))), _1411945))], (33202 ^ _782464) ^ [_1412108, _1412110, _1412112] : [class_Int_Onumber__ring(_1412108), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412108), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1412110), _1412112)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1412108), hAPP(c_Int_Onumber__class_Onumber__of(_1412108), _1412110)), hAPP(c_Int_Onumber__class_Onumber__of(_1412108), _1412112)))], (33208 ^ _782464) ^ [_1412243, _1412245] : [class_Int_Onumber__ring(_1412243), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412243), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412245)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1412243), hAPP(c_Int_Onumber__class_Onumber__of(_1412243), _1412245)))], (33214 ^ _782464) ^ [_1412354, _1412356] : [class_Int_Onumber__ring(_1412354), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1412354), hAPP(c_Int_Onumber__class_Onumber__of(_1412354), _1412356)) = hAPP(c_Int_Onumber__class_Onumber__of(_1412354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412356)))], (33220 ^ _782464) ^ [_1412465, _1412467] : [class_Int_Onumber__ring(_1412465), -(hBOOL(hAPP(hAPP(c_member(_1412465), hAPP(c_Int_Onumber__class_Onumber__of(_1412465), _1412467)), c_Int_Oring__1__class_OInts(_1412465))))], (33226 ^ _782464) ^ [_1412568, _1412570, _1412572, _1412574] : [class_Fields_Ofield__inverse__zero(_1412568), class_Int_Onumber(_1412568), 33233 ^ _782464 : [(33250 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1412568), _1412570), hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572)) = _1412574), 33253 ^ _782464 : [(33254 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572) = c_Groups_Ozero__class_Ozero(_1412568)], (33256 ^ _782464) ^ [] : [_1412570 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412568), _1412574), hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572))]], 33257 ^ _782464 : [(33258 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572) = c_Groups_Ozero__class_Ozero(_1412568))], (33260 ^ _782464) ^ [] : [_1412574 = c_Groups_Ozero__class_Ozero(_1412568)]]], (33234 ^ _782464) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1412568), _1412570), hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572)) = _1412574, 33237 ^ _782464 : [(33238 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572) = c_Groups_Ozero__class_Ozero(_1412568)), -(_1412570 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412568), _1412574), hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572)))], (33244 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412568), _1412572) = c_Groups_Ozero__class_Ozero(_1412568), -(_1412574 = c_Groups_Ozero__class_Ozero(_1412568))]]]]], (33264 ^ _782464) ^ [_1413178, _1413180, _1413182, _1413184] : [class_Fields_Ofield__inverse__zero(_1413178), class_Int_Onumber(_1413178), 33271 ^ _782464 : [(33288 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413178), _1413180), _1413182) = hAPP(c_Int_Onumber__class_Onumber__of(_1413178), _1413184)), 33291 ^ _782464 : [(33292 ^ _782464) ^ [] : [_1413182 = c_Groups_Ozero__class_Ozero(_1413178)], (33294 ^ _782464) ^ [] : [_1413180 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413178), hAPP(c_Int_Onumber__class_Onumber__of(_1413178), _1413184)), _1413182)]], 33295 ^ _782464 : [(33296 ^ _782464) ^ [] : [-(_1413182 = c_Groups_Ozero__class_Ozero(_1413178))], (33298 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413178), _1413184) = c_Groups_Ozero__class_Ozero(_1413178)]]], (33272 ^ _782464) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413178), _1413180), _1413182) = hAPP(c_Int_Onumber__class_Onumber__of(_1413178), _1413184), 33275 ^ _782464 : [(33276 ^ _782464) ^ [] : [-(_1413182 = c_Groups_Ozero__class_Ozero(_1413178)), -(_1413180 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413178), hAPP(c_Int_Onumber__class_Onumber__of(_1413178), _1413184)), _1413182))], (33282 ^ _782464) ^ [] : [_1413182 = c_Groups_Ozero__class_Ozero(_1413178), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413178), _1413184) = c_Groups_Ozero__class_Ozero(_1413178))]]]]], (33302 ^ _782464) ^ [_1413773, _1413775, _1413777, _1413779] : [class_Fields_Ofield__inverse__zero(_1413773), class_Int_Onumber(_1413773), 33309 ^ _782464 : [(33326 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1413773), _1413775) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413773), _1413777), _1413779)), 33329 ^ _782464 : [(33330 ^ _782464) ^ [] : [_1413779 = c_Groups_Ozero__class_Ozero(_1413773)], (33332 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413773), hAPP(c_Int_Onumber__class_Onumber__of(_1413773), _1413775)), _1413779) = _1413777]], 33333 ^ _782464 : [(33334 ^ _782464) ^ [] : [-(_1413779 = c_Groups_Ozero__class_Ozero(_1413773))], (33336 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413773), _1413775) = c_Groups_Ozero__class_Ozero(_1413773)]]], (33310 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413773), _1413775) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413773), _1413777), _1413779), 33313 ^ _782464 : [(33314 ^ _782464) ^ [] : [-(_1413779 = c_Groups_Ozero__class_Ozero(_1413773)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413773), hAPP(c_Int_Onumber__class_Onumber__of(_1413773), _1413775)), _1413779) = _1413777)], (33320 ^ _782464) ^ [] : [_1413779 = c_Groups_Ozero__class_Ozero(_1413773), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413773), _1413775) = c_Groups_Ozero__class_Ozero(_1413773))]]]]], (33340 ^ _782464) ^ [_1414368, _1414370, _1414372, _1414374] : [class_Fields_Ofield__inverse__zero(_1414368), class_Int_Onumber(_1414368), 33347 ^ _782464 : [(33364 ^ _782464) ^ [] : [-(_1414370 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1414368), _1414372), hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374))), 33367 ^ _782464 : [(33368 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374) = c_Groups_Ozero__class_Ozero(_1414368)], (33370 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414368), _1414370), hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374)) = _1414372]], 33371 ^ _782464 : [(33372 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374) = c_Groups_Ozero__class_Ozero(_1414368))], (33374 ^ _782464) ^ [] : [_1414370 = c_Groups_Ozero__class_Ozero(_1414368)]]], (33348 ^ _782464) ^ [] : [_1414370 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1414368), _1414372), hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374)), 33351 ^ _782464 : [(33352 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374) = c_Groups_Ozero__class_Ozero(_1414368)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414368), _1414370), hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374)) = _1414372)], (33358 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1414368), _1414374) = c_Groups_Ozero__class_Ozero(_1414368), -(_1414370 = c_Groups_Ozero__class_Ozero(_1414368))]]]]], (33378 ^ _782464) ^ [_1414978, _1414980, _1414982, _1414984] : [class_Int_Onumber__ring(_1414978), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414978), hAPP(c_Int_Onumber__class_Onumber__of(_1414978), _1414980)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414978), hAPP(c_Int_Onumber__class_Onumber__of(_1414978), _1414982)), _1414984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414978), hAPP(c_Int_Onumber__class_Onumber__of(_1414978), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414980), _1414982))), _1414984))], (33384 ^ _782464) ^ [_1415147, _1415149, _1415151] : [class_Int_Onumber__ring(_1415147), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415147), hAPP(c_Groups_Ouminus__class_Ouminus(_1415147), hAPP(c_Int_Onumber__class_Onumber__of(_1415147), _1415149))), _1415151) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415147), hAPP(c_Int_Onumber__class_Onumber__of(_1415147), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1415149))), _1415151))], (33390 ^ _782464) ^ [_1415292, _1415294, _1415296] : [class_Int_Onumber__ring(_1415292), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1415292), hAPP(c_Int_Onumber__class_Onumber__of(_1415292), _1415294)), hAPP(c_Int_Onumber__class_Onumber__of(_1415292), _1415296)) = hAPP(c_Int_Onumber__class_Onumber__of(_1415292), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415294), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1415296))))], (33396 ^ _782464) ^ [_1415433, _1415435, _1415437, _1415439] : [class_Fields_Olinordered__field__inverse__zero(_1415433), class_Int_Onumber(_1415433), 33403 ^ _782464 : [(33430 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415433), _1415435), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))), _1415439))), 33433 ^ _782464 : [(33434 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), c_Groups_Ozero__class_Ozero(_1415433)), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))))], (33436 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), _1415435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415433), _1415439), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))))]], 33437 ^ _782464 : [(33438 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), c_Groups_Ozero__class_Ozero(_1415433)), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)))], (33440 ^ _782464) ^ [] : [33441 ^ _782464 : [(33442 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)), c_Groups_Ozero__class_Ozero(_1415433))))], (33444 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415433), _1415439), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))), _1415435))]], 33445 ^ _782464 : [(33446 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)), c_Groups_Ozero__class_Ozero(_1415433)))], (33448 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), c_Groups_Ozero__class_Ozero(_1415433)), _1415439))]]]]], (33404 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415433), _1415435), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))), _1415439)), 33407 ^ _782464 : [(33408 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), c_Groups_Ozero__class_Ozero(_1415433)), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), _1415435), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415433), _1415439), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)))))], (33414 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), c_Groups_Ozero__class_Ozero(_1415433)), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)))), 33417 ^ _782464 : [(33418 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)), c_Groups_Ozero__class_Ozero(_1415433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415433), _1415439), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437))), _1415435)))], (33424 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), hAPP(c_Int_Onumber__class_Onumber__of(_1415433), _1415437)), c_Groups_Ozero__class_Ozero(_1415433)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415433), c_Groups_Ozero__class_Ozero(_1415433)), _1415439)))]]]]]]], (33452 ^ _782464) ^ [_1416547, _1416549, _1416551, _1416553] : [class_Fields_Olinordered__field__inverse__zero(_1416547), class_Int_Onumber(_1416547), 33459 ^ _782464 : [(33486 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1416547), _1416549), _1416551)), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553)))), 33489 ^ _782464 : [(33490 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), c_Groups_Ozero__class_Ozero(_1416547)), _1416551)))], (33492 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), _1416549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416547), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553)), _1416551)))]], 33493 ^ _782464 : [(33494 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), c_Groups_Ozero__class_Ozero(_1416547)), _1416551))], (33496 ^ _782464) ^ [] : [33497 ^ _782464 : [(33498 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), _1416551), c_Groups_Ozero__class_Ozero(_1416547))))], (33500 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416547), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553)), _1416551)), _1416549))]], 33501 ^ _782464 : [(33502 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), _1416551), c_Groups_Ozero__class_Ozero(_1416547)))], (33504 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), c_Groups_Ozero__class_Ozero(_1416547)), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553)))]]]]], (33460 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1416547), _1416549), _1416551)), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553))), 33463 ^ _782464 : [(33464 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), c_Groups_Ozero__class_Ozero(_1416547)), _1416551)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), _1416549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416547), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553)), _1416551))))], (33470 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), c_Groups_Ozero__class_Ozero(_1416547)), _1416551))), 33473 ^ _782464 : [(33474 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), _1416551), c_Groups_Ozero__class_Ozero(_1416547))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416547), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553)), _1416551)), _1416549)))], (33480 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), _1416551), c_Groups_Ozero__class_Ozero(_1416547)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416547), c_Groups_Ozero__class_Ozero(_1416547)), hAPP(c_Int_Onumber__class_Onumber__of(_1416547), _1416553))))]]]]]]], (33508 ^ _782464) ^ [_1417616, _1417618, _1417620, _1417622] : [class_Fields_Olinordered__field__inverse__zero(_1417616), class_Int_Onumber(_1417616), 33515 ^ _782464 : [(33542 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417616), _1417620), _1417622)))), 33545 ^ _782464 : [(33546 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), c_Groups_Ozero__class_Ozero(_1417616)), _1417622)))], (33548 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), _1417622)), _1417620))]], 33549 ^ _782464 : [(33550 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), c_Groups_Ozero__class_Ozero(_1417616)), _1417622))], (33552 ^ _782464) ^ [] : [33553 ^ _782464 : [(33554 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), _1417622), c_Groups_Ozero__class_Ozero(_1417616))))], (33556 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), _1417620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), _1417622)))]], 33557 ^ _782464 : [(33558 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), _1417622), c_Groups_Ozero__class_Ozero(_1417616)))], (33560 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), c_Groups_Ozero__class_Ozero(_1417616)))]]]]], (33516 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417616), _1417620), _1417622))), 33519 ^ _782464 : [(33520 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), c_Groups_Ozero__class_Ozero(_1417616)), _1417622)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), _1417622)), _1417620)))], (33526 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), c_Groups_Ozero__class_Ozero(_1417616)), _1417622))), 33529 ^ _782464 : [(33530 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), _1417622), c_Groups_Ozero__class_Ozero(_1417616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), _1417620), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), _1417622))))], (33536 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), _1417622), c_Groups_Ozero__class_Ozero(_1417616)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417616), hAPP(c_Int_Onumber__class_Onumber__of(_1417616), _1417618)), c_Groups_Ozero__class_Ozero(_1417616))))]]]]]]], (33564 ^ _782464) ^ [_1418685, _1418687, _1418689, _1418691] : [class_Fields_Olinordered__field__inverse__zero(_1418685), class_Int_Onumber(_1418685), 33571 ^ _782464 : [(33598 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), _1418687), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418685), _1418689), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691))))), 33601 ^ _782464 : [(33602 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), c_Groups_Ozero__class_Ozero(_1418685)), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691))))], (33604 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418685), _1418687), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691))), _1418689))]], 33605 ^ _782464 : [(33606 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), c_Groups_Ozero__class_Ozero(_1418685)), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)))], (33608 ^ _782464) ^ [] : [33609 ^ _782464 : [(33610 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)), c_Groups_Ozero__class_Ozero(_1418685))))], (33612 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), _1418689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418685), _1418687), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691))))]], 33613 ^ _782464 : [(33614 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)), c_Groups_Ozero__class_Ozero(_1418685)))], (33616 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), _1418687), c_Groups_Ozero__class_Ozero(_1418685)))]]]]], (33572 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), _1418687), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418685), _1418689), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)))), 33575 ^ _782464 : [(33576 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), c_Groups_Ozero__class_Ozero(_1418685)), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418685), _1418687), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691))), _1418689)))], (33582 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), c_Groups_Ozero__class_Ozero(_1418685)), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)))), 33585 ^ _782464 : [(33586 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)), c_Groups_Ozero__class_Ozero(_1418685))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), _1418689), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418685), _1418687), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)))))], (33592 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), hAPP(c_Int_Onumber__class_Onumber__of(_1418685), _1418691)), c_Groups_Ozero__class_Ozero(_1418685)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418685), _1418687), c_Groups_Ozero__class_Ozero(_1418685))))]]]]]]], (33620 ^ _782464) ^ [_1419799, _1419801] : [class_Int_Onumber__ring(_1419799), class_Rings_Olinordered__idom(_1419799), 33627 ^ _782464 : [(33628 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419799), hAPP(c_Int_Onumber__class_Onumber__of(_1419799), _1419801)), c_Groups_Ozero__class_Ozero(_1419799))), -(hAPP(c_Groups_Oabs__class_Oabs(_1419799), hAPP(c_Int_Onumber__class_Onumber__of(_1419799), _1419801)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1419799), hAPP(c_Int_Onumber__class_Onumber__of(_1419799), _1419801)))], (33634 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419799), hAPP(c_Int_Onumber__class_Onumber__of(_1419799), _1419801)), c_Groups_Ozero__class_Ozero(_1419799)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1419799), hAPP(c_Int_Onumber__class_Onumber__of(_1419799), _1419801)) = hAPP(c_Int_Onumber__class_Onumber__of(_1419799), _1419801))]]], (33640 ^ _782464) ^ [_1420151, _1420153, _1420155, _1420157] : [class_Int_Onumber__ring(_1420151), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420151), hAPP(c_Int_Onumber__class_Onumber__of(_1420151), _1420153)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1420151), _1420155), hAPP(c_Int_Onumber__class_Onumber__of(_1420151), _1420157))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420151), hAPP(c_Int_Onumber__class_Onumber__of(_1420151), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1420153), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1420157)))), _1420155))], (33646 ^ _782464) ^ [_1420326, _1420328, _1420330, _1420332] : [class_Fields_Olinordered__field__inverse__zero(_1420326), class_Int_Onumber(_1420326), 33653 ^ _782464 : [(33680 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420326), _1420328), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))), _1420332))), 33683 ^ _782464 : [(33684 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), c_Groups_Ozero__class_Ozero(_1420326)), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))))], (33686 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), _1420328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420326), _1420332), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))))]], 33687 ^ _782464 : [(33688 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), c_Groups_Ozero__class_Ozero(_1420326)), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)))], (33690 ^ _782464) ^ [] : [33691 ^ _782464 : [(33692 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)), c_Groups_Ozero__class_Ozero(_1420326))))], (33694 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420326), _1420332), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))), _1420328))]], 33695 ^ _782464 : [(33696 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)), c_Groups_Ozero__class_Ozero(_1420326)))], (33698 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), c_Groups_Ozero__class_Ozero(_1420326)), _1420332))]]]]], (33654 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420326), _1420328), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))), _1420332)), 33657 ^ _782464 : [(33658 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), c_Groups_Ozero__class_Ozero(_1420326)), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), _1420328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420326), _1420332), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)))))], (33664 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), c_Groups_Ozero__class_Ozero(_1420326)), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)))), 33667 ^ _782464 : [(33668 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)), c_Groups_Ozero__class_Ozero(_1420326))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420326), _1420332), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330))), _1420328)))], (33674 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420326), hAPP(c_Int_Onumber__class_Onumber__of(_1420326), _1420330)), c_Groups_Ozero__class_Ozero(_1420326)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420326), c_Groups_Ozero__class_Ozero(_1420326)), _1420332)))]]]]]]], (33702 ^ _782464) ^ [_1421440, _1421442, _1421444, _1421446] : [class_Fields_Olinordered__field__inverse__zero(_1421440), class_Int_Onumber(_1421440), 33709 ^ _782464 : [(33736 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421440), _1421442), _1421444)), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446)))), 33739 ^ _782464 : [(33740 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), c_Groups_Ozero__class_Ozero(_1421440)), _1421444)))], (33742 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), _1421442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421440), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446)), _1421444)))]], 33743 ^ _782464 : [(33744 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), c_Groups_Ozero__class_Ozero(_1421440)), _1421444))], (33746 ^ _782464) ^ [] : [33747 ^ _782464 : [(33748 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), _1421444), c_Groups_Ozero__class_Ozero(_1421440))))], (33750 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421440), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446)), _1421444)), _1421442))]], 33751 ^ _782464 : [(33752 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), _1421444), c_Groups_Ozero__class_Ozero(_1421440)))], (33754 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), c_Groups_Ozero__class_Ozero(_1421440)), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446)))]]]]], (33710 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421440), _1421442), _1421444)), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446))), 33713 ^ _782464 : [(33714 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), c_Groups_Ozero__class_Ozero(_1421440)), _1421444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), _1421442), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421440), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446)), _1421444))))], (33720 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), c_Groups_Ozero__class_Ozero(_1421440)), _1421444))), 33723 ^ _782464 : [(33724 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), _1421444), c_Groups_Ozero__class_Ozero(_1421440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421440), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446)), _1421444)), _1421442)))], (33730 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421440), _1421444), c_Groups_Ozero__class_Ozero(_1421440)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421440), c_Groups_Ozero__class_Ozero(_1421440)), hAPP(c_Int_Onumber__class_Onumber__of(_1421440), _1421446))))]]]]]]], (33758 ^ _782464) ^ [_1422509, _1422511, _1422513, _1422515] : [class_Fields_Olinordered__field__inverse__zero(_1422509), class_Int_Onumber(_1422509), 33765 ^ _782464 : [(33792 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422509), _1422513), _1422515)))), 33795 ^ _782464 : [(33796 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), c_Groups_Ozero__class_Ozero(_1422509)), _1422515)))], (33798 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), _1422515)), _1422513))]], 33799 ^ _782464 : [(33800 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), c_Groups_Ozero__class_Ozero(_1422509)), _1422515))], (33802 ^ _782464) ^ [] : [33803 ^ _782464 : [(33804 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), _1422515), c_Groups_Ozero__class_Ozero(_1422509))))], (33806 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), _1422513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), _1422515)))]], 33807 ^ _782464 : [(33808 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), _1422515), c_Groups_Ozero__class_Ozero(_1422509)))], (33810 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), c_Groups_Ozero__class_Ozero(_1422509)))]]]]], (33766 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422509), _1422513), _1422515))), 33769 ^ _782464 : [(33770 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), c_Groups_Ozero__class_Ozero(_1422509)), _1422515)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), _1422515)), _1422513)))], (33776 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), c_Groups_Ozero__class_Ozero(_1422509)), _1422515))), 33779 ^ _782464 : [(33780 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), _1422515), c_Groups_Ozero__class_Ozero(_1422509))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), _1422513), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), _1422515))))], (33786 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422509), _1422515), c_Groups_Ozero__class_Ozero(_1422509)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422509), hAPP(c_Int_Onumber__class_Onumber__of(_1422509), _1422511)), c_Groups_Ozero__class_Ozero(_1422509))))]]]]]]], (33814 ^ _782464) ^ [_1423578, _1423580, _1423582, _1423584] : [class_Fields_Olinordered__field__inverse__zero(_1423578), class_Int_Onumber(_1423578), 33821 ^ _782464 : [(33848 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), _1423580), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423578), _1423582), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584))))), 33851 ^ _782464 : [(33852 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), c_Groups_Ozero__class_Ozero(_1423578)), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584))))], (33854 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423578), _1423580), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584))), _1423582))]], 33855 ^ _782464 : [(33856 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), c_Groups_Ozero__class_Ozero(_1423578)), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)))], (33858 ^ _782464) ^ [] : [33859 ^ _782464 : [(33860 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)), c_Groups_Ozero__class_Ozero(_1423578))))], (33862 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), _1423582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423578), _1423580), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584))))]], 33863 ^ _782464 : [(33864 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)), c_Groups_Ozero__class_Ozero(_1423578)))], (33866 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), _1423580), c_Groups_Ozero__class_Ozero(_1423578)))]]]]], (33822 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), _1423580), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423578), _1423582), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)))), 33825 ^ _782464 : [(33826 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), c_Groups_Ozero__class_Ozero(_1423578)), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423578), _1423580), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584))), _1423582)))], (33832 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), c_Groups_Ozero__class_Ozero(_1423578)), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)))), 33835 ^ _782464 : [(33836 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)), c_Groups_Ozero__class_Ozero(_1423578))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), _1423582), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423578), _1423580), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)))))], (33842 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423578), hAPP(c_Int_Onumber__class_Onumber__of(_1423578), _1423584)), c_Groups_Ozero__class_Ozero(_1423578)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423578), _1423580), c_Groups_Ozero__class_Ozero(_1423578))))]]]]]]], (33870 ^ _782464) ^ [_1424698] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1424698))), -(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), _1424698)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33876 ^ _782464) ^ [_1424791] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1424791)))), -(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), _1424791)) = 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), _1424791))))], (33882 ^ _782464) ^ [_1424849] : [-(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), _1424849)) = 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), _1424849))))], (33884 ^ _782464) ^ [_1424887, _1424889, _1424891] : [class_Int_Onumber__ring(_1424887), 33887 ^ _782464 : [(33888 ^ _782464) ^ [] : [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), _1424889))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424887), hAPP(c_Int_Onumber__class_Onumber__of(_1424887), _1424891)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1424889))) = hAPP(hAPP(c_HOL_OLet(_1424887, _1424887), hAPP(hAPP(c_Power_Opower__class_Opower(_1424887), hAPP(c_Int_Onumber__class_Onumber__of(_1424887), _1424891)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424889))), hAPP(hAPP(c_COMBS(_1424887, _1424887, _1424887), hAPP(hAPP(c_COMBB(_1424887, tc_fun(_1424887, _1424887), _1424887), c_Groups_Otimes__class_Otimes(_1424887)), hAPP(c_Groups_Otimes__class_Otimes(_1424887), hAPP(c_Int_Onumber__class_Onumber__of(_1424887), _1424891)))), c_COMBI(_1424887))))], (33894 ^ _782464) ^ [] : [-(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), _1424889)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424887), hAPP(c_Int_Onumber__class_Onumber__of(_1424887), _1424891)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1424889))) = c_Groups_Oone__class_Oone(_1424887))]]], (33900 ^ _782464) ^ [_1425294, _1425296] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425294))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425294)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425296)) = 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), _1425296)))], (33906 ^ _782464) ^ [_1425411, _1425413] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425411)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425411)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425413)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425411)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425413))))], (33912 ^ _782464) ^ [_1425496, _1425498] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425496)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425498))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425496), _1425498)))], (33918 ^ _782464) ^ [_1425601, _1425603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425601), _1425603)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425601)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425603))))], (33924 ^ _782464) ^ [_1425712] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425712) = _1425712)], (33926 ^ _782464) ^ [_1425753, _1425755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425753)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425753), _1425755)))], (33932 ^ _782464) ^ [_1425858, _1425860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425858), _1425860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425858)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425860))))], (33938 ^ _782464) ^ [_1425969, _1425971] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425969)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425971)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1425969), _1425971)))], (33940 ^ _782464) ^ [_1426015, _1426017] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426015)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426017)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1426015), _1426017)))], (33942 ^ _782464) ^ [_1426061] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426061)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426061)))], (33944 ^ _782464) ^ [_1426108] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1426108)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426108))))], (33950 ^ _782464) ^ [_1426203] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426203))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1426203)))))], (33956 ^ _782464) ^ [_1426319, _1426321] : [c_Int_OBit1(_1426319) = c_Int_OBit1(_1426321), -(_1426319 = _1426321)], (33962 ^ _782464) ^ [_1426400, _1426402] : [_1426400 = _1426402, -(c_Int_OBit1(_1426400) = c_Int_OBit1(_1426402))], (33968 ^ _782464) ^ [_1426502, _1426504] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426502)), c_Int_OBit1(_1426504))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426502), _1426504)))], (33974 ^ _782464) ^ [_1426603, _1426605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426603), _1426605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426603)), c_Int_OBit1(_1426605))))], (33980 ^ _782464) ^ [_1426725, _1426727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426725)), c_Int_OBit1(_1426727))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426725), _1426727)))], (33986 ^ _782464) ^ [_1426826, _1426828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426826), _1426828)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426826)), c_Int_OBit1(_1426828))))], (33992 ^ _782464) ^ [_1426948, _1426950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1426948)), c_Int_OBit1(_1426950))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1426948), _1426950)))], (33998 ^ _782464) ^ [_1427049, _1427051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427049), _1427051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427049)), c_Int_OBit1(_1427051))))], (34004 ^ _782464) ^ [_1427171, _1427173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427171)), c_Int_OBit1(_1427173))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427171), _1427173)))], (34010 ^ _782464) ^ [_1427272, _1427274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427272), _1427274)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427272)), c_Int_OBit1(_1427274))))], (34016 ^ _782464) ^ [_1427379] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427379) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1427379))], (34018 ^ _782464) ^ [_1427420] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1427420)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427420), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34024 ^ _782464) ^ [_1427515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427515), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1427515)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34030 ^ _782464) ^ [_1427616] : [-(c_Int_OBit1(_1427616) = 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)), _1427616)), _1427616))], (34032 ^ _782464) ^ [_1427650] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427650)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427650))], (34034 ^ _782464) ^ [_1427682] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427682) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427682)))], (34036 ^ _782464) ^ [_1427720] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427720))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427720)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34042 ^ _782464) ^ [_1427809] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427809)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427809)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427809)), 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)))))], (34048 ^ _782464) ^ [_1427864, _1427866] : [class_Int_Onumber__ring(_1427864), -(hAPP(c_Int_Onumber__class_Onumber__of(_1427864), c_Int_OBit1(_1427866)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427864), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427864), c_Groups_Oone__class_Oone(_1427864)), hAPP(c_Int_Onumber__class_Onumber__of(_1427864), _1427866))), hAPP(c_Int_Onumber__class_Onumber__of(_1427864), _1427866)))], (34054 ^ _782464) ^ [_1428009, _1428011, _1428013] : [class_Int_Onumber__ring(_1428009), 34057 ^ _782464 : [(34058 ^ _782464) ^ [] : [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), _1428011))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428009), _1428013), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428011))) = hAPP(hAPP(c_HOL_OLet(_1428009, _1428009), hAPP(hAPP(c_Power_Opower__class_Opower(_1428009), _1428013), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428011))), hAPP(hAPP(c_COMBS(_1428009, _1428009, _1428009), hAPP(hAPP(c_COMBB(_1428009, tc_fun(_1428009, _1428009), _1428009), c_Groups_Otimes__class_Otimes(_1428009)), hAPP(c_Groups_Otimes__class_Otimes(_1428009), _1428013))), c_COMBI(_1428009))))], (34064 ^ _782464) ^ [] : [-(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), _1428011)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1428009), _1428013), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428011))) = c_Groups_Oone__class_Oone(_1428009))]]], (34070 ^ _782464) ^ [_1428376, _1428378] : [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), _1428376))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428378), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428376))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428378), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428376))), 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), _1428378))), c_COMBI(tc_Int_Oint))))], (34076 ^ _782464) ^ [_1428533, _1428535] : [-(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), _1428533)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428535), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428533))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (34082 ^ _782464) ^ [_1428587, _1428589] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428587)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428589)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428587), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428589))))], (34084 ^ _782464) ^ [_1428636] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428636))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428636) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34090 ^ _782464) ^ [_1428742, _1428744] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428742) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428744), 34093 ^ _782464 : [(34094 ^ _782464) ^ [] : [-(_1428742 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428744)))], (34096 ^ _782464) ^ [] : [-(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), _1428744))))]]], (34098 ^ _782464) ^ [_1428875, _1428877] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428875) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428877)), _1428875 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428877)), 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), _1428877)))], (34134 ^ _782464) ^ [_1429440, _1429442] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429440) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429442)), 34137 ^ _782464 : [(34138 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429440))))], (34140 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429442)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 34141 ^ _782464 : [(34142 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429440)))], (34144 ^ _782464) ^ [] : [34145 ^ _782464 : [(34146 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429442))))], (34148 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429440) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 34149 ^ _782464 : [(34150 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429442)))], (34152 ^ _782464) ^ [] : [_1429440 = _1429442]]]]], (34108 ^ _782464) ^ [_1429055, _1429057] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429055) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429057), 34111 ^ _782464 : [(34112 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429055))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429057)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34118 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429055)))), 34121 ^ _782464 : [(34122 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429057))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429055) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34128 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429057)))), -(_1429055 = _1429057)]]]]], (34156 ^ _782464) ^ [_1429853, _1429855, _1429857] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429853))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429853)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429855)), _1429857)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429855)), _1429857))], (34162 ^ _782464) ^ [_1429991, _1429993, _1429995] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429991)))), 34165 ^ _782464 : [(34166 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429993))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429991)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429993)), _1429995)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429991)), _1429995))], (34172 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429993)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429991)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429993)), _1429995)) = 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), _1429991), _1429993))), _1429995))]]], (34178 ^ _782464) ^ [_1430322] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430322))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430322)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34184 ^ _782464) ^ [_1430413] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430413)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430413)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430413))], (34190 ^ _782464) ^ [_1430472, _1430474] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430472))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430472), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430474)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34196 ^ _782464) ^ [_1430574, _1430576] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430574)))), 34199 ^ _782464 : [(34200 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430576))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430576)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430574))], (34206 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430576)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430576)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430576))))]]], (34212 ^ _782464) ^ [_1430856, _1430858] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430856))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430856)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430858)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34218 ^ _782464) ^ [_1430961, _1430963] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430961)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430961)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430963)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430961)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430963))))], (34224 ^ _782464) ^ [_1431040, _1431042] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431040))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431040)), _1431042) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1431042))], (34230 ^ _782464) ^ [_1431145, _1431147] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431145)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431145)), _1431147) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431145)), _1431147)))], (34236 ^ _782464) ^ [_1431218, _1431220] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431218))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431218)), _1431220)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1431220))], (34242 ^ _782464) ^ [_1431329, _1431331] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431329)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431329)), _1431331)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1431329))), _1431331))], (34248 ^ _782464) ^ [_1431404, _1431406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431404), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431406)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431404)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431406))], (34254 ^ _782464) ^ [_1431515, _1431517] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431515), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431517)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431515)) = 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), _1431517), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1431515)))), 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)))], (34260 ^ _782464) ^ [_1431588, _1431590] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431588)), hAPP(c_Nat_OSuc, _1431590)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431588))), 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)), _1431590)))))], (34262 ^ _782464) ^ [_1431645, _1431647] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431645)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431647)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431647))), 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), _1431645)), c_Int_Onat)))))], (34264 ^ _782464) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (34266 ^ _782464) ^ [_1431735] : [c_Int_OPls = c_Int_OBit1(_1431735)], (34268 ^ _782464) ^ [_1431769] : [c_Int_OBit1(_1431769) = c_Int_OPls], (34270 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (34272 ^ _782464) ^ [_1431812] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1431812), c_Int_OPls) = _1431812)], (34274 ^ _782464) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (34276 ^ _782464) ^ [_1431859] : [-(c_Int_Osucc(c_Int_Opred(_1431859)) = _1431859)], (34278 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (34280 ^ _782464) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34282 ^ _782464) ^ [_1431928] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1431928) = c_Int_OPls)], (34284 ^ _782464) ^ [_1431954] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1431954) = _1431954)], (34286 ^ _782464) ^ [_1431980] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1431980), c_Int_OPls) = _1431980)], (34288 ^ _782464) ^ [_1432009] : [class_Int_Onumber__ring(_1432009), -(hAPP(c_Int_Onumber__class_Onumber__of(_1432009), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1432009))], (34294 ^ _782464) ^ [_1432096] : [class_Int_Onumber__ring(_1432096), -(c_Groups_Ozero__class_Ozero(_1432096) = hAPP(c_Int_Onumber__class_Onumber__of(_1432096), c_Int_OPls))], (34300 ^ _782464) ^ [_1432183, _1432185] : [class_Int_Onumber__ring(_1432183), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432183), _1432185), hAPP(c_Int_Onumber__class_Onumber__of(_1432183), c_Int_OPls)) = _1432185)], (34306 ^ _782464) ^ [_1432284, _1432286] : [class_Int_Onumber__ring(_1432284), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432284), hAPP(c_Int_Onumber__class_Onumber__of(_1432284), c_Int_OPls)), _1432286) = _1432286)], (34312 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34314 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34316 ^ _782464) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (34318 ^ _782464) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (34320 ^ _782464) ^ [_1432475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432475)))], (34326 ^ _782464) ^ [_1432558] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432558)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432558))))], (34332 ^ _782464) ^ [_1432659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432659)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432659), c_Int_OPls)))], (34338 ^ _782464) ^ [_1432754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432754), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432754)), c_Int_OPls)))], (34344 ^ _782464) ^ [_1432855, _1432857] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1432855)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1432857)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1432855)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1432857), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1432855))))], (34350 ^ _782464) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (34352 ^ _782464) ^ [_1433012] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433012), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433012)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34358 ^ _782464) ^ [_1433109] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433109), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433109)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1433109)))], (34364 ^ _782464) ^ [_1433170] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433170), 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), _1433170)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34370 ^ _782464) ^ [_1433261] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433261), 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), _1433261)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1433261)))], (34376 ^ _782464) ^ [_1433328, _1433330] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433328), _1433330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1433328)), _1433330)))], (34382 ^ _782464) ^ [_1433425, _1433427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1433425)), _1433427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433425), _1433427)))], (34388 ^ _782464) ^ [_1433528] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1433528)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1433528))))], (34390 ^ _782464) ^ [_1433563] : [-(c_Int_Opred(_1433563) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1433563), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34392 ^ _782464) ^ [_1433600] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433600), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433600)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34398 ^ _782464) ^ [_1433697] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433697), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433697)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1433697)))], (34404 ^ _782464) ^ [_1433752, _1433754] : [class_Int_Onumber__ring(_1433752), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433752), hAPP(c_Int_Onumber__class_Onumber__of(_1433752), c_Int_OBit1(c_Int_OPls))), _1433754) = _1433754)], (34410 ^ _782464) ^ [_1433853, _1433855] : [class_Int_Onumber__ring(_1433853), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433853), _1433855), hAPP(c_Int_Onumber__class_Onumber__of(_1433853), c_Int_OBit1(c_Int_OPls))) = _1433855)], (34416 ^ _782464) ^ [_1433954, _1433956] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1433954), _1433956), hAPP(c_Int_Onumber__class_Onumber__of(_1433954), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1433954)), class_Fields_Ofield__inverse__zero(_1433954), class_Int_Onumber__ring(_1433954)], (34426 ^ _782464) ^ [_1434109] : [class_Int_Onumber__ring(_1434109), -(hAPP(c_Int_Onumber__class_Onumber__of(_1434109), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1434109))], (34432 ^ _782464) ^ [_1434196] : [class_Int_Onumber__ring(_1434196), -(c_Groups_Oone__class_Oone(_1434196) = hAPP(c_Int_Onumber__class_Onumber__of(_1434196), c_Int_OBit1(c_Int_OPls)))], (34438 ^ _782464) ^ [_1434295] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434295), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434295), c_Int_OPls)))], (34444 ^ _782464) ^ [_1434382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434382), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434382))], (34450 ^ _782464) ^ [_1434487] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434487) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434487), c_Int_OPls)))], (34456 ^ _782464) ^ [_1434574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434574), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434574) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34462 ^ _782464) ^ [] : [-(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))))], (34464 ^ _782464) ^ [_1434697] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1434697))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1434697)))], (34470 ^ _782464) ^ [_1434780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1434780)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1434780))))], (34476 ^ _782464) ^ [_1434881] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1434881)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434881), c_Int_OPls)))], (34482 ^ _782464) ^ [_1434976] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434976), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1434976)), c_Int_OPls)))], (34488 ^ _782464) ^ [_1435092, _1435094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435092)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435094))), 34491 ^ _782464 : [(34498 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435092), _1435094)))], (34492 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435092), _1435094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1435094)))]]], (34500 ^ _782464) ^ [_1435295, _1435297] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435295)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435297)))), 34503 ^ _782464 : [(34504 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435295), _1435297)))], (34506 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1435297))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435295), _1435297))], (34512 ^ _782464) ^ [_1435505, _1435507] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435505), _1435507), hAPP(c_Int_Onumber__class_Onumber__of(_1435505), c_Int_OBit1(c_Int_OPls))) = _1435507), class_Fields_Ofield(_1435505), class_Int_Onumber__ring(_1435505)], (34522 ^ _782464) ^ [_1435656, _1435658] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435656), _1435658), hAPP(c_Int_Onumber__class_Onumber__of(_1435656), c_Int_OBit1(c_Int_OPls))) = _1435658), class_Fields_Ofield(_1435656), class_Int_Onumber__ring(_1435656)], (34542 ^ _782464) ^ [_1435952, _1435954] : [34543 ^ _782464 : [(34544 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435952), _1435954))], (34546 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435952), 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), _1435952)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435954))))], (34532 ^ _782464) ^ [_1435822, _1435824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435822)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435822), _1435824))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435822), c_Int_OPls)))], (34550 ^ _782464) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))], (34552 ^ _782464) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34554 ^ _782464) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))], (34556 ^ _782464) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))], (34558 ^ _782464) ^ [_1436185] : [-(c_Int_Osucc(_1436185) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436185), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34560 ^ _782464) ^ [_1436216, _1436218] : [class_Int_Onumber__ring(_1436216), class_Rings_Olinordered__idom(_1436216), 34567 ^ _782464 : [(34568 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436216), hAPP(c_Int_Onumber__class_Onumber__of(_1436216), _1436218)), c_Groups_Ozero__class_Ozero(_1436216))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436218), c_Int_OPls)))], (34574 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436218), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436216), hAPP(c_Int_Onumber__class_Onumber__of(_1436216), _1436218)), c_Groups_Ozero__class_Ozero(_1436216))))]]], (34580 ^ _782464) ^ [_1436530, _1436532] : [class_Int_Onumber__ring(_1436530), class_Rings_Olinordered__idom(_1436530), 34587 ^ _782464 : [(34588 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436530), c_Groups_Ozero__class_Ozero(_1436530)), hAPP(c_Int_Onumber__class_Onumber__of(_1436530), _1436532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436532)))], (34594 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436530), c_Groups_Ozero__class_Ozero(_1436530)), hAPP(c_Int_Onumber__class_Onumber__of(_1436530), _1436532))))]]], (34600 ^ _782464) ^ [_1436835, _1436837] : [class_Int_Onumber__ring(_1436835), class_Rings_Olinordered__idom(_1436835), 34607 ^ _782464 : [(34608 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436835), c_Groups_Ozero__class_Ozero(_1436835)), hAPP(c_Int_Onumber__class_Onumber__of(_1436835), _1436837))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1436837)))], (34614 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1436837)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436835), c_Groups_Ozero__class_Ozero(_1436835)), hAPP(c_Int_Onumber__class_Onumber__of(_1436835), _1436837))))]]], (34620 ^ _782464) ^ [_1437140, _1437142] : [class_Int_Onumber__ring(_1437140), class_Rings_Olinordered__idom(_1437140), 34627 ^ _782464 : [(34628 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437140), hAPP(c_Int_Onumber__class_Onumber__of(_1437140), _1437142)), c_Groups_Ozero__class_Ozero(_1437140))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437142), c_Int_OPls)))], (34634 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437142), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437140), hAPP(c_Int_Onumber__class_Onumber__of(_1437140), _1437142)), c_Groups_Ozero__class_Ozero(_1437140))))]]], (34640 ^ _782464) ^ [_1437466] : [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), _1437466))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1437466)))], (34646 ^ _782464) ^ [_1437551] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1437551)), -(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), _1437551))))], (34652 ^ _782464) ^ [] : [-(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)))))], (34654 ^ _782464) ^ [] : [-(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)))], (34656 ^ _782464) ^ [_1437678, _1437680] : [class_Groups_Omonoid__mult(_1437678), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1437678), _1437680), 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(_1437678), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1437678), _1437680), _1437680)), _1437680))], (34662 ^ _782464) ^ [] : [-(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))))))], (34664 ^ _782464) ^ [_1437819] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1437819))) = 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)))), _1437819))], (34666 ^ _782464) ^ [_1437863, _1437865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437863), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437863)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437865)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437865))], (34672 ^ _782464) ^ [_1437975, _1437977] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437975), c_Int_OPls))), 34675 ^ _782464 : [(34676 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437977), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437975)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437977)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437975))], (34682 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437977), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437975)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437977)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1437975), _1437977)))]]], (34688 ^ _782464) ^ [] : [-(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)))))], (34690 ^ _782464) ^ [] : [-(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)))))], (34692 ^ _782464) ^ [_1438284, _1438286] : [class_Int_Onumber__ring(_1438284), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438284), c_Int_Osucc(_1438286)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438284), c_Groups_Oone__class_Oone(_1438284)), hAPP(c_Int_Onumber__class_Onumber__of(_1438284), _1438286)))], (34698 ^ _782464) ^ [_1438403, _1438405] : [class_Int_Onumber__ring(_1438403), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438403), c_Int_Opred(_1438405)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438403), hAPP(c_Groups_Ouminus__class_Ouminus(_1438403), c_Groups_Oone__class_Oone(_1438403))), hAPP(c_Int_Onumber__class_Onumber__of(_1438403), _1438405)))], (34704 ^ _782464) ^ [_1438532, _1438534] : [class_Int_Onumber__ring(_1438532), class_Rings_Olinordered__idom(_1438532), 34711 ^ _782464 : [(34712 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438532), hAPP(c_Int_Onumber__class_Onumber__of(_1438532), _1438534)), c_Groups_Oone__class_Oone(_1438532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438534), c_Int_OBit1(c_Int_OPls))))], (34718 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438534), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438532), hAPP(c_Int_Onumber__class_Onumber__of(_1438532), _1438534)), c_Groups_Oone__class_Oone(_1438532))))]]], (34724 ^ _782464) ^ [_1438846, _1438848] : [class_Int_Onumber__ring(_1438846), class_Rings_Olinordered__idom(_1438846), 34731 ^ _782464 : [(34732 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438846), c_Groups_Oone__class_Oone(_1438846)), hAPP(c_Int_Onumber__class_Onumber__of(_1438846), _1438848))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1438848)))], (34738 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1438848)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438846), c_Groups_Oone__class_Oone(_1438846)), hAPP(c_Int_Onumber__class_Onumber__of(_1438846), _1438848))))]]], (34744 ^ _782464) ^ [_1439151, _1439153] : [class_Int_Onumber__ring(_1439151), class_Rings_Olinordered__idom(_1439151), 34751 ^ _782464 : [(34752 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439151), hAPP(c_Int_Onumber__class_Onumber__of(_1439151), _1439153)), c_Groups_Oone__class_Oone(_1439151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439153), c_Int_OBit1(c_Int_OPls))))], (34758 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439153), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439151), hAPP(c_Int_Onumber__class_Onumber__of(_1439151), _1439153)), c_Groups_Oone__class_Oone(_1439151))))]]], (34764 ^ _782464) ^ [_1439465, _1439467] : [class_Int_Onumber__ring(_1439465), class_Rings_Olinordered__idom(_1439465), 34771 ^ _782464 : [(34772 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439465), c_Groups_Oone__class_Oone(_1439465)), hAPP(c_Int_Onumber__class_Onumber__of(_1439465), _1439467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439467)))], (34778 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439465), c_Groups_Oone__class_Oone(_1439465)), hAPP(c_Int_Onumber__class_Onumber__of(_1439465), _1439467))))]]], (34784 ^ _782464) ^ [_1439770, _1439772] : [class_Int_Onumber__ring(_1439770), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439770), hAPP(c_Int_Onumber__class_Onumber__of(_1439770), _1439772)), c_Groups_Oone__class_Oone(_1439770)) = hAPP(c_Int_Onumber__class_Onumber__of(_1439770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1439772), c_Int_OBit1(c_Int_OPls))))], (34790 ^ _782464) ^ [_1439897, _1439899] : [class_Int_Onumber__ring(_1439897), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439897), c_Groups_Oone__class_Oone(_1439897)), hAPP(c_Int_Onumber__class_Onumber__of(_1439897), _1439899)) = hAPP(c_Int_Onumber__class_Onumber__of(_1439897), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439899)))], (34796 ^ _782464) ^ [_1440018, _1440020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1440018)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1440020)), _1440018) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1440020), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1440018), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (34802 ^ _782464) ^ [_1440153, _1440155, _1440157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440153), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440153)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440155)), _1440157)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34808 ^ _782464) ^ [_1440272, _1440274, _1440276] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440272), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440274)), _1440276)) = 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), _1440272), _1440274))), _1440276))], (34814 ^ _782464) ^ [_1440359, _1440361] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440359), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440359)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440361)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34820 ^ _782464) ^ [_1440464, _1440466] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440464), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440464)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440466)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1440464), _1440466)))], (34826 ^ _782464) ^ [_1440540] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1440540)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440540) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34832 ^ _782464) ^ [_1440631] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440631) = 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(_1440631)))))], (34838 ^ _782464) ^ [_1440728, _1440730] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440728, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440730)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440728, 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)))), _1440730)))], (34840 ^ _782464) ^ [_1440773, _1440775] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440773))), _1440775) = 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)))), _1440773), _1440775))], (34842 ^ _782464) ^ [_1440818, _1440820] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440818))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440820)) = 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)))), _1440818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440820)))], (34844 ^ _782464) ^ [_1440869, _1440871] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440869), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440871)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440869), 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)))), _1440871)))], (34846 ^ _782464) ^ [_1440918, _1440920] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440918)))), _1440920) = 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)))), _1440918)), _1440920))], (34848 ^ _782464) ^ [_1440967, _1440969] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440967)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440969)) = 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)))), _1440967)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440969)))], (34850 ^ _782464) ^ [_1441022, _1441024] : [class_Int_Onumber__ring(_1441022), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1441022), c_Groups_Oone__class_Oone(_1441022)), hAPP(c_Int_Onumber__class_Onumber__of(_1441022), _1441024)) = hAPP(c_Int_Onumber__class_Onumber__of(_1441022), 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), _1441024))))], (34856 ^ _782464) ^ [_1441149, _1441151] : [class_Int_Onumber__ring(_1441149), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1441149), hAPP(c_Int_Onumber__class_Onumber__of(_1441149), _1441151)), c_Groups_Oone__class_Oone(_1441149)) = hAPP(c_Int_Onumber__class_Onumber__of(_1441149), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1441151), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (34862 ^ _782464) ^ [_1441291, _1441293] : [hAPP(c_Nat_OSuc, _1441291) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441293), -(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(_1441293))), 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)), _1441291))))))], (34868 ^ _782464) ^ [_1441414, _1441416] : [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(_1441416))), 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)), _1441414))))), -(hAPP(c_Nat_OSuc, _1441414) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441416))], (34874 ^ _782464) ^ [_1441558, _1441560] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441558) = hAPP(c_Nat_OSuc, _1441560), -(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(_1441558))), 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)), _1441560))))))], (34880 ^ _782464) ^ [_1441681, _1441683] : [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(_1441681))), 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)), _1441683))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441681) = hAPP(c_Nat_OSuc, _1441683))], (34886 ^ _782464) ^ [_1441810, _1441812, _1441814, _1441816] : [-(c_Nat_Onat_Onat__case(_1441810, _1441812, _1441814, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441816)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1441810), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1441816))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1441810, _1441810), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1441810, tc_fun(_1441810, _1441810)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1441810, tc_fun(_1441810, _1441810)), tc_Int_Oint), c_If(_1441810)), c_Nat__Numeral_Oneg)), _1441812)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1441810, tc_Int_Oint), _1441814), c_Int_Onat))))], (34888 ^ _782464) ^ [_1441927, _1441929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441927)), hAPP(c_Nat_OSuc, _1441929))), -(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(_1441927))), 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)), _1441929)))))], (34894 ^ _782464) ^ [_1442054, _1442056] : [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(_1442054))), 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)), _1442056)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442054)), hAPP(c_Nat_OSuc, _1442056))))], (34900 ^ _782464) ^ [_1442202, _1442204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442202)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442204))), -(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(_1442204))), 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), _1442202)), c_Int_Onat))))))], (34906 ^ _782464) ^ [_1442347, _1442349] : [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(_1442349))), 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), _1442347)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442347)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442349))))], (34912 ^ _782464) ^ [_1442513, _1442515] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442513)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442515))), -(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(_1442515))), 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), _1442513)), c_Int_Onat))))))], (34918 ^ _782464) ^ [_1442658, _1442660] : [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(_1442660))), 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), _1442658)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442658)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442660))))], (34924 ^ _782464) ^ [_1442824, _1442826] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442824)), hAPP(c_Nat_OSuc, _1442826))), -(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(_1442824))), 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)), _1442826)))))], (34930 ^ _782464) ^ [_1442951, _1442953] : [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(_1442951))), 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)), _1442953)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442951)), hAPP(c_Nat_OSuc, _1442953))))], (34936 ^ _782464) ^ [_1443090] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1443090))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443090)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34942 ^ _782464) ^ [_1443181] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1443181)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443181)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1443181)))], (34948 ^ _782464) ^ [_1443233, _1443235] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443233)), hAPP(c_Nat_OSuc, _1443235)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443233))), 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, _1443235))), 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)), _1443235)))))], (34950 ^ _782464) ^ [_1443299, _1443301] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1443299)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443301)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443301))), 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, _1443299))), 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), _1443299)), c_Int_Onat)))))], (34952 ^ _782464) ^ [_1443371, _1443373, _1443375, _1443377, _1443379] : [-(c_Nat_Onat_Onat__case(_1443371, _1443373, _1443375, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443377)), _1443379)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1443371), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443377))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443371, _1443371), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1443371, tc_fun(_1443371, _1443371)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443371, tc_fun(_1443371, _1443371)), tc_Int_Oint), c_If(_1443371)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1443371, _1443373, _1443375, _1443379))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443371, tc_Int_Oint), _1443375), 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)), _1443379)))))], (34954 ^ _782464) ^ [_1443489, _1443491, _1443493, _1443495, _1443497] : [-(hAPP(c_Nat_Onat_Onat__rec(_1443489, _1443491, _1443493), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443495)), _1443497)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1443489), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443495))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443489, _1443489), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1443489, tc_fun(_1443489, _1443489)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443489, tc_fun(_1443489, _1443489)), tc_Int_Oint), c_If(_1443489)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1443489, _1443491, _1443493), _1443497))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443489, _1443489), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1443489, _1443489), tc_Int_Oint), _1443493), 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)), _1443497))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443489, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1443489, _1443491, _1443493)), 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)), _1443497))))))], (34956 ^ _782464) ^ [_1443641, _1443643] : [class_Int_Onumber__ring(_1443641), 34959 ^ _782464 : [(34960 ^ _782464) ^ [] : [c_Groups_Oone__class_Oone(_1443641) = hAPP(c_Int_Onumber__class_Onumber__of(_1443641), _1443643), -(c_Int_Oiszero(_1443641, hAPP(c_Int_Onumber__class_Onumber__of(_1443641), 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), _1443643)))))], (34966 ^ _782464) ^ [] : [c_Int_Oiszero(_1443641, hAPP(c_Int_Onumber__class_Onumber__of(_1443641), 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), _1443643)))), -(c_Groups_Oone__class_Oone(_1443641) = hAPP(c_Int_Onumber__class_Onumber__of(_1443641), _1443643))]]], (34972 ^ _782464) ^ [_1443900, _1443902] : [class_Int_Onumber__ring(_1443900), 34975 ^ _782464 : [(34976 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1443900), _1443902) = c_Groups_Oone__class_Oone(_1443900), -(c_Int_Oiszero(_1443900, hAPP(c_Int_Onumber__class_Onumber__of(_1443900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443902), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (34982 ^ _782464) ^ [] : [c_Int_Oiszero(_1443900, hAPP(c_Int_Onumber__class_Onumber__of(_1443900), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443902), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1443900), _1443902) = c_Groups_Oone__class_Oone(_1443900))]]], (34988 ^ _782464) ^ [_1444159, _1444161, _1444163, _1444165] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444159, _1444161, _1444163), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1444165)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1444159), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1444165))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1444159, _1444159), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1444159, tc_fun(_1444159, _1444159)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1444159, tc_fun(_1444159, _1444159)), tc_Int_Oint), c_If(_1444159)), c_Nat__Numeral_Oneg)), _1444161)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1444159, _1444159), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1444159, _1444159), tc_Int_Oint), _1444163), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1444159, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1444159, _1444161, _1444163)), c_Int_Onat)))))], (34990 ^ _782464) ^ [_1444290, _1444292] : [class_Rings_Osemiring__1(_1444290), 34993 ^ _782464 : [(34994 ^ _782464) ^ [] : [c_Int_Oiszero(_1444290, _1444292), -(_1444292 = c_Groups_Ozero__class_Ozero(_1444290))], (35000 ^ _782464) ^ [] : [_1444292 = c_Groups_Ozero__class_Ozero(_1444290), -(c_Int_Oiszero(_1444290, _1444292))]]], (35006 ^ _782464) ^ [_1444501] : [class_Rings_Osemiring__1(_1444501), -(c_Int_Oiszero(_1444501, c_Groups_Ozero__class_Ozero(_1444501)))], (35012 ^ _782464) ^ [_1444578] : [class_Rings_Osemiring__1(_1444578), c_Int_Oiszero(_1444578, c_Groups_Oone__class_Oone(_1444578))], (35018 ^ _782464) ^ [_1444656, _1444658, _1444660] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444656, _1444658, _1444660), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1444658)], (35020 ^ _782464) ^ [_1444690, _1444692, _1444694, _1444696] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444690, _1444692, _1444694), hAPP(c_Nat_OSuc, _1444696)) = hAPP(hAPP(_1444694, _1444696), hAPP(c_Nat_Onat_Onat__rec(_1444690, _1444692, _1444694), _1444696)))], (35022 ^ _782464) ^ [_1444742] : [class_Int_Onumber__ring(_1444742), -(c_Int_Oiszero(_1444742, hAPP(c_Int_Onumber__class_Onumber__of(_1444742), c_Int_OPls)))], (35028 ^ _782464) ^ [_1444825, _1444827] : [c_Int_Oiszero(_1444825, hAPP(c_Int_Onumber__class_Onumber__of(_1444825), c_Int_OBit1(_1444827))), class_Int_Onumber__ring(_1444825), class_Int_Oring__char__0(_1444825)], (35038 ^ _782464) ^ [_1444965] : [class_Int_Onumber__ring(_1444965), c_Int_Oiszero(_1444965, hAPP(c_Int_Onumber__class_Onumber__of(_1444965), c_Int_OBit1(c_Int_OPls)))], (35044 ^ _782464) ^ [_1445049, _1445051, _1445053] : [class_Int_Onumber__ring(_1445049), 35047 ^ _782464 : [(35048 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1445049), _1445051) = hAPP(c_Int_Onumber__class_Onumber__of(_1445049), _1445053), -(c_Int_Oiszero(_1445049, hAPP(c_Int_Onumber__class_Onumber__of(_1445049), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445051), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445053)))))], (35054 ^ _782464) ^ [] : [c_Int_Oiszero(_1445049, hAPP(c_Int_Onumber__class_Onumber__of(_1445049), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445051), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445053)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1445049), _1445051) = hAPP(c_Int_Onumber__class_Onumber__of(_1445049), _1445053))]]], (35060 ^ _782464) ^ [_1445332, _1445334] : [class_Int_Onumber__ring(_1445332), 35063 ^ _782464 : [(35064 ^ _782464) ^ [] : [c_Groups_Ozero__class_Ozero(_1445332) = hAPP(c_Int_Onumber__class_Onumber__of(_1445332), _1445334), -(c_Int_Oiszero(_1445332, hAPP(c_Int_Onumber__class_Onumber__of(_1445332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445334)))))], (35070 ^ _782464) ^ [] : [c_Int_Oiszero(_1445332, hAPP(c_Int_Onumber__class_Onumber__of(_1445332), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445334)))), -(c_Groups_Ozero__class_Ozero(_1445332) = hAPP(c_Int_Onumber__class_Onumber__of(_1445332), _1445334))]]], (35076 ^ _782464) ^ [_1445591, _1445593] : [class_Int_Onumber__ring(_1445591), 35079 ^ _782464 : [(35080 ^ _782464) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1445591), _1445593) = c_Groups_Ozero__class_Ozero(_1445591), -(c_Int_Oiszero(_1445591, hAPP(c_Int_Onumber__class_Onumber__of(_1445591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445593), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (35086 ^ _782464) ^ [] : [c_Int_Oiszero(_1445591, hAPP(c_Int_Onumber__class_Onumber__of(_1445591), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445593), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1445591), _1445593) = c_Groups_Ozero__class_Ozero(_1445591))]]], (35092 ^ _782464) ^ [_1445850, _1445852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445850), 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)))), _1445852)), 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)))), _1445850)) = 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), _1445852), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1445850))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35098 ^ _782464) ^ [_1446010, _1446012] : [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), _1446010))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1446012)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1446010))) = 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), _1446012), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1446010)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35104 ^ _782464) ^ [_1446157, _1446159] : [-(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), _1446157)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1446159)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1446157))) = 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), _1446159)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1446157)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35110 ^ _782464) ^ [_1446239, _1446241, _1446243] : [-(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), _1446239)), 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))), _1446241))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1446243))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1446243)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446239), 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), _1446243), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1446241)))))], (35112 ^ _782464) ^ [_1446338, _1446340] : [c_Int_OBit0(_1446338) = c_Int_OBit1(_1446340)], (35114 ^ _782464) ^ [_1446379, _1446381] : [c_Int_OBit1(_1446379) = c_Int_OBit0(_1446381)], (35116 ^ _782464) ^ [_1446423, _1446425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446423)), c_Int_OBit0(_1446425))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446423), _1446425)))], (35122 ^ _782464) ^ [_1446524, _1446526] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446524), _1446526)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446524)), c_Int_OBit0(_1446526))))], (35128 ^ _782464) ^ [_1446646, _1446648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446646)), c_Int_OBit0(_1446648))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446646), _1446648)))], (35134 ^ _782464) ^ [_1446747, _1446749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446747), _1446749)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446747)), c_Int_OBit0(_1446749))))], (35140 ^ _782464) ^ [_1446854, _1446856] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1446854)), c_Int_OBit0(_1446856)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1446854), _1446856)))], (35142 ^ _782464) ^ [_1446897, _1446899] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1446897)), _1446899) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1446897), _1446899)))], (35144 ^ _782464) ^ [_1446953, _1446955] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1446953)), c_Int_OBit0(_1446955))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446953), _1446955)))], (35150 ^ _782464) ^ [_1447054, _1447056] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447054), _1447056)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447054)), c_Int_OBit0(_1447056))))], (35156 ^ _782464) ^ [_1447176, _1447178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447176)), c_Int_OBit0(_1447178))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447176), _1447178)))], (35162 ^ _782464) ^ [_1447277, _1447279] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447277), _1447279)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447277)), c_Int_OBit0(_1447279))))], (35168 ^ _782464) ^ [_1447384] : [-(c_Int_OBit0(_1447384) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447384), _1447384))], (35170 ^ _782464) ^ [_1447415, _1447417] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1447415)), c_Int_OBit0(_1447417)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447415), _1447417)))], (35172 ^ _782464) ^ [_1447473, _1447475] : [c_Int_OBit0(_1447473) = c_Int_OBit0(_1447475), -(_1447473 = _1447475)], (35178 ^ _782464) ^ [_1447554, _1447556] : [_1447554 = _1447556, -(c_Int_OBit0(_1447554) = c_Int_OBit0(_1447556))], (35184 ^ _782464) ^ [_1447641] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1447641)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1447641)))], (35186 ^ _782464) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (35188 ^ _782464) ^ [_1447704] : [c_Int_OPls = c_Int_OBit0(_1447704), -(c_Int_OPls = _1447704)], (35194 ^ _782464) ^ [_1447779] : [c_Int_OPls = _1447779, -(c_Int_OPls = c_Int_OBit0(_1447779))], (35200 ^ _782464) ^ [_1447872] : [c_Int_OBit0(_1447872) = c_Int_OPls, -(_1447872 = c_Int_OPls)], (35206 ^ _782464) ^ [_1447947] : [_1447947 = c_Int_OPls, -(c_Int_OBit0(_1447947) = c_Int_OPls)], (35212 ^ _782464) ^ [_1448040] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448040)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448040), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35218 ^ _782464) ^ [_1448135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448135), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448135)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35224 ^ _782464) ^ [_1448248] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448248)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448248), c_Int_OPls)))], (35230 ^ _782464) ^ [_1448343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448343), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448343)), c_Int_OPls)))], (35236 ^ _782464) ^ [_1448456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1448456))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1448456)))], (35242 ^ _782464) ^ [_1448539] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1448539)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1448539))))], (35248 ^ _782464) ^ [_1448643, _1448645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448643)), c_Int_OBit1(_1448645))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448643), _1448645)))], (35254 ^ _782464) ^ [_1448744, _1448746] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448744), _1448746)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448744)), c_Int_OBit1(_1448746))))], (35260 ^ _782464) ^ [_1448866, _1448868] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448866)), c_Int_OBit1(_1448868))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448866), _1448868)))], (35266 ^ _782464) ^ [_1448967, _1448969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448967), _1448969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448967)), c_Int_OBit1(_1448969))))], (35272 ^ _782464) ^ [_1449086] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1449086)))], (35278 ^ _782464) ^ [_1449169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1449169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449169))))], (35284 ^ _782464) ^ [_1449270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1449270)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449270), c_Int_OPls)))], (35290 ^ _782464) ^ [_1449365] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449365), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1449365)), c_Int_OPls)))], (35296 ^ _782464) ^ [_1449481, _1449483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449481)), c_Int_OBit0(_1449483))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449481), _1449483)))], (35302 ^ _782464) ^ [_1449582, _1449584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449582), _1449584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449582)), c_Int_OBit0(_1449584))))], (35308 ^ _782464) ^ [_1449704, _1449706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449704)), c_Int_OBit0(_1449706))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449704), _1449706)))], (35314 ^ _782464) ^ [_1449805, _1449807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449805), _1449807)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449805)), c_Int_OBit0(_1449807))))], (35320 ^ _782464) ^ [_1449912, _1449914] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1449912)), c_Int_OBit1(_1449914)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449912), _1449914)))], (35322 ^ _782464) ^ [_1449955, _1449957] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1449955)), c_Int_OBit0(_1449957)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449955), _1449957)))], (35324 ^ _782464) ^ [_1449998] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449998)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1449998)))], (35326 ^ _782464) ^ [_1450031, _1450033] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1450031)), c_Int_OBit1(_1450033)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450031), _1450033)))], (35328 ^ _782464) ^ [_1450074, _1450076] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1450074)), c_Int_OBit0(_1450076)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450074), _1450076)))], (35330 ^ _782464) ^ [_1450117, _1450119] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450117))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450119))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450117)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450119)))], (35332 ^ _782464) ^ [_1450182] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450182)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450182))))], (35338 ^ _782464) ^ [_1450277] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450277))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450277)))))], (35344 ^ _782464) ^ [_1450378] : [-(c_Int_Opred(c_Int_OBit1(_1450378)) = c_Int_OBit0(_1450378))], (35346 ^ _782464) ^ [_1450407] : [-(c_Int_Opred(c_Int_OBit0(_1450407)) = c_Int_OBit1(c_Int_Opred(_1450407)))], (35348 ^ _782464) ^ [_1450438, _1450440] : [class_Int_Onumber__ring(_1450438), class_Int_Oring__char__0(_1450438), 35355 ^ _782464 : [(35356 ^ _782464) ^ [] : [c_Int_Oiszero(_1450438, hAPP(c_Int_Onumber__class_Onumber__of(_1450438), c_Int_OBit0(_1450440))), -(c_Int_Oiszero(_1450438, hAPP(c_Int_Onumber__class_Onumber__of(_1450438), _1450440)))], (35362 ^ _782464) ^ [] : [c_Int_Oiszero(_1450438, hAPP(c_Int_Onumber__class_Onumber__of(_1450438), _1450440)), -(c_Int_Oiszero(_1450438, hAPP(c_Int_Onumber__class_Onumber__of(_1450438), c_Int_OBit0(_1450440))))]]], (35368 ^ _782464) ^ [_1450731] : [-(c_Int_Osucc(c_Int_OBit0(_1450731)) = c_Int_OBit1(_1450731))], (35370 ^ _782464) ^ [_1450760] : [-(c_Int_Osucc(c_Int_OBit1(_1450760)) = c_Int_OBit0(c_Int_Osucc(_1450760)))], (35372 ^ _782464) ^ [_1450791] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1450791)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1450791)), 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))))], (35374 ^ _782464) ^ [_1450828, _1450830] : [class_Int_Onumber__ring(_1450828), -(hAPP(c_Int_Onumber__class_Onumber__of(_1450828), c_Int_OBit0(_1450830)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450828), c_Groups_Ozero__class_Ozero(_1450828)), hAPP(c_Int_Onumber__class_Onumber__of(_1450828), _1450830))), hAPP(c_Int_Onumber__class_Onumber__of(_1450828), _1450830)))], (35380 ^ _782464) ^ [_1450988, _1450990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1450988)), c_Int_OBit1(_1450990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1450988), _1450990)))], (35386 ^ _782464) ^ [_1451089, _1451091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451089), _1451091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451089)), c_Int_OBit1(_1451091))))], (35392 ^ _782464) ^ [_1451211, _1451213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451211)), c_Int_OBit1(_1451213))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451211), _1451213)))], (35398 ^ _782464) ^ [_1451312, _1451314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451312), _1451314)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451312)), c_Int_OBit1(_1451314))))], (35404 ^ _782464) ^ [_1451434, _1451436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451434)), c_Int_OBit0(_1451436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451434), _1451436)))], (35410 ^ _782464) ^ [_1451535, _1451537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451535), _1451537)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451535)), c_Int_OBit0(_1451537))))], (35416 ^ _782464) ^ [_1451657, _1451659] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451657)), c_Int_OBit0(_1451659))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451657), _1451659)))], (35422 ^ _782464) ^ [_1451758, _1451760] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451758), _1451760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451758)), c_Int_OBit0(_1451760))))], (35428 ^ _782464) ^ [] : [-(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))))], (35430 ^ _782464) ^ [_1451883, _1451885] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1451883)), _1451885) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1451883), _1451885))), _1451885))], (35432 ^ _782464) ^ [_1451930, _1451932] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1451930)), c_Int_OBit1(_1451932)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1451930)), _1451932)))], (35434 ^ _782464) ^ [_1451975, _1451977] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1451975)), c_Int_OBit1(_1451977)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451975), c_Int_Osucc(_1451977))))], (35436 ^ _782464) ^ [_1452020, _1452022, _1452024] : [class_Int_Onumber__ring(_1452020), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1452020), _1452022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452024))) = hAPP(hAPP(c_HOL_OLet(_1452020, _1452020), hAPP(hAPP(c_Power_Opower__class_Opower(_1452020), _1452022), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452024))), hAPP(hAPP(c_COMBS(_1452020, _1452020, _1452020), c_Groups_Otimes__class_Otimes(_1452020)), c_COMBI(_1452020))))], (35442 ^ _782464) ^ [_1452191, _1452193] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1452191), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452193))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1452191), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452193))), 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))))], (35444 ^ _782464) ^ [_1452242, _1452244] : [class_Int_Onumber__ring(_1452242), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452242), c_Groups_Oone__class_Oone(_1452242)), c_Groups_Oone__class_Oone(_1452242))), hAPP(c_Int_Onumber__class_Onumber__of(_1452242), _1452244)) = hAPP(c_Int_Onumber__class_Onumber__of(_1452242), c_Int_OBit0(_1452244)))], (35450 ^ _782464) ^ [_1452381] : [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), _1452381))), 35453 ^ _782464 : [(35454 ^ _782464) ^ [] : [-(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(_1452381)))))], (35456 ^ _782464) ^ [] : [-(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(_1452381)))))]]], (35458 ^ _782464) ^ [] : [-(c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35460 ^ _782464) ^ [_1452538, _1452540, _1452542] : [class_Int_Onumber__ring(_1452538), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1452538), hAPP(c_Int_Onumber__class_Onumber__of(_1452538), _1452540)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452542))) = hAPP(hAPP(c_HOL_OLet(_1452538, _1452538), hAPP(hAPP(c_Power_Opower__class_Opower(_1452538), hAPP(c_Int_Onumber__class_Onumber__of(_1452538), _1452540)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452542))), hAPP(hAPP(c_COMBS(_1452538, _1452538, _1452538), c_Groups_Otimes__class_Otimes(_1452538)), c_COMBI(_1452538))))], (35466 ^ _782464) ^ [_1452729, _1452731] : [class_Int_Onumber__ring(_1452729), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452729), _1452731), hAPP(c_Int_Onumber__class_Onumber__of(_1452729), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452729), _1452731), _1452731))], (35472 ^ _782464) ^ [_1452846, _1452848] : [class_Int_Onumber__ring(_1452846), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452846), hAPP(c_Int_Onumber__class_Onumber__of(_1452846), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1452848) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452846), _1452848), _1452848))], (35478 ^ _782464) ^ [_1452963] : [class_Int_Onumber__ring(_1452963), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452963), c_Groups_Oone__class_Oone(_1452963)), c_Groups_Oone__class_Oone(_1452963)) = hAPP(c_Int_Onumber__class_Onumber__of(_1452963), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (35484 ^ _782464) ^ [_1453070] : [class_Rings_Osemiring__1(_1453070), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453070), c_Groups_Ozero__class_Ozero(_1453070)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453070))], (35490 ^ _782464) ^ [_1453167, _1453169] : [class_Rings_Oring__1__no__zero__divisors(_1453167), 35493 ^ _782464 : [(35494 ^ _782464) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1453167), _1453169), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453167), -(_1453169 = c_Groups_Ozero__class_Ozero(_1453167))], (35500 ^ _782464) ^ [] : [_1453169 = c_Groups_Ozero__class_Ozero(_1453167), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453167), _1453169), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453167))]]], (35506 ^ _782464) ^ [] : [-(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))))], (35508 ^ _782464) ^ [] : [-(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))))], (35510 ^ _782464) ^ [_1453444, _1453446] : [class_Rings_Ocomm__semiring__1(_1453444), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453444), _1453446), _1453446) = hAPP(hAPP(c_Power_Opower__class_Opower(_1453444), _1453446), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35516 ^ _782464) ^ [_1453551, _1453553] : [class_Groups_Omonoid__mult(_1453551), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453551), _1453553), 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(_1453551), _1453553), _1453553))], (35522 ^ _782464) ^ [] : [-(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))))))], (35524 ^ _782464) ^ [_1453676] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1453676), 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, _1453676)))], (35526 ^ _782464) ^ [_1453711] : [-(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)))), _1453711) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1453711)))], (35528 ^ _782464) ^ [_1453743] : [class_Rings_Osemiring__1(_1453743), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453743), c_Groups_Oone__class_Oone(_1453743)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1453743))], (35534 ^ _782464) ^ [_1453840, _1453842] : [class_Rings_Oring__1(_1453840), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453840), hAPP(c_Groups_Ouminus__class_Ouminus(_1453840), _1453842)), 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(_1453840), _1453842), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35540 ^ _782464) ^ [_1453957] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1453957), 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), _1453957), _1453957))], (35542 ^ _782464) ^ [_1453992] : [-(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)))), _1453992) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1453992), _1453992))], (35544 ^ _782464) ^ [_1454024, _1454026, _1454028] : [class_Groups_Omonoid__mult(_1454024), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1454024), _1454026), 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)))), _1454028)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1454024), hAPP(hAPP(c_Power_Opower__class_Opower(_1454024), _1454026), _1454028)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35550 ^ _782464) ^ [] : [-(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)))))], (35552 ^ _782464) ^ [] : [-(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)))))], (35554 ^ _782464) ^ [_1454191, _1454193] : [class_Rings_Olinordered__idom(_1454191), -(hAPP(c_Groups_Oabs__class_Oabs(_1454191), hAPP(hAPP(c_Power_Opower__class_Opower(_1454191), _1454193), 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(_1454191), _1454193), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35560 ^ _782464) ^ [_1454308, _1454310] : [class_Rings_Olinordered__idom(_1454308), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1454308), hAPP(c_Groups_Oabs__class_Oabs(_1454308), _1454310)), 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(_1454308), _1454310), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35566 ^ _782464) ^ [] : [-(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))))], (35568 ^ _782464) ^ [_1454443] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1454443)), 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, _1454443, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35570 ^ _782464) ^ [_1454480] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1454480))), 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), _1454480), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35572 ^ _782464) ^ [_1454524, _1454526] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1454524)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1454526))) = 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), _1454524), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1454526))))], (35574 ^ _782464) ^ [_1454576] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1454576), _1454576)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1454576)], (35576 ^ _782464) ^ [_1454611, _1454613] : [class_Fields_Olinordered__field__inverse__zero(_1454611), class_Int_Onumber__ring(_1454611), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454611), c_Groups_Ozero__class_Ozero(_1454611)), _1454613)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454611), c_Groups_Ozero__class_Ozero(_1454611)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454611), _1454613), hAPP(c_Int_Onumber__class_Onumber__of(_1454611), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35590 ^ _782464) ^ [_1454852, _1454854] : [class_Fields_Olinordered__field__inverse__zero(_1454852), class_Int_Onumber__ring(_1454852), 35597 ^ _782464 : [(35598 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454852), c_Groups_Ozero__class_Ozero(_1454852)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454852), _1454854), hAPP(c_Int_Onumber__class_Onumber__of(_1454852), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454852), c_Groups_Ozero__class_Ozero(_1454852)), _1454854)))], (35604 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454852), c_Groups_Ozero__class_Ozero(_1454852)), _1454854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454852), c_Groups_Ozero__class_Ozero(_1454852)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454852), _1454854), hAPP(c_Int_Onumber__class_Onumber__of(_1454852), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (35610 ^ _782464) ^ [_1455202, _1455204, _1455206] : [class_Rings_Olinordered__semidom(_1455202), hAPP(hAPP(c_Power_Opower__class_Opower(_1455202), _1455204), 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(_1455202), _1455206), 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(_1455202), c_Groups_Ozero__class_Ozero(_1455202)), _1455204)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455202), c_Groups_Ozero__class_Ozero(_1455202)), _1455206)), -(_1455204 = _1455206)], (35628 ^ _782464) ^ [_1455509, _1455511, _1455513] : [class_Rings_Olinordered__semidom(_1455509), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455509), hAPP(hAPP(c_Power_Opower__class_Opower(_1455509), _1455511), 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(_1455509), _1455513), 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(_1455509), c_Groups_Ozero__class_Ozero(_1455509)), _1455513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455509), _1455511), _1455513)))], (35642 ^ _782464) ^ [_1455772, _1455774] : [class_Rings_Olinordered__idom(_1455772), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455772), c_Groups_Ozero__class_Ozero(_1455772)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455772), _1455774), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35648 ^ _782464) ^ [_1455881, _1455883] : [class_Rings_Olinordered__idom(_1455881), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455881), hAPP(hAPP(c_Power_Opower__class_Opower(_1455881), _1455883), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1455881)))], (35654 ^ _782464) ^ [_1455991, _1455993] : [class_Rings_Olinordered__idom(_1455991), 35657 ^ _782464 : [(35658 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455991), c_Groups_Ozero__class_Ozero(_1455991)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455991), _1455993), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1455993 = c_Groups_Ozero__class_Ozero(_1455991)], (35664 ^ _782464) ^ [] : [-(_1455993 = c_Groups_Ozero__class_Ozero(_1455991)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455991), c_Groups_Ozero__class_Ozero(_1455991)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455991), _1455993), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (35670 ^ _782464) ^ [_1456215, _1456217, _1456219] : [class_Rings_Olinordered__idom(_1456215), 35673 ^ _782464 : [(35674 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456215), hAPP(hAPP(c_Power_Opower__class_Opower(_1456215), _1456217), 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(_1456215), _1456219), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1456215), 35677 ^ _782464 : [(35678 ^ _782464) ^ [] : [-(_1456217 = c_Groups_Ozero__class_Ozero(_1456215))], (35680 ^ _782464) ^ [] : [-(_1456219 = c_Groups_Ozero__class_Ozero(_1456215))]]], (35682 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456215), hAPP(hAPP(c_Power_Opower__class_Opower(_1456215), _1456217), 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(_1456215), _1456219), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1456215)), _1456217 = c_Groups_Ozero__class_Ozero(_1456215), _1456219 = c_Groups_Ozero__class_Ozero(_1456215)]]], (35692 ^ _782464) ^ [_1456590, _1456592] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1456590), hAPP(c_Int_Onumber__class_Onumber__of(_1456590), _1456592)), 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(_1456590), hAPP(c_Int_Onumber__class_Onumber__of(_1456590), _1456592)), hAPP(c_Int_Onumber__class_Onumber__of(_1456590), _1456592))), class_Groups_Omonoid__mult(_1456590), class_Int_Onumber(_1456590)], (35702 ^ _782464) ^ [_1456777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1456777), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1456777 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1456777 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35712 ^ _782464) ^ [] : [-(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))))], (35714 ^ _782464) ^ [_1456893, _1456895] : [class_Rings_Oring__1__no__zero__divisors(_1456893), 35717 ^ _782464 : [(35728 ^ _782464) ^ [] : [35729 ^ _782464 : [(35730 ^ _782464) ^ [] : [_1456895 = c_Groups_Oone__class_Oone(_1456893)], (35732 ^ _782464) ^ [] : [_1456895 = hAPP(c_Groups_Ouminus__class_Ouminus(_1456893), c_Groups_Oone__class_Oone(_1456893))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1456893), _1456895), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1456893))], (35718 ^ _782464) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1456893), _1456895), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1456893), -(_1456895 = c_Groups_Oone__class_Oone(_1456893)), -(_1456895 = hAPP(c_Groups_Ouminus__class_Ouminus(_1456893), c_Groups_Oone__class_Oone(_1456893)))]]], (35736 ^ _782464) ^ [_1457200, _1457202, _1457204] : [class_Rings_Ocomm__semiring__1(_1457200), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1457200), _1457202), 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)))), _1457204)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1457200), hAPP(hAPP(c_Power_Opower__class_Opower(_1457200), _1457202), _1457204)), hAPP(hAPP(c_Power_Opower__class_Opower(_1457200), _1457202), _1457204)))], (35742 ^ _782464) ^ [_1457347, _1457349, _1457351] : [class_Rings_Oring__1(_1457347), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1457347), hAPP(c_Groups_Ouminus__class_Ouminus(_1457347), _1457349)), 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)))), _1457351)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1457347), _1457349), 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)))), _1457351)))], (35748 ^ _782464) ^ [_1457478, _1457480, _1457482] : [class_Rings_Olinordered__semidom(_1457478), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457478), hAPP(hAPP(c_Power_Opower__class_Opower(_1457478), _1457480), 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(_1457478), _1457482), 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(_1457478), c_Groups_Ozero__class_Ozero(_1457478)), _1457482)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457478), _1457480), _1457482)))], (35762 ^ _782464) ^ [_1457741, _1457743, _1457745] : [class_Rings_Olinordered__idom(_1457741), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457741), c_Groups_Ozero__class_Ozero(_1457741)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457741), hAPP(hAPP(c_Power_Opower__class_Opower(_1457741), _1457743), 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(_1457741), _1457745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (35768 ^ _782464) ^ [_1457884, _1457886, _1457888] : [class_Rings_Olinordered__idom(_1457884), 35771 ^ _782464 : [(35772 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457884), hAPP(hAPP(c_Power_Opower__class_Opower(_1457884), _1457886), 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(_1457884), _1457888), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1457884))), 35775 ^ _782464 : [(35776 ^ _782464) ^ [] : [-(_1457886 = c_Groups_Ozero__class_Ozero(_1457884))], (35778 ^ _782464) ^ [] : [-(_1457888 = c_Groups_Ozero__class_Ozero(_1457884))]]], (35780 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457884), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457884), hAPP(hAPP(c_Power_Opower__class_Opower(_1457884), _1457886), 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(_1457884), _1457888), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1457884)))), _1457886 = c_Groups_Ozero__class_Ozero(_1457884), _1457888 = c_Groups_Ozero__class_Ozero(_1457884)]]], (35790 ^ _782464) ^ [_1458280, _1458282, _1458284] : [class_Rings_Olinordered__idom(_1458280), 35793 ^ _782464 : [(35804 ^ _782464) ^ [] : [35805 ^ _782464 : [(35806 ^ _782464) ^ [] : [-(_1458282 = c_Groups_Ozero__class_Ozero(_1458280))], (35808 ^ _782464) ^ [] : [-(_1458284 = c_Groups_Ozero__class_Ozero(_1458280))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458280), c_Groups_Ozero__class_Ozero(_1458280)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458280), hAPP(hAPP(c_Power_Opower__class_Opower(_1458280), _1458282), 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(_1458280), _1458284), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (35794 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458280), c_Groups_Ozero__class_Ozero(_1458280)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458280), hAPP(hAPP(c_Power_Opower__class_Opower(_1458280), _1458282), 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(_1458280), _1458284), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1458282 = c_Groups_Ozero__class_Ozero(_1458280), _1458284 = c_Groups_Ozero__class_Ozero(_1458280)]]], (35812 ^ _782464) ^ [_1458655, _1458657, _1458659] : [class_Rings_Olinordered__idom(_1458655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458655), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458655), hAPP(hAPP(c_Power_Opower__class_Opower(_1458655), _1458657), 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(_1458655), _1458659), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1458655)))], (35818 ^ _782464) ^ [_1458799, _1458801, _1458803] : [class_Int_Onumber__ring(_1458799), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1458799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458799), _1458801), _1458803)), 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(_1458799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458799), hAPP(hAPP(c_Power_Opower__class_Opower(_1458799), _1458801), 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(_1458799), _1458803), 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(_1458799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458799), hAPP(c_Int_Onumber__class_Onumber__of(_1458799), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1458801)), _1458803)))], (35824 ^ _782464) ^ [_1459014, _1459016, _1459018] : [class_Rings_Olinordered__idom(_1459014), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1459014), c_Groups_Ozero__class_Ozero(_1459014)), hAPP(hAPP(c_Power_Opower__class_Opower(_1459014), _1459016), 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)))), _1459018)))))], (35830 ^ _782464) ^ [_1459131, _1459133, _1459135] : [class_Groups_Omonoid__mult(_1459131), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459131), _1459133), 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)))), _1459135))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459131), _1459133), hAPP(hAPP(c_Power_Opower__class_Opower(_1459131), hAPP(hAPP(c_Power_Opower__class_Opower(_1459131), _1459133), _1459135)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35836 ^ _782464) ^ [_1459284, _1459286, _1459288] : [class_Rings_Ocomm__semiring__1(_1459284), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459284), _1459286), 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)))), _1459288))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459284), _1459286), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459284), hAPP(hAPP(c_Power_Opower__class_Opower(_1459284), _1459286), _1459288)), hAPP(hAPP(c_Power_Opower__class_Opower(_1459284), _1459286), _1459288))))], (35842 ^ _782464) ^ [_1459453, _1459455] : [class_Rings_Oring__1(_1459453), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459453), hAPP(c_Groups_Ouminus__class_Ouminus(_1459453), c_Groups_Oone__class_Oone(_1459453))), 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)))), _1459455)) = c_Groups_Oone__class_Oone(_1459453))], (35848 ^ _782464) ^ [_1459577, _1459579] : [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), _1459577))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1459579))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1459577))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459579)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459577)))], (35854 ^ _782464) ^ [_1459714, _1459716] : [-(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), _1459714)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1459716))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1459714))) = 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), _1459716)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459714)))], (35860 ^ _782464) ^ [_1459803] : [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, _1459803, 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, _1459803, 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))], (35866 ^ _782464) ^ [_1459894] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1459894, 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, _1459894, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35872 ^ _782464) ^ [_1459991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1459991)), -(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), _1459991), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35878 ^ _782464) ^ [_1460086, _1460088, _1460090] : [class_Int_Onumber__ring(_1460086), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1460086), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1460086), _1460088), _1460090)), 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(_1460086), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460086), hAPP(hAPP(c_Power_Opower__class_Opower(_1460086), _1460088), 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(_1460086), _1460090), 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(_1460086), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1460086), hAPP(c_Int_Onumber__class_Onumber__of(_1460086), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1460088)), _1460090)))], (35884 ^ _782464) ^ [_1460301, _1460303, _1460305] : [class_Rings_Olinordered__idom(_1460301), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460301), c_Groups_Ozero__class_Ozero(_1460301)), hAPP(hAPP(c_Power_Opower__class_Opower(_1460301), _1460303), 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)))), _1460305))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460301), c_Groups_Ozero__class_Ozero(_1460301)), _1460303)))], (35894 ^ _782464) ^ [_1460496, _1460498, _1460500] : [class_Rings_Olinordered__idom(_1460496), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460496), _1460498), c_Groups_Ozero__class_Ozero(_1460496))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460496), hAPP(hAPP(c_Power_Opower__class_Opower(_1460496), _1460498), 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)))), _1460500)))), c_Groups_Ozero__class_Ozero(_1460496))))], (35904 ^ _782464) ^ [_1460691, _1460693] : [class_Rings_Oring__1(_1460691), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1460691), hAPP(c_Groups_Ouminus__class_Ouminus(_1460691), c_Groups_Oone__class_Oone(_1460691))), 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)))), _1460693))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1460691), c_Groups_Oone__class_Oone(_1460691)))], (35910 ^ _782464) ^ [_1460822] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1460822)), -(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), _1460822), 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)))))))], (35916 ^ _782464) ^ [_1460929, _1460931] : [class_Rings_Osemiring__1(_1460929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460931)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460929), 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)))), _1460931))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460929), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460929), hAPP(c_Int_Onat, _1460931))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460929), hAPP(c_Int_Onat, _1460931))))], (35926 ^ _782464) ^ [_1461130, _1461132] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461130)), -(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)))), _1461132)), 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)))), _1461130)) = 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, _1461132, _1461130))))], (35932 ^ _782464) ^ [_1461257, _1461259] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461257)), -(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)))), _1461259))), 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)))), _1461257)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1461259), _1461257))], (35938 ^ _782464) ^ [_1461380, _1461382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1461380), 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)))), _1461382))), 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)))), _1461380)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461382), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1461380))], (35944 ^ _782464) ^ [_1461527] : [_1461527 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1461527) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35950 ^ _782464) ^ [_1461603] : [-(_1461603 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 35953 ^ _782464 : [(35954 ^ _782464) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1461603, 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, _1461603) = 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), _1461603), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35960 ^ _782464) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1461603, 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, _1461603) = 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), _1461603), 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)))]]], (35966 ^ _782464) ^ [_1461863, _1461865] : [class_Rings_Oring__1(_1461863), 35969 ^ _782464 : [(35970 ^ _782464) ^ [] : [_1461865 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461863), _1461865) = c_Groups_Ozero__class_Ozero(_1461863))], (35976 ^ _782464) ^ [] : [-(_1461865 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35979 ^ _782464 : [(35980 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461865), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461863), _1461865) = hAPP(c_Groups_Ouminus__class_Ouminus(_1461863), hAPP(c_Int_Oring__1__class_Oof__int(_1461863), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1461865))))], (35986 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461865), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461863), _1461865) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1461863), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1461863, _1461863)), tc_fun(tc_Int_Oint, _1461863)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1461863, _1461863), _1461863), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1461863, _1461863)), tc_fun(tc_Int_Oint, _1461863)), tc_Int_Oint), c_COMBB(tc_fun(_1461863, _1461863), _1461863, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1461863, tc_fun(tc_fun(_1461863, _1461863), _1461863), tc_Int_Oint), c_HOL_OLet(_1461863, _1461863)), c_Int_Oring__1__class_Oof__int(_1461863)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1461863, _1461863), tc_fun(_1461863, _1461863)), hAPP(hAPP(c_COMBB(tc_fun(_1461863, tc_fun(_1461863, _1461863)), tc_fun(tc_fun(_1461863, _1461863), tc_fun(_1461863, _1461863)), tc_Int_Oint), c_COMBS(_1461863, _1461863, _1461863)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1461863, _1461863), tc_fun(_1461863, tc_fun(_1461863, _1461863))), hAPP(hAPP(c_COMBB(tc_fun(_1461863, tc_fun(_1461863, _1461863)), tc_fun(tc_fun(_1461863, _1461863), tc_fun(_1461863, tc_fun(_1461863, _1461863))), tc_Int_Oint), c_COMBB(_1461863, tc_fun(_1461863, _1461863), _1461863)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1461863, tc_fun(_1461863, _1461863)), tc_Int_Oint), c_If(_1461863)), 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(_1461863, _1461863, _1461863), c_Groups_Oplus__class_Oplus(_1461863)), c_COMBI(_1461863))))), hAPP(hAPP(c_COMBC(_1461863, _1461863, _1461863), hAPP(hAPP(c_COMBB(_1461863, tc_fun(_1461863, _1461863), _1461863), c_Groups_Oplus__class_Oplus(_1461863)), hAPP(hAPP(c_COMBS(_1461863, _1461863, _1461863), c_Groups_Oplus__class_Oplus(_1461863)), c_COMBI(_1461863)))), c_Groups_Oone__class_Oone(_1461863))))), c_Divides_Odivmod__int(_1461865, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (35992 ^ _782464) ^ [_1462776, _1462778] : [class_Int_Onumber__ring(_1462776), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1462776), hAPP(c_Int_Onumber__class_Onumber__of(_1462776), 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)))), _1462778))) = hAPP(c_Int_Onumber__class_Onumber__of(_1462776), c_Int_OMin))], (35998 ^ _782464) ^ [_1462908] : [c_Int_OBit0(_1462908) = c_Int_OMin], (36000 ^ _782464) ^ [_1462942] : [c_Int_OMin = c_Int_OBit0(_1462942)], (36002 ^ _782464) ^ [] : [c_Int_OPls = c_Int_OMin], (36004 ^ _782464) ^ [] : [c_Int_OMin = c_Int_OPls], (36006 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (36008 ^ _782464) ^ [] : [-(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))], (36010 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (36012 ^ _782464) ^ [_1463087] : [c_Int_OBit1(_1463087) = c_Int_OMin, -(_1463087 = c_Int_OMin)], (36018 ^ _782464) ^ [_1463162] : [_1463162 = c_Int_OMin, -(c_Int_OBit1(_1463162) = c_Int_OMin)], (36024 ^ _782464) ^ [_1463255] : [c_Int_OMin = c_Int_OBit1(_1463255), -(c_Int_OMin = _1463255)], (36030 ^ _782464) ^ [_1463330] : [c_Int_OMin = _1463330, -(c_Int_OMin = c_Int_OBit1(_1463330))], (36036 ^ _782464) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (36038 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36040 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (36042 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (36044 ^ _782464) ^ [_1463501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1463501))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1463501)))], (36050 ^ _782464) ^ [_1463584] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1463584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1463584))))], (36056 ^ _782464) ^ [_1463685] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1463685)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1463685), c_Int_OMin)))], (36062 ^ _782464) ^ [_1463780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1463780), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1463780)), c_Int_OMin)))], (36068 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (36070 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (36072 ^ _782464) ^ [_1463935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1463935)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1463935), c_Int_OMin)))], (36078 ^ _782464) ^ [_1464030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464030), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1464030)), c_Int_OMin)))], (36084 ^ _782464) ^ [_1464143] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1464143))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464143)))], (36090 ^ _782464) ^ [_1464226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1464226))))], (36096 ^ _782464) ^ [_1464327] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1464327)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464327), c_Int_OMin)))], (36102 ^ _782464) ^ [_1464422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464422), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1464422)), c_Int_OMin)))], (36108 ^ _782464) ^ [_1464535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1464535))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464535)))], (36114 ^ _782464) ^ [_1464618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1464618))))], (36120 ^ _782464) ^ [] : [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)], (36122 ^ _782464) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36124 ^ _782464) ^ [_1464749] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1464749) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464749))], (36126 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (36128 ^ _782464) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (36130 ^ _782464) ^ [_1464814] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1464814), c_Int_OMin) = c_Int_Opred(_1464814))], (36132 ^ _782464) ^ [_1464845] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1464845) = c_Int_Opred(_1464845))], (36134 ^ _782464) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (36136 ^ _782464) ^ [_1464891] : [class_Int_Onumber__ring(_1464891), c_Int_Oiszero(_1464891, hAPP(c_Int_Onumber__class_Onumber__of(_1464891), c_Int_OMin))], (36142 ^ _782464) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (36144 ^ _782464) ^ [_1464993] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1464993), c_Int_OMin) = c_Int_Osucc(_1464993))], (36146 ^ _782464) ^ [_1465024, _1465026] : [class_Int_Onumber__ring(_1465024), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465024), hAPP(c_Int_Onumber__class_Onumber__of(_1465024), c_Int_OMin)), _1465026) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465024), _1465026))], (36152 ^ _782464) ^ [_1465135, _1465137] : [class_Int_Onumber__ring(_1465135), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465135), _1465137), hAPP(c_Int_Onumber__class_Onumber__of(_1465135), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465135), _1465137))], (36158 ^ _782464) ^ [_1465246] : [class_Int_Onumber__ring(_1465246), -(hAPP(c_Int_Onumber__class_Onumber__of(_1465246), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465246), c_Groups_Oone__class_Oone(_1465246)))], (36164 ^ _782464) ^ [_1465343] : [class_Int_Onumber__ring(_1465343), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1465343), c_Groups_Oone__class_Oone(_1465343)) = hAPP(c_Int_Onumber__class_Onumber__of(_1465343), c_Int_OMin))], (36170 ^ _782464) ^ [_1465440] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1465440), hAPP(c_Int_Onumber__class_Onumber__of(_1465440), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1465440)), class_Int_Onumber__ring(_1465440), class_Rings_Olinordered__idom(_1465440)], (36180 ^ _782464) ^ [_1465585, _1465587] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1465585), _1465587), hAPP(c_Int_Onumber__class_Onumber__of(_1465585), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465585), _1465587)), class_Fields_Ofield__inverse__zero(_1465585), class_Int_Onumber__ring(_1465585)], (36190 ^ _782464) ^ [_1465758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1465758)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1465758), c_Int_OMin)))], (36196 ^ _782464) ^ [_1465853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1465853), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1465853)), c_Int_OMin)))], (36202 ^ _782464) ^ [_1465966] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1465966))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1465966)))], (36208 ^ _782464) ^ [_1466049] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1466049)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1466049))))], (36214 ^ _782464) ^ [_1466138] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1466138, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36216 ^ _782464) ^ [_1466165] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1466165)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466165)))], (36218 ^ _782464) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (36220 ^ _782464) ^ [_1466216, _1466218] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466216), _1466218) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1466216 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1466216 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36230 ^ _782464) ^ [_1466333, _1466335] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466333), _1466335) = c_Groups_Oone__class_Oone(tc_Int_Oint), 36235 ^ _782464 : [(36236 ^ _782464) ^ [] : [-(_1466333 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (36238 ^ _782464) ^ [] : [-(_1466335 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 36239 ^ _782464 : [(36240 ^ _782464) ^ [] : [-(_1466333 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36242 ^ _782464) ^ [] : [-(_1466335 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (36244 ^ _782464) ^ [_1466517, _1466519] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466517), _1466519) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 36245 ^ _782464 : [(36246 ^ _782464) ^ [] : [_1466517 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1466519 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (36252 ^ _782464) ^ [] : [_1466517 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1466519 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (36260 ^ _782464) ^ [_1466743] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1466743)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466743)))], (36262 ^ _782464) ^ [_1466776] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1466776)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466776)))], (36264 ^ _782464) ^ [_1466809] : [class_Int_Onumber__ring(_1466809), -(hAPP(c_Int_Oring__1__class_Oof__int(_1466809), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1466809), c_Int_OMin))], (36270 ^ _782464) ^ [_1466902] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1466902), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1466902))], (36272 ^ _782464) ^ [] : [-(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))], (36274 ^ _782464) ^ [_1466952, _1466954] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1466952), hAPP(c_Int_Onumber__class_Onumber__of(_1466952), c_Int_OMin)), _1466954) = hAPP(c_Groups_Ouminus__class_Ouminus(_1466952), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1466952), c_Groups_Oone__class_Oone(_1466952)), _1466954))), class_Fields_Ofield__inverse__zero(_1466952), class_Int_Onumber__ring(_1466952)], (36284 ^ _782464) ^ [_1467133, _1467135] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1467133), hAPP(hAPP(c_Power_Opower__class_Opower(_1467133), hAPP(c_Int_Onumber__class_Onumber__of(_1467133), c_Int_OMin)), _1467135)) = c_Groups_Oone__class_Oone(_1467133)), class_Int_Onumber__ring(_1467133), class_Rings_Olinordered__idom(_1467133)], (36294 ^ _782464) ^ [_1467298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467298)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1467298) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36300 ^ _782464) ^ [_1467383, _1467385] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467383)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1467383), _1467385)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467383), _1467385) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36310 ^ _782464) ^ [_1467550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467550)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1467550) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1467550), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36316 ^ _782464) ^ [] : [-(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)))], (36318 ^ _782464) ^ [_1467667, _1467669] : [class_Int_Onumber__ring(_1467667), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1467667), hAPP(c_Int_Onumber__class_Onumber__of(_1467667), 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)))), _1467669)) = c_Groups_Oone__class_Oone(_1467667))], (36324 ^ _782464) ^ [] : [-(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)))))], (36326 ^ _782464) ^ [_1467796] : [-(c_Int_Oint__ge__less__than2(_1467796) = 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), _1467796)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36328 ^ _782464) ^ [_1467842] : [-(c_Int_Oint__ge__less__than(_1467842) = 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), _1467842)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36330 ^ _782464) ^ [_1467888, _1467890] : [-(c_Fun_Oinj__on(tc_fun(_1467888, _1467890), tc_fun(tc_prod(_1467888, _1467890), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1467888, _1467890), tc_HOL_Obool), tc_fun(tc_prod(_1467888, _1467890), tc_HOL_Obool), tc_fun(_1467888, _1467890)), c_Set_OCollect(tc_prod(_1467888, _1467890))), hAPP(hAPP(c_COMBB(tc_fun(_1467888, tc_fun(_1467890, tc_HOL_Obool)), tc_fun(tc_prod(_1467888, _1467890), tc_HOL_Obool), tc_fun(_1467888, _1467890)), c_Product__Type_Oprod_Oprod__case(_1467888, _1467890, tc_HOL_Obool)), hAPP(c_COMBB(_1467890, tc_fun(_1467890, tc_HOL_Obool), _1467888), hAPP(c_COMBC(_1467890, _1467890, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1467888, _1467890), tc_HOL_Obool))))], (36332 ^ _782464) ^ [_1468008, _1468010, _1468012, _1468014] : [-(c_Nitpick_Oprod(_1468008, _1468010, _1468012, _1468014) = hAPP(c_Set_OCollect(tc_prod(_1468008, _1468010)), hAPP(c_Product__Type_Oprod_Oprod__case(_1468008, _1468010, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1468008, tc_fun(_1468010, tc_HOL_Obool), tc_fun(_1468010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1468010, tc_HOL_Obool), tc_fun(_1468010, tc_HOL_Obool)), _1468008), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1468010)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1468008), c_fconj), hAPP(hAPP(c_COMBC(_1468008, tc_fun(_1468008, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468008)), _1468012)))), hAPP(hAPP(c_COMBC(_1468010, tc_fun(_1468010, tc_HOL_Obool), tc_HOL_Obool), c_member(_1468010)), _1468014)))))], (36334 ^ _782464) ^ [_1468145, _1468147] : [_1468145 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1468145, _1468147) = _1468147)], (36340 ^ _782464) ^ [_1468222, _1468224] : [-(_1468222 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1468222, _1468224) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1468222), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1468224)))], (36346 ^ _782464) ^ [_1468275, _1468277] : [-(c_Divides_Odivmod__int__rel(_1468275, _1468277) = 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, _1468275))), 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), _1468277)))))), 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)), _1468277))), 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)), _1468277))))), 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)), _1468277)))), 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), _1468277))), 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))))))))], (36348 ^ _782464) ^ [_1468386, _1468388] : [-(_1468386 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468388, _1468386), c_Divides_Odivmod__int(_1468388, _1468386))))], (36354 ^ _782464) ^ [_1468430, _1468432, _1468434, _1468436, _1468438] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468430, _1468432), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468434), _1468436))), -(_1468432 = 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)), _1468438)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468430, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1468432), _1468438)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468434), _1468438)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1468432), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1468434, _1468438))), _1468436)))))], (36368 ^ _782464) ^ [] : [-(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))], (36370 ^ _782464) ^ [_1468754, _1468756] : [class_Int_Onumber__ring(_1468754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1468756)), -(hBOOL(hAPP(hAPP(c_member(_1468754), hAPP(c_Int_Onumber__class_Onumber__of(_1468754), _1468756)), c_Nat_Osemiring__1__class_ONats(_1468754))))], (36380 ^ _782464) ^ [_1468934, _1468936, _1468938, _1468940] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1468934, tc_fun(_1468936, tc_HOL_Obool))), _1468938), _1468940)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1468934, _1468936)), hAPP(hAPP(c_Product__Type_OPair(_1468934, _1468936), _1468938), _1468940)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1468934, _1468936), tc_HOL_Obool)))))], (36386 ^ _782464) ^ [_1469091, _1469093, _1469095, _1469097] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469091, _1469093)), hAPP(hAPP(c_Product__Type_OPair(_1469091, _1469093), _1469095), _1469097)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1469091, _1469093), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1469091, tc_fun(_1469093, tc_HOL_Obool))), _1469095), _1469097)))], (36392 ^ _782464) ^ [_1469275, _1469277, _1469279, _1469281] : [hAPP(hAPP(c_COMBC(_1469275, tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_fun(_1469277, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469277, tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_fun(_1469277, tc_HOL_Obool)), _1469275), c_COMBC(_1469277, tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469277, tc_prod(_1469275, _1469277)), tc_fun(_1469277, tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool)), _1469275), hAPP(c_COMBB(tc_prod(_1469275, _1469277), tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool), _1469277), c_member(tc_prod(_1469275, _1469277)))), c_Product__Type_OPair(_1469275, _1469277)))), _1469279) = hAPP(hAPP(c_COMBC(_1469275, tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_fun(_1469277, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469277, tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_fun(_1469277, tc_HOL_Obool)), _1469275), c_COMBC(_1469277, tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469277, tc_prod(_1469275, _1469277)), tc_fun(_1469277, tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool)), _1469275), hAPP(c_COMBB(tc_prod(_1469275, _1469277), tc_fun(tc_fun(tc_prod(_1469275, _1469277), tc_HOL_Obool), tc_HOL_Obool), _1469277), c_member(tc_prod(_1469275, _1469277)))), c_Product__Type_OPair(_1469275, _1469277)))), _1469281), -(_1469279 = _1469281)], (36398 ^ _782464) ^ [_1469824, _1469826, _1469828, _1469830] : [_1469828 = _1469830, -(hAPP(hAPP(c_COMBC(_1469824, tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_fun(_1469826, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469826, tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_fun(_1469826, tc_HOL_Obool)), _1469824), c_COMBC(_1469826, tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469826, tc_prod(_1469824, _1469826)), tc_fun(_1469826, tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool)), _1469824), hAPP(c_COMBB(tc_prod(_1469824, _1469826), tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool), _1469826), c_member(tc_prod(_1469824, _1469826)))), c_Product__Type_OPair(_1469824, _1469826)))), _1469828) = hAPP(hAPP(c_COMBC(_1469824, tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_fun(_1469826, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469826, tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_fun(_1469826, tc_HOL_Obool)), _1469824), c_COMBC(_1469826, tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469826, tc_prod(_1469824, _1469826)), tc_fun(_1469826, tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool)), _1469824), hAPP(c_COMBB(tc_prod(_1469824, _1469826), tc_fun(tc_fun(tc_prod(_1469824, _1469826), tc_HOL_Obool), tc_HOL_Obool), _1469826), c_member(tc_prod(_1469824, _1469826)))), c_Product__Type_OPair(_1469824, _1469826)))), _1469830))], (36404 ^ _782464) ^ [_1470406, _1470408, _1470410, _1470412, _1470414, _1470416] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470406, tc_fun(_1470408, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1470406, tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_fun(_1470408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470408, tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_fun(_1470408, tc_HOL_Obool)), _1470406), c_COMBC(_1470408, tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470408, tc_prod(_1470406, _1470408)), tc_fun(_1470408, tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool)), _1470406), hAPP(c_COMBB(tc_prod(_1470406, _1470408), tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool), _1470408), c_member(tc_prod(_1470406, _1470408)))), c_Product__Type_OPair(_1470406, _1470408)))), _1470410)), hAPP(hAPP(c_COMBC(_1470406, tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_fun(_1470408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470408, tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_fun(_1470408, tc_HOL_Obool)), _1470406), c_COMBC(_1470408, tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470408, tc_prod(_1470406, _1470408)), tc_fun(_1470408, tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool)), _1470406), hAPP(c_COMBB(tc_prod(_1470406, _1470408), tc_fun(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool), tc_HOL_Obool), _1470408), c_member(tc_prod(_1470406, _1470408)))), c_Product__Type_OPair(_1470406, _1470408)))), _1470412)), _1470414), _1470416)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470406, _1470408)), hAPP(hAPP(c_Product__Type_OPair(_1470406, _1470408), _1470414), _1470416)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1470406, _1470408), tc_HOL_Obool)), _1470410), _1470412))))], (36410 ^ _782464) ^ [_1471063, _1471065, _1471067, _1471069, _1471071, _1471073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471063, _1471065)), hAPP(hAPP(c_Product__Type_OPair(_1471063, _1471065), _1471071), _1471073)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool)), _1471067), _1471069))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471063, tc_fun(_1471065, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471063, tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_fun(_1471065, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471065, tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_fun(_1471065, tc_HOL_Obool)), _1471063), c_COMBC(_1471065, tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471065, tc_prod(_1471063, _1471065)), tc_fun(_1471065, tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool)), _1471063), hAPP(c_COMBB(tc_prod(_1471063, _1471065), tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool), _1471065), c_member(tc_prod(_1471063, _1471065)))), c_Product__Type_OPair(_1471063, _1471065)))), _1471067)), hAPP(hAPP(c_COMBC(_1471063, tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_fun(_1471065, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471065, tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_fun(_1471065, tc_HOL_Obool)), _1471063), c_COMBC(_1471065, tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471065, tc_prod(_1471063, _1471065)), tc_fun(_1471065, tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool)), _1471063), hAPP(c_COMBB(tc_prod(_1471063, _1471065), tc_fun(tc_fun(tc_prod(_1471063, _1471065), tc_HOL_Obool), tc_HOL_Obool), _1471065), c_member(tc_prod(_1471063, _1471065)))), c_Product__Type_OPair(_1471063, _1471065)))), _1471069)), _1471071), _1471073)))], (36416 ^ _782464) ^ [_1471747, _1471749, _1471751, _1471753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471747, tc_fun(_1471749, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471747, tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_fun(_1471749, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471749, tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_fun(_1471749, tc_HOL_Obool)), _1471747), c_COMBC(_1471749, tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471749, tc_prod(_1471747, _1471749)), tc_fun(_1471749, tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool)), _1471747), hAPP(c_COMBB(tc_prod(_1471747, _1471749), tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool), _1471749), c_member(tc_prod(_1471747, _1471749)))), c_Product__Type_OPair(_1471747, _1471749)))), _1471751)), hAPP(hAPP(c_COMBC(_1471747, tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_fun(_1471749, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471749, tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_fun(_1471749, tc_HOL_Obool)), _1471747), c_COMBC(_1471749, tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471749, tc_prod(_1471747, _1471749)), tc_fun(_1471749, tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool)), _1471747), hAPP(c_COMBB(tc_prod(_1471747, _1471749), tc_fun(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool), tc_HOL_Obool), _1471749), c_member(tc_prod(_1471747, _1471749)))), c_Product__Type_OPair(_1471747, _1471749)))), _1471753))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1471747, _1471749), tc_HOL_Obool)), _1471751), _1471753)))], (36422 ^ _782464) ^ [_1472348, _1472350, _1472352, _1472354] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool)), _1472352), _1472354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472348, tc_fun(_1472350, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1472348, tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_fun(_1472350, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472350, tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_fun(_1472350, tc_HOL_Obool)), _1472348), c_COMBC(_1472350, tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472350, tc_prod(_1472348, _1472350)), tc_fun(_1472350, tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool)), _1472348), hAPP(c_COMBB(tc_prod(_1472348, _1472350), tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool), _1472350), c_member(tc_prod(_1472348, _1472350)))), c_Product__Type_OPair(_1472348, _1472350)))), _1472352)), hAPP(hAPP(c_COMBC(_1472348, tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_fun(_1472350, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472350, tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_fun(_1472350, tc_HOL_Obool)), _1472348), c_COMBC(_1472350, tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472350, tc_prod(_1472348, _1472350)), tc_fun(_1472350, tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool)), _1472348), hAPP(c_COMBB(tc_prod(_1472348, _1472350), tc_fun(tc_fun(tc_prod(_1472348, _1472350), tc_HOL_Obool), tc_HOL_Obool), _1472350), c_member(tc_prod(_1472348, _1472350)))), c_Product__Type_OPair(_1472348, _1472350)))), _1472354))))], (36428 ^ _782464) ^ [_1472982, _1472984, _1472986, _1472988, _1472990, _1472992] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472982, tc_fun(_1472984, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1472982, tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_fun(_1472984, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472984, tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_fun(_1472984, tc_HOL_Obool)), _1472982), c_COMBC(_1472984, tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472984, tc_prod(_1472982, _1472984)), tc_fun(_1472984, tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool)), _1472982), hAPP(c_COMBB(tc_prod(_1472982, _1472984), tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool), _1472984), c_member(tc_prod(_1472982, _1472984)))), c_Product__Type_OPair(_1472982, _1472984)))), _1472986)), hAPP(hAPP(c_COMBC(_1472982, tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_fun(_1472984, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472984, tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_fun(_1472984, tc_HOL_Obool)), _1472982), c_COMBC(_1472984, tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472984, tc_prod(_1472982, _1472984)), tc_fun(_1472984, tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool)), _1472982), hAPP(c_COMBB(tc_prod(_1472982, _1472984), tc_fun(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool), tc_HOL_Obool), _1472984), c_member(tc_prod(_1472982, _1472984)))), c_Product__Type_OPair(_1472982, _1472984)))), _1472988)), _1472990), _1472992)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472982, _1472984)), hAPP(hAPP(c_Product__Type_OPair(_1472982, _1472984), _1472990), _1472992)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1472982, _1472984), tc_HOL_Obool)), _1472986), _1472988))))], (36434 ^ _782464) ^ [_1473639, _1473641, _1473643, _1473645, _1473647, _1473649] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473639, _1473641)), hAPP(hAPP(c_Product__Type_OPair(_1473639, _1473641), _1473647), _1473649)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool)), _1473643), _1473645))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473639, tc_fun(_1473641, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1473639, tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_fun(_1473641, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473641, tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_fun(_1473641, tc_HOL_Obool)), _1473639), c_COMBC(_1473641, tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473641, tc_prod(_1473639, _1473641)), tc_fun(_1473641, tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool)), _1473639), hAPP(c_COMBB(tc_prod(_1473639, _1473641), tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool), _1473641), c_member(tc_prod(_1473639, _1473641)))), c_Product__Type_OPair(_1473639, _1473641)))), _1473643)), hAPP(hAPP(c_COMBC(_1473639, tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_fun(_1473641, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473641, tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_fun(_1473641, tc_HOL_Obool)), _1473639), c_COMBC(_1473641, tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473641, tc_prod(_1473639, _1473641)), tc_fun(_1473641, tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool)), _1473639), hAPP(c_COMBB(tc_prod(_1473639, _1473641), tc_fun(tc_fun(tc_prod(_1473639, _1473641), tc_HOL_Obool), tc_HOL_Obool), _1473641), c_member(tc_prod(_1473639, _1473641)))), c_Product__Type_OPair(_1473639, _1473641)))), _1473645)), _1473647), _1473649)))], (36440 ^ _782464) ^ [_1474302, _1474304, _1474306] : [class_Enum_Oenum(_1474302), class_Enum_Oenum(_1474304), 36447 ^ _782464 : [(36448 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1474304, _1474302)), _1474306)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1474304), hAPP(hAPP(c_COMBB(tc_fun(_1474302, tc_HOL_Obool), tc_HOL_Obool, _1474304), c_Enum_Oenum__class_Oenum__ex(_1474302)), hAPP(hAPP(c_COMBB(tc_fun(_1474302, tc_prod(_1474304, _1474302)), tc_fun(_1474302, tc_HOL_Obool), _1474304), hAPP(c_COMBB(tc_prod(_1474304, _1474302), tc_HOL_Obool, _1474302), _1474306)), c_Product__Type_OPair(_1474304, _1474302))))))], (36454 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1474304), hAPP(hAPP(c_COMBB(tc_fun(_1474302, tc_HOL_Obool), tc_HOL_Obool, _1474304), c_Enum_Oenum__class_Oenum__ex(_1474302)), hAPP(hAPP(c_COMBB(tc_fun(_1474302, tc_prod(_1474304, _1474302)), tc_fun(_1474302, tc_HOL_Obool), _1474304), hAPP(c_COMBB(tc_prod(_1474304, _1474302), tc_HOL_Obool, _1474302), _1474306)), c_Product__Type_OPair(_1474304, _1474302))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1474304, _1474302)), _1474306)))]]], (36460 ^ _782464) ^ [_1474741, _1474743, _1474745] : [class_Enum_Oenum(_1474741), class_Enum_Oenum(_1474743), 36467 ^ _782464 : [(36468 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1474743, _1474741)), _1474745)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1474743), hAPP(hAPP(c_COMBB(tc_fun(_1474741, tc_HOL_Obool), tc_HOL_Obool, _1474743), c_Enum_Oenum__class_Oenum__all(_1474741)), hAPP(hAPP(c_COMBB(tc_fun(_1474741, tc_prod(_1474743, _1474741)), tc_fun(_1474741, tc_HOL_Obool), _1474743), hAPP(c_COMBB(tc_prod(_1474743, _1474741), tc_HOL_Obool, _1474741), _1474745)), c_Product__Type_OPair(_1474743, _1474741))))))], (36474 ^ _782464) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1474743), hAPP(hAPP(c_COMBB(tc_fun(_1474741, tc_HOL_Obool), tc_HOL_Obool, _1474743), c_Enum_Oenum__class_Oenum__all(_1474741)), hAPP(hAPP(c_COMBB(tc_fun(_1474741, tc_prod(_1474743, _1474741)), tc_fun(_1474741, tc_HOL_Obool), _1474743), hAPP(c_COMBB(tc_prod(_1474743, _1474741), tc_HOL_Obool, _1474741), _1474745)), c_Product__Type_OPair(_1474743, _1474741))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1474743, _1474741)), _1474745)))]]], (36480 ^ _782464) ^ [_1475204, _1475206, _1475208, _1475210, _1475212] : [hBOOL(hAPP(hAPP(c_member(_1475204), _1475206), hAPP(c_Relation_OImage(_1475208, _1475204, _1475210), _1475212))), 36484 ^ _782464 : [(36485 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475208), 36483 ^ [_1475204, _1475206, _1475208, _1475210, _1475212]), _1475212)))], (36487 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475208, _1475204)), hAPP(hAPP(c_Product__Type_OPair(_1475208, _1475204), 36483 ^ [_1475204, _1475206, _1475208, _1475210, _1475212]), _1475206)), _1475210)))]]], (36489 ^ _782464) ^ [_1475420, _1475422, _1475424, _1475426, _1475428] : [-(hBOOL(hAPP(hAPP(c_member(_1475420), _1475422), hAPP(c_Relation_OImage(_1475424, _1475420, _1475426), _1475428)))), 36490 ^ _782464 : [(36491 ^ _782464) ^ [_1475506] : [hBOOL(hAPP(hAPP(c_member(_1475424), _1475506), _1475428)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475424, _1475420)), hAPP(hAPP(c_Product__Type_OPair(_1475424, _1475420), _1475506), _1475422)), _1475426))]]], (36499 ^ _782464) ^ [_1475686, _1475688, _1475690, _1475692, _1475694, _1475696] : [hBOOL(hAPP(hAPP(c_member(_1475686), _1475688), _1475690)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475686, _1475692)), hAPP(hAPP(c_Product__Type_OPair(_1475686, _1475692), _1475688), _1475694)), _1475696)), -(hBOOL(hAPP(hAPP(c_member(_1475692), _1475694), hAPP(c_Relation_OImage(_1475686, _1475692, _1475696), _1475690))))], (36509 ^ _782464) ^ [_1475911, _1475913, _1475915, _1475917, _1475919, _1475921] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475911, _1475913), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475915), _1475917))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475911, _1475913), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475919), _1475921))), -(_1475913 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1475917 = _1475921)], (36523 ^ _782464) ^ [_1476115, _1476117, _1476119, _1476121, _1476123, _1476125] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476115, _1476117), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476119), _1476121))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476115, _1476117), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476123), _1476125))), -(_1476117 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476119 = _1476123)], (36537 ^ _782464) ^ [_1476319, _1476321, _1476323] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476319, _1476319), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476321), _1476323))), -(_1476319 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476323 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36547 ^ _782464) ^ [_1476431] : [-(_1476431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1476431), 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)))))], (36553 ^ _782464) ^ [_1476497, _1476499, _1476501, _1476503, _1476505, _1476507] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476497, tc_fun(_1476499, tc_fun(_1476501, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1476497, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_fun(_1476499, tc_fun(_1476501, tc_HOL_Obool)), _1476497), hAPP(c_COMBC(_1476499, tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_fun(_1476501, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476501, tc_fun(tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_fun(_1476501, tc_HOL_Obool)), _1476499), c_COMBC(_1476501, tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476501, tc_prod(_1476499, _1476501)), tc_fun(_1476501, tc_fun(tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_HOL_Obool)), _1476499), hAPP(c_COMBB(tc_prod(_1476499, _1476501), tc_fun(tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool), tc_HOL_Obool), _1476501), c_member(tc_prod(_1476499, _1476501)))), c_Product__Type_OPair(_1476499, _1476501))))), _1476503)), _1476505), _1476507)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476499, _1476501)), hAPP(hAPP(c_Product__Type_OPair(_1476499, _1476501), _1476505), _1476507)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476497, tc_fun(tc_prod(_1476499, _1476501), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1476497, tc_HOL_Obool))), _1476503))))], (36559 ^ _782464) ^ [_1476980, _1476982, _1476984, _1476986, _1476988, _1476990] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476982, _1476984)), hAPP(hAPP(c_Product__Type_OPair(_1476982, _1476984), _1476988), _1476990)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476980, tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1476980, tc_HOL_Obool))), _1476986))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476980, tc_fun(_1476982, tc_fun(_1476984, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1476980, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_fun(_1476982, tc_fun(_1476984, tc_HOL_Obool)), _1476980), hAPP(c_COMBC(_1476982, tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_fun(_1476984, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476984, tc_fun(tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_fun(_1476984, tc_HOL_Obool)), _1476982), c_COMBC(_1476984, tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476984, tc_prod(_1476982, _1476984)), tc_fun(_1476984, tc_fun(tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_HOL_Obool)), _1476982), hAPP(c_COMBB(tc_prod(_1476982, _1476984), tc_fun(tc_fun(tc_prod(_1476982, _1476984), tc_HOL_Obool), tc_HOL_Obool), _1476984), c_member(tc_prod(_1476982, _1476984)))), c_Product__Type_OPair(_1476982, _1476984))))), _1476986)), _1476988), _1476990)))], (36565 ^ _782464) ^ [_1477496, _1477498, _1477500, _1477502, _1477504, _1477506] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477496, tc_fun(_1477498, tc_fun(_1477500, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477496, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_fun(_1477498, tc_fun(_1477500, tc_HOL_Obool)), _1477496), hAPP(c_COMBC(_1477498, tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_fun(_1477500, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477500, tc_fun(tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_fun(_1477500, tc_HOL_Obool)), _1477498), c_COMBC(_1477500, tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477500, tc_prod(_1477498, _1477500)), tc_fun(_1477500, tc_fun(tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_HOL_Obool)), _1477498), hAPP(c_COMBB(tc_prod(_1477498, _1477500), tc_fun(tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool), tc_HOL_Obool), _1477500), c_member(tc_prod(_1477498, _1477500)))), c_Product__Type_OPair(_1477498, _1477500))))), _1477502)), _1477504), _1477506)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477498, _1477500)), hAPP(hAPP(c_Product__Type_OPair(_1477498, _1477500), _1477504), _1477506)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477496, tc_fun(tc_prod(_1477498, _1477500), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477496, tc_HOL_Obool))), _1477502))))], (36571 ^ _782464) ^ [_1477979, _1477981, _1477983, _1477985, _1477987, _1477989] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477981, _1477983)), hAPP(hAPP(c_Product__Type_OPair(_1477981, _1477983), _1477987), _1477989)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477979, tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477979, tc_HOL_Obool))), _1477985))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477979, tc_fun(_1477981, tc_fun(_1477983, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477979, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_fun(_1477981, tc_fun(_1477983, tc_HOL_Obool)), _1477979), hAPP(c_COMBC(_1477981, tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_fun(_1477983, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477983, tc_fun(tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_fun(_1477983, tc_HOL_Obool)), _1477981), c_COMBC(_1477983, tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477983, tc_prod(_1477981, _1477983)), tc_fun(_1477983, tc_fun(tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_HOL_Obool)), _1477981), hAPP(c_COMBB(tc_prod(_1477981, _1477983), tc_fun(tc_fun(tc_prod(_1477981, _1477983), tc_HOL_Obool), tc_HOL_Obool), _1477983), c_member(tc_prod(_1477981, _1477983)))), c_Product__Type_OPair(_1477981, _1477983))))), _1477985)), _1477987), _1477989)))], (36577 ^ _782464) ^ [_1478468, _1478470, _1478472] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478468, _1478468), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478470), _1478472))), -(_1478468 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1478470 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (36587 ^ _782464) ^ [_1478584, _1478586, _1478588, _1478590] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478584, _1478586), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478588), _1478590))), -(_1478586 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1478584, _1478586) = _1478590)], (36597 ^ _782464) ^ [_1478710, _1478712, _1478714, _1478716] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478710, _1478712), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478714), _1478716))), -(_1478712 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1478710), _1478712) = _1478714)], (36607 ^ _782464) ^ [_1478840] : [class_Rings_Osemiring__1(_1478840), -(hBOOL(hAPP(hAPP(c_member(_1478840), c_Groups_Ozero__class_Ozero(_1478840)), c_Nat_Osemiring__1__class_ONats(_1478840))))], (36613 ^ _782464) ^ [_1478935, _1478937] : [-(c_Divides_Odivmod__int(_1478935, _1478937) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1478935), _1478937)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1478935, _1478937)))], (36615 ^ _782464) ^ [_1478979, _1478981, _1478983] : [class_Rings_Osemiring__1(_1478979), hBOOL(hAPP(hAPP(c_member(_1478979), _1478981), c_Nat_Osemiring__1__class_ONats(_1478979))), hBOOL(hAPP(hAPP(c_member(_1478979), _1478983), c_Nat_Osemiring__1__class_ONats(_1478979))), -(hBOOL(hAPP(hAPP(c_member(_1478979), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478979), _1478981), _1478983)), c_Nat_Osemiring__1__class_ONats(_1478979))))], (36629 ^ _782464) ^ [_1479234, _1479236, _1479238] : [class_Rings_Osemiring__1(_1479234), hBOOL(hAPP(hAPP(c_member(_1479234), _1479236), c_Nat_Osemiring__1__class_ONats(_1479234))), hBOOL(hAPP(hAPP(c_member(_1479234), _1479238), c_Nat_Osemiring__1__class_ONats(_1479234))), -(hBOOL(hAPP(hAPP(c_member(_1479234), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1479234), _1479236), _1479238)), c_Nat_Osemiring__1__class_ONats(_1479234))))], (36643 ^ _782464) ^ [_1479489] : [class_Rings_Osemiring__1(_1479489), -(hBOOL(hAPP(hAPP(c_member(_1479489), c_Groups_Oone__class_Oone(_1479489)), c_Nat_Osemiring__1__class_ONats(_1479489))))], (36649 ^ _782464) ^ [_1479584, _1479586] : [class_Rings_Osemiring__1(_1479584), -(hBOOL(hAPP(hAPP(c_member(_1479584), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1479584), _1479586)), c_Nat_Osemiring__1__class_ONats(_1479584))))], (36655 ^ _782464) ^ [_1479711, _1479713, _1479715, _1479717, _1479719] : [hBOOL(hAPP(hAPP(c_member(_1479711), _1479713), hAPP(c_Relation_OImage(_1479715, _1479711, _1479717), hAPP(hAPP(c_Set_Oinsert(_1479715), _1479719), c_Orderings_Obot__class_Obot(tc_fun(_1479715, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1479715, _1479711)), hAPP(hAPP(c_Product__Type_OPair(_1479715, _1479711), _1479719), _1479713)), _1479717)))], (36661 ^ _782464) ^ [_1479882, _1479884, _1479886, _1479888, _1479890] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1479886, _1479882)), hAPP(hAPP(c_Product__Type_OPair(_1479886, _1479882), _1479890), _1479884)), _1479888)), -(hBOOL(hAPP(hAPP(c_member(_1479882), _1479884), hAPP(c_Relation_OImage(_1479886, _1479882, _1479888), hAPP(hAPP(c_Set_Oinsert(_1479886), _1479890), c_Orderings_Obot__class_Obot(tc_fun(_1479886, tc_HOL_Obool)))))))], (36667 ^ _782464) ^ [_1480055, _1480057] : [-(_1480055 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480057, _1480055), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1480057), _1480055)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1480057, _1480055)))))], (36673 ^ _782464) ^ [_1480112, _1480114, _1480116, _1480118] : [-(hAPP(c_Relation_OImage(_1480112, _1480114, _1480116), hAPP(hAPP(c_Set_Oinsert(_1480112), _1480118), c_Orderings_Obot__class_Obot(tc_fun(_1480112, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1480114), hAPP(hAPP(c_COMBC(_1480114, tc_fun(tc_prod(_1480112, _1480114), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1480112, _1480114), tc_fun(tc_fun(tc_prod(_1480112, _1480114), tc_HOL_Obool), tc_HOL_Obool), _1480114), c_member(tc_prod(_1480112, _1480114))), hAPP(c_Product__Type_OPair(_1480112, _1480114), _1480118))), _1480116)))], (36675 ^ _782464) ^ [_1480215, _1480217, _1480219, _1480221, _1480223, _1480225, _1480227] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480215, _1480217), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480219), _1480221))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480223, _1480217), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480225), _1480227))), -(_1480217 = 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), _1480215), _1480223), _1480217), 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), _1480219), _1480225)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480221), _1480227)), _1480217))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480221), _1480227), _1480217)))))], (36689 ^ _782464) ^ [_1480525, _1480527, _1480529, _1480531] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480525, _1480527), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480529), _1480531))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480525), _1480527), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1480531), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480529)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480529)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1480531), 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), _1480527), _1480531))))))], (36695 ^ _782464) ^ [_1480752, _1480754, _1480756, _1480758] : [_1480752 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1480754), _1480756)), _1480758), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480752, _1480754), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480756), _1480758)))), 36702 ^ _782464 : [(36703 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480754)))], (36705 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480758), _1480754))]], 36710 ^ _782464 : [(36711 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480754))], (36713 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480754), _1480758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480758), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (36721 ^ _782464) ^ [_1481214, _1481216, _1481218, _1481220, _1481222] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1481214, _1481216), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1481218), _1481220))), -(_1481216 = 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), _1481222), _1481214), _1481216), 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), _1481222), _1481218)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1481222), _1481220)), _1481216))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1481222), _1481220), _1481216)))))], (36731 ^ _782464) ^ [_1481436, _1481438, _1481440, _1481442, _1481444, _1481446, _1481448] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481436, _1481438)), hAPP(hAPP(c_Product__Type_OPair(_1481436, _1481438), _1481440), _1481442)), _1481444)), -(hBOOL(hAPP(hAPP(c_member(_1481446), hAPP(hAPP(_1481448, _1481440), _1481442)), hAPP(c_Set_Oimage(tc_prod(_1481436, _1481438), _1481446, hAPP(c_Product__Type_Oprod_Oprod__case(_1481436, _1481438, _1481446), _1481448)), _1481444))))], (36737 ^ _782464) ^ [_1481630, _1481632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481630), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1481632, _1481630) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481632), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481630)))], (36743 ^ _782464) ^ [_1481736, _1481738] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481736), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36746 ^ _782464 : [(36747 ^ _782464) ^ [] : [36748 ^ _782464 : [(36749 ^ _782464) ^ [] : [_1481738 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36751 ^ _782464) ^ [] : [_1481736 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1481738, _1481736) = 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)))], (36755 ^ _782464) ^ [] : [-(c_Nitpick_Onorm__frac(_1481738, _1481736) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1481738), _1481736)), 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), _1481738))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481736)))), -(_1481738 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1481736 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (36765 ^ _782464) ^ [_1482034, _1482036, _1482038] : [-(hAPP(c_Divides_Oadjust(_1482034), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1482036), _1482038)) = 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), _1482038), _1482034)), 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)))), _1482036)), 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)))), _1482036)), _1482038))))], (36767 ^ _782464) ^ [_1482114, _1482116, _1482118, _1482120, _1482122, _1482124] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482114, tc_fun(_1482116, tc_HOL_Obool))), _1482118), _1482120), _1482122), _1482124)), -(hBOOL(hAPP(hAPP(_1482118, _1482122), _1482124))), -(hBOOL(hAPP(hAPP(_1482120, _1482122), _1482124)))], (36777 ^ _782464) ^ [_1482272, _1482274, _1482276, _1482278, _1482280, _1482282] : [36778 ^ _782464 : [(36779 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1482272, _1482274), _1482276))], (36781 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1482278, _1482274), _1482276))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482280, tc_fun(_1482282, tc_HOL_Obool))), _1482278), _1482272), _1482274), _1482276)))], (36785 ^ _782464) ^ [_1482455, _1482457, _1482459, _1482461, _1482463, _1482465] : [hBOOL(hAPP(hAPP(_1482455, _1482457), _1482459)), hBOOL(hAPP(hAPP(_1482461, _1482457), _1482459)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482463, tc_fun(_1482465, tc_HOL_Obool))), _1482455), _1482461), _1482457), _1482459)))], (36795 ^ _782464) ^ [_1482658, _1482660, _1482662, _1482664, _1482666, _1482668] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482658, tc_fun(_1482660, tc_HOL_Obool))), _1482662), _1482664), _1482666), _1482668)), 36798 ^ _782464 : [(36799 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1482662, _1482666), _1482668)))], (36801 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1482664, _1482666), _1482668)))]]], (36803 ^ _782464) ^ [_1482831, _1482833, _1482835, _1482837, _1482839, _1482841, _1482843] : [hBOOL(hAPP(hAPP(c_member(_1482831), _1482833), hAPP(hAPP(_1482835, _1482837), _1482839))), -(hBOOL(hAPP(hAPP(c_member(_1482831), _1482833), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1482841, _1482843, tc_fun(_1482831, tc_HOL_Obool)), _1482835), hAPP(hAPP(c_Product__Type_OPair(_1482841, _1482843), _1482837), _1482839)))))], (36809 ^ _782464) ^ [_1483002, _1483004, _1483006, _1483008, _1483010] : [hBOOL(hAPP(hAPP(_1483002, _1483004), _1483006)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483008, _1483010, tc_HOL_Obool), _1483002), hAPP(hAPP(c_Product__Type_OPair(_1483008, _1483010), _1483004), _1483006))))], (36815 ^ _782464) ^ [_1483131, _1483133, _1483135, _1483137, _1483139] : [hBOOL(hAPP(hAPP(_1483131, _1483133), _1483135)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483137, _1483139, tc_HOL_Obool), _1483131), hAPP(hAPP(c_Product__Type_OPair(_1483137, _1483139), _1483133), _1483135))))], (36821 ^ _782464) ^ [_1483278, _1483280, _1483282, _1483284] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1483278, tc_fun(_1483280, tc_HOL_Obool))), _1483282), _1483284))], (36823 ^ _782464) ^ [_1483320, _1483322, _1483324] : [-(c_Fun_Oinj__on(tc_prod(_1483320, _1483322), tc_prod(_1483322, _1483320), hAPP(c_Product__Type_Oprod_Oprod__case(_1483320, _1483322, tc_prod(_1483322, _1483320)), hAPP(c_COMBC(_1483322, _1483320, tc_prod(_1483322, _1483320)), c_Product__Type_OPair(_1483322, _1483320))), _1483324))], (36825 ^ _782464) ^ [_1483378, _1483380, _1483382, _1483384, _1483386, _1483388, _1483390] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483378, _1483380, tc_fun(_1483382, tc_HOL_Obool)), _1483384), hAPP(hAPP(c_Product__Type_OPair(_1483378, _1483380), _1483386), _1483388)), _1483390)), -(hBOOL(hAPP(hAPP(hAPP(_1483384, _1483386), _1483388), _1483390)))], (36831 ^ _782464) ^ [_1483529, _1483531, _1483533, _1483535, _1483537, _1483539] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483529, tc_fun(_1483531, tc_HOL_Obool))), _1483533), _1483535), _1483537), _1483539)), -(hBOOL(hAPP(hAPP(_1483533, _1483537), _1483539)))], (36837 ^ _782464) ^ [_1483662, _1483664, _1483666, _1483668, _1483670, _1483672] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483662, tc_fun(_1483664, tc_HOL_Obool))), _1483666), _1483668), _1483670), _1483672)), -(hBOOL(hAPP(hAPP(_1483668, _1483670), _1483672)))], (36843 ^ _782464) ^ [_1483795, _1483797, _1483799, _1483801, _1483803, _1483805] : [hBOOL(hAPP(hAPP(_1483795, _1483797), _1483799)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483801, tc_fun(_1483803, tc_HOL_Obool))), _1483795), _1483805), _1483797), _1483799)))], (36849 ^ _782464) ^ [_1483928, _1483930, _1483932, _1483934, _1483936, _1483938] : [hBOOL(hAPP(hAPP(_1483928, _1483930), _1483932)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483934, tc_fun(_1483936, tc_HOL_Obool))), _1483938), _1483928), _1483930), _1483932)))], (36855 ^ _782464) ^ [_1484061, _1484063, _1484065, _1484067, _1484069, _1484071] : [hBOOL(hAPP(hAPP(_1484061, _1484063), _1484065)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484067, tc_fun(_1484069, tc_HOL_Obool))), _1484061), _1484071)), -(hBOOL(hAPP(hAPP(_1484071, _1484063), _1484065)))], (36865 ^ _782464) ^ [_1484252, _1484254, _1484256, _1484258, _1484260, _1484262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484252, tc_fun(_1484254, tc_HOL_Obool))), _1484256), _1484258)), hBOOL(hAPP(hAPP(_1484256, _1484260), _1484262)), -(hBOOL(hAPP(hAPP(_1484258, _1484260), _1484262)))], (36875 ^ _782464) ^ [_1484443, _1484445, _1484447, _1484449, _1484451, _1484453] : [hAPP(hAPP(c_Product__Type_OPair(_1484443, _1484445), _1484447), _1484449) = hAPP(hAPP(c_Product__Type_OPair(_1484443, _1484445), _1484451), _1484453), 36878 ^ _782464 : [(36879 ^ _782464) ^ [] : [-(_1484447 = _1484451)], (36881 ^ _782464) ^ [] : [-(_1484449 = _1484453)]]], (36883 ^ _782464) ^ [_1484621, _1484623, _1484625, _1484627, _1484629, _1484631] : [hAPP(hAPP(c_Product__Type_OPair(_1484621, _1484623), _1484625), _1484627) = hAPP(hAPP(c_Product__Type_OPair(_1484621, _1484623), _1484629), _1484631), 36886 ^ _782464 : [(36887 ^ _782464) ^ [] : [-(_1484625 = _1484629)], (36889 ^ _782464) ^ [] : [-(_1484627 = _1484631)]]], (36891 ^ _782464) ^ [_1484764, _1484766, _1484768, _1484770, _1484772, _1484774] : [-(hAPP(hAPP(c_Product__Type_OPair(_1484764, _1484766), _1484768), _1484770) = hAPP(hAPP(c_Product__Type_OPair(_1484764, _1484766), _1484772), _1484774)), _1484768 = _1484772, _1484770 = _1484774], (36901 ^ _782464) ^ [_1484965, _1484967, _1484969] : [hBOOL(hAPP(_1484965, 36902 ^ [_1484965, _1484967, _1484969])), 36905 ^ _782464 : [(36906 ^ _782464) ^ [_1485076, _1485078] : [-(hBOOL(hAPP(_1484965, hAPP(hAPP(c_Product__Type_OPair(_1484967, _1484969), _1485078), _1485076))))]]], (36908 ^ _782464) ^ [_1485112, _1485114, _1485116] : [hBOOL(hAPP(_1485112, hAPP(hAPP(c_Product__Type_OPair(_1485114, _1485116), 36909 ^ [_1485112, _1485114, _1485116]), 36910 ^ [_1485112, _1485114, _1485116]))), 36913 ^ _782464 : [(36914 ^ _782464) ^ [_1485259] : [-(hBOOL(hAPP(_1485112, _1485259)))]]], (36916 ^ _782464) ^ [_1485290, _1485292, _1485294, _1485296, _1485298, _1485300] : [_1485290 = _1485292, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485294, _1485296, _1485298), _1485300), _1485290) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485294, _1485296, _1485298), _1485300), _1485292))], (36922 ^ _782464) ^ [_1485415, _1485417, _1485419, _1485421, _1485423, _1485425, _1485427, _1485429] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485415, _1485417, _1485419), _1485421), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485423, _1485425, tc_prod(_1485415, _1485417)), _1485427), _1485429)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485423, _1485425, _1485419), hAPP(hAPP(c_COMBB(tc_fun(_1485425, tc_prod(_1485415, _1485417)), tc_fun(_1485425, _1485419), _1485423), hAPP(c_COMBB(tc_prod(_1485415, _1485417), _1485419, _1485425), hAPP(c_Product__Type_Oprod_Oprod__case(_1485415, _1485417, _1485419), _1485421))), _1485427)), _1485429))], (36924 ^ _782464) ^ [_1485521, _1485523, _1485525, _1485527, _1485529, _1485531] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485521, _1485523, _1485525), _1485527), hAPP(hAPP(c_Product__Type_OPair(_1485521, _1485523), _1485529), _1485531)) = hAPP(hAPP(_1485527, _1485529), _1485531))], (36926 ^ _782464) ^ [_1485579, _1485581, _1485583, _1485585, _1485587, _1485589] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485579, _1485581, _1485583), _1485585), hAPP(hAPP(c_Product__Type_OPair(_1485579, _1485581), _1485587), _1485589)) = hAPP(hAPP(_1485585, _1485587), _1485589))], (36928 ^ _782464) ^ [_1485637, _1485639, _1485641, _1485643, _1485645] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485637, _1485639, tc_HOL_Obool), _1485641), hAPP(hAPP(c_Product__Type_OPair(_1485637, _1485639), _1485643), _1485645))), -(hBOOL(hAPP(hAPP(_1485641, _1485643), _1485645)))], (36934 ^ _782464) ^ [_1485766, _1485768, _1485770, _1485772] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1485766, _1485768, _1485770), hAPP(hAPP(c_COMBB(tc_fun(_1485768, tc_prod(_1485766, _1485768)), tc_fun(_1485768, _1485770), _1485766), hAPP(c_COMBB(tc_prod(_1485766, _1485768), _1485770, _1485768), _1485772)), c_Product__Type_OPair(_1485766, _1485768))) = _1485772)], (36936 ^ _782464) ^ [_1485834, _1485836, _1485838, _1485840] : [-(c_HOL_OThe(tc_prod(_1485834, _1485836), hAPP(c_Product__Type_Oprod_Oprod__case(_1485834, _1485836, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1485834, tc_fun(_1485836, tc_HOL_Obool), tc_fun(_1485836, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1485836, tc_HOL_Obool), tc_fun(_1485836, tc_HOL_Obool)), _1485834), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1485836)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1485834), c_fconj), hAPP(c_fequal, _1485838)))), hAPP(c_fequal, _1485840)))) = hAPP(hAPP(c_Product__Type_OPair(_1485834, _1485836), _1485838), _1485840))], (36938 ^ _782464) ^ [_1485940, _1485942, _1485944] : [-(c_HOL_OThe(tc_prod(_1485940, _1485942), _1485944) = c_HOL_OThe(tc_prod(_1485940, _1485942), hAPP(c_Product__Type_Oprod_Oprod__case(_1485940, _1485942, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1485942, tc_prod(_1485940, _1485942)), tc_fun(_1485942, tc_HOL_Obool), _1485940), hAPP(c_COMBB(tc_prod(_1485940, _1485942), tc_HOL_Obool, _1485942), _1485944)), c_Product__Type_OPair(_1485940, _1485942)))))], (36940 ^ _782464) ^ [_1486018] : [-(c_Divides_Oadjust(_1486018) = 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)), _1486018))))), 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)), _1486018))))), 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))))))))], (36942 ^ _782464) ^ [_1486103, _1486105, _1486107, _1486109, _1486111] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1486103, _1486105, _1486107), _1486109), _1486111)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486103, _1486105)), hAPP(hAPP(c_Product__Type_OPair(_1486103, _1486105), _1486109), _1486111)), _1486107)))], (36948 ^ _782464) ^ [_1486238, _1486240, _1486242, _1486244, _1486246] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486238, _1486240)), hAPP(hAPP(c_Product__Type_OPair(_1486238, _1486240), _1486244), _1486246)), _1486242)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1486238, _1486240, _1486242), _1486244), _1486246)))], (36954 ^ _782464) ^ [_1486379, _1486381] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1486379, _1486381) = 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), _1486379), _1486381)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1486379, _1486381)))], (36956 ^ _782464) ^ [_1486423] : [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), _1486423))), 36959 ^ _782464 : [(36960 ^ _782464) ^ [] : [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), _1486423)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486423)) = 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), _1486423))))], (36966 ^ _782464) ^ [] : [-(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), _1486423))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486423)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486423)), 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), _1486423)))))]]], (36972 ^ _782464) ^ [_1486713, _1486715] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1486713), 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)), _1486715)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1486713, _1486715), c_Divides_OnegDivAlg(_1486713, _1486715))))], (36982 ^ _782464) ^ [_1486872, _1486874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1486872), 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)), _1486874)), -(c_Divides_OnegDivAlg(_1486872, _1486874) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1486872), _1486874)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1486872, _1486874)))], (36992 ^ _782464) ^ [_1487053] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1487053) = 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), _1487053), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (36994 ^ _782464) ^ [_1487097, _1487099] : [36995 ^ _782464 : [(36996 ^ _782464) ^ [] : [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), _1487097), _1487099)))], (36998 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1487099), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1487097, _1487099) = 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), _1487097), _1487099)))], (37002 ^ _782464) ^ [_1487256, _1487258] : [-(c_Divides_OnegDivAlg(_1487256, _1487258) = hAPP(c_Divides_Oadjust(_1487258), c_Divides_OnegDivAlg(_1487256, 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)))), _1487258)))), -(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), _1487256), _1487258)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1487258), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37012 ^ _782464) ^ [_1487328, _1487330] : [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), _1487328))), 37015 ^ _782464 : [(37016 ^ _782464) ^ [] : [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), _1487330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487328)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487330), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487328)) = 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), _1487330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487328))))], (37022 ^ _782464) ^ [] : [-(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), _1487330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487328))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487330), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487328)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487328)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487330), 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), _1487328)))))]]], (37028 ^ _782464) ^ [_1487676, _1487678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1487676)), 37031 ^ _782464 : [(37032 ^ _782464) ^ [] : [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), _1487678), _1487676))), -(c_Divides_OnegDivAlg(_1487678, _1487676) = 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), _1487678), _1487676)))], (37038 ^ _782464) ^ [] : [-(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), _1487678), _1487676)))), -(c_Divides_OnegDivAlg(_1487678, _1487676) = hAPP(c_Divides_Oadjust(_1487676), c_Divides_OnegDivAlg(_1487678, 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)))), _1487676))))]]], (37044 ^ _782464) ^ [_1487955, _1487957] : [c_Nitpick_Orefl_H(_1487955, _1487957), 37047 ^ _782464 : [(37048 ^ _782464) ^ [_1488033] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487955, _1487955)), hAPP(hAPP(c_Product__Type_OPair(_1487955, _1487955), _1488033), _1488033)), _1487957)))]]], (37050 ^ _782464) ^ [_1488075, _1488077] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488075, _1488075)), hAPP(hAPP(c_Product__Type_OPair(_1488075, _1488075), 37051 ^ [_1488075, _1488077]), 37051 ^ [_1488075, _1488077])), _1488077)), -(c_Nitpick_Orefl_H(_1488075, _1488077))], (37057 ^ _782464) ^ [_1488242] : [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), _1488242))), 37060 ^ _782464 : [(37061 ^ _782464) ^ [] : [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), _1488242))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488242)) = 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)))], (37067 ^ _782464) ^ [] : [-(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), _1488242)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488242)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488242)), 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), _1488242)))))]]], (37073 ^ _782464) ^ [_1488511, _1488513] : [37074 ^ _782464 : [(37075 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488511), _1488513))], (37077 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1488513), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1488511, _1488513) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488511))], (37081 ^ _782464) ^ [_1488652, _1488654] : [-(c_Divides_OposDivAlg(_1488652, _1488654) = hAPP(c_Divides_Oadjust(_1488654), c_Divides_OposDivAlg(_1488652, 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)))), _1488654)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488652), _1488654))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1488654), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37091 ^ _782464) ^ [_1488721] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1488721) = 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)))], (37093 ^ _782464) ^ [_1488747, _1488749] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488747)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488749)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1488747, _1488749), c_Divides_OposDivAlg(_1488747, _1488749))))], (37103 ^ _782464) ^ [_1488900, _1488902] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488900)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488902)), -(c_Divides_OposDivAlg(_1488900, _1488902) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488900), _1488902)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1488900, _1488902)))], (37113 ^ _782464) ^ [_1489075, _1489077] : [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), _1489075))), 37116 ^ _782464 : [(37117 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489077)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489075))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489077), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489075)) = 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), _1489077)))], (37123 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489077)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489075)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489077), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489075)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489075)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489077), 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), _1489075)))))]]], (37129 ^ _782464) ^ [_1489393, _1489395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489393)), 37132 ^ _782464 : [(37133 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489395), _1489393)), -(c_Divides_OposDivAlg(_1489395, _1489393) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489395))], (37139 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489395), _1489393))), -(c_Divides_OposDivAlg(_1489395, _1489393) = hAPP(c_Divides_Oadjust(_1489393), c_Divides_OposDivAlg(_1489395, 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)))), _1489393))))]]], (37171 ^ _782464) ^ [_1490012, _1490014] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490012))), 37174 ^ _782464 : [(37175 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490014)), -(c_Divides_Odivmod__int(_1490012, _1490014) = c_Divides_OnegDivAlg(_1490012, _1490014))], (37181 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490014))), -(c_Divides_Odivmod__int(_1490012, _1490014) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1490012), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1490014))))]]], (37145 ^ _782464) ^ [_1489642, _1489644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489642)), 37148 ^ _782464 : [(37149 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489644)), -(c_Divides_Odivmod__int(_1489642, _1489644) = c_Divides_OposDivAlg(_1489642, _1489644))], (37155 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489644))), 37158 ^ _782464 : [(37159 ^ _782464) ^ [] : [_1489642 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1489642, _1489644) = 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)))], (37165 ^ _782464) ^ [] : [-(_1489642 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1489642, _1489644) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489642), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489644))))]]]]], (37187 ^ _782464) ^ [_1490240, _1490242] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490240)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1490240), _1490242)), -(c_Divides_Odivmod__nat(_1490242, _1490240) = 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), _1490242), _1490240)), _1490240))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1490242), _1490240), _1490240)))], (37197 ^ _782464) ^ [_1490460, _1490462] : [_1490460 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1490460, _1490462) = 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)))], (37203 ^ _782464) ^ [_1490538, _1490540] : [-(_1490538 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37206 ^ _782464 : [(37207 ^ _782464) ^ [] : [_1490540 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1490538, _1490540) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490538))], (37213 ^ _782464) ^ [] : [-(_1490540 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1490538, _1490540) = 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, _1490540))), 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)), _1490540)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490538))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490540), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490538), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1490538, _1490540)), 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), _1490540))))), c_Divides_Opdivmod(_1490538, _1490540)))))]]], (37219 ^ _782464) ^ [_1490898, _1490900, _1490902, _1490904, _1490906, _1490908, _1490910] : [-(hAPP(c_Product__Type_Oapsnd(_1490898, _1490900, _1490902, _1490904), hAPP(c_Product__Type_Oapsnd(_1490906, _1490898, _1490902, _1490908), _1490910)) = hAPP(c_Product__Type_Oapsnd(_1490906, _1490900, _1490902, hAPP(c_Fun_Ocomp(_1490898, _1490900, _1490906, _1490904), _1490908)), _1490910))], (37221 ^ _782464) ^ [] : [-(c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint, tc_Int_Oint, tc_Int_Oint, c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)))], (37223 ^ _782464) ^ [_1490983, _1490985, _1490987, _1490989, _1490991, _1490993] : [-(hAPP(c_Product__Type_Oapsnd(_1490983, _1490985, _1490987, _1490989), hAPP(hAPP(c_Product__Type_OPair(_1490987, _1490983), _1490991), _1490993)) = hAPP(hAPP(c_Product__Type_OPair(_1490987, _1490985), _1490991), hAPP(_1490989, _1490993)))], (37225 ^ _782464) ^ [_1491045] : [-(c_Divides_Odivmod__nat(_1491045, 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)), _1491045))], (37227 ^ _782464) ^ [_1491074, _1491076] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491074), _1491076)), -(c_Divides_Odivmod__nat(_1491074, _1491076) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491074))], (37233 ^ _782464) ^ [_1491173, _1491175] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1491173), _1491175)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1491173), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491175)))], (37235 ^ _782464) ^ [_1491216, _1491218] : [-(c_Divides_Odivmod__nat(_1491216, _1491218) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1491216), _1491218)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1491216, _1491218)))], (37237 ^ _782464) ^ [_1491260, _1491262, _1491264] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491260), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491262)), _1491264)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1491260, _1491262), hAPP(c_Divides_OnegateSnd, _1491264))))], (37243 ^ _782464) ^ [_1491386, _1491388] : [37244 ^ _782464 : [(37245 ^ _782464) ^ [] : [_1491386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37247 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491388), _1491386))]], -(c_Divides_Odivmod__nat(_1491388, _1491386) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491388))], (37251 ^ _782464) ^ [_1491517, _1491519] : [-(c_Divides_Odivmod__nat(_1491519, _1491517) = 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), _1491519), _1491517), _1491517))), -(_1491517 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491519), _1491517)))], (37261 ^ _782464) ^ [_1491582, _1491584] : [-(c_Divides_Opdivmod(_1491582, _1491584) = 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), _1491582)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491584))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491582), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491584))))], (37263 ^ _782464) ^ [_1491647, _1491649] : [_1491647 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1491649, _1491647) = 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), _1491649)))], (37269 ^ _782464) ^ [_1491736, _1491738] : [-(_1491736 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1491738, _1491736) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491738), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491736)))], (37275 ^ _782464) ^ [_1491795, _1491797] : [_1491795 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1491795, _1491797) = 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)))], (37281 ^ _782464) ^ [_1491873, _1491875] : [-(_1491873 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37284 ^ _782464 : [(37285 ^ _782464) ^ [] : [_1491875 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1491873, _1491875) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1491873))], (37291 ^ _782464) ^ [] : [-(_1491875 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1491873, _1491875) = 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, _1491875))), 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, _1491873)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1491875))), c_Divides_Opdivmod(_1491873, _1491875)), 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), _1491875))))), c_Divides_Opdivmod(_1491873, _1491875)))))]]], (37297 ^ _782464) ^ [_1492185, _1492187, _1492189, _1492191, _1492193] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492185, _1492187), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492189), _1492191))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492187)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492193), _1492185), _1492187), 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), _1492193), _1492189)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492193), _1492191)), _1492187))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492193), _1492191), _1492187)))))], (37307 ^ _782464) ^ [_1492454, _1492456, _1492458, _1492460, _1492462] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492454, _1492456), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492458), _1492460))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492462)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492454, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492456), _1492462)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1492458), _1492462)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492456), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1492458, _1492462))), _1492460)))))], (37321 ^ _782464) ^ [_1492761, _1492763] : [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), _1492761), _1492763))), 37324 ^ _782464 : [(37325 ^ _782464) ^ [] : [37326 ^ _782464 : [(37327 ^ _782464) ^ [] : [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), _1492761), _1492763)))], (37329 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1492763), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1492761, _1492763) = 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), _1492761), _1492763)))], (37333 ^ _782464) ^ [] : [-(c_Divides_OnegDivAlg(_1492761, _1492763) = hAPP(c_Divides_Oadjust(_1492763), c_Divides_OnegDivAlg(_1492761, 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)))), _1492763)))), -(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), _1492761), _1492763)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1492763), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37343 ^ _782464) ^ [_1493108, _1493110, _1493112, _1493114] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493108, _1493110), _1493112)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493108, _1493110), _1493114)), -(_1493112 = _1493114)], (37353 ^ _782464) ^ [_1493265, _1493267] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493265, _1493267), c_Divides_Odivmod__nat(_1493265, _1493267))))], (37355 ^ _782464) ^ [_1493298, _1493300, _1493302] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493298, _1493300), _1493302)), -(c_Divides_Odivmod__nat(_1493298, _1493300) = _1493302)], (37361 ^ _782464) ^ [_1493393, _1493395] : [-(c_Divides_Odivmod__nat(_1493393, _1493395) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1493393, _1493395)))], (37363 ^ _782464) ^ [_1493427, _1493429, _1493431, _1493433] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493427, _1493429), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493431), _1493433))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1493427, _1493429) = _1493433)], (37369 ^ _782464) ^ [_1493538, _1493540, _1493542, _1493544] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493538, _1493540), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493542), _1493544))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1493538), _1493540) = _1493542)], (37375 ^ _782464) ^ [_1493653, _1493655] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493653, _1493655), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1493653), _1493655)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1493653, _1493655)))))], (37377 ^ _782464) ^ [_1493699, _1493701, _1493703, _1493705, _1493707, _1493709, _1493711] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493699, _1493701), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493703), _1493705))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493707, _1493701), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493709), _1493711))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1493701)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493699), _1493707), _1493701), 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), _1493703), _1493709)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493705), _1493711)), _1493701))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493705), _1493711), _1493701)))))], (37391 ^ _782464) ^ [_1494060, _1494062] : [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), _1494060), _1494062))), 37394 ^ _782464 : [(37395 ^ _782464) ^ [] : [37396 ^ _782464 : [(37397 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494060), _1494062))], (37399 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494062), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1494060, _1494062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1494060))], (37403 ^ _782464) ^ [] : [-(c_Divides_OposDivAlg(_1494060, _1494062) = hAPP(c_Divides_Oadjust(_1494062), c_Divides_OposDivAlg(_1494060, 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)))), _1494062)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494060), _1494062))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494062), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37413 ^ _782464) ^ [_1494383, _1494385] : [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), _1494383), _1494385))), 37416 ^ _782464 : [(37417 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494385), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1494383, _1494385) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494383), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494385)))], (37423 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494385), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 37426 ^ _782464 : [(37427 ^ _782464) ^ [] : [37428 ^ _782464 : [(37429 ^ _782464) ^ [] : [_1494383 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (37431 ^ _782464) ^ [] : [_1494385 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1494383, _1494385) = 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)))], (37435 ^ _782464) ^ [] : [-(c_Nitpick_Onorm__frac(_1494383, _1494385) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1494383), _1494385)), 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), _1494383))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1494385)))), -(_1494383 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1494385 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (37445 ^ _782464) ^ [_1494875, _1494877, _1494879] : [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), _1494875), _1494877))), -(hBOOL(hAPP(hAPP(_1494879, _1494875), _1494877))), 37452 ^ _782464 : [(37453 ^ _782464) ^ [] : [-(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), 37450 ^ [_1494875, _1494877, _1494879]), 37451 ^ [_1494875, _1494877, _1494879]))))], (37465 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1494879, 37450 ^ [_1494875, _1494877, _1494879]), 37451 ^ [_1494875, _1494877, _1494879]))], (37455 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1494879, 37450 ^ [_1494875, _1494877, _1494879]), 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)))), 37451 ^ [_1494875, _1494877, _1494879])))), -(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), 37450 ^ [_1494875, _1494877, _1494879]), 37451 ^ [_1494875, _1494877, _1494879])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37451 ^ [_1494875, _1494877, _1494879]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37469 ^ _782464) ^ [_1495370, _1495372, _1495374] : [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), _1495370), _1495372))), -(hBOOL(hAPP(hAPP(_1495374, _1495370), _1495372))), 37476 ^ _782464 : [(37477 ^ _782464) ^ [] : [-(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), 37474 ^ [_1495370, _1495372, _1495374]), 37475 ^ [_1495370, _1495372, _1495374]))))], (37489 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1495374, 37474 ^ [_1495370, _1495372, _1495374]), 37475 ^ [_1495370, _1495372, _1495374]))], (37479 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1495374, 37474 ^ [_1495370, _1495372, _1495374]), 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)))), 37475 ^ [_1495370, _1495372, _1495374])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37474 ^ [_1495370, _1495372, _1495374]), 37475 ^ [_1495370, _1495372, _1495374]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37475 ^ [_1495370, _1495372, _1495374]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37493 ^ _782464) ^ [_1495856, _1495858, _1495860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495856, tc_fun(_1495856, tc_HOL_Obool))), _1495858), _1495860)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495856, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1495856, _1495860)), c_Wellfounded_Oaccp(_1495856, _1495858))))], (37499 ^ _782464) ^ [_1495993] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1495993)), 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), _1495993)) = 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), _1495993))))))], (37505 ^ _782464) ^ [_1496128, _1496130, _1496132, _1496134, _1496136] : [hAPP(c_Product__Type_Osnd(_1496128, _1496130), hAPP(hAPP(c_Product__Type_OPair(_1496128, _1496130), _1496132), _1496134)) = _1496136, -(_1496134 = _1496136)], (37511 ^ _782464) ^ [_1496241, _1496243, _1496245, _1496247] : [-(hAPP(c_Product__Type_Osnd(_1496241, _1496243), hAPP(hAPP(c_Product__Type_OPair(_1496241, _1496243), _1496245), _1496247)) = _1496247)], (37513 ^ _782464) ^ [_1496285, _1496287, _1496289] : [-(hAPP(c_Product__Type_Osnd(_1496285, _1496287), _1496289) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1496285, _1496287, _1496287), hAPP(c_COMBK(tc_fun(_1496287, _1496287), _1496285), c_COMBI(_1496287))), _1496289))], (37515 ^ _782464) ^ [_1496339, _1496341, _1496343, _1496345, _1496347] : [-(hAPP(c_Product__Type_Osnd(_1496339, _1496341), hAPP(c_Product__Type_Oapsnd(_1496343, _1496341, _1496339, _1496345), _1496347)) = hAPP(_1496345, hAPP(c_Product__Type_Osnd(_1496339, _1496343), _1496347)))], (37517 ^ _782464) ^ [_1496420, _1496422, _1496424, _1496426, _1496428, _1496430] : [hAPP(c_Product__Type_Oapsnd(_1496420, _1496422, _1496424, _1496426), _1496428) = hAPP(c_Product__Type_Oapsnd(_1496420, _1496422, _1496424, _1496430), _1496428), -(hAPP(_1496426, hAPP(c_Product__Type_Osnd(_1496424, _1496420), _1496428)) = hAPP(_1496430, hAPP(c_Product__Type_Osnd(_1496424, _1496420), _1496428)))], (37523 ^ _782464) ^ [_1496569, _1496571, _1496573, _1496575, _1496577, _1496579] : [hAPP(_1496575, hAPP(c_Product__Type_Osnd(_1496573, _1496569), _1496577)) = hAPP(_1496579, hAPP(c_Product__Type_Osnd(_1496573, _1496569), _1496577)), -(hAPP(c_Product__Type_Oapsnd(_1496569, _1496571, _1496573, _1496575), _1496577) = hAPP(c_Product__Type_Oapsnd(_1496569, _1496571, _1496573, _1496579), _1496577))], (37529 ^ _782464) ^ [_1496724, _1496726] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1496724, _1496726) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1496724, _1496726)))], (37531 ^ _782464) ^ [_1496759, _1496761, _1496763, _1496765] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496759, _1496761), _1496763)), hBOOL(hAPP(hAPP(_1496761, _1496765), _1496763)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496759, _1496761), _1496765)))], (37551 ^ _782464) ^ [_1497130, _1497132, _1497134] : [37553 ^ _782464 : [(37554 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1497132, 37552 ^ [_1497130, _1497132, _1497134]), _1497134)))], (37556 ^ _782464) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497130, _1497132), 37552 ^ [_1497130, _1497132, _1497134]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497130, _1497132), _1497134)))], (37541 ^ _782464) ^ [_1496944, _1496946, _1496948] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496944, _1496946), _1496948)), 37544 ^ _782464 : [(37545 ^ _782464) ^ [_1497029] : [hBOOL(hAPP(hAPP(_1496946, _1497029), _1496948)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496944, _1496946), _1497029)))]]], (37570 ^ _782464) ^ [_1497520, _1497522, _1497524] : [37572 ^ _782464 : [(37573 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1497522, 37571 ^ [_1497520, _1497522, _1497524]), _1497524)))], (37575 ^ _782464) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497520, _1497522), 37571 ^ [_1497520, _1497522, _1497524]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497520, _1497522), _1497524)))], (37560 ^ _782464) ^ [_1497334, _1497336, _1497338] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497334, _1497336), _1497338)), 37563 ^ _782464 : [(37564 ^ _782464) ^ [_1497419] : [hBOOL(hAPP(hAPP(_1497336, _1497419), _1497338)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497334, _1497336), _1497419)))]]], (37579 ^ _782464) ^ [_1497706, _1497708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1497706), 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)), _1497708)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1497706, _1497708) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1497706, _1497708)))], (37589 ^ _782464) ^ [_1497869, _1497871] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497871)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1497869, _1497871) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1497869, _1497871)))], (37599 ^ _782464) ^ [_1498026] : [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), _1498026))), -(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), _1498026)) = 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), _1498026))))], (37605 ^ _782464) ^ [_1498143, _1498145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1498143)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498145), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1498143, _1498145) = 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), _1498143), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498145)))))], (37615 ^ _782464) ^ [_1498324, _1498326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498324), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1498326), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1498324, _1498326) = 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), _1498324), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498326)))))], (37625 ^ _782464) ^ [_1498511, _1498513] : [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), _1498511), _1498513))), 37628 ^ _782464 : [(37629 ^ _782464) ^ [] : [_1498513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1498511, _1498513) = _1498511)], (37635 ^ _782464) ^ [] : [-(_1498513 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1498511, _1498513) = c_Nitpick_Onat__gcd(_1498513, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1498511, _1498513)))]]], (37641 ^ _782464) ^ [_1498729] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1498729)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1498729)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37643 ^ _782464) ^ [_1498786, _1498788, _1498790, _1498792] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498786, _1498786)), hAPP(hAPP(c_Product__Type_OPair(_1498786, _1498786), _1498788), _1498790)), hAPP(c_Wellfounded_Omeasure(_1498786), _1498792))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1498792, _1498788)), hAPP(_1498792, _1498790))))], (37649 ^ _782464) ^ [_1498933, _1498935, _1498937, _1498939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1498939, _1498935)), hAPP(_1498939, _1498937))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498933, _1498933)), hAPP(hAPP(c_Product__Type_OPair(_1498933, _1498933), _1498935), _1498937)), hAPP(c_Wellfounded_Omeasure(_1498933), _1498939))))], (37655 ^ _782464) ^ [_1499086, _1499088] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1499086, _1499088) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1499086, _1499088)))], (37657 ^ _782464) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37659 ^ _782464) ^ [_1499154, _1499156] : [c_Relation_Oirrefl(_1499154, _1499156), 37662 ^ _782464 : [(37663 ^ _782464) ^ [_1499236] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499154, _1499154)), hAPP(hAPP(c_Product__Type_OPair(_1499154, _1499154), _1499236), _1499236)), _1499156))]]], (37665 ^ _782464) ^ [_1499276, _1499278] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499276, _1499276)), hAPP(hAPP(c_Product__Type_OPair(_1499276, _1499276), 37666 ^ [_1499276, _1499278]), 37666 ^ [_1499276, _1499278])), _1499278))), -(c_Relation_Oirrefl(_1499276, _1499278))], (37672 ^ _782464) ^ [_1499347, _1499349, _1499351] : [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), _1499347), _1499349))), -(hBOOL(hAPP(hAPP(_1499351, _1499347), _1499349))), 37679 ^ _782464 : [(37680 ^ _782464) ^ [] : [-(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), 37677 ^ [_1499347, _1499349, _1499351]), 37678 ^ [_1499347, _1499349, _1499351]))))], (37688 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1499351, 37677 ^ [_1499347, _1499349, _1499351]), 37678 ^ [_1499347, _1499349, _1499351]))], (37682 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37678 ^ [_1499347, _1499349, _1499351]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1499351, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37677 ^ [_1499347, _1499349, _1499351])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37678 ^ [_1499347, _1499349, _1499351]))))]]], (37692 ^ _782464) ^ [_1499820] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1499820)), 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), _1499820)) = 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), _1499820))))))], (37698 ^ _782464) ^ [_1499974, _1499976, _1499978, _1499980] : [_1499974 = _1499976, 37701 ^ _782464 : [(37702 ^ _782464) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1499978, _1499980), _1499974) = hAPP(c_Product__Type_Ofst(_1499978, _1499980), _1499976))], (37704 ^ _782464) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1499978, _1499980), _1499974) = hAPP(c_Product__Type_Osnd(_1499978, _1499980), _1499976))]]], (37706 ^ _782464) ^ [_1500125, _1500127, _1500129, _1500131] : [-(_1500125 = _1500127), hAPP(c_Product__Type_Ofst(_1500129, _1500131), _1500125) = hAPP(c_Product__Type_Ofst(_1500129, _1500131), _1500127), hAPP(c_Product__Type_Osnd(_1500129, _1500131), _1500125) = hAPP(c_Product__Type_Osnd(_1500129, _1500131), _1500127)], (37716 ^ _782464) ^ [_1500312, _1500314, _1500316, _1500318] : [hAPP(c_Product__Type_Ofst(_1500312, _1500314), _1500316) = hAPP(c_Product__Type_Ofst(_1500312, _1500314), _1500318), hAPP(c_Product__Type_Osnd(_1500312, _1500314), _1500316) = hAPP(c_Product__Type_Osnd(_1500312, _1500314), _1500318), -(_1500316 = _1500318)], (37726 ^ _782464) ^ [_1500497, _1500499, _1500501, _1500503, _1500505] : [hAPP(c_Product__Type_Ofst(_1500497, _1500499), hAPP(hAPP(c_Product__Type_OPair(_1500497, _1500499), _1500501), _1500503)) = _1500505, -(_1500501 = _1500505)], (37732 ^ _782464) ^ [_1500610, _1500612, _1500614, _1500616] : [-(hAPP(c_Product__Type_Ofst(_1500610, _1500612), hAPP(hAPP(c_Product__Type_OPair(_1500610, _1500612), _1500614), _1500616)) = _1500614)], (37734 ^ _782464) ^ [_1500654, _1500656, _1500658] : [-(hAPP(c_Product__Type_Ofst(_1500654, _1500656), _1500658) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500654, _1500656, _1500654), c_COMBK(_1500654, _1500656)), _1500658))], (37736 ^ _782464) ^ [_1500700, _1500702, _1500704, _1500706, _1500708] : [-(hAPP(c_Product__Type_Ofst(_1500700, _1500702), hAPP(c_Product__Type_Oapsnd(_1500704, _1500702, _1500700, _1500706), _1500708)) = hAPP(c_Product__Type_Ofst(_1500700, _1500704), _1500708))], (37738 ^ _782464) ^ [_1500751, _1500753, _1500755] : [-(hAPP(hAPP(c_Product__Type_OPair(_1500751, _1500753), hAPP(c_Product__Type_Ofst(_1500751, _1500753), _1500755)), hAPP(c_Product__Type_Osnd(_1500751, _1500753), _1500755)) = _1500755)], (37740 ^ _782464) ^ [_1500799, _1500801, _1500803] : [-(_1500799 = hAPP(hAPP(c_Product__Type_OPair(_1500801, _1500803), hAPP(c_Product__Type_Ofst(_1500801, _1500803), _1500799)), hAPP(c_Product__Type_Osnd(_1500801, _1500803), _1500799)))], (37742 ^ _782464) ^ [_1500847, _1500849, _1500851, _1500853, _1500855] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500847, _1500849, _1500851), _1500853), _1500855) = hAPP(hAPP(_1500853, hAPP(c_Product__Type_Ofst(_1500847, _1500849), _1500855)), hAPP(c_Product__Type_Osnd(_1500847, _1500849), _1500855)))], (37744 ^ _782464) ^ [_1500906, _1500908] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1500906), _1500908) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1500906, _1500908)))], (37746 ^ _782464) ^ [_1500943, _1500945, _1500947, _1500949, _1500951] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500943, _1500945, _1500947), _1500949), _1500951) = hAPP(hAPP(_1500949, hAPP(c_Product__Type_Ofst(_1500943, _1500945), _1500951)), hAPP(c_Product__Type_Osnd(_1500943, _1500945), _1500951)))], (37748 ^ _782464) ^ [_1501002, _1501004, _1501006, _1501008, _1501010, _1501012] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1501002, _1501004), _1501004, _1501006), hAPP(hAPP(c_COMBB(_1501008, tc_fun(_1501004, _1501006), tc_prod(_1501002, _1501004)), _1501010), hAPP(hAPP(c_COMBB(_1501002, _1501008, tc_prod(_1501002, _1501004)), _1501012), c_Product__Type_Ofst(_1501002, _1501004)))), c_Product__Type_Osnd(_1501002, _1501004)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1501002, _1501004, _1501006), hAPP(hAPP(c_COMBB(_1501008, tc_fun(_1501004, _1501006), _1501002), _1501010), _1501012)))], (37750 ^ _782464) ^ [_1501103, _1501105, _1501107, _1501109, _1501111] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501103, _1501105, _1501107), _1501109), _1501111) = hAPP(hAPP(_1501109, hAPP(c_Product__Type_Ofst(_1501103, _1501105), _1501111)), hAPP(c_Product__Type_Osnd(_1501103, _1501105), _1501111)))], (37752 ^ _782464) ^ [_1501162, _1501164, _1501166, _1501168, _1501170, _1501172, _1501174] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501162, _1501164, _1501166), hAPP(c_Fun_Ocomp(_1501168, tc_fun(_1501164, _1501166), _1501162, _1501170), _1501172)), _1501174) = hAPP(hAPP(_1501170, hAPP(_1501172, hAPP(c_Product__Type_Ofst(_1501162, _1501164), _1501174))), hAPP(c_Product__Type_Osnd(_1501162, _1501164), _1501174)))], (37754 ^ _782464) ^ [_1501239, _1501241, _1501243] : [-(c_HOL_OThe(tc_prod(_1501239, _1501241), hAPP(c_Product__Type_Oprod_Oprod__case(_1501239, _1501241, tc_HOL_Obool), _1501243)) = c_HOL_OThe(tc_prod(_1501239, _1501241), hAPP(hAPP(c_COMBS(tc_prod(_1501239, _1501241), _1501241, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1501239, tc_fun(_1501241, tc_HOL_Obool), tc_prod(_1501239, _1501241)), _1501243), c_Product__Type_Ofst(_1501239, _1501241))), c_Product__Type_Osnd(_1501239, _1501241))))], (37756 ^ _782464) ^ [_1501320, _1501322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501320), 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)), _1501322)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501320), _1501322) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1501320, _1501322)))], (37766 ^ _782464) ^ [_1501487, _1501489] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501489)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501487), _1501489) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1501487, _1501489)))], (37776 ^ _782464) ^ [_1501648] : [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), _1501648))), -(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), _1501648)) = 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), _1501648))))], (37782 ^ _782464) ^ [_1501763, _1501765] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501763)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501765), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501763), _1501765) = 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), _1501763), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501765)))))], (37792 ^ _782464) ^ [_1501948, _1501950] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501948), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1501950), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501948), _1501950) = 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), _1501948), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501950)))))], (37802 ^ _782464) ^ [_1502139, _1502141, _1502143, _1502145, _1502147] : [-(c_Product__Type_Oprod_Oprod__size(_1502139, _1502141, _1502143, _1502145, _1502147) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1502143, hAPP(c_Product__Type_Ofst(_1502139, _1502141), _1502147))), hAPP(_1502145, hAPP(c_Product__Type_Osnd(_1502139, _1502141), _1502147)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37804 ^ _782464) ^ [_1502206, _1502208, _1502210, _1502212, _1502214] : [hBOOL(hAPP(hAPP(_1502206, _1502208), _1502210)), -(hBOOL(hAPP(hAPP(_1502206, hAPP(c_Product__Type_Osnd(_1502212, _1502214), hAPP(hAPP(c_Product__Type_OPair(_1502212, _1502214), _1502210), _1502208))), hAPP(c_Product__Type_Ofst(_1502212, _1502214), hAPP(hAPP(c_Product__Type_OPair(_1502212, _1502214), _1502210), _1502208)))))], (37810 ^ _782464) ^ [_1502369, _1502371, _1502373, _1502375, _1502377, _1502379] : [hBOOL(hAPP(_1502369, _1502371)), hBOOL(hAPP(_1502373, _1502375)), 37817 ^ _782464 : [(37818 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1502369, hAPP(c_Product__Type_Ofst(_1502377, _1502379), hAPP(hAPP(c_Product__Type_OPair(_1502377, _1502379), _1502371), _1502375)))))], (37820 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1502373, hAPP(c_Product__Type_Osnd(_1502377, _1502379), hAPP(hAPP(c_Product__Type_OPair(_1502377, _1502379), _1502371), _1502375)))))]]], (37822 ^ _782464) ^ [_1502616, _1502618] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1502616), _1502618) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1502616, _1502618)))], (37856 ^ _782464) ^ [_1503207, _1503209, _1503211] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1503207, _1503209), _1503211))), _1503207 = 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), _1503211)), _1503209)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503211)), 37863 ^ _782464 : [(37864 ^ _782464) ^ [] : [-(_1503209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37866 ^ _782464) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1503211) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 37867 ^ _782464 : [(37868 ^ _782464) ^ [] : [_1503209 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37870 ^ _782464) ^ [] : [37871 ^ _782464 : [(37872 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1503209)))], (37874 ^ _782464) ^ [] : [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), _1503211))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503211)), _1503209))]], 37879 ^ _782464 : [(37880 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1503209))], (37882 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1503209), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503211))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503211)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (37824 ^ _782464) ^ [_1502671, _1502673, _1502675] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1502671, _1502673), _1502675)), 37827 ^ _782464 : [(37828 ^ _782464) ^ [] : [-(_1502671 = 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), _1502675)), _1502673)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502675)))], (37830 ^ _782464) ^ [] : [_1502673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1502675) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37836 ^ _782464) ^ [] : [-(_1502673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37839 ^ _782464 : [(37840 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1502673)), 37843 ^ _782464 : [(37844 ^ _782464) ^ [] : [-(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), _1502675))))], (37846 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502675)), _1502673)))]]], (37848 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1502673))), 37851 ^ _782464 : [(37852 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1502673), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502675))))], (37854 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502675)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (37890 ^ _782464) ^ [_1503816] : [-(hAPP(c_Int_Onat, _1503816) = 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, _1503816)), 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)))))))], (37892 ^ _782464) ^ [_1503854, _1503856, _1503858] : [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), _1503854), _1503856))), -(hBOOL(hAPP(hAPP(_1503858, _1503854), _1503856))), 37899 ^ _782464 : [(37900 ^ _782464) ^ [] : [-(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), 37897 ^ [_1503854, _1503856, _1503858]), 37898 ^ [_1503854, _1503856, _1503858]))))], (37908 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1503858, 37897 ^ [_1503854, _1503856, _1503858]), 37898 ^ [_1503854, _1503856, _1503858]))], (37902 ^ _782464) ^ [] : [-(37898 ^ [_1503854, _1503856, _1503858] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1503858, 37898 ^ [_1503854, _1503856, _1503858]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37897 ^ [_1503854, _1503856, _1503858], 37898 ^ [_1503854, _1503856, _1503858]))))]]], (37912 ^ _782464) ^ [_1504276, _1504278, _1504280, _1504282] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1504276, _1504278), _1504280), _1504282) = hAPP(c_Set_OCollect(tc_prod(_1504278, _1504278)), hAPP(c_Product__Type_Oprod_Oprod__case(_1504278, _1504278, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1504278, tc_fun(tc_prod(_1504276, _1504276), tc_HOL_Obool), tc_fun(_1504278, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504278, tc_fun(tc_fun(tc_prod(_1504276, _1504276), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504276, _1504276), tc_HOL_Obool), tc_fun(_1504278, tc_HOL_Obool)), _1504278), c_COMBC(_1504278, tc_fun(tc_prod(_1504276, _1504276), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504278, tc_prod(_1504276, _1504276)), tc_fun(_1504278, tc_fun(tc_fun(tc_prod(_1504276, _1504276), tc_HOL_Obool), tc_HOL_Obool)), _1504278), hAPP(c_COMBB(tc_prod(_1504276, _1504276), tc_fun(tc_fun(tc_prod(_1504276, _1504276), tc_HOL_Obool), tc_HOL_Obool), _1504278), c_member(tc_prod(_1504276, _1504276)))), hAPP(hAPP(c_COMBC(_1504278, tc_fun(_1504278, _1504276), tc_fun(_1504278, tc_prod(_1504276, _1504276))), hAPP(hAPP(c_COMBB(tc_fun(_1504276, tc_prod(_1504276, _1504276)), tc_fun(tc_fun(_1504278, _1504276), tc_fun(_1504278, tc_prod(_1504276, _1504276))), _1504278), c_COMBB(_1504276, tc_prod(_1504276, _1504276), _1504278)), hAPP(hAPP(c_COMBB(_1504276, tc_fun(_1504276, tc_prod(_1504276, _1504276)), _1504278), c_Product__Type_OPair(_1504276, _1504276)), _1504282))), _1504282)))), _1504280))))], (37914 ^ _782464) ^ [_1504532, _1504534] : [hAPP(c_Int_ORep__Integ, _1504532) = hAPP(c_Int_ORep__Integ, _1504534), -(_1504532 = _1504534)], (37920 ^ _782464) ^ [_1504617, _1504619] : [_1504617 = _1504619, -(hAPP(c_Int_ORep__Integ, _1504617) = hAPP(c_Int_ORep__Integ, _1504619))], (37926 ^ _782464) ^ [_1504735, _1504737, _1504739, _1504741, _1504743, _1504745] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504735, _1504735)), hAPP(hAPP(c_Product__Type_OPair(_1504735, _1504735), _1504737), _1504739)), hAPP(hAPP(c_Relation_Oinv__image(_1504741, _1504735), _1504743), _1504745))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504741, _1504741)), hAPP(hAPP(c_Product__Type_OPair(_1504741, _1504741), hAPP(_1504745, _1504737)), hAPP(_1504745, _1504739))), _1504743)))], (37932 ^ _782464) ^ [_1504922, _1504924, _1504926, _1504928, _1504930, _1504932] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504928, _1504928)), hAPP(hAPP(c_Product__Type_OPair(_1504928, _1504928), hAPP(_1504932, _1504924)), hAPP(_1504932, _1504926))), _1504930)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504922, _1504922)), hAPP(hAPP(c_Product__Type_OPair(_1504922, _1504922), _1504924), _1504926)), hAPP(hAPP(c_Relation_Oinv__image(_1504928, _1504922), _1504930), _1504932))))], (37938 ^ _782464) ^ [_1505115, _1505117] : [-(c_FunDef_Orp__inv__image(_1505115, _1505117) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_fun(_1505117, _1505115), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_fun(_1505117, _1505115), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)), tc_fun(tc_fun(_1505117, _1505115), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool), tc_fun(tc_fun(_1505117, _1505115), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool))))), tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)), tc_fun(tc_fun(_1505117, _1505115), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool))), tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)), tc_fun(tc_fun(_1505117, _1505115), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool)), c_COMBS(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)), tc_fun(tc_fun(_1505117, _1505115), tc_fun(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), tc_fun(tc_prod(_1505115, _1505115), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool))), tc_fun(_1505117, _1505115)), c_Product__Type_OPair(tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool), tc_fun(tc_prod(_1505117, _1505117), tc_HOL_Obool)))), c_Relation_Oinv__image(_1505115, _1505117))))), c_Relation_Oinv__image(_1505115, _1505117))))], (37940 ^ _782464) ^ [_1505628, _1505630, _1505632, _1505634, _1505636, _1505638] : [c_Equiv__Relations_Oequiv(_1505628, _1505630, _1505632), hBOOL(hAPP(hAPP(c_member(_1505628), _1505634), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505628, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1505628, _1505628, _1505632), hAPP(hAPP(c_Set_Oinsert(_1505628), _1505636), c_Orderings_Obot__class_Obot(tc_fun(_1505628, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1505628, _1505628, _1505632), hAPP(hAPP(c_Set_Oinsert(_1505628), _1505638), c_Orderings_Obot__class_Obot(tc_fun(_1505628, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505628, _1505628)), hAPP(hAPP(c_Product__Type_OPair(_1505628, _1505628), _1505636), _1505638)), _1505632)))], (37950 ^ _782464) ^ [_1505929, _1505931, _1505933, _1505935, _1505937] : [c_Equiv__Relations_Oequiv(_1505929, _1505931, _1505933), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505929, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1505929, _1505929, _1505933), hAPP(hAPP(c_Set_Oinsert(_1505929), _1505935), c_Orderings_Obot__class_Obot(tc_fun(_1505929, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1505929, _1505929, _1505933), hAPP(hAPP(c_Set_Oinsert(_1505929), _1505937), c_Orderings_Obot__class_Obot(tc_fun(_1505929, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1505929), _1505935), _1505931)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505929, _1505929)), hAPP(hAPP(c_Product__Type_OPair(_1505929, _1505929), _1505937), _1505935)), _1505933)))], (37964 ^ _782464) ^ [_1506282, _1506284, _1506286] : [c_Equiv__Relations_Oequiv(_1506282, _1506284, _1506286), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1506282, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506282), _1506284), _1506286)) = _1506284)], (37970 ^ _782464) ^ [_1506391, _1506393, _1506395, _1506397] : [c_Equiv__Relations_Oequiv(_1506391, _1506393, _1506395), hBOOL(hAPP(hAPP(c_member(_1506391), _1506397), _1506393)), -(hBOOL(hAPP(hAPP(c_member(_1506391), _1506397), hAPP(c_Relation_OImage(_1506391, _1506391, _1506395), hAPP(hAPP(c_Set_Oinsert(_1506391), _1506397), c_Orderings_Obot__class_Obot(tc_fun(_1506391, tc_HOL_Obool)))))))], (37980 ^ _782464) ^ [_1506598, _1506600, _1506602, _1506604, _1506606] : [c_Equiv__Relations_Oequiv(_1506598, _1506600, _1506602), hBOOL(hAPP(hAPP(c_member(tc_fun(_1506598, tc_HOL_Obool)), _1506604), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506598), _1506600), _1506602))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1506598, tc_HOL_Obool)), _1506606), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506598), _1506600), _1506602))), -(_1506604 = _1506606), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506598, tc_HOL_Obool)), _1506604), _1506606) = c_Orderings_Obot__class_Obot(tc_fun(_1506598, tc_HOL_Obool)))], (37998 ^ _782464) ^ [_1506916, _1506918, _1506920, _1506922, _1506924] : [c_Equiv__Relations_Oequiv(_1506916, _1506918, _1506920), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506916, _1506916)), hAPP(hAPP(c_Product__Type_OPair(_1506916, _1506916), _1506922), _1506924)), _1506920)), -(hAPP(c_Relation_OImage(_1506916, _1506916, _1506920), hAPP(hAPP(c_Set_Oinsert(_1506916), _1506922), c_Orderings_Obot__class_Obot(tc_fun(_1506916, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1506916, _1506916, _1506920), hAPP(hAPP(c_Set_Oinsert(_1506916), _1506924), c_Orderings_Obot__class_Obot(tc_fun(_1506916, tc_HOL_Obool)))))], (38008 ^ _782464) ^ [_1507177, _1507179, _1507181, _1507183, _1507185, _1507187, _1507189] : [c_Equiv__Relations_Oequiv(_1507177, _1507179, _1507181), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507177, tc_HOL_Obool)), _1507183), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507177), _1507179), _1507181))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507177, tc_HOL_Obool)), _1507185), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507177), _1507179), _1507181))), hBOOL(hAPP(hAPP(c_member(_1507177), _1507187), _1507183)), hBOOL(hAPP(hAPP(c_member(_1507177), _1507189), _1507185)), 38027 ^ _782464 : [(38028 ^ _782464) ^ [] : [_1507183 = _1507185, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507177, _1507177)), hAPP(hAPP(c_Product__Type_OPair(_1507177, _1507177), _1507187), _1507189)), _1507181)))], (38034 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507177, _1507177)), hAPP(hAPP(c_Product__Type_OPair(_1507177, _1507177), _1507187), _1507189)), _1507181)), -(_1507183 = _1507185)]]], (38040 ^ _782464) ^ [_1507821, _1507823, _1507825, _1507827, _1507829, _1507831, _1507833] : [c_Equiv__Relations_Oequiv(_1507821, _1507823, _1507825), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507821, tc_HOL_Obool)), _1507827), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507821), _1507823), _1507825))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507821, tc_HOL_Obool)), _1507829), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507821), _1507823), _1507825))), hBOOL(hAPP(hAPP(c_member(_1507821), _1507831), _1507827)), hBOOL(hAPP(hAPP(c_member(_1507821), _1507833), _1507829)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1507821, _1507821)), hAPP(hAPP(c_Product__Type_OPair(_1507821, _1507821), _1507831), _1507833)), _1507825)), -(_1507827 = _1507829)], (38066 ^ _782464) ^ [_1508358, _1508360, _1508362, _1508364, _1508366] : [c_Equiv__Relations_Oequiv(_1508358, _1508360, _1508362), 38069 ^ _782464 : [(38070 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508358, _1508358)), hAPP(hAPP(c_Product__Type_OPair(_1508358, _1508358), _1508364), _1508366)), _1508362)), 38073 ^ _782464 : [(38074 ^ _782464) ^ [] : [-(hAPP(c_Relation_OImage(_1508358, _1508358, _1508362), hAPP(hAPP(c_Set_Oinsert(_1508358), _1508364), c_Orderings_Obot__class_Obot(tc_fun(_1508358, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508358, _1508358, _1508362), hAPP(hAPP(c_Set_Oinsert(_1508358), _1508366), c_Orderings_Obot__class_Obot(tc_fun(_1508358, tc_HOL_Obool)))))], (38076 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508358), _1508364), _1508360)))], (38078 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508358), _1508366), _1508360)))]]], (38080 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508358, _1508358)), hAPP(hAPP(c_Product__Type_OPair(_1508358, _1508358), _1508364), _1508366)), _1508362))), hAPP(c_Relation_OImage(_1508358, _1508358, _1508362), hAPP(hAPP(c_Set_Oinsert(_1508358), _1508364), c_Orderings_Obot__class_Obot(tc_fun(_1508358, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508358, _1508358, _1508362), hAPP(hAPP(c_Set_Oinsert(_1508358), _1508366), c_Orderings_Obot__class_Obot(tc_fun(_1508358, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1508358), _1508364), _1508360)), hBOOL(hAPP(hAPP(c_member(_1508358), _1508366), _1508360))]]], (38094 ^ _782464) ^ [_1508958, _1508960, _1508962, _1508964, _1508966] : [hAPP(c_Relation_OImage(_1508958, _1508958, _1508960), hAPP(hAPP(c_Set_Oinsert(_1508958), _1508962), c_Orderings_Obot__class_Obot(tc_fun(_1508958, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508958, _1508958, _1508960), hAPP(hAPP(c_Set_Oinsert(_1508958), _1508964), c_Orderings_Obot__class_Obot(tc_fun(_1508958, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1508958, _1508966, _1508960), hBOOL(hAPP(hAPP(c_member(_1508958), _1508964), _1508966)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508958, _1508958)), hAPP(hAPP(c_Product__Type_OPair(_1508958, _1508958), _1508962), _1508964)), _1508960)))], (38108 ^ _782464) ^ [_1509291, _1509293, _1509295, _1509297, _1509299] : [c_Equiv__Relations_Oequiv(_1509291, _1509293, _1509295), hBOOL(hAPP(hAPP(c_member(_1509291), _1509297), _1509293)), hBOOL(hAPP(hAPP(c_member(_1509291), _1509299), _1509293)), 38119 ^ _782464 : [(38120 ^ _782464) ^ [] : [hAPP(c_Relation_OImage(_1509291, _1509291, _1509295), hAPP(hAPP(c_Set_Oinsert(_1509291), _1509297), c_Orderings_Obot__class_Obot(tc_fun(_1509291, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509291, _1509291, _1509295), hAPP(hAPP(c_Set_Oinsert(_1509291), _1509299), c_Orderings_Obot__class_Obot(tc_fun(_1509291, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509291, _1509291)), hAPP(hAPP(c_Product__Type_OPair(_1509291, _1509291), _1509297), _1509299)), _1509295)))], (38126 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509291, _1509291)), hAPP(hAPP(c_Product__Type_OPair(_1509291, _1509291), _1509297), _1509299)), _1509295)), -(hAPP(c_Relation_OImage(_1509291, _1509291, _1509295), hAPP(hAPP(c_Set_Oinsert(_1509291), _1509297), c_Orderings_Obot__class_Obot(tc_fun(_1509291, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509291, _1509291, _1509295), hAPP(hAPP(c_Set_Oinsert(_1509291), _1509299), c_Orderings_Obot__class_Obot(tc_fun(_1509291, tc_HOL_Obool)))))]]], (38132 ^ _782464) ^ [_1509839, _1509841, _1509843, _1509845, _1509847] : [c_Equiv__Relations_Oequiv(_1509839, _1509841, _1509843), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509839, _1509839)), hAPP(hAPP(c_Product__Type_OPair(_1509839, _1509839), _1509845), _1509847)), _1509843)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509839, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1509839, _1509839, _1509843), hAPP(hAPP(c_Set_Oinsert(_1509839), _1509845), c_Orderings_Obot__class_Obot(tc_fun(_1509839, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1509839, _1509839, _1509843), hAPP(hAPP(c_Set_Oinsert(_1509839), _1509847), c_Orderings_Obot__class_Obot(tc_fun(_1509839, tc_HOL_Obool)))))))], (38142 ^ _782464) ^ [_1510120, _1510122, _1510124, _1510126, _1510128] : [c_Equiv__Relations_Oequiv(_1510120, _1510122, _1510124), hBOOL(hAPP(hAPP(c_member(_1510120), _1510126), _1510122)), hBOOL(hAPP(hAPP(c_member(_1510120), _1510128), _1510122)), 38153 ^ _782464 : [(38154 ^ _782464) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510120), hAPP(hAPP(c_Set_Oinsert(_1510120), _1510126), c_Orderings_Obot__class_Obot(tc_fun(_1510120, tc_HOL_Obool)))), _1510124) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510120), hAPP(hAPP(c_Set_Oinsert(_1510120), _1510128), c_Orderings_Obot__class_Obot(tc_fun(_1510120, tc_HOL_Obool)))), _1510124), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510120, _1510120)), hAPP(hAPP(c_Product__Type_OPair(_1510120, _1510120), _1510126), _1510128)), _1510124)))], (38160 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510120, _1510120)), hAPP(hAPP(c_Product__Type_OPair(_1510120, _1510120), _1510126), _1510128)), _1510124)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510120), hAPP(hAPP(c_Set_Oinsert(_1510120), _1510126), c_Orderings_Obot__class_Obot(tc_fun(_1510120, tc_HOL_Obool)))), _1510124) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510120), hAPP(hAPP(c_Set_Oinsert(_1510120), _1510128), c_Orderings_Obot__class_Obot(tc_fun(_1510120, tc_HOL_Obool)))), _1510124))]]], (38166 ^ _782464) ^ [_1510674, _1510676, _1510678, _1510680, _1510682, _1510684] : [c_Equiv__Relations_Oequiv(_1510674, _1510676, _1510678), c_Equiv__Relations_Ocongruent(_1510674, tc_fun(_1510680, tc_HOL_Obool), _1510678, _1510682), hBOOL(hAPP(hAPP(c_member(_1510674), _1510684), _1510676)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510674, tc_fun(_1510680, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510674, _1510674, _1510678), hAPP(hAPP(c_Set_Oinsert(_1510674), _1510684), c_Orderings_Obot__class_Obot(tc_fun(_1510674, tc_HOL_Obool))))), _1510682) = hAPP(_1510682, _1510684))], (38180 ^ _782464) ^ [_1510975, _1510977, _1510979, _1510981, _1510983, _1510985, _1510987, _1510989, _1510991, _1510993] : [c_Equiv__Relations_Oequiv(_1510975, _1510977, _1510979), c_Equiv__Relations_Oequiv(_1510981, _1510983, _1510985), c_Equiv__Relations_Ocongruent2(_1510975, _1510981, tc_fun(_1510987, tc_HOL_Obool), _1510979, _1510985, _1510989), hBOOL(hAPP(hAPP(c_member(_1510975), _1510991), _1510977)), hBOOL(hAPP(hAPP(c_member(_1510981), _1510993), _1510983)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510975, tc_fun(_1510987, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510975, _1510975, _1510979), hAPP(hAPP(c_Set_Oinsert(_1510975), _1510991), c_Orderings_Obot__class_Obot(tc_fun(_1510975, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1510981, tc_fun(_1510987, tc_HOL_Obool)), tc_fun(_1510987, tc_HOL_Obool), _1510975), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510981, tc_fun(_1510987, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510981, _1510981, _1510985), hAPP(hAPP(c_Set_Oinsert(_1510981), _1510993), c_Orderings_Obot__class_Obot(tc_fun(_1510981, tc_HOL_Obool)))))), _1510989)) = hAPP(hAPP(_1510989, _1510991), _1510993))], (38202 ^ _782464) ^ [_1511576, _1511578, _1511580] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511576, tc_HOL_Obool), tc_fun(_1511576, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511576, tc_HOL_Obool), tc_fun(_1511576, tc_HOL_Obool)), _1511578), _1511580)), c_Wellfounded_Ofinite__psubset(_1511576))), 38205 ^ _782464 : [(38206 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1511576, tc_HOL_Obool)), _1511578), _1511580)))], (38208 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1511576), _1511580)))]]], (38210 ^ _782464) ^ [_1511771, _1511773, _1511775] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511771, tc_HOL_Obool), tc_fun(_1511771, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511771, tc_HOL_Obool), tc_fun(_1511771, tc_HOL_Obool)), _1511773), _1511775)), c_Wellfounded_Ofinite__psubset(_1511771)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1511771, tc_HOL_Obool)), _1511773), _1511775)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511771), _1511775))], (38220 ^ _782464) ^ [_1512000, _1512002, _1512004, _1512006, _1512008, _1512010, _1512012, _1512014] : [c_Equiv__Relations_Oequiv(_1512000, _1512002, _1512004), c_Equiv__Relations_Ocongruent2(_1512000, _1512006, _1512008, _1512004, _1512010, _1512012), hBOOL(hAPP(hAPP(c_member(_1512000), _1512014), _1512002)), -(c_Equiv__Relations_Ocongruent(_1512006, _1512008, _1512010, hAPP(_1512012, _1512014)))], (38234 ^ _782464) ^ [_1512251, _1512253, _1512255, _1512257, _1512259, _1512261, _1512263, _1512265, _1512267, _1512269] : [c_Equiv__Relations_Ocongruent2(_1512251, _1512253, _1512255, _1512257, _1512259, _1512261), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512251, _1512251)), hAPP(hAPP(c_Product__Type_OPair(_1512251, _1512251), _1512263), _1512265)), _1512257)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512253, _1512253)), hAPP(hAPP(c_Product__Type_OPair(_1512253, _1512253), _1512267), _1512269)), _1512259)), -(hAPP(hAPP(_1512261, _1512263), _1512267) = hAPP(hAPP(_1512261, _1512265), _1512269))], (38248 ^ _782464) ^ [_1512588, _1512590, _1512592, _1512594, _1512596, _1512598] : [c_Equiv__Relations_Ocongruent(_1512588, _1512590, _1512592, _1512594), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512588, _1512588)), hAPP(hAPP(c_Product__Type_OPair(_1512588, _1512588), _1512596), _1512598)), _1512592)), -(hAPP(_1512594, _1512596) = hAPP(_1512594, _1512598))], (38258 ^ _782464) ^ [_1512787, _1512789, _1512791, _1512793, _1512795, _1512797, _1512799, _1512801, _1512803] : [c_Equiv__Relations_Oequiv(_1512787, _1512789, _1512791), c_Equiv__Relations_Oequiv(_1512793, _1512795, _1512797), c_Equiv__Relations_Ocongruent2(_1512787, _1512793, tc_fun(_1512799, tc_HOL_Obool), _1512791, _1512797, _1512801), hBOOL(hAPP(hAPP(c_member(_1512793), _1512803), _1512795)), -(c_Equiv__Relations_Ocongruent(_1512787, tc_fun(_1512799, tc_HOL_Obool), _1512791, hAPP(hAPP(c_COMBB(tc_fun(_1512793, tc_fun(_1512799, tc_HOL_Obool)), tc_fun(_1512799, tc_HOL_Obool), _1512787), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512793, tc_fun(_1512799, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1512793, _1512793, _1512797), hAPP(hAPP(c_Set_Oinsert(_1512793), _1512803), c_Orderings_Obot__class_Obot(tc_fun(_1512793, tc_HOL_Obool)))))), _1512801)))], (38276 ^ _782464) ^ [_1513214] : [-(c_Wellfounded_Ofinite__psubset(_1513214) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1513214, tc_HOL_Obool), tc_fun(_1513214, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1513214, tc_HOL_Obool), tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1513214, tc_HOL_Obool), tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1513214, tc_HOL_Obool)), c_COMBS(tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513214, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1513214, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1513214, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1513214, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1513214)))))], (38278 ^ _782464) ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386] : [c_Equiv__Relations_Oequiv(_1513374, _1513376, _1513378), c_Equiv__Relations_Ocongruent(_1513374, tc_fun(_1513380, tc_HOL_Obool), _1513378, _1513382), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513374, tc_fun(_1513380, tc_HOL_Obool)), _1513384), _1513382) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513374, tc_fun(_1513380, tc_HOL_Obool)), _1513386), _1513382), hBOOL(hAPP(hAPP(c_member(tc_fun(_1513374, tc_HOL_Obool)), _1513384), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513374), _1513376), _1513378))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1513374, tc_HOL_Obool)), _1513386), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513374), _1513376), _1513378))), 38300 ^ _782464 : [(38301 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513374), 38299 ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386]), _1513376)))], (38304 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513374), 38302 ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386]), _1513376)))], (38306 ^ _782464) ^ [] : [-(hAPP(_1513382, 38299 ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386]) = hAPP(_1513382, 38302 ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386]))], (38308 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513374, _1513374)), hAPP(hAPP(c_Product__Type_OPair(_1513374, _1513374), 38299 ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386]), 38302 ^ [_1513374, _1513376, _1513378, _1513380, _1513382, _1513384, _1513386])), _1513378))]], -(_1513384 = _1513386)], (38312 ^ _782464) ^ [_1514344, _1514346, _1514348, _1514350, _1514352, _1514354, _1514356, _1514358, _1514360, _1514362, _1514364] : [c_Equiv__Relations_Oequiv(_1514344, _1514346, _1514348), c_Equiv__Relations_Oequiv(_1514350, _1514352, _1514354), c_Equiv__Relations_Ocongruent2(_1514344, _1514350, tc_fun(_1514356, tc_HOL_Obool), _1514348, _1514354, _1514358), hBOOL(hAPP(hAPP(c_member(tc_fun(_1514344, tc_HOL_Obool)), _1514360), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1514344), _1514346), _1514348))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1514350, tc_HOL_Obool)), _1514362), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1514350), _1514352), _1514354))), 38334 ^ _782464 : [(38335 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514344), 38333 ^ [_1514344, _1514346, _1514348, _1514350, _1514352, _1514354, _1514356, _1514358, _1514360, _1514362, _1514364]), _1514346)))], (38338 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514350), 38336 ^ [_1514344, _1514346, _1514348, _1514350, _1514352, _1514354, _1514356, _1514358, _1514360, _1514362, _1514364]), _1514352)))], (38340 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1514356, tc_HOL_Obool)), hAPP(hAPP(_1514358, 38333 ^ [_1514344, _1514346, _1514348, _1514350, _1514352, _1514354, _1514356, _1514358, _1514360, _1514362, _1514364]), 38336 ^ [_1514344, _1514346, _1514348, _1514350, _1514352, _1514354, _1514356, _1514358, _1514360, _1514362, _1514364])), _1514364))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1514356, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1514344, tc_fun(_1514356, tc_HOL_Obool)), _1514360), hAPP(hAPP(c_COMBB(tc_fun(_1514350, tc_fun(_1514356, tc_HOL_Obool)), tc_fun(_1514356, tc_HOL_Obool), _1514344), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1514350, tc_fun(_1514356, tc_HOL_Obool)), _1514362)), _1514358))), _1514364)))], (38344 ^ _782464) ^ [_1515346, _1515348, _1515350, _1515352, _1515354, _1515356, _1515358] : [c_Equiv__Relations_Oequiv(_1515346, _1515348, _1515350), c_Equiv__Relations_Ocongruent(_1515346, tc_fun(_1515352, tc_HOL_Obool), _1515350, _1515354), hBOOL(hAPP(hAPP(c_member(tc_fun(_1515346, tc_HOL_Obool)), _1515356), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1515346), _1515348), _1515350))), 38358 ^ _782464 : [(38359 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515346), 38357 ^ [_1515346, _1515348, _1515350, _1515352, _1515354, _1515356, _1515358]), _1515348)))], (38361 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1515352, tc_HOL_Obool)), hAPP(_1515354, 38357 ^ [_1515346, _1515348, _1515350, _1515352, _1515354, _1515356, _1515358])), _1515358))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1515352, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1515346, tc_fun(_1515352, tc_HOL_Obool)), _1515356), _1515354)), _1515358)))], (38365 ^ _782464) ^ [_1515857, _1515859, _1515861, _1515863, _1515865] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1515857, _1515859)), hAPP(_1515857, _1515861))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515863, _1515863)), hAPP(hAPP(c_Product__Type_OPair(_1515863, _1515863), _1515859), _1515861)), _1515865)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515863, _1515863)), hAPP(hAPP(c_Product__Type_OPair(_1515863, _1515863), _1515859), _1515861)), c_Wellfounded_Omlex__prod(_1515863, _1515857, _1515865))))], (38375 ^ _782464) ^ [_1516104] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1516104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1516104)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38377 ^ _782464) ^ [_1516139, _1516141, _1516143, _1516145, _1516147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1516139, _1516141)), hAPP(_1516139, _1516143))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516145, _1516145)), hAPP(hAPP(c_Product__Type_OPair(_1516145, _1516145), _1516141), _1516143)), c_Wellfounded_Omlex__prod(_1516145, _1516139, _1516147))))], (38383 ^ _782464) ^ [_1516305, _1516307] : [c_Code__Numeral_OSuc__code__numeral(_1516305) = c_Code__Numeral_OSuc__code__numeral(_1516307), -(_1516305 = _1516307)], (38389 ^ _782464) ^ [_1516386, _1516388] : [_1516386 = _1516388, -(c_Code__Numeral_OSuc__code__numeral(_1516386) = c_Code__Numeral_OSuc__code__numeral(_1516388))], (38395 ^ _782464) ^ [_1516482] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1516482)], (38397 ^ _782464) ^ [_1516516] : [c_Code__Numeral_OSuc__code__numeral(_1516516) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (38399 ^ _782464) ^ [_1516541] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1516541)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1516541)], (38401 ^ _782464) ^ [_1516572] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1516572)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1516572)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38403 ^ _782464) ^ [_1516609] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1516609)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1516609)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38405 ^ _782464) ^ [_1516647, _1516649, _1516651, _1516653, _1516655, _1516657] : [-(c_Product__Type_Oprod_Oprod__rec(_1516647, _1516649, _1516651, _1516653, hAPP(hAPP(c_Product__Type_OPair(_1516647, _1516649), _1516655), _1516657)) = hAPP(hAPP(_1516653, _1516655), _1516657))], (38407 ^ _782464) ^ [_1516701] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1516701) = _1516701)], (38409 ^ _782464) ^ [] : [-(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))], (38411 ^ _782464) ^ [] : [-(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))], (38413 ^ _782464) ^ [_1516763, _1516765, _1516767, _1516769, _1516771, _1516773] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516763, _1516765)), hAPP(hAPP(c_Product__Type_OPair(_1516763, _1516765), _1516767), _1516769)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1516763, _1516765), tc_HOL_Obool), _1516771))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1516763, _1516765), tc_HOL_Obool), tc_fun(tc_prod(_1516763, _1516765), tc_HOL_Obool), _1516771), 38424 ^ _782464 : [(38425 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516763, _1516765)), hAPP(hAPP(c_Product__Type_OPair(_1516763, _1516765), 38422 ^ [_1516763, _1516765, _1516767, _1516769, _1516771, _1516773]), 38423 ^ [_1516763, _1516765, _1516767, _1516769, _1516771, _1516773])), hAPP(_1516771, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1516763, _1516765), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1516763, _1516765), tc_HOL_Obool), _1516771)), hAPP(c_Set_OCollect(tc_prod(_1516763, _1516765)), hAPP(c_Product__Type_Oprod_Oprod__case(_1516763, _1516765, tc_HOL_Obool), _1516773)))))))], (38427 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1516773, 38422 ^ [_1516763, _1516765, _1516767, _1516769, _1516771, _1516773]), 38423 ^ [_1516763, _1516765, _1516767, _1516769, _1516771, _1516773]))]], -(hBOOL(hAPP(hAPP(_1516773, _1516767), _1516769)))], (38431 ^ _782464) ^ [_1517371, _1517373, _1517375, _1517377, _1517379, _1517381, _1517383, _1517385] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1517371, _1517373), tc_prod(_1517371, _1517373))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1517371, _1517373), tc_prod(_1517371, _1517373)), hAPP(hAPP(c_Product__Type_OPair(_1517371, _1517373), _1517375), _1517377)), hAPP(hAPP(c_Product__Type_OPair(_1517371, _1517373), _1517379), _1517381))), c_Wellfounded_Olex__prod(_1517371, _1517373, _1517383, _1517385))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517371, _1517371)), hAPP(hAPP(c_Product__Type_OPair(_1517371, _1517371), _1517375), _1517379)), _1517383))), 38438 ^ _782464 : [(38439 ^ _782464) ^ [] : [-(_1517375 = _1517379)], (38441 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517373, _1517373)), hAPP(hAPP(c_Product__Type_OPair(_1517373, _1517373), _1517377), _1517381)), _1517385)))]]], (38443 ^ _782464) ^ [_1517696, _1517698, _1517700, _1517702, _1517704, _1517706, _1517708, _1517710] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1517696, _1517698), tc_prod(_1517696, _1517698))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1517696, _1517698), tc_prod(_1517696, _1517698)), hAPP(hAPP(c_Product__Type_OPair(_1517696, _1517698), _1517700), _1517702)), hAPP(hAPP(c_Product__Type_OPair(_1517696, _1517698), _1517704), _1517706))), c_Wellfounded_Olex__prod(_1517696, _1517698, _1517708, _1517710)))), 38444 ^ _782464 : [(38445 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517696, _1517696)), hAPP(hAPP(c_Product__Type_OPair(_1517696, _1517696), _1517700), _1517704)), _1517708))], (38447 ^ _782464) ^ [] : [_1517700 = _1517704, hBOOL(hAPP(hAPP(c_member(tc_prod(_1517698, _1517698)), hAPP(hAPP(c_Product__Type_OPair(_1517698, _1517698), _1517702), _1517706)), _1517710))]]], (38455 ^ _782464) ^ [_1518086, _1518088] : [c_Equiv__Relations_Oequiv(_1518086, c_Orderings_Otop__class_Otop(tc_fun(_1518086, tc_HOL_Obool)), _1518088), -(c_Equiv__Relations_Oequivp(_1518086, hAPP(hAPP(c_COMBC(_1518086, tc_fun(tc_prod(_1518086, _1518086), tc_HOL_Obool), tc_fun(_1518086, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518086, tc_fun(tc_fun(tc_prod(_1518086, _1518086), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518086, _1518086), tc_HOL_Obool), tc_fun(_1518086, tc_HOL_Obool)), _1518086), c_COMBC(_1518086, tc_fun(tc_prod(_1518086, _1518086), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518086, tc_prod(_1518086, _1518086)), tc_fun(_1518086, tc_fun(tc_fun(tc_prod(_1518086, _1518086), tc_HOL_Obool), tc_HOL_Obool)), _1518086), hAPP(c_COMBB(tc_prod(_1518086, _1518086), tc_fun(tc_fun(tc_prod(_1518086, _1518086), tc_HOL_Obool), tc_HOL_Obool), _1518086), c_member(tc_prod(_1518086, _1518086)))), c_Product__Type_OPair(_1518086, _1518086)))), _1518088)))], (38461 ^ _782464) ^ [_1518407, _1518409] : [c_Equiv__Relations_Oequivp(_1518407, hAPP(hAPP(c_COMBC(_1518407, tc_fun(tc_prod(_1518407, _1518407), tc_HOL_Obool), tc_fun(_1518407, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518407, tc_fun(tc_fun(tc_prod(_1518407, _1518407), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518407, _1518407), tc_HOL_Obool), tc_fun(_1518407, tc_HOL_Obool)), _1518407), c_COMBC(_1518407, tc_fun(tc_prod(_1518407, _1518407), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518407, tc_prod(_1518407, _1518407)), tc_fun(_1518407, tc_fun(tc_fun(tc_prod(_1518407, _1518407), tc_HOL_Obool), tc_HOL_Obool)), _1518407), hAPP(c_COMBB(tc_prod(_1518407, _1518407), tc_fun(tc_fun(tc_prod(_1518407, _1518407), tc_HOL_Obool), tc_HOL_Obool), _1518407), c_member(tc_prod(_1518407, _1518407)))), c_Product__Type_OPair(_1518407, _1518407)))), _1518409)), -(c_Equiv__Relations_Oequiv(_1518407, c_Orderings_Otop__class_Otop(tc_fun(_1518407, tc_HOL_Obool)), _1518409))], (38467 ^ _782464) ^ [_1518734] : [-(c_Equiv__Relations_Oequivp(_1518734, c_fequal))], (38485 ^ _782464) ^ [_1519070, _1519072] : [-(c_Equiv__Relations_Oequivp(_1519070, _1519072)), 38490 ^ _782464 : [(38491 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1519072, 38486 ^ [_1519070, _1519072]), 38487 ^ [_1519070, _1519072])))], (38493 ^ _782464) ^ [] : [hAPP(_1519072, 38486 ^ [_1519070, _1519072]) = hAPP(_1519072, 38487 ^ [_1519070, _1519072])]], 38494 ^ _782464 : [(38495 ^ _782464) ^ [] : [-(hAPP(_1519072, 38486 ^ [_1519070, _1519072]) = hAPP(_1519072, 38487 ^ [_1519070, _1519072]))], (38497 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1519072, 38486 ^ [_1519070, _1519072]), 38487 ^ [_1519070, _1519072]))]]], (38469 ^ _782464) ^ [_1518772, _1518774] : [c_Equiv__Relations_Oequivp(_1518772, _1518774), 38472 ^ _782464 : [(38473 ^ _782464) ^ [_1518866, _1518868] : [hBOOL(hAPP(hAPP(_1518774, _1518868), _1518866)), -(hAPP(_1518774, _1518868) = hAPP(_1518774, _1518866))], (38479 ^ _782464) ^ [_1518965, _1518967] : [hAPP(_1518774, _1518967) = hAPP(_1518774, _1518965), -(hBOOL(hAPP(hAPP(_1518774, _1518967), _1518965)))]]], (38501 ^ _782464) ^ [_1519399, _1519401, _1519403] : [c_Equiv__Relations_Oequivp(_1519399, _1519401), -(hBOOL(hAPP(hAPP(_1519401, _1519403), _1519403)))], (38507 ^ _782464) ^ [_1519488, _1519490, _1519492, _1519494] : [c_Equiv__Relations_Oequivp(_1519488, _1519490), hBOOL(hAPP(hAPP(_1519490, _1519492), _1519494)), -(hBOOL(hAPP(hAPP(_1519490, _1519494), _1519492)))], (38517 ^ _782464) ^ [_1519645, _1519647, _1519649, _1519651, _1519653] : [c_Equiv__Relations_Oequivp(_1519645, _1519647), hBOOL(hAPP(hAPP(_1519647, _1519649), _1519651)), hBOOL(hAPP(hAPP(_1519647, _1519651), _1519653)), -(hBOOL(hAPP(hAPP(_1519647, _1519649), _1519653)))], (38531 ^ _782464) ^ [_1519874, _1519876, _1519878, _1519880, _1519882, _1519884, _1519886] : [hBOOL(hAPP(_1519874, _1519876)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519878, _1519878)), hAPP(hAPP(c_Product__Type_OPair(_1519878, _1519878), _1519880), _1519882)), hAPP(_1519884, _1519876))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1519886, _1519878), tc_prod(_1519886, _1519878))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1519886, _1519878), tc_prod(_1519886, _1519878)), hAPP(hAPP(c_Product__Type_OPair(_1519886, _1519878), _1519876), _1519880)), hAPP(hAPP(c_Product__Type_OPair(_1519886, _1519878), _1519876), _1519882))), c_Recdef_Osame__fst(_1519886, _1519878, _1519874, _1519884))))], (38541 ^ _782464) ^ [_1520179, _1520181, _1520183, _1520185, _1520187, _1520189, _1520191] : [-(hAPP(c_Product__Type_Oapfst(_1520179, _1520181, _1520183, _1520185), hAPP(c_Product__Type_Oapsnd(_1520187, _1520183, _1520179, _1520189), _1520191)) = hAPP(hAPP(c_Product__Type_OPair(_1520181, _1520183), hAPP(_1520185, hAPP(c_Product__Type_Ofst(_1520179, _1520187), _1520191))), hAPP(_1520189, hAPP(c_Product__Type_Osnd(_1520179, _1520187), _1520191))))], (38543 ^ _782464) ^ [_1520257, _1520259, _1520261, _1520263, _1520265, _1520267, _1520269] : [-(hAPP(c_Product__Type_Oapsnd(_1520257, _1520259, _1520261, _1520263), hAPP(c_Product__Type_Oapfst(_1520265, _1520261, _1520257, _1520267), _1520269)) = hAPP(hAPP(c_Product__Type_OPair(_1520261, _1520259), hAPP(_1520267, hAPP(c_Product__Type_Ofst(_1520265, _1520257), _1520269))), hAPP(_1520263, hAPP(c_Product__Type_Osnd(_1520265, _1520257), _1520269))))], (38545 ^ _782464) ^ [_1520335, _1520337, _1520339, _1520341, _1520343, _1520345] : [-(hAPP(c_Product__Type_Oapfst(_1520335, _1520337, _1520339, _1520341), hAPP(hAPP(c_Product__Type_OPair(_1520335, _1520339), _1520343), _1520345)) = hAPP(hAPP(c_Product__Type_OPair(_1520337, _1520339), hAPP(_1520341, _1520343)), _1520345))], (38547 ^ _782464) ^ [_1520397, _1520399, _1520401, _1520403, _1520405] : [-(hAPP(c_Product__Type_Ofst(_1520397, _1520399), hAPP(c_Product__Type_Oapfst(_1520401, _1520397, _1520399, _1520403), _1520405)) = hAPP(_1520403, hAPP(c_Product__Type_Ofst(_1520401, _1520399), _1520405)))], (38549 ^ _782464) ^ [_1520478, _1520480, _1520482, _1520484, _1520486, _1520488] : [hAPP(c_Product__Type_Oapfst(_1520478, _1520480, _1520482, _1520484), _1520486) = hAPP(c_Product__Type_Oapfst(_1520478, _1520480, _1520482, _1520488), _1520486), -(hAPP(_1520484, hAPP(c_Product__Type_Ofst(_1520478, _1520482), _1520486)) = hAPP(_1520488, hAPP(c_Product__Type_Ofst(_1520478, _1520482), _1520486)))], (38555 ^ _782464) ^ [_1520627, _1520629, _1520631, _1520633, _1520635, _1520637] : [hAPP(_1520633, hAPP(c_Product__Type_Ofst(_1520627, _1520631), _1520635)) = hAPP(_1520637, hAPP(c_Product__Type_Ofst(_1520627, _1520631), _1520635)), -(hAPP(c_Product__Type_Oapfst(_1520627, _1520629, _1520631, _1520633), _1520635) = hAPP(c_Product__Type_Oapfst(_1520627, _1520629, _1520631, _1520637), _1520635))], (38561 ^ _782464) ^ [_1520782, _1520784, _1520786, _1520788, _1520790] : [-(hAPP(c_Product__Type_Osnd(_1520782, _1520784), hAPP(c_Product__Type_Oapfst(_1520786, _1520782, _1520784, _1520788), _1520790)) = hAPP(c_Product__Type_Osnd(_1520786, _1520784), _1520790))], (38563 ^ _782464) ^ [_1520833, _1520835, _1520837, _1520839, _1520841, _1520843, _1520845] : [-(hAPP(c_Product__Type_Oapfst(_1520833, _1520835, _1520837, _1520839), hAPP(c_Product__Type_Oapfst(_1520841, _1520833, _1520837, _1520843), _1520845)) = hAPP(c_Product__Type_Oapfst(_1520841, _1520835, _1520837, hAPP(c_Fun_Ocomp(_1520833, _1520835, _1520841, _1520839), _1520843)), _1520845))], (38565 ^ _782464) ^ [_1520900, _1520902, _1520904, _1520906, _1520908, _1520910, _1520912] : [-(hAPP(c_Product__Type_Oapsnd(_1520900, _1520902, _1520904, _1520906), hAPP(c_Product__Type_Oapfst(_1520908, _1520904, _1520900, _1520910), _1520912)) = hAPP(c_Product__Type_Oapfst(_1520908, _1520904, _1520902, _1520910), hAPP(c_Product__Type_Oapsnd(_1520900, _1520902, _1520908, _1520906), _1520912)))], (38567 ^ _782464) ^ [_1520967, _1520969, _1520971, _1520973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1520967), _1520969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1520971), _1520973)), -(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), _1520967), _1520971)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1520969), _1520973))), c_FunDef_Opair__less)))], (38577 ^ _782464) ^ [_1521170, _1521172, _1521174, _1521176, _1521178] : [hBOOL(hAPP(hAPP(c_member(_1521170), _1521172), hAPP(c_Relation_OImage(_1521174, _1521170, _1521176), _1521178))), 38581 ^ _782464 : [(38582 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521174, _1521170)), hAPP(hAPP(c_Product__Type_OPair(_1521174, _1521170), 38580 ^ [_1521170, _1521172, _1521174, _1521176, _1521178]), _1521172)), _1521176)))], (38584 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521174), 38580 ^ [_1521170, _1521172, _1521174, _1521176, _1521178]), _1521178)))]]], (38586 ^ _782464) ^ [_1521394, _1521396, _1521398] : [-(c_Wellfounded_Omlex__prod(_1521394, _1521396, _1521398) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1521394), _1521394), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1521394, c_Wellfounded_Oless__than, _1521398)), hAPP(hAPP(c_COMBS(_1521394, _1521394, tc_prod(tc_Nat_Onat, _1521394)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1521394, tc_prod(tc_Nat_Onat, _1521394)), _1521394), c_Product__Type_OPair(tc_Nat_Onat, _1521394)), _1521396)), c_COMBI(_1521394))))], (38588 ^ _782464) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (38590 ^ _782464) ^ [_1521494] : [-(c_Wellfounded_Omeasure(_1521494) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1521494), c_Wellfounded_Oless__than))], (38592 ^ _782464) ^ [_1521540, _1521542] : [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), _1521540), _1521542)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521540), _1521542)))], (38598 ^ _782464) ^ [_1521645, _1521647] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521645), _1521647)), -(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), _1521645), _1521647)), c_Wellfounded_Oless__than)))], (38604 ^ _782464) ^ [_1521756, _1521758, _1521760, _1521762] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521756), _1521758)), -(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), _1521756), _1521760)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521758), _1521762))), c_FunDef_Opair__less)))], (38610 ^ _782464) ^ [_1521893, _1521895, _1521897, _1521899] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521893), _1521895)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521897), _1521899)), -(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), _1521893), _1521897)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521895), _1521899))), c_FunDef_Opair__leq)))], (38620 ^ _782464) ^ [_1522096, _1522098, _1522100, _1522102] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522096), _1522098)), 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)), _1522096), _1522100)), 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)), _1522098), _1522102)), 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)), _1522098), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522100), _1522102))), c_FunDef_Omin__strict)))], (38634 ^ _782464) ^ [_1522377, _1522379, _1522381, _1522383] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522377), _1522379)), 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)), _1522381), _1522377)), 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)), _1522383), _1522379)), 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)), _1522381), _1522383)), _1522379)), c_FunDef_Omax__strict)))], (38648 ^ _782464) ^ [_1522658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522658)), -(_1522658 = 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))), _1522658)), c_FunDef_Omax__strict)))], (38658 ^ _782464) ^ [_1522764] : [-(_1522764 = 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)), _1522764), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (38664 ^ _782464) ^ [_1522809, _1522811, _1522813, _1522815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1522809), _1522811)), -(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), _1522809), _1522813)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1522811), _1522815))), c_FunDef_Opair__leq)))], (38670 ^ _782464) ^ [_1522946, _1522948, _1522950, _1522952] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522946), _1522948)), 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)), _1522950), _1522946)), 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)), _1522952), _1522948)), 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)), _1522950), _1522952)), _1522948)), c_FunDef_Omax__weak)))], (38684 ^ _782464) ^ [_1523227, _1523229, _1523231, _1523233] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1523227), _1523229)), 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)), _1523227), _1523231)), 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)), _1523229), _1523233)), 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)), _1523229), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1523231), _1523233))), c_FunDef_Omin__weak)))], (38698 ^ _782464) ^ [_1523508, _1523510, _1523512, _1523514] : [-(hAPP(c_Relation_OField(_1523508), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1523508, _1523508)), hAPP(hAPP(c_Product__Type_OPair(_1523508, _1523508), _1523510), _1523512)), _1523514)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523508, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1523508), _1523510), hAPP(hAPP(c_Set_Oinsert(_1523508), _1523512), c_Orderings_Obot__class_Obot(tc_fun(_1523508, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1523508), _1523514)))], (38700 ^ _782464) ^ [_1523599, _1523601] : [-(hAPP(c_Relation_OField(_1523599), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1523599, _1523599), tc_HOL_Obool), _1523601)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1523599, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1523599, _1523599), tc_HOL_Obool), tc_fun(_1523599, tc_HOL_Obool), c_Relation_OField(_1523599)), _1523601)))], (38702 ^ _782464) ^ [_1523662] : [-(hAPP(c_Relation_OField(_1523662), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523662, _1523662), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1523662, tc_HOL_Obool)))], (38704 ^ _782464) ^ [_1523703, _1523705, _1523707] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1523703, _1523703), tc_HOL_Obool)), _1523705), _1523707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523703, tc_HOL_Obool)), hAPP(c_Relation_OField(_1523703), _1523705)), hAPP(c_Relation_OField(_1523703), _1523707))))], (38710 ^ _782464) ^ [_1523848, _1523850, _1523852] : [-(hAPP(c_Relation_OField(_1523848), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523848, _1523848), tc_HOL_Obool)), _1523850), _1523852)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523848, tc_HOL_Obool)), hAPP(c_Relation_OField(_1523848), _1523850)), hAPP(c_Relation_OField(_1523848), _1523852)))], (38712 ^ _782464) ^ [_1523915, _1523917] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523915, _1523915)), _1523917)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523915), hAPP(c_Relation_OField(_1523915), _1523917))))], (38718 ^ _782464) ^ [_1524024] : [-(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)), _1524024), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (38720 ^ _782464) ^ [_1524058] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1524058)), -(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))), _1524058)), c_FunDef_Omax__weak)))], (38726 ^ _782464) ^ [] : [-(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)))))], (38728 ^ _782464) ^ [] : [-(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)))))], (38730 ^ _782464) ^ [_1524189, _1524191] : [-(c_Relation_OId__on(_1524189, _1524191) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524189, tc_fun(tc_prod(_1524189, _1524189), tc_HOL_Obool)), _1524191), hAPP(hAPP(c_COMBC(_1524189, tc_fun(tc_prod(_1524189, _1524189), tc_HOL_Obool), tc_fun(tc_prod(_1524189, _1524189), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1524189, _1524189), tc_fun(tc_fun(tc_prod(_1524189, _1524189), tc_HOL_Obool), tc_fun(tc_prod(_1524189, _1524189), tc_HOL_Obool)), _1524189), c_Set_Oinsert(tc_prod(_1524189, _1524189))), hAPP(hAPP(c_COMBS(_1524189, _1524189, tc_prod(_1524189, _1524189)), c_Product__Type_OPair(_1524189, _1524189)), c_COMBI(_1524189)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524189, _1524189), tc_HOL_Obool)))))], (38732 ^ _782464) ^ [_1524313, _1524315] : [-(c_Relation_OId__on(_1524313, _1524315) = hAPP(c_Product__Type_Oprod_Oprod__case(_1524313, _1524313, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1524313, tc_HOL_Obool, tc_fun(_1524313, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524313, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1524313, tc_HOL_Obool)), _1524313), c_COMBC(_1524313, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524313, tc_HOL_Obool), tc_fun(_1524313, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1524313), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524313), c_fconj)), c_fequal))), _1524315)))], (38734 ^ _782464) ^ [_1524407] : [-(c_Relation_OId__on(_1524407, c_Orderings_Obot__class_Obot(tc_fun(_1524407, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524407, _1524407), tc_HOL_Obool)))], (38736 ^ _782464) ^ [_1524446, _1524448, _1524450] : [-(hAPP(c_Relation_OImage(_1524446, _1524446, c_Relation_OId__on(_1524446, _1524448)), _1524450) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524446, tc_HOL_Obool)), _1524448), _1524450))], (38738 ^ _782464) ^ [_1524515, _1524517, _1524519, _1524521] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524515, _1524515)), hAPP(hAPP(c_Product__Type_OPair(_1524515, _1524515), _1524517), _1524519)), c_Relation_OId__on(_1524515, _1524521))), 38741 ^ _782464 : [(38742 ^ _782464) ^ [] : [-(_1524517 = _1524519)], (38744 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524515), _1524517), _1524521)))]]], (38746 ^ _782464) ^ [_1524676, _1524678, _1524680, _1524682] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524676, _1524676)), hAPP(hAPP(c_Product__Type_OPair(_1524676, _1524676), _1524678), _1524680)), c_Relation_OId__on(_1524676, _1524682)))), _1524678 = _1524680, hBOOL(hAPP(hAPP(c_member(_1524676), _1524678), _1524682))], (38756 ^ _782464) ^ [_1524873, _1524875, _1524877, _1524879] : [_1524873 = _1524875, hBOOL(hAPP(hAPP(c_member(_1524877), _1524873), _1524879)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524877, _1524877)), hAPP(hAPP(c_Product__Type_OPair(_1524877, _1524877), _1524873), _1524875)), c_Relation_OId__on(_1524877, _1524879))))], (38766 ^ _782464) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38768 ^ _782464) ^ [_1525086, _1525088, _1525090, _1525092, _1525094, _1525096] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525086, tc_HOL_Obool), tc_fun(_1525086, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525086, tc_HOL_Obool), tc_fun(_1525086, tc_HOL_Obool)), _1525088), _1525090)), c_Wellfounded_Omax__ext(_1525086, _1525092))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525086, tc_HOL_Obool), tc_fun(_1525086, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525086, tc_HOL_Obool), tc_fun(_1525086, tc_HOL_Obool)), _1525094), _1525096)), c_Wellfounded_Omax__ext(_1525086, _1525092))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525086, tc_HOL_Obool), tc_fun(_1525086, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525086, tc_HOL_Obool), tc_fun(_1525086, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525086, tc_HOL_Obool)), _1525088), _1525094)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525086, tc_HOL_Obool)), _1525090), _1525096))), c_Wellfounded_Omax__ext(_1525086, _1525092))))], (38778 ^ _782464) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38780 ^ _782464) ^ [_1525518, _1525520, _1525522, _1525524] : [c_Wellfounded_Omax__extp(_1525518, hAPP(hAPP(c_COMBC(_1525518, tc_fun(tc_prod(_1525518, _1525518), tc_HOL_Obool), tc_fun(_1525518, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525518, tc_fun(tc_fun(tc_prod(_1525518, _1525518), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525518, _1525518), tc_HOL_Obool), tc_fun(_1525518, tc_HOL_Obool)), _1525518), c_COMBC(_1525518, tc_fun(tc_prod(_1525518, _1525518), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525518, tc_prod(_1525518, _1525518)), tc_fun(_1525518, tc_fun(tc_fun(tc_prod(_1525518, _1525518), tc_HOL_Obool), tc_HOL_Obool)), _1525518), hAPP(c_COMBB(tc_prod(_1525518, _1525518), tc_fun(tc_fun(tc_prod(_1525518, _1525518), tc_HOL_Obool), tc_HOL_Obool), _1525518), c_member(tc_prod(_1525518, _1525518)))), c_Product__Type_OPair(_1525518, _1525518)))), _1525520), _1525522, _1525524), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525518, tc_HOL_Obool), tc_fun(_1525518, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525518, tc_HOL_Obool), tc_fun(_1525518, tc_HOL_Obool)), _1525522), _1525524)), c_Wellfounded_Omax__ext(_1525518, _1525520))))], (38786 ^ _782464) ^ [_1525903, _1525905, _1525907, _1525909] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525903, tc_HOL_Obool), tc_fun(_1525903, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525903, tc_HOL_Obool), tc_fun(_1525903, tc_HOL_Obool)), _1525907), _1525909)), c_Wellfounded_Omax__ext(_1525903, _1525905))), -(c_Wellfounded_Omax__extp(_1525903, hAPP(hAPP(c_COMBC(_1525903, tc_fun(tc_prod(_1525903, _1525903), tc_HOL_Obool), tc_fun(_1525903, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525903, tc_fun(tc_fun(tc_prod(_1525903, _1525903), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525903, _1525903), tc_HOL_Obool), tc_fun(_1525903, tc_HOL_Obool)), _1525903), c_COMBC(_1525903, tc_fun(tc_prod(_1525903, _1525903), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525903, tc_prod(_1525903, _1525903)), tc_fun(_1525903, tc_fun(tc_fun(tc_prod(_1525903, _1525903), tc_HOL_Obool), tc_HOL_Obool)), _1525903), hAPP(c_COMBB(tc_prod(_1525903, _1525903), tc_fun(tc_fun(tc_prod(_1525903, _1525903), tc_HOL_Obool), tc_HOL_Obool), _1525903), c_member(tc_prod(_1525903, _1525903)))), c_Product__Type_OPair(_1525903, _1525903)))), _1525905), _1525907, _1525909))], (38792 ^ _782464) ^ [] : [-(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)))], (38794 ^ _782464) ^ [] : [-(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)))], (38796 ^ _782464) ^ [_1526330, _1526332, _1526334, _1526336] : [c_FunDef_Oreduction__pair(_1526330, _1526332), -(c_FunDef_Oreduction__pair(_1526334, hAPP(hAPP(c_FunDef_Orp__inv__image(_1526330, _1526334), _1526332), _1526336)))], (38802 ^ _782464) ^ [_1526444, _1526446] : [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)), _1526444), 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)), _1526446), 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)), _1526444), _1526446)), c_Int_Ointrel)))], (38808 ^ _782464) ^ [_1526575, _1526577] : [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)), _1526575), _1526577)), 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)), _1526575), 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)), _1526577), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (38814 ^ _782464) ^ [_1526733, _1526735, _1526737, _1526739] : [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), _1526733), _1526735)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1526737), _1526739))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526733), _1526739) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526737), _1526735))], (38820 ^ _782464) ^ [_1526880, _1526882, _1526884, _1526886] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526880), _1526886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526884), _1526882), -(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), _1526880), _1526882)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1526884), _1526886))), c_Int_Ointrel)))], (38826 ^ _782464) ^ [_1527033, _1527035, _1527037] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527033, _1527033)), _1527035), c_Relation_OId__on(_1527033, _1527037))), 38830 ^ _782464 : [(38831 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527033), 38829 ^ [_1527033, _1527035, _1527037]), _1527037)))], (38833 ^ _782464) ^ [] : [-(_1527035 = hAPP(hAPP(c_Product__Type_OPair(_1527033, _1527033), 38829 ^ [_1527033, _1527035, _1527037]), 38829 ^ [_1527033, _1527035, _1527037]))]]], (38835 ^ _782464) ^ [] : [-(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))], (38837 ^ _782464) ^ [_1527250, _1527252, _1527254] : [class_Rings_Oring__1(_1527250), -(hAPP(c_Int_Oring__1__class_Oof__int(_1527250), 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), _1527252), _1527254)), 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(_1527250), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1527250), _1527252)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1527250), _1527254)))], (38843 ^ _782464) ^ [] : [-(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))))))], (38845 ^ _782464) ^ [_1527427, _1527429, _1527431, _1527433] : [-(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), _1527427), _1527429)), 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), _1527431), _1527433)), 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), _1527427), _1527431)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527429), _1527433))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527427), _1527433)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527429), _1527431)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38847 ^ _782464) ^ [_1527552] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1527552)) = _1527552)], (38849 ^ _782464) ^ [_1527581, _1527583] : [-(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), _1527581), _1527583)), 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), _1527583), _1527581)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38851 ^ _782464) ^ [] : [-(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))))))], (38853 ^ _782464) ^ [_1527663] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1527663) = 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), _1527663), 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))))))], (38855 ^ _782464) ^ [_1527707, _1527709, _1527711, _1527713] : [-(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), _1527707), _1527709)), 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), _1527711), _1527713)), 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), _1527707), _1527711)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1527709), _1527713))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38857 ^ _782464) ^ [_1527808, _1527810] : [-(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), _1527808), _1527810)), 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), _1527808), _1527810))], (38859 ^ _782464) ^ [_1527860] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1527860) = 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, _1527860)), 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))))))))], (38861 ^ _782464) ^ [_1527919, _1527921, _1527923, _1527925] : [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), _1527919), _1527921)), 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), _1527923), _1527925)), 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), _1527919), _1527925)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1527923), _1527921))))], (38867 ^ _782464) ^ [_1528112, _1528114, _1528116, _1528118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528112), _1528118)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528116), _1528114))), -(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), _1528112), _1528114)), 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), _1528116), _1528118)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (38873 ^ _782464) ^ [_1528332, _1528334, _1528336, _1528338] : [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), _1528332), _1528334)), 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), _1528336), _1528338)), 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), _1528332), _1528338)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528336), _1528334))))], (38879 ^ _782464) ^ [_1528525, _1528527, _1528529, _1528531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528525), _1528531)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528529), _1528527))), -(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), _1528525), _1528527)), 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), _1528529), _1528531)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (38887 ^ _782464) ^ [_1528724] : [-(_1528724 = 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), 38884 ^ [_1528724]), 38885 ^ [_1528724])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38889 ^ _782464) ^ [] : [-(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))], (38891 ^ _782464) ^ [_1528793, _1528795, _1528797, _1528799] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1528793, _1528795, _1528797, c_Code__Numeral_OSuc__code__numeral(_1528799)) = hAPP(_1528797, _1528799))], (38893 ^ _782464) ^ [_1528832] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1528832)), c_Int_OInteg)))], (38895 ^ _782464) ^ [_1528863, _1528865, _1528867] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1528863, _1528865, _1528867, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1528865)], (38897 ^ _782464) ^ [] : [-(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))], (38899 ^ _782464) ^ [_1528931, _1528933, _1528935] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1528931, hAPP(hAPP(c_COMBC(_1528931, tc_fun(tc_prod(_1528931, _1528931), tc_HOL_Obool), tc_fun(_1528931, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528931, tc_fun(tc_fun(tc_prod(_1528931, _1528931), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1528931, _1528931), tc_HOL_Obool), tc_fun(_1528931, tc_HOL_Obool)), _1528931), c_COMBC(_1528931, tc_fun(tc_prod(_1528931, _1528931), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528931, tc_prod(_1528931, _1528931)), tc_fun(_1528931, tc_fun(tc_fun(tc_prod(_1528931, _1528931), tc_HOL_Obool), tc_HOL_Obool)), _1528931), hAPP(c_COMBB(tc_prod(_1528931, _1528931), tc_fun(tc_fun(tc_prod(_1528931, _1528931), tc_HOL_Obool), tc_HOL_Obool), _1528931), c_member(tc_prod(_1528931, _1528931)))), c_Product__Type_OPair(_1528931, _1528931)))), _1528933)), _1528935)), -(hBOOL(hAPP(hAPP(c_member(_1528931), _1528935), c_Wellfounded_Oacc(_1528931, _1528933))))], (38905 ^ _782464) ^ [_1529272, _1529274, _1529276] : [hBOOL(hAPP(hAPP(c_member(_1529272), _1529276), c_Wellfounded_Oacc(_1529272, _1529274))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1529272, hAPP(hAPP(c_COMBC(_1529272, tc_fun(tc_prod(_1529272, _1529272), tc_HOL_Obool), tc_fun(_1529272, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529272, tc_fun(tc_fun(tc_prod(_1529272, _1529272), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529272, _1529272), tc_HOL_Obool), tc_fun(_1529272, tc_HOL_Obool)), _1529272), c_COMBC(_1529272, tc_fun(tc_prod(_1529272, _1529272), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529272, tc_prod(_1529272, _1529272)), tc_fun(_1529272, tc_fun(tc_fun(tc_prod(_1529272, _1529272), tc_HOL_Obool), tc_HOL_Obool)), _1529272), hAPP(c_COMBB(tc_prod(_1529272, _1529272), tc_fun(tc_fun(tc_prod(_1529272, _1529272), tc_HOL_Obool), tc_HOL_Obool), _1529272), c_member(tc_prod(_1529272, _1529272)))), c_Product__Type_OPair(_1529272, _1529272)))), _1529274)), _1529276)))], (38911 ^ _782464) ^ [_1529619, _1529621, _1529623, _1529625, _1529627] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1529619, _1529621, _1529623), _1529625), _1529627) = hAPP(c_Set_OCollect(tc_prod(_1529619, _1529623)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529619, _1529623, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1529623, tc_fun(_1529621, tc_HOL_Obool)), tc_fun(_1529623, tc_HOL_Obool), _1529619), hAPP(c_COMBB(tc_fun(_1529621, tc_HOL_Obool), tc_HOL_Obool, _1529623), c_HOL_OEx(_1529621))), hAPP(hAPP(c_COMBC(_1529619, tc_fun(_1529623, tc_fun(_1529621, tc_HOL_Obool)), tc_fun(_1529623, tc_fun(_1529621, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1529621, tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool)), tc_fun(tc_fun(_1529623, tc_fun(_1529621, tc_HOL_Obool)), tc_fun(_1529623, tc_fun(_1529621, tc_HOL_Obool))), _1529619), c_COMBB(tc_fun(_1529621, tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool), _1529623)), hAPP(hAPP(c_COMBB(tc_fun(_1529621, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529621, tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool)), _1529619), c_COMBS(_1529621, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529621, tc_HOL_Obool), tc_fun(_1529621, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529619), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529621), c_fconj)), hAPP(hAPP(c_COMBC(_1529619, tc_fun(tc_prod(_1529619, _1529621), tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529621, tc_fun(tc_fun(tc_prod(_1529619, _1529621), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529619, _1529621), tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool)), _1529619), c_COMBC(_1529621, tc_fun(tc_prod(_1529619, _1529621), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529621, tc_prod(_1529619, _1529621)), tc_fun(_1529621, tc_fun(tc_fun(tc_prod(_1529619, _1529621), tc_HOL_Obool), tc_HOL_Obool)), _1529619), hAPP(c_COMBB(tc_prod(_1529619, _1529621), tc_fun(tc_fun(tc_prod(_1529619, _1529621), tc_HOL_Obool), tc_HOL_Obool), _1529621), c_member(tc_prod(_1529619, _1529621)))), c_Product__Type_OPair(_1529619, _1529621)))), _1529625))))), hAPP(hAPP(c_COMBC(_1529623, tc_fun(tc_prod(_1529621, _1529623), tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529621, tc_fun(tc_fun(tc_prod(_1529621, _1529623), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529621, _1529623), tc_HOL_Obool), tc_fun(_1529621, tc_HOL_Obool)), _1529623), c_COMBC(_1529621, tc_fun(tc_prod(_1529621, _1529623), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529621, tc_prod(_1529621, _1529623)), tc_fun(_1529621, tc_fun(tc_fun(tc_prod(_1529621, _1529623), tc_HOL_Obool), tc_HOL_Obool)), _1529623), hAPP(c_COMBB(tc_prod(_1529621, _1529623), tc_fun(tc_fun(tc_prod(_1529621, _1529623), tc_HOL_Obool), tc_HOL_Obool), _1529621), c_member(tc_prod(_1529621, _1529623)))), hAPP(c_COMBC(_1529621, _1529623, tc_prod(_1529621, _1529623)), c_Product__Type_OPair(_1529621, _1529623))))), _1529627))))))], (38913 ^ _782464) ^ [_1530067, _1530069, _1530071, _1530073, _1530075, _1530077, _1530079, _1530081] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530067, _1530069)), hAPP(hAPP(c_Product__Type_OPair(_1530067, _1530069), _1530071), _1530073)), _1530075)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530069, _1530077)), hAPP(hAPP(c_Product__Type_OPair(_1530069, _1530077), _1530073), _1530079)), _1530081)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530067, _1530077)), hAPP(hAPP(c_Product__Type_OPair(_1530067, _1530077), _1530071), _1530079)), hAPP(hAPP(c_Relation_Orel__comp(_1530067, _1530069, _1530077), _1530075), _1530081))))], (38923 ^ _782464) ^ [_1530354, _1530356, _1530358, _1530360, _1530362, _1530364, _1530366] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530354, _1530356, _1530358), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530360, tc_fun(tc_prod(_1530354, _1530356), tc_HOL_Obool)), _1530362), _1530364)), _1530366) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530360, tc_fun(tc_prod(_1530354, _1530358), tc_HOL_Obool)), _1530362), hAPP(hAPP(c_COMBC(_1530360, tc_fun(tc_prod(_1530356, _1530358), tc_HOL_Obool), tc_fun(tc_prod(_1530354, _1530358), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530354, _1530356), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1530356, _1530358), tc_HOL_Obool), tc_fun(tc_prod(_1530354, _1530358), tc_HOL_Obool)), _1530360), c_Relation_Orel__comp(_1530354, _1530356, _1530358)), _1530364)), _1530366)))], (38925 ^ _782464) ^ [_1530486, _1530488, _1530490, _1530492, _1530494, _1530496, _1530498] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530486, _1530488, _1530490), _1530492), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530494, tc_fun(tc_prod(_1530488, _1530490), tc_HOL_Obool)), _1530496), _1530498)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530494, tc_fun(tc_prod(_1530486, _1530490), tc_HOL_Obool)), _1530496), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530488, _1530490), tc_HOL_Obool), tc_fun(tc_prod(_1530486, _1530490), tc_HOL_Obool), _1530494), hAPP(c_Relation_Orel__comp(_1530486, _1530488, _1530490), _1530492)), _1530498)))], (38927 ^ _782464) ^ [_1530590, _1530592, _1530594, _1530596] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530590, _1530592, _1530594), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530590, _1530592), tc_HOL_Obool))), _1530596) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530590, _1530594), tc_HOL_Obool)))], (38929 ^ _782464) ^ [_1530645, _1530647, _1530649, _1530651] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530645, _1530647, _1530649), _1530651), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530647, _1530649), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530645, _1530649), tc_HOL_Obool)))], (38931 ^ _782464) ^ [_1530700, _1530702, _1530704, _1530706, _1530708, _1530710] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530700, _1530702, _1530704), _1530706), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530702, _1530704), tc_HOL_Obool)), _1530708), _1530710)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530700, _1530704), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530700, _1530702, _1530704), _1530706), _1530708)), hAPP(hAPP(c_Relation_Orel__comp(_1530700, _1530702, _1530704), _1530706), _1530710)))], (38933 ^ _782464) ^ [_1530791, _1530793, _1530795, _1530797, _1530799, _1530801] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530791, _1530793, _1530795), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530791, _1530793), tc_HOL_Obool)), _1530797), _1530799)), _1530801) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530791, _1530795), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530791, _1530793, _1530795), _1530797), _1530801)), hAPP(hAPP(c_Relation_Orel__comp(_1530791, _1530793, _1530795), _1530799), _1530801)))], (38935 ^ _782464) ^ [_1530882, _1530884, _1530886, _1530888, _1530890, _1530892, _1530894] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530882, _1530884, _1530886), hAPP(hAPP(c_Relation_Orel__comp(_1530882, _1530888, _1530884), _1530890), _1530892)), _1530894) = hAPP(hAPP(c_Relation_Orel__comp(_1530882, _1530888, _1530886), _1530890), hAPP(hAPP(c_Relation_Orel__comp(_1530888, _1530884, _1530886), _1530892), _1530894)))], (38937 ^ _782464) ^ [_1530957, _1530959, _1530961, _1530963, _1530965, _1530967, _1530969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530957, _1530959), tc_HOL_Obool)), _1530961), _1530963)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530959, _1530965), tc_HOL_Obool)), _1530967), _1530969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530957, _1530965), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530957, _1530959, _1530965), _1530961), _1530967)), hAPP(hAPP(c_Relation_Orel__comp(_1530957, _1530959, _1530965), _1530963), _1530969))))], (38947 ^ _782464) ^ [_1531224, _1531226, _1531228, _1531230] : [hAPP(hAPP(c_Relation_Orel__comp(_1531224, _1531224, _1531224), _1531226), _1531228) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531224, _1531224), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531224, _1531224, _1531224), _1531226), _1531230) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531224, _1531224), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531224, _1531224, _1531224), _1531226), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531224, _1531224), tc_HOL_Obool)), _1531228), _1531230)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531224, _1531224), tc_HOL_Obool)))], (38957 ^ _782464) ^ [_1531497, _1531499, _1531501, _1531503] : [hAPP(hAPP(c_Relation_Orel__comp(_1531497, _1531497, _1531497), _1531499), _1531501) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531497, _1531497), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531497, _1531497, _1531497), _1531503), _1531501) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531497, _1531497), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531497, _1531497, _1531497), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531497, _1531497), tc_HOL_Obool)), _1531499), _1531503)), _1531501) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531497, _1531497), tc_HOL_Obool)))], (38967 ^ _782464) ^ [_1531770, _1531772, _1531774] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531770, _1531770), tc_HOL_Obool)), _1531772), _1531774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531770, tc_HOL_Obool)), c_Wellfounded_Oacc(_1531770, _1531774)), c_Wellfounded_Oacc(_1531770, _1531772))))], (38973 ^ _782464) ^ [_1531907, _1531909, _1531911, _1531913] : [hBOOL(hAPP(hAPP(c_member(_1531907), _1531909), c_Wellfounded_Oacc(_1531907, _1531911))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531907, _1531907)), hAPP(hAPP(c_Product__Type_OPair(_1531907, _1531907), _1531913), _1531909)), _1531911)), -(hBOOL(hAPP(hAPP(c_member(_1531907), _1531913), c_Wellfounded_Oacc(_1531907, _1531911))))], (38993 ^ _782464) ^ [_1532393, _1532395, _1532397] : [38995 ^ _782464 : [(38996 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532393, _1532393)), hAPP(hAPP(c_Product__Type_OPair(_1532393, _1532393), 38994 ^ [_1532393, _1532395, _1532397]), _1532395)), _1532397)))], (38998 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1532393), 38994 ^ [_1532393, _1532395, _1532397]), c_Wellfounded_Oacc(_1532393, _1532397)))]], -(hBOOL(hAPP(hAPP(c_member(_1532393), _1532395), c_Wellfounded_Oacc(_1532393, _1532397))))], (38983 ^ _782464) ^ [_1532140, _1532142, _1532144] : [hBOOL(hAPP(hAPP(c_member(_1532140), _1532142), c_Wellfounded_Oacc(_1532140, _1532144))), 38986 ^ _782464 : [(38987 ^ _782464) ^ [_1532254] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532140, _1532140)), hAPP(hAPP(c_Product__Type_OPair(_1532140, _1532140), _1532254), _1532142)), _1532144)), -(hBOOL(hAPP(hAPP(c_member(_1532140), _1532254), c_Wellfounded_Oacc(_1532140, _1532144))))]]], (39002 ^ _782464) ^ [_1532633, _1532635, _1532637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532633, _1532633), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532633, _1532633, _1532633), _1532635), _1532637)), _1532635)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1532633, _1532635)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1532633, _1532637)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1532633, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1532633, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1532633, tc_HOL_Obool), tc_fun(_1532633, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1532633, _1532635))))], (39008 ^ _782464) ^ [_1533004, _1533006, _1533008] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1533004, _1533004), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1533004, _1533004, _1533004), _1533006), _1533008)), _1533006)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1533004, _1533006)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1533004, _1533008)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1533004, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1533004, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1533004, tc_HOL_Obool), tc_fun(_1533004, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1533004, _1533006))))], (39014 ^ _782464) ^ [_1533375, _1533377, _1533379, _1533381, _1533383] : [c_Typedef_Otype__definition(_1533375, _1533377, _1533379, _1533381, _1533383), -(hAPP(c_Set_Oimage(_1533377, _1533375, _1533381), _1533383) = c_Orderings_Otop__class_Otop(tc_fun(_1533375, tc_HOL_Obool)))], (39020 ^ _782464) ^ [_1533488, _1533490, _1533492, _1533494, _1533496] : [c_Typedef_Otype__definition(_1533488, _1533490, _1533492, _1533494, _1533496), -(hAPP(c_Set_Oimage(_1533488, _1533490, _1533492), c_Orderings_Otop__class_Otop(tc_fun(_1533488, tc_HOL_Obool))) = _1533496)], (39026 ^ _782464) ^ [_1533601, _1533603, _1533605, _1533607, _1533609, _1533611] : [c_Typedef_Otype__definition(_1533601, _1533603, _1533605, _1533607, _1533609), -(hBOOL(hAPP(hAPP(c_member(_1533603), hAPP(_1533605, _1533611)), _1533609)))], (39032 ^ _782464) ^ [_1533712, _1533714, _1533716, _1533718, _1533720, _1533722] : [c_Typedef_Otype__definition(_1533712, _1533714, _1533716, _1533718, _1533720), -(hAPP(_1533718, hAPP(_1533716, _1533722)) = _1533722)], (39038 ^ _782464) ^ [_1533815, _1533817, _1533819, _1533821, _1533823, _1533825, _1533827] : [c_Typedef_Otype__definition(_1533815, _1533817, _1533819, _1533821, _1533823), 39041 ^ _782464 : [(39042 ^ _782464) ^ [] : [hAPP(_1533819, _1533825) = hAPP(_1533819, _1533827), -(_1533825 = _1533827)], (39048 ^ _782464) ^ [] : [_1533825 = _1533827, -(hAPP(_1533819, _1533825) = hAPP(_1533819, _1533827))]]], (39054 ^ _782464) ^ [_1534076, _1534078, _1534080, _1534082, _1534084, _1534086, _1534088] : [c_Typedef_Otype__definition(_1534076, _1534078, _1534080, _1534082, _1534084), hBOOL(hAPP(hAPP(c_member(_1534078), _1534086), _1534084)), hBOOL(hAPP(hAPP(c_member(_1534078), _1534088), _1534084)), 39065 ^ _782464 : [(39066 ^ _782464) ^ [] : [hAPP(_1534082, _1534086) = hAPP(_1534082, _1534088), -(_1534086 = _1534088)], (39072 ^ _782464) ^ [] : [_1534086 = _1534088, -(hAPP(_1534082, _1534086) = hAPP(_1534082, _1534088))]]], (39078 ^ _782464) ^ [_1534489, _1534491, _1534493, _1534495, _1534497, _1534499] : [c_Typedef_Otype__definition(_1534489, _1534491, _1534493, _1534495, _1534497), hBOOL(hAPP(hAPP(c_member(_1534491), _1534499), _1534497)), -(hAPP(_1534493, hAPP(_1534495, _1534499)) = _1534499)], (39088 ^ _782464) ^ [_1534696, _1534698, _1534700, _1534702, _1534704, _1534706, _1534708] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1534696, _1534698, _1534700, hAPP(hAPP(c_COMBC(_1534696, tc_fun(tc_prod(_1534696, _1534698), tc_HOL_Obool), tc_fun(_1534698, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534698, tc_fun(tc_fun(tc_prod(_1534696, _1534698), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534696, _1534698), tc_HOL_Obool), tc_fun(_1534698, tc_HOL_Obool)), _1534696), c_COMBC(_1534698, tc_fun(tc_prod(_1534696, _1534698), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534698, tc_prod(_1534696, _1534698)), tc_fun(_1534698, tc_fun(tc_fun(tc_prod(_1534696, _1534698), tc_HOL_Obool), tc_HOL_Obool)), _1534696), hAPP(c_COMBB(tc_prod(_1534696, _1534698), tc_fun(tc_fun(tc_prod(_1534696, _1534698), tc_HOL_Obool), tc_HOL_Obool), _1534698), c_member(tc_prod(_1534696, _1534698)))), c_Product__Type_OPair(_1534696, _1534698)))), _1534702), hAPP(hAPP(c_COMBC(_1534698, tc_fun(tc_prod(_1534698, _1534700), tc_HOL_Obool), tc_fun(_1534700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534700, tc_fun(tc_fun(tc_prod(_1534698, _1534700), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534698, _1534700), tc_HOL_Obool), tc_fun(_1534700, tc_HOL_Obool)), _1534698), c_COMBC(_1534700, tc_fun(tc_prod(_1534698, _1534700), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534700, tc_prod(_1534698, _1534700)), tc_fun(_1534700, tc_fun(tc_fun(tc_prod(_1534698, _1534700), tc_HOL_Obool), tc_HOL_Obool)), _1534698), hAPP(c_COMBB(tc_prod(_1534698, _1534700), tc_fun(tc_fun(tc_prod(_1534698, _1534700), tc_HOL_Obool), tc_HOL_Obool), _1534700), c_member(tc_prod(_1534698, _1534700)))), c_Product__Type_OPair(_1534698, _1534700)))), _1534704)), _1534706), _1534708)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534696, _1534700)), hAPP(hAPP(c_Product__Type_OPair(_1534696, _1534700), _1534706), _1534708)), hAPP(hAPP(c_Relation_Orel__comp(_1534696, _1534698, _1534700), _1534702), _1534704))))], (39094 ^ _782464) ^ [_1535331, _1535333, _1535335, _1535337, _1535339, _1535341, _1535343] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535331, _1535335)), hAPP(hAPP(c_Product__Type_OPair(_1535331, _1535335), _1535341), _1535343)), hAPP(hAPP(c_Relation_Orel__comp(_1535331, _1535333, _1535335), _1535337), _1535339))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1535331, _1535333, _1535335, hAPP(hAPP(c_COMBC(_1535331, tc_fun(tc_prod(_1535331, _1535333), tc_HOL_Obool), tc_fun(_1535333, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535333, tc_fun(tc_fun(tc_prod(_1535331, _1535333), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535331, _1535333), tc_HOL_Obool), tc_fun(_1535333, tc_HOL_Obool)), _1535331), c_COMBC(_1535333, tc_fun(tc_prod(_1535331, _1535333), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535333, tc_prod(_1535331, _1535333)), tc_fun(_1535333, tc_fun(tc_fun(tc_prod(_1535331, _1535333), tc_HOL_Obool), tc_HOL_Obool)), _1535331), hAPP(c_COMBB(tc_prod(_1535331, _1535333), tc_fun(tc_fun(tc_prod(_1535331, _1535333), tc_HOL_Obool), tc_HOL_Obool), _1535333), c_member(tc_prod(_1535331, _1535333)))), c_Product__Type_OPair(_1535331, _1535333)))), _1535337), hAPP(hAPP(c_COMBC(_1535333, tc_fun(tc_prod(_1535333, _1535335), tc_HOL_Obool), tc_fun(_1535335, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535335, tc_fun(tc_fun(tc_prod(_1535333, _1535335), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535333, _1535335), tc_HOL_Obool), tc_fun(_1535335, tc_HOL_Obool)), _1535333), c_COMBC(_1535335, tc_fun(tc_prod(_1535333, _1535335), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535335, tc_prod(_1535333, _1535335)), tc_fun(_1535335, tc_fun(tc_fun(tc_prod(_1535333, _1535335), tc_HOL_Obool), tc_HOL_Obool)), _1535333), hAPP(c_COMBB(tc_prod(_1535333, _1535335), tc_fun(tc_fun(tc_prod(_1535333, _1535335), tc_HOL_Obool), tc_HOL_Obool), _1535335), c_member(tc_prod(_1535333, _1535335)))), c_Product__Type_OPair(_1535333, _1535335)))), _1535339)), _1535341), _1535343)))], (39100 ^ _782464) ^ [_1535972, _1535974, _1535976] : [c_Wellfounded_Owf(_1535972, _1535974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535972, _1535972), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1535972, _1535972, _1535972), _1535974), _1535976)), _1535974)), -(c_FunDef_Oreduction__pair(_1535972, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1535972, _1535972), tc_HOL_Obool), tc_fun(tc_prod(_1535972, _1535972), tc_HOL_Obool)), _1535974), _1535976)))], (39110 ^ _782464) ^ [_1536214, _1536216, _1536218, _1536220] : [c_Wellfounded_Omax__extp(_1536214, _1536216, _1536218, _1536220), 39113 ^ _782464 : [(39114 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536214), _1536218)))], (39116 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536214), _1536220)))], (39118 ^ _782464) ^ [] : [_1536220 = c_Orderings_Obot__class_Obot(tc_fun(_1536214, tc_HOL_Obool))], (39120 ^ _782464) ^ [_1536430] : [hBOOL(hAPP(hAPP(c_member(_1536214), _1536430), _1536218)), 39124 ^ _782464 : [(39125 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536214), 39123 ^ [_1536214, _1536216, _1536218, _1536220, _1536430]), _1536220)))], (39127 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1536216, _1536430), 39123 ^ [_1536214, _1536216, _1536218, _1536220, _1536430])))]]]]], (39129 ^ _782464) ^ [_1536614, _1536616, _1536618, _1536620] : [-(c_Wellfounded_Omax__extp(_1536614, _1536616, _1536618, _1536620)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536614), _1536618)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536614), _1536620)), -(_1536620 = c_Orderings_Obot__class_Obot(tc_fun(_1536614, tc_HOL_Obool))), 39143 ^ _782464 : [(39144 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536614), 39142 ^ [_1536614, _1536616, _1536618, _1536620]), _1536618)))], (39146 ^ _782464) ^ [_1536959] : [hBOOL(hAPP(hAPP(c_member(_1536614), _1536959), _1536620)), hBOOL(hAPP(hAPP(_1536616, 39142 ^ [_1536614, _1536616, _1536618, _1536620]), _1536959))]]], (39154 ^ _782464) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (39156 ^ _782464) ^ [_1537145, _1537147, _1537149, _1537151, _1537153, _1537155, _1537157, _1537159] : [hBOOL(hAPP(hAPP(_1537145, _1537147), _1537149)), hBOOL(hAPP(hAPP(_1537151, _1537149), _1537153)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1537155, _1537157, _1537159, _1537145, _1537151), _1537147), _1537153)))], (39166 ^ _782464) ^ [_1537340] : [-(c_Wellfounded_Owf(_1537340, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537340, _1537340), tc_HOL_Obool))))], (39168 ^ _782464) ^ [_1537371, _1537373, _1537375, _1537377] : [c_Wellfounded_Owf(_1537371, _1537373), -(c_Wellfounded_Owf(_1537375, hAPP(hAPP(c_Relation_Oinv__image(_1537371, _1537375), _1537373), _1537377)))], (39174 ^ _782464) ^ [_1537470, _1537472, _1537474, _1537476] : [c_Wellfounded_Owf(_1537470, _1537472), c_Wellfounded_Owf(_1537474, _1537476), -(c_Wellfounded_Owf(tc_prod(_1537470, _1537474), c_Wellfounded_Olex__prod(_1537470, _1537474, _1537472, _1537476)))], (39184 ^ _782464) ^ [_1537623, _1537625] : [-(c_Wellfounded_Owf(_1537623, hAPP(c_Wellfounded_Omeasure(_1537623), _1537625)))], (39186 ^ _782464) ^ [_1537668, _1537670] : [c_Wellfounded_Owf(_1537668, _1537670), -(c_Wellfounded_Owf(_1537668, hAPP(hAPP(c_Relation_Orel__comp(_1537668, _1537668, _1537668), _1537670), _1537670)))], (39192 ^ _782464) ^ [_1537761, _1537763] : [c_Wellfounded_Owf(_1537761, hAPP(hAPP(c_Relation_Orel__comp(_1537761, _1537761, _1537761), _1537763), _1537763)), -(c_Wellfounded_Owf(_1537761, _1537763))], (39198 ^ _782464) ^ [_1537860, _1537862, _1537864] : [c_Wellfounded_Owf(_1537860, _1537862), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537860, _1537860), tc_HOL_Obool)), _1537864), _1537862)), -(c_Wellfounded_Owf(_1537860, _1537864))], (39208 ^ _782464) ^ [_1538019, _1538021] : [c_Wellfounded_Owf(_1538019, _1538021), -(c_Wellfounded_Owf(tc_fun(_1538019, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1538019, _1538021)))], (39214 ^ _782464) ^ [] : [-(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)))))], (39216 ^ _782464) ^ [_1538156, _1538158, _1538160, _1538162, _1538164, _1538166, _1538168] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1538156, _1538158, _1538160, _1538162, _1538164), _1538166), _1538168)), 39220 ^ _782464 : [(39221 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1538162, _1538166), 39219 ^ [_1538156, _1538158, _1538160, _1538162, _1538164, _1538166, _1538168])))], (39223 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1538164, 39219 ^ [_1538156, _1538158, _1538160, _1538162, _1538164, _1538166, _1538168]), _1538168)))]]], (39225 ^ _782464) ^ [_1538346, _1538348, _1538350, _1538352, _1538354, _1538356, _1538358] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1538346, _1538348, _1538350, _1538352, _1538354), _1538356), _1538358))), 39226 ^ _782464 : [(39227 ^ _782464) ^ [_1538417] : [hBOOL(hAPP(hAPP(_1538352, _1538356), _1538417)), hBOOL(hAPP(hAPP(_1538354, _1538417), _1538358))]]], (39235 ^ _782464) ^ [_1538566, _1538568, _1538570] : [c_Wellfounded_Owf(_1538566, _1538568), -(c_Wellfounded_Owf(_1538566, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538566, _1538566), tc_HOL_Obool)), _1538570), _1538568)))], (39241 ^ _782464) ^ [_1538673, _1538675, _1538677] : [c_Wellfounded_Owf(_1538673, _1538675), -(c_Wellfounded_Owf(_1538673, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538673, _1538673), tc_HOL_Obool)), _1538675), _1538677)))], (39247 ^ _782464) ^ [_1538780] : [-(c_Wellfounded_Owf(tc_fun(_1538780, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1538780)))], (39249 ^ _782464) ^ [_1538808, _1538810, _1538812] : [c_Wellfounded_Owf(_1538808, _1538810), -(c_Wellfounded_Owf(_1538808, c_Wellfounded_Omlex__prod(_1538808, _1538812, _1538810)))], (39255 ^ _782464) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (39257 ^ _782464) ^ [_1538913, _1538915] : [c_Wellfounded_Owf(_1538913, _1538915), -(c_Wellfounded_Owf(tc_fun(_1538913, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1538913, _1538915)))], (39263 ^ _782464) ^ [_1539002, _1539004, _1539006] : [c_Wellfounded_Owf(_1539002, _1539004), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539002, _1539002)), hAPP(hAPP(c_Product__Type_OPair(_1539002, _1539002), _1539006), _1539006)), _1539004))], (39269 ^ _782464) ^ [_1539120, _1539122, _1539124, _1539126] : [c_Wellfounded_Owf(_1539120, _1539122), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539120, _1539120)), hAPP(hAPP(c_Product__Type_OPair(_1539120, _1539120), _1539124), _1539126)), _1539122)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539120, _1539120)), hAPP(hAPP(c_Product__Type_OPair(_1539120, _1539120), _1539126), _1539124)), _1539122))], (39279 ^ _782464) ^ [_1539334, _1539336, _1539338, _1539340] : [c_Wellfounded_Owf(_1539334, _1539336), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539334, _1539334)), hAPP(hAPP(c_Product__Type_OPair(_1539334, _1539334), _1539338), _1539340)), _1539336)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539334, _1539334)), hAPP(hAPP(c_Product__Type_OPair(_1539334, _1539334), _1539340), _1539338)), _1539336))], (39289 ^ _782464) ^ [_1539548, _1539550, _1539552] : [c_Wellfounded_Owf(_1539548, _1539550), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539548, _1539548)), hAPP(hAPP(c_Product__Type_OPair(_1539548, _1539548), _1539552), _1539552)), _1539550))], (39295 ^ _782464) ^ [_1539666] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1539666)))], (39297 ^ _782464) ^ [_1539691] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1539691)))], (39299 ^ _782464) ^ [_1539731, _1539733] : [c_Wellfounded_Owf(_1539731, _1539733), 39302 ^ _782464 : [(39303 ^ _782464) ^ [_1539800] : [-(hBOOL(hAPP(hAPP(c_member(_1539731), _1539800), c_Wellfounded_Oacc(_1539731, _1539733))))]]], (39305 ^ _782464) ^ [_1539833, _1539835] : [hBOOL(hAPP(hAPP(c_member(_1539833), 39306 ^ [_1539833, _1539835]), c_Wellfounded_Oacc(_1539833, _1539835))), -(c_Wellfounded_Owf(_1539833, _1539835))], (39312 ^ _782464) ^ [_1539966, _1539968, _1539970] : [c_Wellfounded_Owf(_1539966, _1539968), -(hBOOL(hAPP(hAPP(c_member(_1539966), _1539970), c_Wellfounded_Oacc(_1539966, _1539968))))], (39318 ^ _782464) ^ [_1540065, _1540067] : [hAPP(hAPP(c_Relation_Orel__comp(_1540065, _1540065, _1540065), _1540067), _1540067) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540065, _1540065), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1540065, _1540067))], (39324 ^ _782464) ^ [_1540196, _1540198, _1540200] : [c_Wellfounded_Owf(_1540196, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540196, _1540196), tc_HOL_Obool)), _1540198), _1540200)), -(c_Wellfounded_Owf(_1540196, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540196, _1540196), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540196, _1540196), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540196, _1540196, _1540196), _1540198), _1540198)), hAPP(hAPP(c_Relation_Orel__comp(_1540196, _1540196, _1540196), _1540200), _1540198))), _1540200)))], (39330 ^ _782464) ^ [_1540395, _1540397, _1540399] : [c_Wellfounded_Owf(_1540395, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540395, _1540395), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540395, _1540395), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540395, _1540395, _1540395), _1540397), _1540397)), hAPP(hAPP(c_Relation_Orel__comp(_1540395, _1540395, _1540395), _1540399), _1540397))), _1540399)), -(c_Wellfounded_Owf(_1540395, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540395, _1540395), tc_HOL_Obool)), _1540397), _1540399)))], (39336 ^ _782464) ^ [_1540615, _1540617] : [c_Wellfounded_Owf(_1540615, _1540617), 39340 ^ _782464 : [(39341 ^ _782464) ^ [_1540751] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540615, _1540615)), hAPP(hAPP(c_Product__Type_OPair(_1540615, _1540615), hAPP(_1540751, hAPP(c_Nat_OSuc, 39339 ^ [_1540615, _1540617, _1540751]))), hAPP(_1540751, 39339 ^ [_1540615, _1540617, _1540751]))), _1540617))]]], (39343 ^ _782464) ^ [_1540818, _1540820] : [39345 ^ _782464 : [(39346 ^ _782464) ^ [_1540843] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540818, _1540818)), hAPP(hAPP(c_Product__Type_OPair(_1540818, _1540818), hAPP(39344 ^ [_1540818, _1540820], hAPP(c_Nat_OSuc, _1540843))), hAPP(39344 ^ [_1540818, _1540820], _1540843))), _1540820)))]], -(c_Wellfounded_Owf(_1540818, _1540820))], (39350 ^ _782464) ^ [_1540919, _1540921, _1540923] : [c_Wellfounded_Owf(_1540919, _1540921), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540919, tc_HOL_Obool)), _1540923), hAPP(c_Relation_OImage(_1540919, _1540919, _1540921), _1540923))), -(_1540923 = c_Orderings_Obot__class_Obot(tc_fun(_1540919, tc_HOL_Obool)))], (39360 ^ _782464) ^ [_1541096, _1541098, _1541100] : [c_Wellfounded_Owf(_1541096, _1541098), c_Wellfounded_Owf(_1541096, _1541100), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541096, _1541096), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541096, _1541096, _1541096), _1541098), _1541100)), _1541098)), -(c_Wellfounded_Owf(_1541096, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541096, _1541096), tc_HOL_Obool)), _1541098), _1541100)))], (39374 ^ _782464) ^ [_1541357] : [class_Orderings_Owellorder(_1541357), -(c_Wellfounded_Owf(_1541357, hAPP(c_Set_OCollect(tc_prod(_1541357, _1541357)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541357, _1541357, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1541357)))))], (39380 ^ _782464) ^ [_1541479, _1541481] : [c_FunDef_Oreduction__pair(_1541479, _1541481), 39383 ^ _782464 : [(39384 ^ _782464) ^ [] : [-(c_Wellfounded_Owf(_1541479, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool), tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool)), _1541481)))], (39386 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541479, _1541479, _1541479), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool), tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool)), _1541481)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool), tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool)), _1541481))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool), tc_fun(tc_prod(_1541479, _1541479), tc_HOL_Obool)), _1541481))))]]], (39388 ^ _782464) ^ [_1541768, _1541770] : [-(c_FunDef_Oreduction__pair(_1541768, _1541770)), c_Wellfounded_Owf(_1541768, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool), tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool)), _1541770)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541768, _1541768, _1541768), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool), tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool)), _1541770)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool), tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool)), _1541770))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool), tc_fun(tc_prod(_1541768, _1541768), tc_HOL_Obool)), _1541770)))], (39398 ^ _782464) ^ [_1542089, _1542091, _1542093, _1542095] : [c_FunDef_Oreduction__pair(_1542089, _1542091), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool)), _1542093), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool), tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool)), _1542091))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool)), _1542095), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool), tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool)), _1542091))), c_Wellfounded_Owf(_1542089, _1542095), -(c_Wellfounded_Owf(_1542089, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542089, _1542089), tc_HOL_Obool)), _1542093), _1542095)))], (39416 ^ _782464) ^ [_1542490, _1542492] : [c_Wellfounded_Owf(_1542490, _1542492), -(c_Wellfounded_Owf(tc_List_Olist(_1542490), c_List_Olenlex(_1542490, _1542492)))], (39422 ^ _782464) ^ [_1542577, _1542579, _1542581, _1542583] : [39424 ^ _782464 : [(39425 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1542577, 39423 ^ [_1542577, _1542579, _1542581, _1542583])))], (39427 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1542579, hAPP(_1542581, 39423 ^ [_1542577, _1542579, _1542581, _1542583]))), hAPP(_1542579, 39423 ^ [_1542577, _1542579, _1542581, _1542583])))]], -(c_Wellfounded_Owf(_1542583, hAPP(c_Set_OCollect(tc_prod(_1542583, _1542583)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542583, _1542583, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1542583, tc_HOL_Obool), tc_fun(_1542583, tc_HOL_Obool), _1542583), hAPP(c_COMBS(_1542583, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542583), c_fconj), _1542577))), hAPP(hAPP(c_COMBC(_1542583, tc_fun(_1542583, _1542583), tc_fun(_1542583, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542583, tc_HOL_Obool), tc_fun(tc_fun(_1542583, _1542583), tc_fun(_1542583, tc_HOL_Obool)), _1542583), c_COMBB(_1542583, tc_HOL_Obool, _1542583)), c_fequal)), _1542581))))))], (39431 ^ _782464) ^ [_1542970, _1542972, _1542974, _1542976] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542970), _1542972)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542970), _1542974)), -(_1542974 = c_Orderings_Obot__class_Obot(tc_fun(_1542970, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1542970, tc_HOL_Obool), tc_fun(_1542970, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1542970, tc_HOL_Obool), tc_fun(_1542970, tc_HOL_Obool)), _1542972), _1542974)), c_Wellfounded_Omax__ext(_1542970, _1542976)))), 39445 ^ _782464 : [(39446 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542970), 39444 ^ [_1542970, _1542972, _1542974, _1542976]), _1542972)))], (39448 ^ _782464) ^ [_1543375] : [hBOOL(hAPP(hAPP(c_member(_1542970), _1543375), _1542974)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1542970, _1542970)), hAPP(hAPP(c_Product__Type_OPair(_1542970, _1542970), 39444 ^ [_1542970, _1542972, _1542974, _1542976]), _1543375)), _1542976))]]], (39456 ^ _782464) ^ [] : [-(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))))], (39458 ^ _782464) ^ [_1543619, _1543621] : [c_Wellfounded_Owf(_1543619, _1543621), -(c_Wellfounded_Owf(tc_List_Olist(_1543619), c_List_Olex(_1543619, _1543621)))], (39464 ^ _782464) ^ [_1543706, _1543708, _1543710] : [c_Wellfounded_Owf(_1543706, _1543708), -(c_Wellfounded_Owf(tc_List_Olist(_1543706), hAPP(c_List_Olexn(_1543706, _1543708), _1543710)))], (39470 ^ _782464) ^ [_1543801, _1543803] : [-(c_List_Olex(_1543801, _1543803) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1543801), tc_List_Olist(_1543801)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1543801, _1543803)))], (39472 ^ _782464) ^ [_1543851, _1543853] : [-(hAPP(c_List_Olexn(_1543851, _1543853), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1543851), tc_List_Olist(_1543851)), tc_HOL_Obool)))], (39474 ^ _782464) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (39476 ^ _782464) ^ [_1543912, _1543914, _1543916, _1543918] : [39478 ^ _782464 : [(39479 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1543912, 39477 ^ [_1543912, _1543914, _1543916, _1543918])))], (39481 ^ _782464) ^ [] : [c_Wellfounded_Owf(_1543914, hAPP(_1543916, 39477 ^ [_1543912, _1543914, _1543916, _1543918]))]], -(c_Wellfounded_Owf(tc_prod(_1543918, _1543914), c_Recdef_Osame__fst(_1543918, _1543914, _1543912, _1543916)))], (39485 ^ _782464) ^ [_1544097] : [-(c_Nitpick_Ozero__frac(_1544097) = c_Nitpick_OAbs__Frac(_1544097, 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))))], (39487 ^ _782464) ^ [_1544125, _1544127, _1544129] : [-(hAPP(c_Relation_ORange(_1544125, _1544127), hAPP(c_Set_OCollect(tc_prod(_1544125, _1544127)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544125, _1544127, tc_HOL_Obool), _1544129))) = hAPP(c_Set_OCollect(_1544127), hAPP(hAPP(c_COMBB(tc_fun(_1544125, tc_HOL_Obool), tc_HOL_Obool, _1544127), c_HOL_OEx(_1544125)), hAPP(c_COMBC(_1544125, _1544127, tc_HOL_Obool), _1544129))))], (39489 ^ _782464) ^ [_1544200, _1544202, _1544204, _1544206, _1544208] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544200, _1544202)), hAPP(hAPP(c_Product__Type_OPair(_1544200, _1544202), _1544204), _1544206)), _1544208)), -(hBOOL(hAPP(hAPP(c_member(_1544202), _1544206), hAPP(c_Relation_ORange(_1544200, _1544202), _1544208))))], (39495 ^ _782464) ^ [_1544347, _1544349] : [-(hAPP(c_Relation_ORange(_1544347, _1544347), c_Relation_OId__on(_1544347, _1544349)) = _1544349)], (39497 ^ _782464) ^ [_1544381, _1544383, _1544385, _1544387] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544381, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1544381, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544383, _1544381), _1544385)), hAPP(c_Relation_ORange(_1544383, _1544381), _1544387))), hAPP(c_Relation_ORange(_1544383, _1544381), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1544383, _1544381), tc_HOL_Obool)), _1544385), _1544387)))))], (39499 ^ _782464) ^ [_1544463, _1544465, _1544467] : [-(hAPP(c_Relation_ORange(_1544463, _1544465), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1544463, _1544465), tc_HOL_Obool), _1544467)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1544463, _1544465), tc_HOL_Obool), tc_fun(_1544465, tc_HOL_Obool)), _1544467), c_Relation_ORange(_1544463, _1544465)))], (39501 ^ _782464) ^ [_1544526, _1544528] : [-(hAPP(c_Relation_ORange(_1544526, _1544528), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544526, _1544528), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1544528, tc_HOL_Obool)))], (39503 ^ _782464) ^ [_1544588, _1544590, _1544592] : [hAPP(c_Relation_ORange(_1544588, _1544590), _1544592) = c_Orderings_Obot__class_Obot(tc_fun(_1544590, tc_HOL_Obool)), -(_1544592 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544588, _1544590), tc_HOL_Obool)))], (39509 ^ _782464) ^ [_1544701, _1544703, _1544705] : [_1544705 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544701, _1544703), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1544701, _1544703), _1544705) = c_Orderings_Obot__class_Obot(tc_fun(_1544703, tc_HOL_Obool)))], (39515 ^ _782464) ^ [_1544820, _1544822, _1544824, _1544826] : [-(hAPP(c_Relation_ORange(_1544820, _1544822), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1544820, _1544822), tc_HOL_Obool)), _1544824), _1544826)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544822, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544820, _1544822), _1544824)), hAPP(c_Relation_ORange(_1544820, _1544822), _1544826)))], (39517 ^ _782464) ^ [_1544892, _1544894, _1544896] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1544892, _1544894)), _1544896)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544894), hAPP(c_Relation_ORange(_1544892, _1544894), _1544896))))], (39523 ^ _782464) ^ [_1545005, _1545007, _1545009] : [-(hAPP(c_Set_Oimage(tc_prod(_1545005, _1545007), _1545007, c_Product__Type_Osnd(_1545005, _1545007)), _1545009) = hAPP(c_Relation_ORange(_1545005, _1545007), _1545009))], (39525 ^ _782464) ^ [_1545072, _1545074, _1545076, _1545078] : [hBOOL(hAPP(hAPP(c_member(_1545072), _1545074), hAPP(c_Relation_ORange(_1545076, _1545072), _1545078))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545076, _1545072)), hAPP(hAPP(c_Product__Type_OPair(_1545076, _1545072), 39528 ^ [_1545072, _1545074, _1545076, _1545078]), _1545074)), _1545078)))], (39532 ^ _782464) ^ [_1545229, _1545231, _1545233, _1545235] : [39533 ^ _782464 : [(39534 ^ _782464) ^ [_1545304] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545233, _1545229)), hAPP(hAPP(c_Product__Type_OPair(_1545233, _1545229), _1545304), _1545231)), _1545235))]], -(hBOOL(hAPP(hAPP(c_member(_1545229), _1545231), hAPP(c_Relation_ORange(_1545233, _1545229), _1545235))))], (39538 ^ _782464) ^ [_1545389, _1545391, _1545393, _1545395, _1545397] : [-(hAPP(c_Relation_ORange(_1545389, _1545391), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1545389, _1545391)), hAPP(hAPP(c_Product__Type_OPair(_1545389, _1545391), _1545393), _1545395)), _1545397)) = hAPP(hAPP(c_Set_Oinsert(_1545391), _1545395), hAPP(c_Relation_ORange(_1545389, _1545391), _1545397)))], (39540 ^ _782464) ^ [_1545460, _1545462, _1545464, _1545466] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1545460, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545462, _1545460), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1545462, _1545460), tc_HOL_Obool)), _1545464), _1545466))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545460, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545462, _1545460), _1545464)), hAPP(c_Relation_ORange(_1545462, _1545460), _1545466)))))], (39542 ^ _782464) ^ [_1545542] : [-(c_Nitpick_Oone__frac(_1545542) = c_Nitpick_OAbs__Frac(_1545542, 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))))], (39544 ^ _782464) ^ [_1545570, _1545572] : [-(c_Nitpick_Onumber__of__frac(_1545570, _1545572) = c_Nitpick_OAbs__Frac(_1545570, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1545572), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (39546 ^ _782464) ^ [_1545628, _1545630, _1545632, _1545634] : [hBOOL(hAPP(c_Predicate_ORangeP(_1545628, _1545630, hAPP(hAPP(c_COMBC(_1545628, tc_fun(tc_prod(_1545628, _1545630), tc_HOL_Obool), tc_fun(_1545630, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545630, tc_fun(tc_fun(tc_prod(_1545628, _1545630), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545628, _1545630), tc_HOL_Obool), tc_fun(_1545630, tc_HOL_Obool)), _1545628), c_COMBC(_1545630, tc_fun(tc_prod(_1545628, _1545630), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545630, tc_prod(_1545628, _1545630)), tc_fun(_1545630, tc_fun(tc_fun(tc_prod(_1545628, _1545630), tc_HOL_Obool), tc_HOL_Obool)), _1545628), hAPP(c_COMBB(tc_prod(_1545628, _1545630), tc_fun(tc_fun(tc_prod(_1545628, _1545630), tc_HOL_Obool), tc_HOL_Obool), _1545630), c_member(tc_prod(_1545628, _1545630)))), c_Product__Type_OPair(_1545628, _1545630)))), _1545632)), _1545634)), -(hBOOL(hAPP(hAPP(c_member(_1545630), _1545634), hAPP(c_Relation_ORange(_1545628, _1545630), _1545632))))], (39552 ^ _782464) ^ [_1545979, _1545981, _1545983, _1545985] : [hBOOL(hAPP(hAPP(c_member(_1545981), _1545985), hAPP(c_Relation_ORange(_1545979, _1545981), _1545983))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1545979, _1545981, hAPP(hAPP(c_COMBC(_1545979, tc_fun(tc_prod(_1545979, _1545981), tc_HOL_Obool), tc_fun(_1545981, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545981, tc_fun(tc_fun(tc_prod(_1545979, _1545981), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545979, _1545981), tc_HOL_Obool), tc_fun(_1545981, tc_HOL_Obool)), _1545979), c_COMBC(_1545981, tc_fun(tc_prod(_1545979, _1545981), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545981, tc_prod(_1545979, _1545981)), tc_fun(_1545981, tc_fun(tc_fun(tc_prod(_1545979, _1545981), tc_HOL_Obool), tc_HOL_Obool)), _1545979), hAPP(c_COMBB(tc_prod(_1545979, _1545981), tc_fun(tc_fun(tc_prod(_1545979, _1545981), tc_HOL_Obool), tc_HOL_Obool), _1545981), c_member(tc_prod(_1545979, _1545981)))), c_Product__Type_OPair(_1545979, _1545981)))), _1545983)), _1545985)))], (39558 ^ _782464) ^ [_1546336, _1546338, _1546340, _1546342, _1546344] : [hBOOL(hAPP(hAPP(_1546336, _1546338), _1546340)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1546342, _1546344, _1546336), _1546340)))], (39564 ^ _782464) ^ [_1546462, _1546464, _1546466, _1546468] : [hBOOL(hAPP(c_Predicate_ORangeP(_1546462, _1546464, _1546466), _1546468)), -(hBOOL(hAPP(hAPP(_1546466, 39567 ^ [_1546462, _1546464, _1546466, _1546468]), _1546468)))], (39571 ^ _782464) ^ [_1546577, _1546579, _1546581, _1546583] : [39572 ^ _782464 : [(39573 ^ _782464) ^ [_1546631] : [hBOOL(hAPP(hAPP(_1546581, _1546631), _1546583))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1546577, _1546579, _1546581), _1546583)))], (39577 ^ _782464) ^ [_1546695, _1546697, _1546699] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1546695), _1546697), _1546699) = c_Nitpick_OAbs__Frac(_1546695, c_Nitpick_Onorm__frac(_1546697, _1546699)))], (39579 ^ _782464) ^ [_1546736, _1546738, _1546740, _1546742] : [hBOOL(hAPP(hAPP(c_member(_1546736), _1546738), hAPP(c_Relation_ORange(_1546740, _1546736), _1546742))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546740, _1546736)), hAPP(hAPP(c_Product__Type_OPair(_1546740, _1546736), 39582 ^ [_1546736, _1546738, _1546740, _1546742]), _1546738)), _1546742)))], (39586 ^ _782464) ^ [_1546901, _1546903, _1546905] : [c_Wellfounded_Owf(_1546901, _1546903), c_Wellfounded_Owf(_1546901, _1546905), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1546901, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1546901, _1546901), _1546903)), hAPP(c_Relation_ORange(_1546901, _1546901), _1546905)) = c_Orderings_Obot__class_Obot(tc_fun(_1546901, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1546901, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1546901, _1546901), tc_HOL_Obool)), _1546903), _1546905)))], (39600 ^ _782464) ^ [_1547172, _1547174, _1547176, _1547178, _1547180] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547172, _1547174)), hAPP(hAPP(c_Product__Type_OPair(_1547172, _1547174), _1547176), _1547178)), _1547180)), -(hBOOL(hAPP(hAPP(c_member(_1547172), _1547176), hAPP(c_Relation_ODomain(_1547172, _1547174), _1547180))))], (39606 ^ _782464) ^ [_1547319, _1547321] : [-(hAPP(c_Relation_ODomain(_1547319, _1547319), c_Relation_OId__on(_1547319, _1547321)) = _1547321)], (39608 ^ _782464) ^ [_1547353, _1547355] : [-(hAPP(c_Relation_ODomain(_1547353, _1547355), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547353, _1547355), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1547353, tc_HOL_Obool)))], (39610 ^ _782464) ^ [_1547415, _1547417, _1547419] : [hAPP(c_Relation_ODomain(_1547415, _1547417), _1547419) = c_Orderings_Obot__class_Obot(tc_fun(_1547415, tc_HOL_Obool)), -(_1547419 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547415, _1547417), tc_HOL_Obool)))], (39616 ^ _782464) ^ [_1547528, _1547530, _1547532] : [_1547532 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547528, _1547530), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1547528, _1547530), _1547532) = c_Orderings_Obot__class_Obot(tc_fun(_1547528, tc_HOL_Obool)))], (39622 ^ _782464) ^ [_1547647, _1547649, _1547651, _1547653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547647, _1547649), tc_HOL_Obool)), _1547651), _1547653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1547647, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1547647, _1547649), _1547651)), hAPP(c_Relation_ODomain(_1547647, _1547649), _1547653))))], (39628 ^ _782464) ^ [_1547798, _1547800, _1547802, _1547804] : [-(hAPP(c_Relation_ODomain(_1547798, _1547800), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1547798, _1547800), tc_HOL_Obool)), _1547802), _1547804)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547798, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1547798, _1547800), _1547802)), hAPP(c_Relation_ODomain(_1547798, _1547800), _1547804)))], (39630 ^ _782464) ^ [_1547870, _1547872, _1547874] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1547870, _1547872)), _1547874)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547870), hAPP(c_Relation_ODomain(_1547870, _1547872), _1547874))))], (39636 ^ _782464) ^ [_1547983, _1547985, _1547987] : [-(hAPP(c_Set_Oimage(tc_prod(_1547983, _1547985), _1547983, c_Product__Type_Ofst(_1547983, _1547985)), _1547987) = hAPP(c_Relation_ODomain(_1547983, _1547985), _1547987))], (39638 ^ _782464) ^ [_1548050, _1548052, _1548054, _1548056] : [hBOOL(hAPP(hAPP(c_member(_1548050), _1548052), hAPP(c_Relation_ODomain(_1548050, _1548054), _1548056))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548050, _1548054)), hAPP(hAPP(c_Product__Type_OPair(_1548050, _1548054), _1548052), 39641 ^ [_1548050, _1548052, _1548054, _1548056])), _1548056)))], (39645 ^ _782464) ^ [_1548207, _1548209, _1548211, _1548213] : [39646 ^ _782464 : [(39647 ^ _782464) ^ [_1548282] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548207, _1548211)), hAPP(hAPP(c_Product__Type_OPair(_1548207, _1548211), _1548209), _1548282)), _1548213))]], -(hBOOL(hAPP(hAPP(c_member(_1548207), _1548209), hAPP(c_Relation_ODomain(_1548207, _1548211), _1548213))))], (39651 ^ _782464) ^ [_1548367, _1548369, _1548371, _1548373, _1548375] : [-(hAPP(c_Relation_ODomain(_1548367, _1548369), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1548367, _1548369)), hAPP(hAPP(c_Product__Type_OPair(_1548367, _1548369), _1548371), _1548373)), _1548375)) = hAPP(hAPP(c_Set_Oinsert(_1548367), _1548371), hAPP(c_Relation_ODomain(_1548367, _1548369), _1548375)))], (39653 ^ _782464) ^ [_1548438, _1548440, _1548442, _1548444] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548438, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548438, _1548440), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1548438, _1548440), tc_HOL_Obool)), _1548442), _1548444))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1548438, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548438, _1548440), _1548442)), hAPP(c_Relation_ODomain(_1548438, _1548440), _1548444)))))], (39655 ^ _782464) ^ [_1548520, _1548522, _1548524, _1548526] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548520, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1548520, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548520, _1548522), _1548524)), hAPP(c_Relation_ODomain(_1548520, _1548522), _1548526))), hAPP(c_Relation_ODomain(_1548520, _1548522), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1548520, _1548522), tc_HOL_Obool)), _1548524), _1548526)))))], (39657 ^ _782464) ^ [_1548602, _1548604] : [-(hAPP(c_Relation_OField(_1548602), _1548604) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1548602, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548602, _1548602), _1548604)), hAPP(c_Relation_ORange(_1548602, _1548602), _1548604)))], (39659 ^ _782464) ^ [_1548655, _1548657, _1548659] : [-(hAPP(c_Relation_ODomain(_1548655, _1548657), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1548655, _1548657), tc_HOL_Obool), _1548659)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1548655, _1548657), tc_HOL_Obool), tc_fun(_1548655, tc_HOL_Obool)), _1548659), c_Relation_ODomain(_1548655, _1548657)))], (39661 ^ _782464) ^ [_1548718, _1548720, _1548722] : [-(hAPP(c_Relation_ODomain(_1548718, _1548720), hAPP(c_Set_OCollect(tc_prod(_1548718, _1548720)), hAPP(c_Product__Type_Oprod_Oprod__case(_1548718, _1548720, tc_HOL_Obool), _1548722))) = hAPP(c_Set_OCollect(_1548718), hAPP(hAPP(c_COMBB(tc_fun(_1548720, tc_HOL_Obool), tc_HOL_Obool, _1548718), c_HOL_OEx(_1548720)), _1548722)))], (39663 ^ _782464) ^ [_1548807, _1548809, _1548811, _1548813] : [hBOOL(hAPP(c_Predicate_ODomainP(_1548807, _1548809, hAPP(hAPP(c_COMBC(_1548807, tc_fun(tc_prod(_1548807, _1548809), tc_HOL_Obool), tc_fun(_1548809, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548809, tc_fun(tc_fun(tc_prod(_1548807, _1548809), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1548807, _1548809), tc_HOL_Obool), tc_fun(_1548809, tc_HOL_Obool)), _1548807), c_COMBC(_1548809, tc_fun(tc_prod(_1548807, _1548809), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548809, tc_prod(_1548807, _1548809)), tc_fun(_1548809, tc_fun(tc_fun(tc_prod(_1548807, _1548809), tc_HOL_Obool), tc_HOL_Obool)), _1548807), hAPP(c_COMBB(tc_prod(_1548807, _1548809), tc_fun(tc_fun(tc_prod(_1548807, _1548809), tc_HOL_Obool), tc_HOL_Obool), _1548809), c_member(tc_prod(_1548807, _1548809)))), c_Product__Type_OPair(_1548807, _1548809)))), _1548811)), _1548813)), -(hBOOL(hAPP(hAPP(c_member(_1548807), _1548813), hAPP(c_Relation_ODomain(_1548807, _1548809), _1548811))))], (39669 ^ _782464) ^ [_1549158, _1549160, _1549162, _1549164] : [hBOOL(hAPP(hAPP(c_member(_1549158), _1549164), hAPP(c_Relation_ODomain(_1549158, _1549160), _1549162))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1549158, _1549160, hAPP(hAPP(c_COMBC(_1549158, tc_fun(tc_prod(_1549158, _1549160), tc_HOL_Obool), tc_fun(_1549160, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549160, tc_fun(tc_fun(tc_prod(_1549158, _1549160), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1549158, _1549160), tc_HOL_Obool), tc_fun(_1549160, tc_HOL_Obool)), _1549158), c_COMBC(_1549160, tc_fun(tc_prod(_1549158, _1549160), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549160, tc_prod(_1549158, _1549160)), tc_fun(_1549160, tc_fun(tc_fun(tc_prod(_1549158, _1549160), tc_HOL_Obool), tc_HOL_Obool)), _1549158), hAPP(c_COMBB(tc_prod(_1549158, _1549160), tc_fun(tc_fun(tc_prod(_1549158, _1549160), tc_HOL_Obool), tc_HOL_Obool), _1549160), c_member(tc_prod(_1549158, _1549160)))), c_Product__Type_OPair(_1549158, _1549160)))), _1549162)), _1549164)))], (39675 ^ _782464) ^ [_1549515, _1549517, _1549519, _1549521] : [hBOOL(hAPP(hAPP(c_member(_1549515), _1549517), hAPP(c_Relation_ODomain(_1549515, _1549519), _1549521))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549515, _1549519)), hAPP(hAPP(c_Product__Type_OPair(_1549515, _1549519), _1549517), 39678 ^ [_1549515, _1549517, _1549519, _1549521])), _1549521)))], (39682 ^ _782464) ^ [_1549680, _1549682, _1549684, _1549686, _1549688, _1549690] : [-(hAPP(c_Set_Oimage(_1549680, tc_prod(_1549682, _1549684), hAPP(hAPP(c_COMBS(_1549680, _1549684, tc_prod(_1549682, _1549684)), hAPP(hAPP(c_COMBB(_1549682, tc_fun(_1549684, tc_prod(_1549682, _1549684)), _1549680), c_Product__Type_OPair(_1549682, _1549684)), _1549686)), _1549688)), _1549690) = hAPP(hAPP(c_Product__Type_OSigma(_1549682, _1549684), hAPP(c_Set_Oimage(_1549680, _1549682, _1549686), _1549690)), hAPP(hAPP(c_COMBB(tc_fun(_1549680, tc_HOL_Obool), tc_fun(_1549684, tc_HOL_Obool), _1549682), c_Set_Oimage(_1549680, _1549684, _1549688)), hAPP(hAPP(c_COMBC(_1549682, tc_fun(_1549680, tc_HOL_Obool), tc_fun(_1549680, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549680, tc_HOL_Obool), tc_fun(tc_fun(_1549680, tc_HOL_Obool), tc_fun(_1549680, tc_HOL_Obool)), _1549682), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549680, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1549682, tc_HOL_Obool), tc_fun(_1549680, tc_HOL_Obool), _1549682), c_Set_Ovimage(_1549680, _1549682, _1549686)), hAPP(hAPP(c_COMBC(_1549682, tc_fun(_1549682, tc_HOL_Obool), tc_fun(_1549682, tc_HOL_Obool)), c_Set_Oinsert(_1549682)), c_Orderings_Obot__class_Obot(tc_fun(_1549682, tc_HOL_Obool)))))), _1549690))))], (39684 ^ _782464) ^ [_1549877, _1549879, _1549881, _1549883, _1549885] : [hBOOL(hAPP(hAPP(_1549877, _1549879), _1549881)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1549883, _1549885, _1549877), _1549879)))], (39690 ^ _782464) ^ [_1549982, _1549984, _1549986, _1549988, _1549990, _1549992] : [hBOOL(hAPP(hAPP(c_member(_1549982), _1549984), _1549986)), hBOOL(hAPP(hAPP(c_member(_1549988), _1549990), hAPP(_1549992, _1549984))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549982, _1549988)), hAPP(hAPP(c_Product__Type_OPair(_1549982, _1549988), _1549984), _1549990)), hAPP(hAPP(c_Product__Type_OSigma(_1549982, _1549988), _1549986), _1549992))))], (39700 ^ _782464) ^ [_1550217, _1550219, _1550221] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550217, _1550219), c_Orderings_Obot__class_Obot(tc_fun(_1550217, tc_HOL_Obool))), _1550221) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1550217, _1550219), tc_HOL_Obool)))], (39702 ^ _782464) ^ [_1550266, _1550268, _1550270, _1550272, _1550274, _1550276] : [hBOOL(hAPP(hAPP(c_member(_1550266), _1550268), _1550270)), 39705 ^ _782464 : [(39706 ^ _782464) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1550272, _1550266), _1550274), hAPP(c_COMBK(tc_fun(_1550266, tc_HOL_Obool), _1550272), _1550270)) = hAPP(hAPP(c_Product__Type_OSigma(_1550272, _1550266), _1550276), hAPP(c_COMBK(tc_fun(_1550266, tc_HOL_Obool), _1550272), _1550270)), -(_1550274 = _1550276)], (39712 ^ _782464) ^ [] : [_1550274 = _1550276, -(hAPP(hAPP(c_Product__Type_OSigma(_1550272, _1550266), _1550274), hAPP(c_COMBK(tc_fun(_1550266, tc_HOL_Obool), _1550272), _1550270)) = hAPP(hAPP(c_Product__Type_OSigma(_1550272, _1550266), _1550276), hAPP(c_COMBK(tc_fun(_1550266, tc_HOL_Obool), _1550272), _1550270)))]]], (39718 ^ _782464) ^ [_1550619, _1550621, _1550623, _1550625] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550619, _1550621), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1550619, tc_HOL_Obool), _1550623)), _1550625) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1550619, tc_HOL_Obool), tc_fun(tc_prod(_1550619, _1550621), tc_HOL_Obool)), _1550623), hAPP(hAPP(c_COMBC(tc_fun(_1550619, tc_HOL_Obool), tc_fun(_1550619, tc_fun(_1550621, tc_HOL_Obool)), tc_fun(tc_prod(_1550619, _1550621), tc_HOL_Obool)), c_Product__Type_OSigma(_1550619, _1550621)), _1550625)))], (39720 ^ _782464) ^ [_1550709, _1550711, _1550713, _1550715] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1550709, _1550711)), hAPP(hAPP(c_Product__Type_OSigma(_1550709, _1550711), _1550713), hAPP(c_COMBK(tc_fun(_1550711, tc_HOL_Obool), _1550709), _1550715))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1550709), _1550713)), hAPP(c_Finite__Set_Ocard(_1550711), _1550715)))], (39722 ^ _782464) ^ [_1550780, _1550782, _1550784, _1550786, _1550788, _1550790] : [class_Groups_Ocomm__monoid__add(_1550780), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550782, _1550780), hAPP(hAPP(c_COMBC(_1550782, tc_fun(_1550784, tc_HOL_Obool), _1550780), hAPP(hAPP(c_COMBB(tc_fun(_1550784, _1550780), tc_fun(tc_fun(_1550784, tc_HOL_Obool), _1550780), _1550782), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550784, _1550780)), _1550786)), _1550788)), _1550790) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1550782, _1550784), _1550780), hAPP(c_Product__Type_Oprod_Oprod__case(_1550782, _1550784, _1550780), _1550786)), hAPP(hAPP(c_Product__Type_OSigma(_1550782, _1550784), _1550790), hAPP(c_COMBK(tc_fun(_1550784, tc_HOL_Obool), _1550782), _1550788))))], (39728 ^ _782464) ^ [_1551025, _1551027, _1551029] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551025, _1551027), _1551029), hAPP(c_COMBK(tc_fun(_1551027, tc_HOL_Obool), _1551025), c_Orderings_Obot__class_Obot(tc_fun(_1551027, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551025, _1551027), tc_HOL_Obool)))], (39740 ^ _782464) ^ [_1551266, _1551268, _1551270, _1551272] : [39741 ^ _782464 : [(39742 ^ _782464) ^ [] : [_1551270 = c_Orderings_Obot__class_Obot(tc_fun(_1551266, tc_HOL_Obool))], (39744 ^ _782464) ^ [] : [_1551272 = c_Orderings_Obot__class_Obot(tc_fun(_1551268, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1551266, _1551268), _1551270), hAPP(c_COMBK(tc_fun(_1551268, tc_HOL_Obool), _1551266), _1551272)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551266, _1551268), tc_HOL_Obool)))], (39730 ^ _782464) ^ [_1551104, _1551106, _1551108, _1551110] : [hAPP(hAPP(c_Product__Type_OSigma(_1551104, _1551106), _1551108), hAPP(c_COMBK(tc_fun(_1551106, tc_HOL_Obool), _1551104), _1551110)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551104, _1551106), tc_HOL_Obool)), -(_1551108 = c_Orderings_Obot__class_Obot(tc_fun(_1551104, tc_HOL_Obool))), -(_1551110 = c_Orderings_Obot__class_Obot(tc_fun(_1551106, tc_HOL_Obool)))], (39748 ^ _782464) ^ [_1551459, _1551461, _1551463] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1551459, _1551461), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551459, _1551461), _1551463), hAPP(c_COMBK(tc_fun(_1551461, tc_HOL_Obool), _1551459), c_Orderings_Otop__class_Otop(tc_fun(_1551461, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1551459, _1551461), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1551459, tc_HOL_Obool)), _1551463)), hAPP(c_COMBK(tc_fun(_1551461, tc_HOL_Obool), _1551459), c_Orderings_Otop__class_Otop(tc_fun(_1551461, tc_HOL_Obool)))))], (39750 ^ _782464) ^ [_1551551, _1551553, _1551555] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1551551, _1551553), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551551, _1551553), c_Orderings_Otop__class_Otop(tc_fun(_1551551, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1551553, tc_HOL_Obool), _1551551), _1551555))) = hAPP(hAPP(c_Product__Type_OSigma(_1551551, _1551553), c_Orderings_Otop__class_Otop(tc_fun(_1551551, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1551553, tc_HOL_Obool), _1551551), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1551553, tc_HOL_Obool)), _1551555))))], (39752 ^ _782464) ^ [_1551643, _1551645, _1551647, _1551649, _1551651, _1551653] : [class_Groups_Ocomm__monoid__mult(_1551643), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1551645, _1551643), hAPP(hAPP(c_COMBC(_1551645, tc_fun(_1551647, tc_HOL_Obool), _1551643), hAPP(hAPP(c_COMBB(tc_fun(_1551647, _1551643), tc_fun(tc_fun(_1551647, tc_HOL_Obool), _1551643), _1551645), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1551647, _1551643)), _1551649)), _1551651)), _1551653) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1551645, _1551647), _1551643), hAPP(c_Product__Type_Oprod_Oprod__case(_1551645, _1551647, _1551643), _1551649)), hAPP(hAPP(c_Product__Type_OSigma(_1551645, _1551647), _1551653), hAPP(c_COMBK(tc_fun(_1551647, tc_HOL_Obool), _1551645), _1551651))))], (39758 ^ _782464) ^ [_1551888, _1551890, _1551892, _1551894, _1551896] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551888, _1551890), _1551892), hAPP(hAPP(c_COMBS(_1551888, tc_fun(_1551890, tc_HOL_Obool), tc_fun(_1551890, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551890, tc_HOL_Obool), tc_fun(tc_fun(_1551890, tc_HOL_Obool), tc_fun(_1551890, tc_HOL_Obool)), _1551888), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1551890, tc_HOL_Obool))), _1551894)), _1551896)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551888, _1551890), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551888, _1551890), _1551892), _1551894)), hAPP(hAPP(c_Product__Type_OSigma(_1551888, _1551890), _1551892), _1551896)))], (39760 ^ _782464) ^ [_1552003, _1552005, _1552007, _1552009, _1552011] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1552003, _1552005), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552003, tc_HOL_Obool)), _1552007), _1552009)), hAPP(c_COMBK(tc_fun(_1552005, tc_HOL_Obool), _1552003), _1552011)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552003, _1552005), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552003, _1552005), _1552007), hAPP(c_COMBK(tc_fun(_1552005, tc_HOL_Obool), _1552003), _1552011))), hAPP(hAPP(c_Product__Type_OSigma(_1552003, _1552005), _1552009), hAPP(c_COMBK(tc_fun(_1552005, tc_HOL_Obool), _1552003), _1552011))))], (39762 ^ _782464) ^ [_1552113, _1552115, _1552117, _1552119, _1552121] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1552113, _1552115), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552113, tc_HOL_Obool)), _1552117), _1552119)), _1552121) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552113, _1552115), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552113, _1552115), _1552117), _1552121)), hAPP(hAPP(c_Product__Type_OSigma(_1552113, _1552115), _1552119), _1552121)))], (39764 ^ _782464) ^ [_1552196, _1552198, _1552200, _1552202, _1552204, _1552206, _1552208, _1552210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552196, _1552198), tc_HOL_Obool)), _1552200), hAPP(hAPP(c_Product__Type_OSigma(_1552196, _1552198), _1552202), hAPP(c_COMBK(tc_fun(_1552198, tc_HOL_Obool), _1552196), _1552204)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552198, _1552206), tc_HOL_Obool)), _1552208), hAPP(hAPP(c_Product__Type_OSigma(_1552198, _1552206), _1552204), hAPP(c_COMBK(tc_fun(_1552206, tc_HOL_Obool), _1552198), _1552210)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552196, _1552206), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552196, _1552198, _1552206), _1552200), _1552208)), hAPP(hAPP(c_Product__Type_OSigma(_1552196, _1552206), _1552202), hAPP(c_COMBK(tc_fun(_1552206, tc_HOL_Obool), _1552196), _1552210)))))], (39774 ^ _782464) ^ [_1552555, _1552557, _1552559, _1552561] : [-(hAPP(c_Set_Oimage(tc_prod(_1552555, _1552557), tc_prod(_1552557, _1552555), hAPP(c_Product__Type_Oprod_Oprod__case(_1552555, _1552557, tc_prod(_1552557, _1552555)), hAPP(c_COMBC(_1552557, _1552555, tc_prod(_1552557, _1552555)), c_Product__Type_OPair(_1552557, _1552555)))), hAPP(hAPP(c_Product__Type_OSigma(_1552555, _1552557), _1552559), hAPP(c_COMBK(tc_fun(_1552557, tc_HOL_Obool), _1552555), _1552561))) = hAPP(hAPP(c_Product__Type_OSigma(_1552557, _1552555), _1552561), hAPP(c_COMBK(tc_fun(_1552555, tc_HOL_Obool), _1552557), _1552559)))], (39776 ^ _782464) ^ [_1552656, _1552658, _1552660, _1552662] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552656), _1552658)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552660), _1552662)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1552656, _1552660)), hAPP(hAPP(c_Product__Type_OSigma(_1552656, _1552660), _1552658), hAPP(c_COMBK(tc_fun(_1552660, tc_HOL_Obool), _1552656), _1552662)))))], (39786 ^ _782464) ^ [_1552859, _1552861, _1552863] : [c_Equiv__Relations_Oequiv(_1552859, _1552861, _1552863), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552859, _1552859), tc_HOL_Obool)), _1552863), hAPP(hAPP(c_Product__Type_OSigma(_1552859, _1552859), _1552861), hAPP(c_COMBK(tc_fun(_1552859, tc_HOL_Obool), _1552859), _1552861)))))], (39792 ^ _782464) ^ [_1553002, _1553004, _1553006, _1553008, _1553010] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553002, _1553004), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553002, tc_HOL_Obool)), _1553006), _1553008)), _1553010) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553002, _1553004), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553002, _1553004), _1553006), _1553010)), hAPP(hAPP(c_Product__Type_OSigma(_1553002, _1553004), _1553008), _1553010)))], (39794 ^ _782464) ^ [_1553085, _1553087, _1553089, _1553091, _1553093] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553085, _1553087), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553085, tc_HOL_Obool)), _1553089), _1553091)), hAPP(c_COMBK(tc_fun(_1553087, tc_HOL_Obool), _1553085), _1553093)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553085, _1553087), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553085, _1553087), _1553089), hAPP(c_COMBK(tc_fun(_1553087, tc_HOL_Obool), _1553085), _1553093))), hAPP(hAPP(c_Product__Type_OSigma(_1553085, _1553087), _1553091), hAPP(c_COMBK(tc_fun(_1553087, tc_HOL_Obool), _1553085), _1553093))))], (39796 ^ _782464) ^ [_1553195, _1553197, _1553199, _1553201, _1553203] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553195, _1553197), _1553199), hAPP(hAPP(c_COMBS(_1553195, tc_fun(_1553197, tc_HOL_Obool), tc_fun(_1553197, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553197, tc_HOL_Obool), tc_fun(tc_fun(_1553197, tc_HOL_Obool), tc_fun(_1553197, tc_HOL_Obool)), _1553195), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553197, tc_HOL_Obool))), _1553201)), _1553203)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553195, _1553197), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553195, _1553197), _1553199), _1553201)), hAPP(hAPP(c_Product__Type_OSigma(_1553195, _1553197), _1553199), _1553203)))], (39798 ^ _782464) ^ [_1553310, _1553312] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553310, _1553310), tc_HOL_Obool)), c_Relation_OId__on(_1553310, _1553312)), hAPP(hAPP(c_Product__Type_OSigma(_1553310, _1553310), _1553312), hAPP(c_COMBK(tc_fun(_1553310, tc_HOL_Obool), _1553310), _1553312)))))], (39800 ^ _782464) ^ [_1553369, _1553371, _1553373, _1553375, _1553377] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553369, _1553371), _1553373), hAPP(hAPP(c_COMBS(_1553369, tc_fun(_1553371, tc_HOL_Obool), tc_fun(_1553371, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553371, tc_HOL_Obool), tc_fun(tc_fun(_1553371, tc_HOL_Obool), tc_fun(_1553371, tc_HOL_Obool)), _1553369), c_Groups_Ominus__class_Ominus(tc_fun(_1553371, tc_HOL_Obool))), _1553375)), _1553377)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553369, _1553371), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553369, _1553371), _1553373), _1553375)), hAPP(hAPP(c_Product__Type_OSigma(_1553369, _1553371), _1553373), _1553377)))], (39802 ^ _782464) ^ [_1553484, _1553486, _1553488, _1553490, _1553492] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553484, _1553486), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553484, tc_HOL_Obool)), _1553488), _1553490)), hAPP(c_COMBK(tc_fun(_1553486, tc_HOL_Obool), _1553484), _1553492)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553484, _1553486), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553484, _1553486), _1553488), hAPP(c_COMBK(tc_fun(_1553486, tc_HOL_Obool), _1553484), _1553492))), hAPP(hAPP(c_Product__Type_OSigma(_1553484, _1553486), _1553490), hAPP(c_COMBK(tc_fun(_1553486, tc_HOL_Obool), _1553484), _1553492))))], (39804 ^ _782464) ^ [_1553594, _1553596, _1553598, _1553600, _1553602] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553594, _1553596), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553594, tc_HOL_Obool)), _1553598), _1553600)), _1553602) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553594, _1553596), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553594, _1553596), _1553598), _1553602)), hAPP(hAPP(c_Product__Type_OSigma(_1553594, _1553596), _1553600), _1553602)))], (39806 ^ _782464) ^ [_1553698, _1553700, _1553702, _1553704] : [hBOOL(hAPP(c_Predicate_ODomainP(_1553698, _1553700, _1553702), _1553704)), -(hBOOL(hAPP(hAPP(_1553702, _1553704), 39809 ^ [_1553698, _1553700, _1553702, _1553704])))], (39813 ^ _782464) ^ [_1553813, _1553815, _1553817, _1553819] : [39814 ^ _782464 : [(39815 ^ _782464) ^ [_1553867] : [hBOOL(hAPP(hAPP(_1553817, _1553819), _1553867))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1553813, _1553815, _1553817), _1553819)))], (39819 ^ _782464) ^ [_1553931, _1553933] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553931, _1553933), c_Orderings_Otop__class_Otop(tc_fun(_1553931, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1553933, tc_HOL_Obool), _1553931), c_Orderings_Otop__class_Otop(tc_fun(_1553933, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1553931, _1553933), tc_HOL_Obool)))], (39821 ^ _782464) ^ [_1553992, _1553994, _1553996, _1553998, _1554000, _1554002] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553992, _1553994)), hAPP(hAPP(c_Product__Type_OPair(_1553992, _1553994), _1553996), _1553998)), hAPP(hAPP(c_Product__Type_OSigma(_1553992, _1553994), _1554000), _1554002))), 39824 ^ _782464 : [(39825 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553992), _1553996), _1554000)))], (39827 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553994), _1553998), hAPP(_1554002, _1553996))))]]], (39829 ^ _782464) ^ [_1554197, _1554199, _1554201, _1554203, _1554205, _1554207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554197, _1554199)), hAPP(hAPP(c_Product__Type_OPair(_1554197, _1554199), _1554201), _1554203)), hAPP(hAPP(c_Product__Type_OSigma(_1554197, _1554199), _1554205), _1554207))), -(hBOOL(hAPP(hAPP(c_member(_1554199), _1554203), hAPP(_1554207, _1554201))))], (39835 ^ _782464) ^ [_1554358, _1554360, _1554362, _1554364, _1554366, _1554368] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554358, _1554360)), hAPP(hAPP(c_Product__Type_OPair(_1554358, _1554360), _1554362), _1554364)), hAPP(hAPP(c_Product__Type_OSigma(_1554358, _1554360), _1554366), _1554368))), -(hBOOL(hAPP(hAPP(c_member(_1554358), _1554362), _1554366)))], (39841 ^ _782464) ^ [_1554540, _1554542, _1554544, _1554546, _1554548, _1554550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554540, _1554542)), hAPP(hAPP(c_Product__Type_OPair(_1554540, _1554542), _1554544), _1554546)), hAPP(hAPP(c_Product__Type_OSigma(_1554540, _1554542), _1554548), _1554550))), 39844 ^ _782464 : [(39845 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554540), _1554544), _1554548)))], (39847 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554542), _1554546), hAPP(_1554550, _1554544))))]]], (39849 ^ _782464) ^ [_1554737, _1554739, _1554741, _1554743, _1554745, _1554747] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1554737, _1554739)), hAPP(hAPP(c_Product__Type_OPair(_1554737, _1554739), _1554741), _1554743)), hAPP(hAPP(c_Product__Type_OSigma(_1554737, _1554739), _1554745), _1554747)))), hBOOL(hAPP(hAPP(c_member(_1554737), _1554741), _1554745)), hBOOL(hAPP(hAPP(c_member(_1554739), _1554743), hAPP(_1554747, _1554741)))], (39859 ^ _782464) ^ [_1554974, _1554976, _1554978, _1554980] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1554974, _1554976)), hAPP(hAPP(c_Product__Type_OSigma(_1554974, _1554976), hAPP(hAPP(c_Set_Oinsert(_1554974), _1554978), c_Orderings_Obot__class_Obot(tc_fun(_1554974, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1554976, tc_HOL_Obool), _1554974), _1554980))) = hAPP(c_Finite__Set_Ocard(_1554976), _1554980))], (39861 ^ _782464) ^ [_1555047, _1555049, _1555051, _1555053, _1555055, _1555057] : [hBOOL(hAPP(hAPP(c_member(_1555047), _1555049), _1555051)), 39864 ^ _782464 : [(39865 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555053, _1555047), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555053, _1555047), _1555055), hAPP(c_COMBK(tc_fun(_1555047, tc_HOL_Obool), _1555053), _1555051))), hAPP(hAPP(c_Product__Type_OSigma(_1555053, _1555047), _1555057), hAPP(c_COMBK(tc_fun(_1555047, tc_HOL_Obool), _1555053), _1555051)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555053, tc_HOL_Obool)), _1555055), _1555057)))], (39871 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555053, tc_HOL_Obool)), _1555055), _1555057)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555053, _1555047), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555053, _1555047), _1555055), hAPP(c_COMBK(tc_fun(_1555047, tc_HOL_Obool), _1555053), _1555051))), hAPP(hAPP(c_Product__Type_OSigma(_1555053, _1555047), _1555057), hAPP(c_COMBK(tc_fun(_1555047, tc_HOL_Obool), _1555053), _1555051)))))]]], (39877 ^ _782464) ^ [_1555469, _1555471, _1555473, _1555475, _1555477, _1555479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555469, _1555471), tc_HOL_Obool)), _1555473), hAPP(hAPP(c_Product__Type_OSigma(_1555469, _1555471), _1555475), hAPP(c_COMBK(tc_fun(_1555471, tc_HOL_Obool), _1555469), _1555477)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555471, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1555469, _1555471, _1555473), _1555479)), _1555477)))], (39883 ^ _782464) ^ [_1555650, _1555652, _1555654, _1555656] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555650, _1555652)), hAPP(hAPP(c_Product__Type_OSigma(_1555650, _1555652), _1555654), hAPP(c_COMBK(tc_fun(_1555652, tc_HOL_Obool), _1555650), _1555656)))), -(_1555654 = c_Orderings_Obot__class_Obot(tc_fun(_1555650, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555652), _1555656)))], (39893 ^ _782464) ^ [_1555814, _1555816, _1555818, _1555820] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555814, _1555816)), hAPP(hAPP(c_Product__Type_OSigma(_1555814, _1555816), _1555818), hAPP(c_COMBK(tc_fun(_1555816, tc_HOL_Obool), _1555814), _1555820)))), -(_1555820 = c_Orderings_Obot__class_Obot(tc_fun(_1555816, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555814), _1555818)))], (39903 ^ _782464) ^ [_1555978, _1555980, _1555982, _1555984] : [-(hAPP(c_Set_OCollect(tc_prod(_1555978, _1555980)), hAPP(c_Product__Type_Oprod_Oprod__case(_1555978, _1555980, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1555978, tc_fun(_1555980, tc_HOL_Obool), tc_fun(_1555980, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555980, tc_HOL_Obool), tc_fun(_1555980, tc_HOL_Obool)), _1555978), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555980)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555978), c_fconj), _1555982))), _1555984))) = hAPP(hAPP(c_Product__Type_OSigma(_1555978, _1555980), hAPP(c_Set_OCollect(_1555978), _1555982)), hAPP(hAPP(c_COMBB(tc_fun(_1555980, tc_HOL_Obool), tc_fun(_1555980, tc_HOL_Obool), _1555978), c_Set_OCollect(_1555980)), _1555984)))], (39905 ^ _782464) ^ [_1556103, _1556105, _1556107, _1556109] : [-(hAPP(c_Set_OCollect(tc_prod(_1556103, _1556105)), hAPP(c_Product__Type_Oprod_Oprod__case(_1556103, _1556105, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1556103, tc_fun(_1556105, tc_HOL_Obool), tc_fun(_1556105, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1556105, tc_HOL_Obool), tc_fun(_1556105, tc_HOL_Obool)), _1556103), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1556105)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556103), c_fconj), _1556107))), _1556109))) = hAPP(hAPP(c_Product__Type_OSigma(_1556103, _1556105), hAPP(c_Set_OCollect(_1556103), _1556107)), hAPP(c_COMBK(tc_fun(_1556105, tc_HOL_Obool), _1556103), hAPP(c_Set_OCollect(_1556105), _1556109))))], (39907 ^ _782464) ^ [_1556239, _1556241, _1556243, _1556245] : [_1556239 = c_Orderings_Obot__class_Obot(tc_fun(_1556241, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1556243, _1556241), _1556243, c_Product__Type_Ofst(_1556243, _1556241)), hAPP(hAPP(c_Product__Type_OSigma(_1556243, _1556241), _1556245), hAPP(c_COMBK(tc_fun(_1556241, tc_HOL_Obool), _1556243), _1556239))) = c_Orderings_Obot__class_Obot(tc_fun(_1556243, tc_HOL_Obool)))], (39913 ^ _782464) ^ [_1556396, _1556398, _1556400, _1556402] : [-(_1556396 = c_Orderings_Obot__class_Obot(tc_fun(_1556398, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1556400, _1556398), _1556400, c_Product__Type_Ofst(_1556400, _1556398)), hAPP(hAPP(c_Product__Type_OSigma(_1556400, _1556398), _1556402), hAPP(c_COMBK(tc_fun(_1556398, tc_HOL_Obool), _1556400), _1556396))) = _1556402)], (39919 ^ _782464) ^ [_1556489, _1556491, _1556493, _1556495] : [_1556489 = c_Orderings_Obot__class_Obot(tc_fun(_1556491, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1556491, _1556493), _1556493, c_Product__Type_Osnd(_1556491, _1556493)), hAPP(hAPP(c_Product__Type_OSigma(_1556491, _1556493), _1556489), hAPP(c_COMBK(tc_fun(_1556493, tc_HOL_Obool), _1556491), _1556495))) = c_Orderings_Obot__class_Obot(tc_fun(_1556493, tc_HOL_Obool)))], (39925 ^ _782464) ^ [_1556646, _1556648, _1556650, _1556652] : [-(_1556646 = c_Orderings_Obot__class_Obot(tc_fun(_1556648, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1556648, _1556650), _1556650, c_Product__Type_Osnd(_1556648, _1556650)), hAPP(hAPP(c_Product__Type_OSigma(_1556648, _1556650), _1556646), hAPP(c_COMBK(tc_fun(_1556650, tc_HOL_Obool), _1556648), _1556652))) = _1556652)], (39931 ^ _782464) ^ [_1556724, _1556726, _1556728, _1556730, _1556732, _1556734] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1556724, _1556726), hAPP(hAPP(c_Set_Oinsert(_1556724), _1556728), _1556730)), hAPP(c_COMBK(tc_fun(_1556726, tc_HOL_Obool), _1556724), hAPP(hAPP(c_Set_Oinsert(_1556726), _1556732), _1556734))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1556724, _1556726)), hAPP(hAPP(c_Product__Type_OPair(_1556724, _1556726), _1556728), _1556732)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556724, _1556726), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1556724, _1556726), _1556730), hAPP(c_COMBK(tc_fun(_1556726, tc_HOL_Obool), _1556724), hAPP(hAPP(c_Set_Oinsert(_1556726), _1556732), _1556734)))), hAPP(hAPP(c_Product__Type_OSigma(_1556724, _1556726), hAPP(hAPP(c_Set_Oinsert(_1556724), _1556728), _1556730)), hAPP(c_COMBK(tc_fun(_1556726, tc_HOL_Obool), _1556724), _1556734)))))], (39933 ^ _782464) ^ [_1556877, _1556879, _1556881, _1556883] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1556877), _1556879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556877, _1556877), tc_HOL_Obool)), _1556881), hAPP(hAPP(c_Product__Type_OSigma(_1556877, _1556877), _1556879), hAPP(c_COMBK(tc_fun(_1556877, tc_HOL_Obool), _1556877), _1556879)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1556877, tc_HOL_Obool)), _1556883), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1556877), _1556879), _1556881))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1556877), _1556883)))], (39947 ^ _782464) ^ [_1557184, _1557186, _1557188, _1557190, _1557192, _1557194] : [-(hAPP(c_Set_Ovimage(_1557184, tc_prod(_1557186, _1557188), _1557190), hAPP(hAPP(c_Product__Type_OSigma(_1557186, _1557188), _1557192), hAPP(c_COMBK(tc_fun(_1557188, tc_HOL_Obool), _1557186), _1557194))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1557184, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1557184, _1557186, hAPP(c_Fun_Ocomp(tc_prod(_1557186, _1557188), _1557186, _1557184, c_Product__Type_Ofst(_1557186, _1557188)), _1557190)), _1557192)), hAPP(c_Set_Ovimage(_1557184, _1557188, hAPP(c_Fun_Ocomp(tc_prod(_1557186, _1557188), _1557188, _1557184, c_Product__Type_Osnd(_1557186, _1557188)), _1557190)), _1557194)))], (39949 ^ _782464) ^ [_1557298, _1557300, _1557302, _1557304, _1557306, _1557308, _1557310, _1557312] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1557298, _1557300), tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1557298, _1557300), _1557306), hAPP(c_COMBK(tc_fun(_1557300, tc_HOL_Obool), _1557298), _1557308))), hAPP(c_Product__Type_Oprod_Oprod__case(_1557298, _1557300, tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1557298, tc_fun(_1557300, tc_fun(_1557302, tc_fun(_1557304, tc_HOL_Obool))), tc_fun(_1557300, tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1557302, tc_fun(_1557304, tc_HOL_Obool)), tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool)), tc_fun(tc_fun(_1557300, tc_fun(_1557302, tc_fun(_1557304, tc_HOL_Obool))), tc_fun(_1557300, tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool))), _1557298), c_COMBB(tc_fun(_1557302, tc_fun(_1557304, tc_HOL_Obool)), tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool), _1557300)), hAPP(hAPP(c_COMBB(tc_fun(_1557302, tc_HOL_Obool), tc_fun(tc_fun(_1557302, tc_fun(_1557304, tc_HOL_Obool)), tc_fun(tc_prod(_1557302, _1557304), tc_HOL_Obool)), _1557298), c_Product__Type_OSigma(_1557302, _1557304)), _1557310))), hAPP(hAPP(c_COMBB(tc_fun(_1557304, tc_HOL_Obool), tc_fun(_1557302, tc_fun(_1557304, tc_HOL_Obool)), _1557300), c_COMBK(tc_fun(_1557304, tc_HOL_Obool), _1557302)), _1557312)))) = hAPP(hAPP(c_Product__Type_OSigma(_1557302, _1557304), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557298, tc_fun(_1557302, tc_HOL_Obool)), _1557306), _1557310)), hAPP(c_COMBK(tc_fun(_1557304, tc_HOL_Obool), _1557302), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557300, tc_fun(_1557304, tc_HOL_Obool)), _1557308), _1557312))))], (39951 ^ _782464) ^ [_1557572, _1557574, _1557576, _1557578] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1557572, _1557574), _1557576), _1557578) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557572, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool)), _1557576), hAPP(hAPP(c_COMBS(_1557572, tc_fun(_1557574, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool)), tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1557574, tc_HOL_Obool), tc_fun(tc_fun(_1557574, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool)), tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool)), _1557572), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557574, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))), _1557578)), hAPP(hAPP(c_COMBC(_1557572, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool), tc_fun(_1557574, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557574, tc_fun(tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool), tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool), tc_fun(_1557574, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))), _1557572), c_COMBC(_1557574, tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool), tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557574, tc_prod(_1557572, _1557574)), tc_fun(_1557574, tc_fun(tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool), tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))), _1557572), hAPP(c_COMBB(tc_prod(_1557572, _1557574), tc_fun(tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool), tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool)), _1557574), c_Set_Oinsert(tc_prod(_1557572, _1557574)))), c_Product__Type_OPair(_1557572, _1557574)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557572, _1557574), tc_HOL_Obool))))))], (39953 ^ _782464) ^ [_1557852, _1557854, _1557856] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1557852), _1557854)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557852, _1557852), tc_HOL_Obool)), _1557856), hAPP(hAPP(c_Product__Type_OSigma(_1557852, _1557852), _1557854), hAPP(c_COMBK(tc_fun(_1557852, tc_HOL_Obool), _1557852), _1557854)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1557852, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1557852), _1557854), _1557856))))], (39963 ^ _782464) ^ [_1558085, _1558087, _1558089, _1558091, _1558093, _1558095, _1558097] : [class_Rings_Osemiring__0(_1558085), c_Fun_Oinj__on(tc_prod(_1558087, _1558089), _1558085, hAPP(c_Product__Type_Oprod_Oprod__case(_1558087, _1558089, _1558085), hAPP(hAPP(c_COMBC(_1558087, tc_fun(_1558089, _1558085), tc_fun(_1558089, _1558085)), hAPP(hAPP(c_COMBB(tc_fun(_1558085, _1558085), tc_fun(tc_fun(_1558089, _1558085), tc_fun(_1558089, _1558085)), _1558087), c_COMBB(_1558085, _1558085, _1558089)), hAPP(hAPP(c_COMBB(_1558085, tc_fun(_1558085, _1558085), _1558087), c_Groups_Otimes__class_Otimes(_1558085)), _1558091))), _1558093)), hAPP(hAPP(c_Product__Type_OSigma(_1558087, _1558089), _1558095), hAPP(c_COMBK(tc_fun(_1558089, tc_HOL_Obool), _1558087), _1558097))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1558085), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558087, _1558085), _1558091), _1558095)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558089, _1558085), _1558093), _1558097)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558085, _1558085), c_Fun_Oid(_1558085)), hAPP(c_Set_OCollect(_1558085), hAPP(hAPP(c_COMBB(tc_fun(_1558087, tc_HOL_Obool), tc_HOL_Obool, _1558085), c_HOL_OEx(_1558087)), hAPP(hAPP(c_COMBB(tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool)), tc_fun(_1558087, tc_HOL_Obool), _1558085), hAPP(c_COMBB(tc_fun(_1558089, tc_HOL_Obool), tc_HOL_Obool, _1558087), c_HOL_OEx(_1558089))), hAPP(hAPP(c_COMBC(_1558085, tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool)), tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558087, tc_fun(tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_HOL_Obool))), tc_fun(tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool)), tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool))), _1558085), c_COMBS(_1558087, tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558087, tc_fun(_1558089, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1558087, tc_fun(tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_HOL_Obool))), _1558085), hAPP(c_COMBB(tc_fun(_1558089, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_HOL_Obool)), _1558087), c_COMBS(_1558089, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool)), tc_fun(_1558087, tc_fun(_1558089, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1558085), hAPP(c_COMBB(tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1558087), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558089), c_fconj))), hAPP(hAPP(c_COMBC(_1558085, tc_fun(_1558087, tc_fun(_1558089, _1558085)), tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1558089, _1558085), tc_fun(_1558089, tc_HOL_Obool)), tc_fun(tc_fun(_1558087, tc_fun(_1558089, _1558085)), tc_fun(_1558087, tc_fun(_1558089, tc_HOL_Obool))), _1558085), c_COMBB(tc_fun(_1558089, _1558085), tc_fun(_1558089, tc_HOL_Obool), _1558087)), hAPP(hAPP(c_COMBB(tc_fun(_1558085, tc_HOL_Obool), tc_fun(tc_fun(_1558089, _1558085), tc_fun(_1558089, tc_HOL_Obool)), _1558085), c_COMBB(_1558085, tc_HOL_Obool, _1558089)), c_fequal))), hAPP(hAPP(c_COMBC(_1558087, tc_fun(_1558089, _1558085), tc_fun(_1558089, _1558085)), hAPP(hAPP(c_COMBB(tc_fun(_1558085, _1558085), tc_fun(tc_fun(_1558089, _1558085), tc_fun(_1558089, _1558085)), _1558087), c_COMBB(_1558085, _1558085, _1558089)), hAPP(hAPP(c_COMBB(_1558085, tc_fun(_1558085, _1558085), _1558087), c_Groups_Otimes__class_Otimes(_1558085)), _1558091))), _1558093)))))), hAPP(hAPP(c_COMBC(_1558087, tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1558089, tc_HOL_Obool), tc_fun(_1558089, tc_HOL_Obool)), _1558087), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1558089)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558087), c_fconj), hAPP(hAPP(c_COMBC(_1558087, tc_fun(_1558087, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558087)), _1558095)))), hAPP(hAPP(c_COMBC(_1558089, tc_fun(_1558089, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558089)), _1558097))))))))], (39974 ^ _782464) ^ [_1559360, _1559362, _1559364, _1559366] : [-(c_Fun_Oinj__on(_1559360, tc_prod(_1559362, _1559360), 39972 ^ [_1559360, _1559362, _1559364, _1559366], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559362, tc_fun(_1559360, tc_HOL_Obool)), _1559364), _1559366)))], (39976 ^ _782464) ^ [_1559414, _1559416, _1559418, _1559420] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559416, _1559414), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1559414, tc_prod(_1559416, _1559414), 39972 ^ [_1559414, _1559416, _1559418, _1559420]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559416, tc_fun(_1559414, tc_HOL_Obool)), _1559418), _1559420))), hAPP(hAPP(c_Product__Type_OSigma(_1559416, _1559414), _1559418), _1559420))))], (39978 ^ _782464) ^ [_1559500, _1559502, _1559504, _1559506, _1559508, _1559510] : [class_Groups_Ocomm__monoid__mult(_1559500), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559502), _1559504)), 39988 ^ _782464 : [(39989 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559502), 39987 ^ [_1559500, _1559502, _1559504, _1559506, _1559508, _1559510]), _1559504)))], (39991 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559506), hAPP(_1559508, 39987 ^ [_1559500, _1559502, _1559504, _1559506, _1559508, _1559510])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559500, _1559502, c_Groups_Otimes__class_Otimes(_1559500)), hAPP(hAPP(c_COMBS(_1559502, tc_fun(_1559506, tc_HOL_Obool), _1559500), hAPP(hAPP(c_COMBC(_1559502, _1559500, tc_fun(tc_fun(_1559506, tc_HOL_Obool), _1559500)), hAPP(hAPP(c_COMBB(tc_fun(_1559506, _1559500), tc_fun(_1559500, tc_fun(tc_fun(_1559506, tc_HOL_Obool), _1559500)), _1559502), c_Finite__Set_Ofold__image(_1559500, _1559506, c_Groups_Otimes__class_Otimes(_1559500))), _1559510)), c_Groups_Oone__class_Oone(_1559500))), _1559508)), c_Groups_Oone__class_Oone(_1559500)), _1559504) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559500, tc_prod(_1559502, _1559506), c_Groups_Otimes__class_Otimes(_1559500)), hAPP(c_Product__Type_Oprod_Oprod__case(_1559502, _1559506, _1559500), _1559510)), c_Groups_Oone__class_Oone(_1559500)), hAPP(hAPP(c_Product__Type_OSigma(_1559502, _1559506), _1559504), _1559508)))], (39995 ^ _782464) ^ [_1560057, _1560059] : [-(c_Fun_Obij__betw(_1560057, _1560057, c_Fun_Oid(_1560057), _1560059, _1560059))], (39997 ^ _782464) ^ [_1560087, _1560089] : [-(hAPP(c_Set_Oimage(_1560087, _1560087, c_Fun_Oid(_1560087)), _1560089) = _1560089)], (39999 ^ _782464) ^ [_1560121, _1560123] : [-(c_Product__Type_Oapsnd(_1560121, _1560121, _1560123, c_Fun_Oid(_1560121)) = c_Fun_Oid(tc_prod(_1560123, _1560121)))], (40001 ^ _782464) ^ [_1560158, _1560160] : [-(hAPP(c_Fun_Oid(_1560158), _1560160) = _1560160)], (40003 ^ _782464) ^ [_1560188, _1560190] : [-(hAPP(c_Fun_Oid(_1560188), _1560190) = _1560190)], (40005 ^ _782464) ^ [_1560218, _1560220] : [-(hAPP(c_Set_Ovimage(_1560218, _1560218, c_Fun_Oid(_1560218)), _1560220) = _1560220)], (40007 ^ _782464) ^ [_1560270, _1560272, _1560274] : [c_Fun_Obij__betw(_1560270, _1560270, c_Fun_Oid(_1560270), _1560272, _1560274), -(_1560272 = _1560274)], (40013 ^ _782464) ^ [_1560355, _1560357, _1560359] : [_1560357 = _1560359, -(c_Fun_Obij__betw(_1560355, _1560355, c_Fun_Oid(_1560355), _1560357, _1560359))], (40019 ^ _782464) ^ [_1560446, _1560448] : [-(c_Fun_Oinj__on(_1560446, _1560446, c_Fun_Oid(_1560446), _1560448))], (40021 ^ _782464) ^ [_1560475, _1560477, _1560479] : [-(hAPP(c_Fun_Ocomp(_1560475, _1560477, _1560475, _1560479), c_Fun_Oid(_1560475)) = _1560479)], (40023 ^ _782464) ^ [_1560512, _1560514, _1560516] : [-(hAPP(c_Fun_Ocomp(_1560512, _1560512, _1560514, c_Fun_Oid(_1560512)), _1560516) = _1560516)], (40025 ^ _782464) ^ [_1560549, _1560551, _1560553, _1560555, _1560557, _1560559, _1560561] : [hAPP(c_Fun_Ocomp(_1560549, _1560551, _1560553, _1560555), _1560557) = hAPP(c_Fun_Ocomp(_1560551, _1560551, _1560553, c_Fun_Oid(_1560551)), _1560559), -(hAPP(_1560555, hAPP(_1560557, _1560561)) = hAPP(_1560559, _1560561))], (40031 ^ _782464) ^ [_1560690, _1560692] : [-(c_Product__Type_Oapfst(_1560690, _1560690, _1560692, c_Fun_Oid(_1560690)) = c_Fun_Oid(tc_prod(_1560690, _1560692)))], (40033 ^ _782464) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (40035 ^ _782464) ^ [_1560745] : [-(hAPP(c_Set_Oimage(_1560745, _1560745, c_Fun_Oid(_1560745)), c_Orderings_Otop__class_Otop(tc_fun(_1560745, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560745, tc_HOL_Obool)))], (40037 ^ _782464) ^ [_1560787] : [-(c_Fun_Obij__betw(_1560787, _1560787, c_Fun_Oid(_1560787), c_Orderings_Otop__class_Otop(tc_fun(_1560787, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1560787, tc_HOL_Obool))))], (40039 ^ _782464) ^ [_1560825, _1560827, _1560829, _1560831] : [c_Finite__Set_Ofolding(_1560825, _1560827, _1560829, _1560831), -(hAPP(_1560831, c_Orderings_Obot__class_Obot(tc_fun(_1560825, tc_HOL_Obool))) = c_Fun_Oid(_1560827))], (40045 ^ _782464) ^ [_1560930, _1560932] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1560930, _1560932, tc_prod(_1560930, _1560932)), c_Product__Type_OPair(_1560930, _1560932)) = c_Fun_Oid(tc_prod(_1560930, _1560932)))], (40047 ^ _782464) ^ [_1560973, _1560975, _1560977, _1560979] : [class_Groups_Ocomm__monoid__add(_1560973), c_Fun_Oinj__on(_1560975, _1560973, _1560977, _1560979), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560975, _1560973), _1560977), _1560979) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560973, _1560973), c_Fun_Oid(_1560973)), hAPP(c_Set_Oimage(_1560975, _1560973, _1560977), _1560979)))], (40057 ^ _782464) ^ [_1561166, _1561168, _1561170, _1561172] : [class_Groups_Ocomm__monoid__mult(_1561166), c_Fun_Oinj__on(_1561168, _1561166, _1561170, _1561172), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561168, _1561166), _1561170), _1561172) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561166, _1561166), c_Fun_Oid(_1561166)), hAPP(c_Set_Oimage(_1561168, _1561166, _1561170), _1561172)))], (40067 ^ _782464) ^ [_1561359, _1561361, _1561363, _1561365, _1561367, _1561369] : [class_Groups_Ocomm__monoid__mult(_1561359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561361), _1561363)), 40077 ^ _782464 : [(40078 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561361), 40076 ^ [_1561359, _1561361, _1561363, _1561365, _1561367, _1561369]), _1561363)))], (40080 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1561365), hAPP(_1561367, 40076 ^ [_1561359, _1561361, _1561363, _1561365, _1561367, _1561369])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561361, _1561359), hAPP(hAPP(c_COMBS(_1561361, tc_fun(_1561365, tc_HOL_Obool), _1561359), hAPP(hAPP(c_COMBB(tc_fun(_1561365, _1561359), tc_fun(tc_fun(_1561365, tc_HOL_Obool), _1561359), _1561361), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561365, _1561359)), _1561369)), _1561367)), _1561363) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1561361, _1561365), _1561359), hAPP(c_Product__Type_Oprod_Oprod__case(_1561361, _1561365, _1561359), _1561369)), hAPP(hAPP(c_Product__Type_OSigma(_1561361, _1561365), _1561363), _1561367)))], (40084 ^ _782464) ^ [_1561836, _1561838, _1561840, _1561842, _1561844, _1561846] : [class_Groups_Ocomm__monoid__add(_1561836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561838), _1561840)), 40094 ^ _782464 : [(40095 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561838), 40093 ^ [_1561836, _1561838, _1561840, _1561842, _1561844, _1561846]), _1561840)))], (40097 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1561842), hAPP(_1561844, 40093 ^ [_1561836, _1561838, _1561840, _1561842, _1561844, _1561846])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561838, _1561836), hAPP(hAPP(c_COMBS(_1561838, tc_fun(_1561842, tc_HOL_Obool), _1561836), hAPP(hAPP(c_COMBB(tc_fun(_1561842, _1561836), tc_fun(tc_fun(_1561842, tc_HOL_Obool), _1561836), _1561838), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561842, _1561836)), _1561846)), _1561844)), _1561840) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1561838, _1561842), _1561836), hAPP(c_Product__Type_Oprod_Oprod__case(_1561838, _1561842, _1561836), _1561846)), hAPP(hAPP(c_Product__Type_OSigma(_1561838, _1561842), _1561840), _1561844)))], (40101 ^ _782464) ^ [_1562313, _1562315, _1562317, _1562319] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562313), _1562315)), 40107 ^ _782464 : [(40108 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562313), 40106 ^ [_1562313, _1562315, _1562317, _1562319]), _1562315)))], (40110 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562317), hAPP(_1562319, 40106 ^ [_1562313, _1562315, _1562317, _1562319])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1562313, _1562317)), hAPP(hAPP(c_Product__Type_OSigma(_1562313, _1562317), _1562315), _1562319)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562313, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1562317, tc_HOL_Obool), tc_Nat_Onat, _1562313), c_Finite__Set_Ocard(_1562317)), _1562319)), _1562315))], (40114 ^ _782464) ^ [_1562650, _1562652, _1562654, _1562656] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562650), _1562652)), 40120 ^ _782464 : [(40121 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562650), 40119 ^ [_1562650, _1562652, _1562654, _1562656]), _1562652)))], (40123 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562654), hAPP(_1562656, 40119 ^ [_1562650, _1562652, _1562654, _1562656])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562650, _1562654)), hAPP(hAPP(c_Product__Type_OSigma(_1562650, _1562654), _1562652), _1562656))))], (40127 ^ _782464) ^ [_1562937, _1562939, _1562941, _1562943, _1562945] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562937, _1562939)), _1562941), hAPP(hAPP(c_Product__Type_OSigma(_1562937, _1562939), _1562943), _1562945))), 40131 ^ _782464 : [(40132 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562937), 40130 ^ [_1562937, _1562939, _1562941, _1562943, _1562945]), _1562943)))], (40135 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562939), 40133 ^ [_1562937, _1562939, _1562941, _1562943, _1562945]), hAPP(_1562945, 40130 ^ [_1562937, _1562939, _1562941, _1562943, _1562945]))))], (40137 ^ _782464) ^ [] : [-(_1562941 = hAPP(hAPP(c_Product__Type_OPair(_1562937, _1562939), 40130 ^ [_1562937, _1562939, _1562941, _1562943, _1562945]), 40133 ^ [_1562937, _1562939, _1562941, _1562943, _1562945]))]]], (40139 ^ _782464) ^ [_1563239, _1563241, _1563243, _1563245, _1563247, _1563249] : [hAPP(c_Set_Oimage(_1563239, _1563241, _1563243), c_Orderings_Otop__class_Otop(tc_fun(_1563239, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1563241, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563245, _1563247, _1563249), c_Orderings_Otop__class_Otop(tc_fun(_1563245, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1563247, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1563239, _1563245), tc_prod(_1563241, _1563247), c_Product__Type_Omap__pair(_1563239, _1563241, _1563245, _1563247, _1563243, _1563249)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1563239, _1563245), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1563241, _1563247), tc_HOL_Obool)))], (40149 ^ _782464) ^ [_1563524, _1563526, _1563528, _1563530, _1563532, _1563534, _1563536, _1563538, _1563540] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563524, _1563526)), hAPP(hAPP(c_Product__Type_OPair(_1563524, _1563526), _1563528), _1563530)), _1563532)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563534, _1563536)), hAPP(hAPP(c_Product__Type_OPair(_1563534, _1563536), hAPP(_1563538, _1563528)), hAPP(_1563540, _1563530))), hAPP(c_Set_Oimage(tc_prod(_1563524, _1563526), tc_prod(_1563534, _1563536), c_Product__Type_Omap__pair(_1563524, _1563534, _1563526, _1563536, _1563538, _1563540)), _1563532))))], (40155 ^ _782464) ^ [_1563743, _1563745, _1563747, _1563749, _1563751, _1563753, _1563755, _1563757] : [-(hAPP(c_Product__Type_Omap__pair(_1563743, _1563745, _1563747, _1563749, _1563751, _1563753), hAPP(hAPP(c_Product__Type_OPair(_1563743, _1563747), _1563755), _1563757)) = hAPP(hAPP(c_Product__Type_OPair(_1563745, _1563749), hAPP(_1563751, _1563755)), hAPP(_1563753, _1563757)))], (40157 ^ _782464) ^ [_1563814, _1563816, _1563818] : [-(hAPP(c_Product__Type_Omap__pair(_1563814, _1563814, _1563816, _1563816, c_COMBI(_1563814), c_COMBI(_1563816)), _1563818) = _1563818)], (40159 ^ _782464) ^ [_1563855, _1563857, _1563859, _1563861, _1563863, _1563865, _1563867] : [-(hAPP(c_Product__Type_Osnd(_1563855, _1563857), hAPP(c_Product__Type_Omap__pair(_1563859, _1563855, _1563861, _1563857, _1563863, _1563865), _1563867)) = hAPP(_1563865, hAPP(c_Product__Type_Osnd(_1563859, _1563861), _1563867)))], (40161 ^ _782464) ^ [_1563915, _1563917, _1563919, _1563921, _1563923, _1563925, _1563927] : [-(hAPP(c_Product__Type_Ofst(_1563915, _1563917), hAPP(c_Product__Type_Omap__pair(_1563919, _1563915, _1563921, _1563917, _1563923, _1563925), _1563927)) = hAPP(_1563923, hAPP(c_Product__Type_Ofst(_1563919, _1563921), _1563927)))], (40163 ^ _782464) ^ [_1563975, _1563977, _1563979, _1563981, _1563983, _1563985] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1563975, _1563977), _1563975, tc_prod(_1563979, _1563981), c_Product__Type_Ofst(_1563975, _1563977)), c_Product__Type_Omap__pair(_1563979, _1563975, _1563981, _1563977, _1563983, _1563985)) = hAPP(c_Fun_Ocomp(_1563979, _1563975, tc_prod(_1563979, _1563981), _1563983), c_Product__Type_Ofst(_1563979, _1563981)))], (40165 ^ _782464) ^ [_1564046, _1564048, _1564050, _1564052, _1564054, _1564056] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1564046, _1564048), _1564048, tc_prod(_1564050, _1564052), c_Product__Type_Osnd(_1564046, _1564048)), c_Product__Type_Omap__pair(_1564050, _1564046, _1564052, _1564048, _1564054, _1564056)) = hAPP(c_Fun_Ocomp(_1564052, _1564048, tc_prod(_1564050, _1564052), _1564056), c_Product__Type_Osnd(_1564050, _1564052)))], (40167 ^ _782464) ^ [_1564117, _1564119, _1564121, _1564123, _1564125, _1564127, _1564129, _1564131, _1564133, _1564135] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1564117, _1564119), tc_prod(_1564121, _1564123), tc_prod(_1564125, _1564127), c_Product__Type_Omap__pair(_1564117, _1564121, _1564119, _1564123, _1564129, _1564131)), c_Product__Type_Omap__pair(_1564125, _1564117, _1564127, _1564119, _1564133, _1564135)) = c_Product__Type_Omap__pair(_1564125, _1564121, _1564127, _1564123, hAPP(c_Fun_Ocomp(_1564117, _1564121, _1564125, _1564129), _1564133), hAPP(c_Fun_Ocomp(_1564119, _1564123, _1564127, _1564131), _1564135)))], (40169 ^ _782464) ^ [_1564212, _1564214, _1564216, _1564218, _1564220, _1564222, _1564224, _1564226, _1564228, _1564230] : [-(c_Product__Type_Omap__pair(_1564212, _1564214, _1564216, _1564218, hAPP(c_Fun_Ocomp(_1564220, _1564214, _1564212, _1564222), _1564224), hAPP(c_Fun_Ocomp(_1564226, _1564218, _1564216, _1564228), _1564230)) = hAPP(c_Fun_Ocomp(tc_prod(_1564220, _1564226), tc_prod(_1564214, _1564218), tc_prod(_1564212, _1564216), c_Product__Type_Omap__pair(_1564220, _1564214, _1564226, _1564218, _1564222, _1564228)), c_Product__Type_Omap__pair(_1564212, _1564220, _1564216, _1564226, _1564224, _1564230)))], (40171 ^ _782464) ^ [_1564307, _1564309, _1564311, _1564313, _1564315, _1564317, _1564319, _1564321, _1564323, _1564325, _1564327] : [-(hAPP(c_Product__Type_Omap__pair(_1564307, _1564309, _1564311, _1564313, _1564315, _1564317), hAPP(c_Product__Type_Omap__pair(_1564319, _1564307, _1564321, _1564311, _1564323, _1564325), _1564327)) = hAPP(c_Product__Type_Omap__pair(_1564319, _1564309, _1564321, _1564313, hAPP(c_Fun_Ocomp(_1564307, _1564309, _1564319, _1564315), _1564323), hAPP(c_Fun_Ocomp(_1564311, _1564313, _1564321, _1564317), _1564325)), _1564327))], (40173 ^ _782464) ^ [_1564396, _1564398] : [-(c_Product__Type_Omap__pair(_1564396, _1564396, _1564398, _1564398, c_COMBI(_1564396), c_COMBI(_1564398)) = c_Fun_Oid(tc_prod(_1564396, _1564398)))], (40175 ^ _782464) ^ [_1564437, _1564439, _1564441, _1564443] : [-(c_Product__Type_Oapsnd(_1564437, _1564439, _1564441, _1564443) = c_Product__Type_Omap__pair(_1564441, _1564441, _1564437, _1564439, c_Fun_Oid(_1564441), _1564443))], (40177 ^ _782464) ^ [_1564480, _1564482, _1564484, _1564486] : [-(c_Product__Type_Oapfst(_1564480, _1564482, _1564484, _1564486) = c_Product__Type_Omap__pair(_1564480, _1564482, _1564484, _1564484, _1564486, c_Fun_Oid(_1564484)))], (40179 ^ _782464) ^ [_1564523, _1564525] : [-(c_Product__Type_Omap__pair(_1564523, _1564523, _1564525, _1564525, c_Fun_Oid(_1564523), c_Fun_Oid(_1564525)) = c_Fun_Oid(tc_prod(_1564523, _1564525)))], (40181 ^ _782464) ^ [_1564564, _1564566, _1564568, _1564570, _1564572, _1564574] : [-(c_Product__Type_Omap__pair(_1564564, _1564566, _1564568, _1564570, _1564572, _1564574) = hAPP(c_Product__Type_Oprod_Oprod__case(_1564564, _1564568, tc_prod(_1564566, _1564570)), hAPP(hAPP(c_COMBC(_1564564, tc_fun(_1564568, _1564570), tc_fun(_1564568, tc_prod(_1564566, _1564570))), hAPP(hAPP(c_COMBB(tc_fun(_1564570, tc_prod(_1564566, _1564570)), tc_fun(tc_fun(_1564568, _1564570), tc_fun(_1564568, tc_prod(_1564566, _1564570))), _1564564), c_COMBB(_1564570, tc_prod(_1564566, _1564570), _1564568)), hAPP(hAPP(c_COMBB(_1564566, tc_fun(_1564570, tc_prod(_1564566, _1564570)), _1564564), c_Product__Type_OPair(_1564566, _1564570)), _1564572))), _1564574)))], (40183 ^ _782464) ^ [_1564687, _1564689, _1564691, _1564693, _1564695, _1564697, _1564699, _1564701, _1564703, _1564705] : [hAPP(c_Set_Oimage(_1564687, _1564689, _1564691), _1564693) = _1564695, hAPP(c_Set_Oimage(_1564697, _1564699, _1564701), _1564703) = _1564705, -(hAPP(c_Set_Oimage(tc_prod(_1564687, _1564697), tc_prod(_1564689, _1564699), c_Product__Type_Omap__pair(_1564687, _1564689, _1564697, _1564699, _1564691, _1564701)), hAPP(hAPP(c_Product__Type_OSigma(_1564687, _1564697), _1564693), hAPP(c_COMBK(tc_fun(_1564697, tc_HOL_Obool), _1564687), _1564703))) = hAPP(hAPP(c_Product__Type_OSigma(_1564689, _1564699), _1564695), hAPP(c_COMBK(tc_fun(_1564699, tc_HOL_Obool), _1564689), _1564705)))], (40193 ^ _782464) ^ [_1564988, _1564990, _1564992, _1564994] : [c_Wellfounded_Owf(_1564988, _1564990), c_Fun_Oinj__on(_1564988, _1564992, _1564994, c_Orderings_Otop__class_Otop(tc_fun(_1564988, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1564992, hAPP(c_Set_Oimage(tc_prod(_1564988, _1564988), tc_prod(_1564992, _1564992), c_Product__Type_Omap__pair(_1564988, _1564992, _1564988, _1564992, _1564994, _1564994)), _1564990)))], (40203 ^ _782464) ^ [_1565179, _1565181, _1565183, _1565185, _1565187, _1565189, _1565191, _1565193] : [c_Fun_Oinj__on(_1565179, _1565181, _1565183, _1565185), c_Fun_Oinj__on(_1565187, _1565189, _1565191, _1565193), -(c_Fun_Oinj__on(tc_prod(_1565179, _1565187), tc_prod(_1565181, _1565189), c_Product__Type_Omap__pair(_1565179, _1565181, _1565187, _1565189, _1565183, _1565191), hAPP(hAPP(c_Product__Type_OSigma(_1565179, _1565187), _1565185), hAPP(c_COMBK(tc_fun(_1565187, tc_HOL_Obool), _1565179), _1565193))))], (40213 ^ _782464) ^ [_1565406, _1565408, _1565410, _1565412, _1565414, _1565416, _1565418, _1565420] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565406, _1565408)), _1565410), hAPP(c_Set_Oimage(tc_prod(_1565412, _1565414), tc_prod(_1565406, _1565408), c_Product__Type_Omap__pair(_1565412, _1565406, _1565414, _1565408, _1565416, _1565418)), _1565420))), 40218 ^ _782464 : [(40219 ^ _782464) ^ [] : [-(_1565410 = hAPP(hAPP(c_Product__Type_OPair(_1565406, _1565408), hAPP(_1565416, 40216 ^ [_1565406, _1565408, _1565410, _1565412, _1565414, _1565416, _1565418, _1565420])), hAPP(_1565418, 40217 ^ [_1565406, _1565408, _1565410, _1565412, _1565414, _1565416, _1565418, _1565420])))], (40221 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565412, _1565414)), hAPP(hAPP(c_Product__Type_OPair(_1565412, _1565414), 40216 ^ [_1565406, _1565408, _1565410, _1565412, _1565414, _1565416, _1565418, _1565420]), 40217 ^ [_1565406, _1565408, _1565410, _1565412, _1565414, _1565416, _1565418, _1565420])), _1565420)))]]], (40223 ^ _782464) ^ [_1565757, _1565759, _1565761] : [c_Relation_Orefl__on(_1565757, _1565759, _1565761), 40226 ^ _782464 : [(40227 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565757, _1565757), tc_HOL_Obool)), _1565761), hAPP(hAPP(c_Product__Type_OSigma(_1565757, _1565757), _1565759), hAPP(c_COMBK(tc_fun(_1565757, tc_HOL_Obool), _1565757), _1565759)))))], (40229 ^ _782464) ^ [_1565939] : [hBOOL(hAPP(hAPP(c_member(_1565757), _1565939), _1565759)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565757, _1565757)), hAPP(hAPP(c_Product__Type_OPair(_1565757, _1565757), _1565939), _1565939)), _1565761)))]]], (40235 ^ _782464) ^ [_1566074, _1566076, _1566078] : [-(c_Relation_Orefl__on(_1566074, _1566076, _1566078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566074, _1566074), tc_HOL_Obool)), _1566078), hAPP(hAPP(c_Product__Type_OSigma(_1566074, _1566074), _1566076), hAPP(c_COMBK(tc_fun(_1566074, tc_HOL_Obool), _1566074), _1566076)))), 40241 ^ _782464 : [(40242 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566074), 40240 ^ [_1566074, _1566076, _1566078]), _1566076)))], (40244 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566074, _1566074)), hAPP(hAPP(c_Product__Type_OPair(_1566074, _1566074), 40240 ^ [_1566074, _1566076, _1566078]), 40240 ^ [_1566074, _1566076, _1566078])), _1566078))]]], (40248 ^ _782464) ^ [_1566438, _1566440] : [c_Wellfounded_OwfP(_1566438, _1566440), -(c_Wellfounded_Owf(_1566438, hAPP(c_Set_OCollect(tc_prod(_1566438, _1566438)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566438, _1566438, tc_HOL_Obool), _1566440))))], (40254 ^ _782464) ^ [_1566541, _1566543] : [c_Wellfounded_Owf(_1566541, hAPP(c_Set_OCollect(tc_prod(_1566541, _1566541)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566541, _1566541, tc_HOL_Obool), _1566543))), -(c_Wellfounded_OwfP(_1566541, _1566543))], (40260 ^ _782464) ^ [_1566650] : [-(c_Wellfounded_OwfP(_1566650, hAPP(c_COMBK(tc_fun(_1566650, tc_HOL_Obool), _1566650), hAPP(c_COMBK(tc_HOL_Obool, _1566650), c_fFalse))))], (40262 ^ _782464) ^ [_1566688, _1566690] : [-(c_Relation_Orefl__on(_1566688, _1566690, c_Relation_OId__on(_1566688, _1566690)))], (40264 ^ _782464) ^ [_1566717, _1566719, _1566721] : [c_Wellfounded_OwfP(_1566717, _1566719), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1566717, _1566719), _1566721)))], (40270 ^ _782464) ^ [_1566821, _1566823] : [c_Wellfounded_OwfP(_1566821, _1566823), 40273 ^ _782464 : [(40274 ^ _782464) ^ [_1566885] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1566821, _1566823), _1566885)))]]], (40276 ^ _782464) ^ [_1566913, _1566915] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1566913, _1566915), 40277 ^ [_1566913, _1566915])), -(c_Wellfounded_OwfP(_1566913, _1566915))], (40283 ^ _782464) ^ [_1567031, _1567033, _1567035] : [c_Wellfounded_OwfP(_1567031, _1567033), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567031, tc_fun(_1567031, tc_HOL_Obool))), _1567035), _1567033)), -(c_Wellfounded_OwfP(_1567031, _1567035))], (40293 ^ _782464) ^ [_1567190] : [-(c_Relation_Orefl__on(_1567190, c_Orderings_Obot__class_Obot(tc_fun(_1567190, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1567190, _1567190), tc_HOL_Obool))))], (40295 ^ _782464) ^ [_1567227, _1567229, _1567231, _1567233, _1567235] : [c_Relation_Orefl__on(_1567227, _1567229, _1567231), c_Relation_Orefl__on(_1567227, _1567233, _1567235), -(c_Relation_Orefl__on(_1567227, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567227, tc_HOL_Obool)), _1567229), _1567233), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567227, _1567227), tc_HOL_Obool)), _1567231), _1567235)))], (40305 ^ _782464) ^ [_1567424, _1567426, _1567428, _1567430, _1567432] : [c_Relation_Orefl__on(_1567424, _1567426, _1567428), c_Relation_Orefl__on(_1567424, _1567430, _1567432), -(c_Relation_Orefl__on(_1567424, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567424, tc_HOL_Obool)), _1567426), _1567430), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1567424, _1567424), tc_HOL_Obool)), _1567428), _1567432)))], (40315 ^ _782464) ^ [_1567621, _1567623, _1567625, _1567627, _1567629] : [c_Relation_Orefl__on(_1567621, _1567623, _1567625), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567621, _1567621)), hAPP(hAPP(c_Product__Type_OPair(_1567621, _1567621), _1567627), _1567629)), _1567625)), -(hBOOL(hAPP(hAPP(c_member(_1567621), _1567629), _1567623)))], (40325 ^ _782464) ^ [_1567816, _1567818, _1567820, _1567822, _1567824] : [c_Relation_Orefl__on(_1567816, _1567818, _1567820), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567816, _1567816)), hAPP(hAPP(c_Product__Type_OPair(_1567816, _1567816), _1567822), _1567824)), _1567820)), -(hBOOL(hAPP(hAPP(c_member(_1567816), _1567822), _1567818)))], (40335 ^ _782464) ^ [_1568011, _1568013, _1568015, _1568017] : [c_Relation_Orefl__on(_1568011, _1568013, _1568015), hBOOL(hAPP(hAPP(c_member(_1568011), _1568017), _1568013)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1568011, _1568011)), hAPP(hAPP(c_Product__Type_OPair(_1568011, _1568011), _1568017), _1568017)), _1568015)))], (40345 ^ _782464) ^ [_1568202, _1568204] : [c_Wellfounded_Owf(_1568202, _1568204), -(c_Wellfounded_OwfP(_1568202, c_FunDef_Oin__rel(_1568202, _1568202, _1568204)))], (40351 ^ _782464) ^ [_1568302, _1568304] : [c_Wellfounded_OwfP(_1568302, hAPP(hAPP(c_COMBC(_1568302, tc_fun(tc_prod(_1568302, _1568302), tc_HOL_Obool), tc_fun(_1568302, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568302, tc_fun(tc_fun(tc_prod(_1568302, _1568302), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568302, _1568302), tc_HOL_Obool), tc_fun(_1568302, tc_HOL_Obool)), _1568302), c_COMBC(_1568302, tc_fun(tc_prod(_1568302, _1568302), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568302, tc_prod(_1568302, _1568302)), tc_fun(_1568302, tc_fun(tc_fun(tc_prod(_1568302, _1568302), tc_HOL_Obool), tc_HOL_Obool)), _1568302), hAPP(c_COMBB(tc_prod(_1568302, _1568302), tc_fun(tc_fun(tc_prod(_1568302, _1568302), tc_HOL_Obool), tc_HOL_Obool), _1568302), c_member(tc_prod(_1568302, _1568302)))), c_Product__Type_OPair(_1568302, _1568302)))), _1568304)), -(c_Wellfounded_Owf(_1568302, _1568304))], (40357 ^ _782464) ^ [_1568611, _1568613] : [c_Wellfounded_Owf(_1568611, _1568613), -(c_Wellfounded_OwfP(_1568611, hAPP(hAPP(c_COMBC(_1568611, tc_fun(tc_prod(_1568611, _1568611), tc_HOL_Obool), tc_fun(_1568611, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568611, tc_fun(tc_fun(tc_prod(_1568611, _1568611), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568611, _1568611), tc_HOL_Obool), tc_fun(_1568611, tc_HOL_Obool)), _1568611), c_COMBC(_1568611, tc_fun(tc_prod(_1568611, _1568611), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568611, tc_prod(_1568611, _1568611)), tc_fun(_1568611, tc_fun(tc_fun(tc_prod(_1568611, _1568611), tc_HOL_Obool), tc_HOL_Obool)), _1568611), hAPP(c_COMBB(tc_prod(_1568611, _1568611), tc_fun(tc_fun(tc_prod(_1568611, _1568611), tc_HOL_Obool), tc_HOL_Obool), _1568611), c_member(tc_prod(_1568611, _1568611)))), c_Product__Type_OPair(_1568611, _1568611)))), _1568613)))], (40363 ^ _782464) ^ [_1568941, _1568943] : [c_Predicate_Oreflp(_1568941, _1568943), -(c_Relation_Orefl__on(_1568941, c_Orderings_Otop__class_Otop(tc_fun(_1568941, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1568941, _1568941)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568941, _1568941, tc_HOL_Obool), _1568943))))], (40369 ^ _782464) ^ [_1569056, _1569058] : [c_Relation_Orefl__on(_1569056, c_Orderings_Otop__class_Otop(tc_fun(_1569056, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569056, _1569056)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569056, _1569056, tc_HOL_Obool), _1569058))), -(c_Predicate_Oreflp(_1569056, _1569058))], (40375 ^ _782464) ^ [_1569177, _1569179, _1569181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569177, _1569177), tc_HOL_Obool)), _1569179), hAPP(hAPP(c_Product__Type_OSigma(_1569177, _1569177), _1569181), hAPP(c_COMBK(tc_fun(_1569177, tc_HOL_Obool), _1569177), _1569181)))), 40381 ^ _782464 : [(40382 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1569177), 40380 ^ [_1569177, _1569179, _1569181]), _1569181)))], (40384 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569177, _1569177)), hAPP(hAPP(c_Product__Type_OPair(_1569177, _1569177), 40380 ^ [_1569177, _1569179, _1569181]), 40380 ^ [_1569177, _1569179, _1569181])), _1569179))]], -(c_Relation_Orefl__on(_1569177, _1569181, _1569179))], (40388 ^ _782464) ^ [_1569524, _1569526] : [c_Wellfounded_OwfP(_1569524, _1569526), -(c_Wellfounded_Oacyclic(_1569524, hAPP(c_Set_OCollect(tc_prod(_1569524, _1569524)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569524, _1569524, tc_HOL_Obool), _1569526))))], (40394 ^ _782464) ^ [_1569631, _1569633, _1569635] : [c_Predicate_Oreflp(_1569631, _1569633), -(hBOOL(hAPP(hAPP(_1569633, _1569635), _1569635)))], (40400 ^ _782464) ^ [_1569720, _1569722, _1569724] : [c_Wellfounded_Oacyclic(_1569720, _1569722), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569720, _1569720), tc_HOL_Obool)), _1569724), _1569722)), -(c_Wellfounded_Oacyclic(_1569720, _1569724))], (40410 ^ _782464) ^ [_1569879, _1569881] : [c_Wellfounded_Owf(_1569879, _1569881), -(c_Wellfounded_Oacyclic(_1569879, _1569881))], (40416 ^ _782464) ^ [_1569956, _1569958] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569956, _1569956)), _1569958)), 40419 ^ _782464 : [(40420 ^ _782464) ^ [] : [c_Wellfounded_Owf(_1569956, _1569958), -(c_Wellfounded_Oacyclic(_1569956, _1569958))], (40426 ^ _782464) ^ [] : [c_Wellfounded_Oacyclic(_1569956, _1569958), -(c_Wellfounded_Owf(_1569956, _1569958))]]], (40432 ^ _782464) ^ [_1570177, _1570179] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570177, _1570177)), _1570179)), c_Wellfounded_Oacyclic(_1570177, _1570179), -(c_Wellfounded_Owf(_1570177, _1570179))], (40442 ^ _782464) ^ [_1570335, _1570337] : [c_Nitpick_Owf_H(_1570335, _1570337), 40445 ^ _782464 : [(40446 ^ _782464) ^ [] : [-(c_Wellfounded_Oacyclic(_1570335, _1570337))], (40448 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570335, _1570335)), _1570337))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (40454 ^ _782464) ^ [_1570455, _1570457] : [-(c_Nitpick_Owf_H(_1570455, _1570457)), c_Wellfounded_Oacyclic(_1570455, _1570457), 40459 ^ _782464 : [(40460 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570455, _1570455)), _1570457))], (40462 ^ _782464) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (40466 ^ _782464) ^ [_1570632, _1570634] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1570632), c_Int_OInteg)), hBOOL(hAPP(_1570634, hAPP(c_Int_ORep__Integ, 40471 ^ [_1570632, _1570634]))), -(hBOOL(hAPP(_1570634, _1570632)))], (40477 ^ _782464) ^ [_1570814] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1570814), c_Int_OInteg)), -(_1570814 = hAPP(c_Int_ORep__Integ, 40480 ^ [_1570814]))], (40500 ^ _782464) ^ [_1571556, _1571558, _1571560] : [-(c_Relation_Orefl__on(_1571556, _1571558, _1571560)), 40504 ^ _782464 : [(40505 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571556, _1571556)), 40503 ^ [_1571556, _1571558, _1571560]), _1571560)))], (40507 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1571556, _1571556, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571556, tc_fun(_1571556, tc_HOL_Obool), tc_fun(_1571556, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571556, tc_HOL_Obool), tc_fun(_1571556, tc_HOL_Obool)), _1571556), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571556)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571556), c_fconj), hAPP(hAPP(c_COMBC(_1571556, tc_fun(_1571556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571556)), _1571558)))), hAPP(hAPP(c_COMBC(_1571556, tc_fun(_1571556, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571556)), _1571558))), 40503 ^ [_1571556, _1571558, _1571560]))]], 40509 ^ _782464 : [(40510 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571556), 40508 ^ [_1571556, _1571558, _1571560]), _1571558)))], (40512 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571556, _1571556)), hAPP(hAPP(c_Product__Type_OPair(_1571556, _1571556), 40508 ^ [_1571556, _1571558, _1571560]), 40508 ^ [_1571556, _1571558, _1571560])), _1571560))]]], (40484 ^ _782464) ^ [_1570937, _1570939, _1570941] : [c_Relation_Orefl__on(_1570937, _1570939, _1570941), 40487 ^ _782464 : [(40488 ^ _782464) ^ [_1571148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570937, _1570937)), _1571148), _1570941)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1570937, _1570937, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1570937, tc_fun(_1570937, tc_HOL_Obool), tc_fun(_1570937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1570937, tc_HOL_Obool), tc_fun(_1570937, tc_HOL_Obool)), _1570937), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570937)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570937), c_fconj), hAPP(hAPP(c_COMBC(_1570937, tc_fun(_1570937, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570937)), _1570939)))), hAPP(hAPP(c_COMBC(_1570937, tc_fun(_1570937, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570937)), _1570939))), _1571148)))], (40494 ^ _782464) ^ [_1571421] : [hBOOL(hAPP(hAPP(c_member(_1570937), _1571421), _1570939)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570937, _1570937)), hAPP(hAPP(c_Product__Type_OPair(_1570937, _1570937), _1571421), _1571421)), _1570941)))]]], (40516 ^ _782464) ^ [_1572197, _1572199] : [40518 ^ _782464 : [(40519 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40517 ^ [_1572197, _1572199]), c_Int_OInteg)))], (40521 ^ _782464) ^ [] : [hBOOL(hAPP(_1572197, hAPP(c_Int_OAbs__Integ, 40517 ^ [_1572197, _1572199])))]], -(hBOOL(hAPP(_1572197, _1572199)))], (40526 ^ _782464) ^ [_1572364] : [-(_1572364 = hAPP(c_Int_OAbs__Integ, 40524 ^ [_1572364]))], (40528 ^ _782464) ^ [_1572392] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40524 ^ [_1572392]), c_Int_OInteg)))], (40540 ^ _782464) ^ [_1572628, _1572630, _1572632] : [40542 ^ _782464 : [(40543 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572628), 40541 ^ [_1572628, _1572630, _1572632]), _1572632)))], (40545 ^ _782464) ^ [] : [hBOOL(hAPP(_1572630, 40541 ^ [_1572628, _1572630, _1572632]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1572628, _1572630), _1572632)))], (40530 ^ _782464) ^ [_1572445, _1572447, _1572449] : [hBOOL(hAPP(c_Predicate_OPowp(_1572445, _1572447), _1572449)), 40533 ^ _782464 : [(40534 ^ _782464) ^ [_1572529] : [hBOOL(hAPP(hAPP(c_member(_1572445), _1572529), _1572449)), -(hBOOL(hAPP(_1572447, _1572529)))]]], (40549 ^ _782464) ^ [_1572808] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1572808, tc_HOL_Obool) = c_Set_OBall(_1572808))], (40551 ^ _782464) ^ [_1572836, _1572838, _1572840] : [hBOOL(hAPP(hAPP(c_member(_1572838), _1572836), c_Orderings_Obot__class_Obot(tc_fun(_1572838, tc_HOL_Obool)))), -(hBOOL(hAPP(_1572840, _1572836)))], (40557 ^ _782464) ^ [_1572943, _1572945, _1572947, _1572949] : [-(hAPP(c_Set_OCollect(_1572943), hAPP(hAPP(c_COMBB(tc_fun(_1572945, tc_HOL_Obool), tc_HOL_Obool, _1572943), c_HOL_OAll(_1572945)), hAPP(hAPP(c_COMBB(tc_fun(_1572945, tc_HOL_Obool), tc_fun(_1572945, tc_HOL_Obool), _1572943), hAPP(c_COMBS(_1572945, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572945), c_fimplies), hAPP(hAPP(c_COMBC(_1572945, tc_fun(_1572945, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572945)), _1572947)))), _1572949))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1572945, tc_fun(_1572943, tc_HOL_Obool)), _1572947), hAPP(hAPP(c_COMBB(tc_fun(_1572943, tc_HOL_Obool), tc_fun(_1572943, tc_HOL_Obool), _1572945), c_Set_OCollect(_1572943)), hAPP(c_COMBC(_1572943, _1572945, tc_HOL_Obool), _1572949))))], (40569 ^ _782464) ^ [_1573474, _1573476, _1573478, _1573480] : [40571 ^ _782464 : [(40572 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573474, _1573474)), 40570 ^ [_1573474, _1573476, _1573478, _1573480]), _1573478)))], (40574 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1573474, _1573474, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1573474, tc_fun(_1573474, _1573476), tc_fun(_1573474, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573476, tc_HOL_Obool), tc_fun(tc_fun(_1573474, _1573476), tc_fun(_1573474, tc_HOL_Obool)), _1573474), c_COMBB(_1573476, tc_HOL_Obool, _1573474)), hAPP(hAPP(c_COMBB(_1573476, tc_fun(_1573476, tc_HOL_Obool), _1573474), c_fequal), _1573480))), _1573480)), 40570 ^ [_1573474, _1573476, _1573478, _1573480]))]], -(c_Equiv__Relations_Ocongruent(_1573474, _1573476, _1573478, _1573480))], (40559 ^ _782464) ^ [_1573098, _1573100, _1573102, _1573104] : [c_Equiv__Relations_Ocongruent(_1573098, _1573100, _1573102, _1573104), 40562 ^ _782464 : [(40563 ^ _782464) ^ [_1573243] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573098, _1573098)), _1573243), _1573102)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1573098, _1573098, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1573098, tc_fun(_1573098, _1573100), tc_fun(_1573098, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573100, tc_HOL_Obool), tc_fun(tc_fun(_1573098, _1573100), tc_fun(_1573098, tc_HOL_Obool)), _1573098), c_COMBB(_1573100, tc_HOL_Obool, _1573098)), hAPP(hAPP(c_COMBB(_1573100, tc_fun(_1573100, tc_HOL_Obool), _1573098), c_fequal), _1573104))), _1573104)), _1573243)))]]], (40578 ^ _782464) ^ [_1573849, _1573851, _1573853, _1573855] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573849, tc_fun(_1573851, tc_HOL_Obool)), _1573853), _1573855) = hAPP(c_Set_OCollect(_1573851), hAPP(hAPP(c_COMBB(tc_fun(_1573849, tc_HOL_Obool), tc_HOL_Obool, _1573851), c_HOL_OAll(_1573849)), hAPP(hAPP(c_COMBB(tc_fun(_1573849, tc_HOL_Obool), tc_fun(_1573849, tc_HOL_Obool), _1573851), hAPP(c_COMBS(_1573849, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573849), c_fimplies), hAPP(hAPP(c_COMBC(_1573849, tc_fun(_1573849, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573849)), _1573853)))), hAPP(hAPP(c_COMBC(_1573851, tc_fun(_1573849, tc_fun(_1573851, tc_HOL_Obool)), tc_fun(_1573849, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573851, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1573849, tc_fun(_1573851, tc_HOL_Obool)), tc_fun(_1573849, tc_HOL_Obool)), _1573851), c_COMBB(tc_fun(_1573851, tc_HOL_Obool), tc_HOL_Obool, _1573849)), c_member(_1573851))), _1573855)))))], (40580 ^ _782464) ^ [_1574014, _1574016] : [class_Complete__Lattice_Ocomplete__lattice(_1574014), -(c_Complete__Lattice_OInf__class_OInf(_1574014, _1574016) = c_Complete__Lattice_OSup__class_OSup(_1574014, hAPP(c_Set_OCollect(_1574014), hAPP(hAPP(c_COMBB(tc_fun(_1574014, tc_HOL_Obool), tc_HOL_Obool, _1574014), c_HOL_OAll(_1574014)), hAPP(hAPP(c_COMBB(tc_fun(_1574014, tc_HOL_Obool), tc_fun(_1574014, tc_HOL_Obool), _1574014), hAPP(c_COMBS(_1574014, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574014), c_fimplies), hAPP(hAPP(c_COMBC(_1574014, tc_fun(_1574014, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574014)), _1574016)))), c_Orderings_Oord__class_Oless__eq(_1574014))))))], (40586 ^ _782464) ^ [_1574241, _1574243] : [class_Complete__Lattice_Ocomplete__lattice(_1574241), -(c_Complete__Lattice_OSup__class_OSup(_1574241, _1574243) = c_Complete__Lattice_OInf__class_OInf(_1574241, hAPP(c_Set_OCollect(_1574241), hAPP(hAPP(c_COMBB(tc_fun(_1574241, tc_HOL_Obool), tc_HOL_Obool, _1574241), c_HOL_OAll(_1574241)), hAPP(hAPP(c_COMBB(tc_fun(_1574241, tc_HOL_Obool), tc_fun(_1574241, tc_HOL_Obool), _1574241), hAPP(c_COMBS(_1574241, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574241), c_fimplies), hAPP(hAPP(c_COMBC(_1574241, tc_fun(_1574241, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574241)), _1574243)))), hAPP(c_COMBC(_1574241, _1574241, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1574241)))))))], (40592 ^ _782464) ^ [_1574482, _1574484, _1574486] : [c_Wellfounded_OwfP(_1574482, hAPP(_1574484, 40593 ^ [_1574482, _1574484, _1574486])), 40600 ^ _782464 : [(40601 ^ _782464) ^ [] : [hAPP(_1574484, 40598 ^ [_1574482, _1574484, _1574486]) = hAPP(_1574484, 40599 ^ [_1574482, _1574484, _1574486])], (40603 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574482, tc_HOL_Obool)), c_Predicate_ODomainP(_1574482, _1574482, hAPP(_1574484, 40598 ^ [_1574482, _1574484, _1574486]))), c_Predicate_ORangeP(_1574482, _1574482, hAPP(_1574484, 40599 ^ [_1574482, _1574484, _1574486]))) = c_Orderings_Obot__class_Obot(tc_fun(_1574482, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1574482, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1574486, tc_fun(_1574482, tc_fun(_1574482, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1574486, tc_HOL_Obool))), _1574484)))], (40607 ^ _782464) ^ [_1574922, _1574924, _1574926, _1574928, _1574930, _1574932] : [hBOOL(hAPP(hAPP(c_member(_1574922), _1574924), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1574926, _1574928, tc_fun(_1574922, tc_HOL_Obool)), _1574930), _1574932))), 40612 ^ _782464 : [(40613 ^ _782464) ^ [] : [-(_1574932 = hAPP(hAPP(c_Product__Type_OPair(_1574926, _1574928), 40610 ^ [_1574922, _1574924, _1574926, _1574928, _1574930, _1574932]), 40611 ^ [_1574922, _1574924, _1574926, _1574928, _1574930, _1574932]))], (40615 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574922), _1574924), hAPP(hAPP(_1574930, 40610 ^ [_1574922, _1574924, _1574926, _1574928, _1574930, _1574932]), 40611 ^ [_1574922, _1574924, _1574926, _1574928, _1574930, _1574932]))))]]], (40617 ^ _782464) ^ [_1575191, _1575193, _1575195, _1575197, _1575199, _1575201] : [40620 ^ _782464 : [(40621 ^ _782464) ^ [] : [-(_1575191 = hAPP(hAPP(c_Product__Type_OPair(_1575193, _1575195), 40618 ^ [_1575191, _1575193, _1575195, _1575197, _1575199, _1575201]), 40619 ^ [_1575191, _1575193, _1575195, _1575197, _1575199, _1575201]))], (40623 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1575197), _1575199), hAPP(hAPP(_1575201, 40618 ^ [_1575191, _1575193, _1575195, _1575197, _1575199, _1575201]), 40619 ^ [_1575191, _1575193, _1575195, _1575197, _1575199, _1575201])))]], -(hBOOL(hAPP(hAPP(c_member(_1575197), _1575199), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1575193, _1575195, tc_fun(_1575197, tc_HOL_Obool)), _1575201), _1575191))))], (40627 ^ _782464) ^ [_1575516, _1575518] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1575516, tc_HOL_Obool), _1575518) = hAPP(c_Set_OCollect(_1575516), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575516, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1575516), c_HOL_OAll(tc_fun(_1575516, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575516, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1575516, tc_HOL_Obool), tc_HOL_Obool), _1575516), hAPP(c_COMBS(tc_fun(_1575516, 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(_1575516, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1575516, tc_HOL_Obool), tc_fun(tc_fun(_1575516, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1575516, tc_HOL_Obool))), _1575518)))), c_member(_1575516)))))], (40629 ^ _782464) ^ [_1575644, _1575646, _1575648] : [-(c_Hilbert__Choice_OEps(tc_prod(_1575644, _1575646), hAPP(c_Product__Type_Oprod_Oprod__case(_1575644, _1575646, tc_HOL_Obool), _1575648)) = c_Hilbert__Choice_OEps(tc_prod(_1575644, _1575646), hAPP(hAPP(c_COMBS(tc_prod(_1575644, _1575646), _1575646, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1575644, tc_fun(_1575646, tc_HOL_Obool), tc_prod(_1575644, _1575646)), _1575648), c_Product__Type_Ofst(_1575644, _1575646))), c_Product__Type_Osnd(_1575644, _1575646))))], (40631 ^ _782464) ^ [_1575725, _1575727] : [40633 ^ _782464 : [(40634 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575725, tc_HOL_Obool)), 40632 ^ [_1575725, _1575727]), hAPP(c_Relation_OImage(_1575725, _1575725, _1575727), 40632 ^ [_1575725, _1575727]))))], (40636 ^ _782464) ^ [] : [40632 ^ [_1575725, _1575727] = c_Orderings_Obot__class_Obot(tc_fun(_1575725, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1575725, _1575727))], (40640 ^ _782464) ^ [_1575922, _1575924, _1575926, _1575928, _1575930, _1575932] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575922, tc_HOL_Obool)), _1575924), _1575926)), 40646 ^ _782464 : [(40647 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575922), 40645 ^ [_1575922, _1575924, _1575926, _1575928, _1575930, _1575932]), _1575924)))], (40649 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575928, tc_HOL_Obool)), hAPP(_1575930, 40645 ^ [_1575922, _1575924, _1575926, _1575928, _1575930, _1575932])), hAPP(_1575932, 40645 ^ [_1575922, _1575924, _1575926, _1575928, _1575930, _1575932])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575922, _1575928), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575922, _1575928), _1575924), _1575930)), hAPP(hAPP(c_Product__Type_OSigma(_1575922, _1575928), _1575926), _1575932))))], (40653 ^ _782464) ^ [_1576313, _1576315] : [-(c_Hilbert__Choice_OEps(_1576313, hAPP(c_fequal, _1576315)) = _1576315)], (40655 ^ _782464) ^ [_1576344, _1576346] : [-(c_Hilbert__Choice_OEps(_1576344, hAPP(hAPP(c_COMBC(_1576344, _1576344, tc_HOL_Obool), c_fequal), _1576346)) = _1576346)], (40657 ^ _782464) ^ [_1576397, _1576399] : [hBOOL(hAPP(_1576397, c_Hilbert__Choice_OEps(_1576399, _1576397))), -(hBOOL(hAPP(_1576397, 40660 ^ [_1576397, _1576399])))], (40664 ^ _782464) ^ [_1576496, _1576498] : [40665 ^ _782464 : [(40666 ^ _782464) ^ [_1576542] : [hBOOL(hAPP(_1576496, _1576542))]], -(hBOOL(hAPP(_1576496, c_Hilbert__Choice_OEps(_1576498, _1576496))))], (40670 ^ _782464) ^ [_1576602, _1576604] : [40671 ^ _782464 : [(40672 ^ _782464) ^ [_1576648] : [hBOOL(hAPP(_1576602, _1576648))]], -(hBOOL(hAPP(_1576602, c_Hilbert__Choice_OEps(_1576604, _1576602))))], (40676 ^ _782464) ^ [_1576706, _1576708, _1576710] : [hBOOL(hAPP(_1576706, _1576708)), -(hBOOL(hAPP(_1576706, c_Hilbert__Choice_OEps(_1576710, _1576706))))], (40682 ^ _782464) ^ [_1576799, _1576801] : [40683 ^ _782464 : [(40684 ^ _782464) ^ [_1576845] : [hBOOL(hAPP(_1576799, _1576845))]], -(hBOOL(hAPP(_1576799, c_Hilbert__Choice_OEps(_1576801, _1576799))))], (40688 ^ _782464) ^ [_1576903, _1576905, _1576907] : [40689 ^ _782464 : [(40690 ^ _782464) ^ [_1576957] : [hBOOL(hAPP(_1576903, _1576957))]], _1576905 = c_Hilbert__Choice_OEps(_1576907, _1576903), -(hBOOL(hAPP(_1576903, _1576905)))], (40698 ^ _782464) ^ [_1577063, _1577065, _1577067] : [-(c_Hilbert__Choice_OEps(tc_prod(_1577063, _1577065), _1577067) = c_Hilbert__Choice_OEps(tc_prod(_1577063, _1577065), hAPP(c_Product__Type_Oprod_Oprod__case(_1577063, _1577065, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1577065, tc_prod(_1577063, _1577065)), tc_fun(_1577065, tc_HOL_Obool), _1577063), hAPP(c_COMBB(tc_prod(_1577063, _1577065), tc_HOL_Obool, _1577065), _1577067)), c_Product__Type_OPair(_1577063, _1577065)))))], (40700 ^ _782464) ^ [_1577141, _1577143, _1577145, _1577147] : [-(c_Hilbert__Choice_OEps(tc_prod(_1577141, _1577143), hAPP(c_Product__Type_Oprod_Oprod__case(_1577141, _1577143, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1577141, tc_fun(_1577143, tc_HOL_Obool), tc_fun(_1577143, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1577143, tc_HOL_Obool), tc_fun(_1577143, tc_HOL_Obool)), _1577141), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1577143)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577141), c_fconj), hAPP(c_fequal, _1577145)))), hAPP(c_fequal, _1577147)))) = hAPP(hAPP(c_Product__Type_OPair(_1577141, _1577143), _1577145), _1577147))], (40702 ^ _782464) ^ [_1577247, _1577249, _1577251] : [40704 ^ _782464 : [(40705 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577247, _1577247)), hAPP(hAPP(c_Product__Type_OPair(_1577247, _1577247), 40703 ^ [_1577247, _1577249, _1577251]), _1577249)), _1577251)))], (40707 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1577247), 40703 ^ [_1577247, _1577249, _1577251]), c_Wellfounded_Oacc(_1577247, _1577251)))]], -(hBOOL(hAPP(hAPP(c_member(_1577247), _1577249), c_Wellfounded_Oacc(_1577247, _1577251))))], (40711 ^ _782464) ^ [_1577484, _1577486, _1577488] : [-(hBOOL(hAPP(hAPP(c_member(_1577484), _1577486), c_Wellfounded_Oacc(_1577484, _1577488)))), 40715 ^ _782464 : [(40716 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577484, _1577484)), hAPP(hAPP(c_Product__Type_OPair(_1577484, _1577484), 40714 ^ [_1577484, _1577486, _1577488]), _1577486)), _1577488)))], (40718 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1577484), 40714 ^ [_1577484, _1577486, _1577488]), c_Wellfounded_Oacc(_1577484, _1577488)))]]], (40720 ^ _782464) ^ [_1577732, _1577734, _1577736, _1577738] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1577732, tc_HOL_Obool), tc_fun(_1577732, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1577732, tc_HOL_Obool), tc_fun(_1577732, tc_HOL_Obool)), _1577734), _1577736)), c_Wellfounded_Omax__ext(_1577732, _1577738))), 40723 ^ _782464 : [(40724 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577732), _1577734)))], (40726 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577732), _1577736)))], (40728 ^ _782464) ^ [] : [_1577736 = c_Orderings_Obot__class_Obot(tc_fun(_1577732, tc_HOL_Obool))], (40730 ^ _782464) ^ [_1578026] : [hBOOL(hAPP(hAPP(c_member(_1577732), _1578026), _1577734)), 40734 ^ _782464 : [(40735 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577732), 40733 ^ [_1577732, _1577734, _1577736, _1577738, _1578026]), _1577736)))], (40737 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577732, _1577732)), hAPP(hAPP(c_Product__Type_OPair(_1577732, _1577732), _1578026), 40733 ^ [_1577732, _1577734, _1577736, _1577738, _1578026])), _1577738)))]]]]], (40739 ^ _782464) ^ [_1578238, _1578240, _1578242, _1578244] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1578238, tc_HOL_Obool), tc_fun(_1578238, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1578238, tc_HOL_Obool), tc_fun(_1578238, tc_HOL_Obool)), _1578240), _1578242)), c_Wellfounded_Omax__ext(_1578238, _1578244)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578238), _1578240)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578238), _1578242)), -(_1578242 = c_Orderings_Obot__class_Obot(tc_fun(_1578238, tc_HOL_Obool))), 40753 ^ _782464 : [(40754 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578238), 40752 ^ [_1578238, _1578240, _1578242, _1578244]), _1578240)))], (40756 ^ _782464) ^ [_1578643] : [hBOOL(hAPP(hAPP(c_member(_1578238), _1578643), _1578242)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578238, _1578238)), hAPP(hAPP(c_Product__Type_OPair(_1578238, _1578238), 40752 ^ [_1578238, _1578240, _1578242, _1578244]), _1578643)), _1578244))]]], (40764 ^ _782464) ^ [_1578871, _1578873, _1578875] : [c_Wellfounded_Owf(_1578871, _1578873), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578871, _1578871)), hAPP(hAPP(c_Product__Type_OPair(_1578871, _1578871), hAPP(_1578875, hAPP(c_Nat_OSuc, 40767 ^ [_1578871, _1578873, _1578875]))), hAPP(_1578875, 40767 ^ [_1578871, _1578873, _1578875]))), _1578873))], (40771 ^ _782464) ^ [_1579072, _1579074, _1579076, _1579078, _1579080, _1579082, _1579084, _1579086] : [class_Groups_Ocomm__monoid__add(_1579072), c_Fun_Oinj__on(_1579074, _1579076, _1579078, _1579080), _1579082 = hAPP(c_Set_Oimage(_1579074, _1579076, _1579078), _1579080), 40785 ^ _782464 : [(40786 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579074), 40784 ^ [_1579072, _1579074, _1579076, _1579078, _1579080, _1579082, _1579084, _1579086]), _1579080)))], (40788 ^ _782464) ^ [] : [hAPP(_1579084, 40784 ^ [_1579072, _1579074, _1579076, _1579078, _1579080, _1579082, _1579084, _1579086]) = hAPP(_1579086, hAPP(_1579078, 40784 ^ [_1579072, _1579074, _1579076, _1579078, _1579080, _1579082, _1579084, _1579086]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579076, _1579072), _1579086), _1579082) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579074, _1579072), _1579084), _1579080))], (40792 ^ _782464) ^ [_1579564, _1579566, _1579568, _1579570, _1579572, _1579574, _1579576] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579564, _1579566, _1579568, _1579570), _1579572), _1579574), _1579576) = hAPP(hAPP(_1579574, hAPP(c_Product__Type_Ofst(_1579566, _1579568), hAPP(_1579572, _1579576))), hAPP(c_Product__Type_Osnd(_1579566, _1579568), hAPP(_1579572, _1579576))))], (40794 ^ _782464) ^ [_1579637, _1579639, _1579641, _1579643] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579637, _1579639, _1579641, tc_prod(_1579639, _1579641)), _1579643), c_Product__Type_OPair(_1579639, _1579641)) = _1579643)], (40796 ^ _782464) ^ [_1579683, _1579685, _1579687, _1579689, _1579691] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579683, _1579685, _1579683, _1579687), hAPP(c_Product__Type_OPair(_1579685, _1579683), _1579689)), _1579691) = hAPP(_1579691, _1579689))], (40798 ^ _782464) ^ [_1579734, _1579736, _1579738, _1579740, _1579742, _1579744, _1579746, _1579748, _1579750] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579734, _1579736, _1579738, _1579740), hAPP(hAPP(c_Product__Type_Oscomp(_1579734, _1579742, _1579744, tc_prod(_1579736, _1579738)), _1579746), _1579748)), _1579750) = hAPP(hAPP(c_Product__Type_Oscomp(_1579734, _1579742, _1579744, _1579740), _1579746), hAPP(hAPP(c_COMBC(_1579742, tc_fun(_1579736, tc_fun(_1579738, _1579740)), tc_fun(_1579744, _1579740)), hAPP(hAPP(c_COMBB(tc_fun(_1579744, tc_prod(_1579736, _1579738)), tc_fun(tc_fun(_1579736, tc_fun(_1579738, _1579740)), tc_fun(_1579744, _1579740)), _1579742), c_Product__Type_Oscomp(_1579744, _1579736, _1579738, _1579740)), _1579748)), _1579750)))], (40800 ^ _782464) ^ [_1579861, _1579863, _1579865, _1579867, _1579869, _1579871, _1579873] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579861, _1579863, _1579865, _1579867), _1579869), _1579871), _1579873) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579863, _1579865, _1579867), _1579871), hAPP(_1579869, _1579873)))], (40802 ^ _782464) ^ [_1579923, _1579925, _1579927, _1579929, _1579931, _1579933, _1579935] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579923, _1579925, _1579927, _1579929), _1579931), _1579933), _1579935) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579925, _1579927, _1579929), _1579933), hAPP(_1579931, _1579935)))], (40804 ^ _782464) ^ [_1580003, _1580005, _1580007, _1580009, _1580011] : [_1580003 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1580005, _1580007, _1580003, _1580009), _1580011) = hAPP(c_Product__Type_OPair(_1580005, _1580007), _1580011))], (40810 ^ _782464) ^ [_1580108, _1580110, _1580112, _1580114, _1580116] : [-(_1580108 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1580110, _1580112, _1580108, _1580114), _1580116) = hAPP(hAPP(c_Product__Type_Oscomp(_1580112, _1580110, _1580112, tc_prod(_1580110, _1580112)), hAPP(_1580114, _1580116)), c_Random_Oiterate(_1580110, _1580112, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1580108), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1580114)))], (40816 ^ _782464) ^ [_1580188, _1580190, _1580192, _1580194, _1580196, _1580198, _1580200, _1580202] : [class_Groups_Ocomm__monoid__add(_1580188), class_Orderings_Oord(_1580190), _1580192 = _1580194, _1580196 = _1580198, 40834 ^ _782464 : [(40835 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1580190), _1580194), 40833 ^ [_1580188, _1580190, _1580192, _1580194, _1580196, _1580198, _1580200, _1580202])))], (40837 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1580190), 40833 ^ [_1580188, _1580190, _1580192, _1580194, _1580196, _1580198, _1580200, _1580202]), _1580198)))], (40839 ^ _782464) ^ [] : [hAPP(_1580200, 40833 ^ [_1580188, _1580190, _1580192, _1580194, _1580196, _1580198, _1580200, _1580202]) = hAPP(_1580202, 40833 ^ [_1580188, _1580190, _1580192, _1580194, _1580196, _1580198, _1580200, _1580202])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580190, _1580188), _1580200), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1580190, _1580192), _1580196)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580190, _1580188), _1580202), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1580190, _1580194), _1580198)))], (40843 ^ _782464) ^ [_1580826, _1580828] : [40844 ^ _782464 : [(40845 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1580826), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40847 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1580828), _1580826))]], -(c_Random_Olog(_1580826, _1580828) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40851 ^ _782464) ^ [_1580961, _1580963] : [-(c_Random_Olog(_1580961, _1580963) = 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(_1580961, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1580963), _1580961)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1580961), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1580963), _1580961)))], (40861 ^ _782464) ^ [_1581043, _1581045, _1581047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1581043), _1581045)), -(c_Random_Ominus__shift(_1581047, _1581043, _1581045) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1581047), _1581043)), _1581045))], (40867 ^ _782464) ^ [_1581158, _1581160, _1581162] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1581158), _1581160))), -(c_Random_Ominus__shift(_1581162, _1581158, _1581160) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1581158), _1581160))], (40873 ^ _782464) ^ [_1581222, _1581224] : [_1581222 = _1581224, -(c_Random_Oinc__shift(_1581222, _1581224) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40879 ^ _782464) ^ [_1581299, _1581301] : [-(_1581299 = _1581301), -(c_Random_Oinc__shift(_1581299, _1581301) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1581301), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40885 ^ _782464) ^ [_1581346, _1581348] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1581346)), -(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(_1581346), _1581348))), _1581346)))], (40891 ^ _782464) ^ [_1581468, _1581470] : [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), _1581468), _1581470)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581468), _1581470)))], (40897 ^ _782464) ^ [_1581573, _1581575] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581573), _1581575)), -(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), _1581573), _1581575)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40903 ^ _782464) ^ [_1581684, _1581686, _1581688, _1581690] : [40905 ^ _782464 : [(40906 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1581684), 40904 ^ [_1581684, _1581686, _1581688, _1581690])))], (40908 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40904 ^ [_1581684, _1581686, _1581688, _1581690]), _1581686)))], (40910 ^ _782464) ^ [] : [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(_1581688, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 40904 ^ [_1581684, _1581686, _1581688, _1581690]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1581688, 40904 ^ [_1581684, _1581686, _1581688, _1581690])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581684), _1581686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1581688, _1581684)), _1581690)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1581690), hAPP(_1581688, _1581686))), 40924 ^ _782464 : [(40925 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1581684), 40923 ^ [_1581684, _1581686, _1581688, _1581690])))], (40927 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 40923 ^ [_1581684, _1581686, _1581688, _1581690]), _1581686)))], (40929 ^ _782464) ^ [] : [-(hAPP(_1581688, 40923 ^ [_1581684, _1581686, _1581688, _1581690]) = _1581690)]]], (40931 ^ _782464) ^ [_1582310, _1582312] : [c_Wellfounded_Owf(_1582310, _1582312), -(c_Wellfounded_Owf(_1582310, c_Transitive__Closure_Otrancl(_1582310, _1582312)))], (40937 ^ _782464) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40939 ^ _782464) ^ [_1582426, _1582428] : [c_Wellfounded_Oacyclic(_1582426, _1582428), 40942 ^ _782464 : [(40943 ^ _782464) ^ [_1582511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582426, _1582426)), hAPP(hAPP(c_Product__Type_OPair(_1582426, _1582426), _1582511), _1582511)), c_Transitive__Closure_Otrancl(_1582426, _1582428)))]]], (40945 ^ _782464) ^ [_1582554, _1582556] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582554, _1582554)), hAPP(hAPP(c_Product__Type_OPair(_1582554, _1582554), 40946 ^ [_1582554, _1582556]), 40946 ^ [_1582554, _1582556])), c_Transitive__Closure_Otrancl(_1582554, _1582556)))), -(c_Wellfounded_Oacyclic(_1582554, _1582556))], (40952 ^ _782464) ^ [_1582628, _1582630, _1582632, _1582634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582628, _1582628)), hAPP(hAPP(c_Product__Type_OPair(_1582628, _1582628), _1582630), _1582632)), _1582634)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582628, _1582628)), hAPP(hAPP(c_Product__Type_OPair(_1582628, _1582628), _1582630), _1582632)), c_Transitive__Closure_Otrancl(_1582628, _1582634))))], (40958 ^ _782464) ^ [_1582791, _1582793] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582791, _1582791), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1582791, _1582793)), hAPP(hAPP(c_Product__Type_OSigma(_1582791, _1582791), hAPP(c_Relation_OField(_1582791), _1582793)), hAPP(c_COMBK(tc_fun(_1582791, tc_HOL_Obool), _1582791), hAPP(c_Relation_OField(_1582791), _1582793))))))], (40960 ^ _782464) ^ [_1582860, _1582862, _1582864] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582860, _1582860)), _1582862), _1582864)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582860, _1582860)), _1582862), c_Transitive__Closure_Otrancl(_1582860, _1582864))))], (40966 ^ _782464) ^ [_1582985] : [-(c_Transitive__Closure_Otrancl(_1582985, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582985, _1582985), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582985, _1582985), tc_HOL_Obool)))], (40968 ^ _782464) ^ [_1583027, _1583029] : [-(hAPP(c_Relation_ODomain(_1583027, _1583027), c_Transitive__Closure_Otrancl(_1583027, _1583029)) = hAPP(c_Relation_ODomain(_1583027, _1583027), _1583029))], (40970 ^ _782464) ^ [_1583067, _1583069] : [-(hAPP(c_Relation_ORange(_1583067, _1583067), c_Transitive__Closure_Otrancl(_1583067, _1583069)) = hAPP(c_Relation_ORange(_1583067, _1583067), _1583069))], (40972 ^ _782464) ^ [_1583122, _1583124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583122, _1583122)), c_Transitive__Closure_Otrancl(_1583122, _1583124))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583122, _1583122)), _1583124)))], (40978 ^ _782464) ^ [_1583229, _1583231] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583229, _1583229)), _1583231)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583229, _1583229)), c_Transitive__Closure_Otrancl(_1583229, _1583231))))], (40984 ^ _782464) ^ [_1583342, _1583344, _1583346, _1583348, _1583350] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583342, _1583342)), hAPP(hAPP(c_Product__Type_OPair(_1583342, _1583342), _1583344), _1583346)), c_Transitive__Closure_Otrancl(_1583342, _1583348))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583342, _1583342)), hAPP(hAPP(c_Product__Type_OPair(_1583342, _1583342), _1583346), _1583350)), c_Transitive__Closure_Otrancl(_1583342, _1583348))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583342, _1583342)), hAPP(hAPP(c_Product__Type_OPair(_1583342, _1583342), _1583344), _1583350)), c_Transitive__Closure_Otrancl(_1583342, _1583348))))], (40994 ^ _782464) ^ [_1583615, _1583617, _1583619, _1583621, _1583623] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583615, _1583615)), hAPP(hAPP(c_Product__Type_OPair(_1583615, _1583615), _1583617), _1583619)), c_Transitive__Closure_Otrancl(_1583615, _1583621))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583615, _1583615)), hAPP(hAPP(c_Product__Type_OPair(_1583615, _1583615), _1583619), _1583623)), _1583621)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583615, _1583615)), hAPP(hAPP(c_Product__Type_OPair(_1583615, _1583615), _1583617), _1583623)), c_Transitive__Closure_Otrancl(_1583615, _1583621))))], (41004 ^ _782464) ^ [_1583882, _1583884, _1583886, _1583888, _1583890] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583882, _1583882)), hAPP(hAPP(c_Product__Type_OPair(_1583882, _1583882), _1583884), _1583886)), _1583888)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583882, _1583882)), hAPP(hAPP(c_Product__Type_OPair(_1583882, _1583882), _1583886), _1583890)), c_Transitive__Closure_Otrancl(_1583882, _1583888))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583882, _1583882)), hAPP(hAPP(c_Product__Type_OPair(_1583882, _1583882), _1583884), _1583890)), c_Transitive__Closure_Otrancl(_1583882, _1583888))))], (41014 ^ _782464) ^ [_1584149, _1584151, _1584153, _1584155, _1584157] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584149, _1584149)), hAPP(hAPP(c_Product__Type_OPair(_1584149, _1584149), _1584151), _1584153)), _1584155)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584149, _1584149)), hAPP(hAPP(c_Product__Type_OPair(_1584149, _1584149), _1584153), _1584157)), _1584155)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584149, _1584149)), hAPP(hAPP(c_Product__Type_OPair(_1584149, _1584149), _1584151), _1584157)), c_Transitive__Closure_Otrancl(_1584149, _1584155))))], (41024 ^ _782464) ^ [_1584410, _1584412, _1584414, _1584416] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584410, _1584410)), _1584412), c_Transitive__Closure_Otrancl(_1584410, _1584414))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584410, _1584410), tc_HOL_Obool)), _1584414), _1584416)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584410, _1584410)), _1584412), c_Transitive__Closure_Otrancl(_1584410, _1584416))))], (41034 ^ _782464) ^ [_1584625, _1584627] : [-(c_Transitive__Closure_Otrancl(_1584625, _1584627) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584625, _1584625), tc_HOL_Obool)), _1584627), hAPP(hAPP(c_Relation_Orel__comp(_1584625, _1584625, _1584625), c_Transitive__Closure_Otrancl(_1584625, _1584627)), _1584627)))], (41036 ^ _782464) ^ [_1584680, _1584682, _1584684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584680, _1584680), tc_HOL_Obool)), _1584682), hAPP(hAPP(c_Product__Type_OSigma(_1584680, _1584680), _1584684), hAPP(c_COMBK(tc_fun(_1584680, tc_HOL_Obool), _1584680), _1584684)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584680, _1584680), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584680, _1584682)), hAPP(hAPP(c_Product__Type_OSigma(_1584680, _1584680), _1584684), hAPP(c_COMBK(tc_fun(_1584680, tc_HOL_Obool), _1584680), _1584684)))))], (41042 ^ _782464) ^ [_1584889, _1584891, _1584893] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584889, _1584889), tc_HOL_Obool)), _1584891), _1584893)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584889, _1584889), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584889, _1584889, _1584889), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1584889, _1584889), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584889, _1584891)), _1584893)), _1584891)), _1584893)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584889, _1584889), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584889, _1584891)), _1584893)))], (41052 ^ _782464) ^ [_1585160, _1585162, _1585164, _1585166] : [-(c_Transitive__Closure_Otrancl(_1585160, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1585160, _1585160)), hAPP(hAPP(c_Product__Type_OPair(_1585160, _1585160), _1585162), _1585164)), _1585166)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585160, _1585160), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585160, _1585166)), hAPP(c_Set_OCollect(tc_prod(_1585160, _1585160)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585160, _1585160, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585160, tc_fun(_1585160, tc_HOL_Obool), tc_fun(_1585160, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1585160, tc_HOL_Obool), tc_fun(_1585160, tc_HOL_Obool)), _1585160), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1585160)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585160), c_fconj), hAPP(hAPP(c_COMBC(_1585160, tc_fun(tc_prod(_1585160, _1585160), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585160, _1585160), tc_fun(tc_fun(tc_prod(_1585160, _1585160), tc_HOL_Obool), tc_HOL_Obool), _1585160), c_member(tc_prod(_1585160, _1585160))), hAPP(hAPP(c_COMBC(_1585160, _1585160, tc_prod(_1585160, _1585160)), c_Product__Type_OPair(_1585160, _1585160)), _1585162))), c_Transitive__Closure_Ortrancl(_1585160, _1585166))))), hAPP(hAPP(c_COMBC(_1585160, tc_fun(tc_prod(_1585160, _1585160), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585160, _1585160), tc_fun(tc_fun(tc_prod(_1585160, _1585160), tc_HOL_Obool), tc_HOL_Obool), _1585160), c_member(tc_prod(_1585160, _1585160))), hAPP(c_Product__Type_OPair(_1585160, _1585160), _1585164))), c_Transitive__Closure_Ortrancl(_1585160, _1585166)))))))], (41054 ^ _782464) ^ [_1585428, _1585430, _1585432, _1585434] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585428, tc_fun(_1585428, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585428, tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool), tc_fun(_1585428, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585428, tc_fun(tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool), tc_fun(_1585428, tc_HOL_Obool)), _1585428), c_COMBC(_1585428, tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585428, tc_prod(_1585428, _1585428)), tc_fun(_1585428, tc_fun(tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool), tc_HOL_Obool)), _1585428), hAPP(c_COMBB(tc_prod(_1585428, _1585428), tc_fun(tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool), tc_HOL_Obool), _1585428), c_member(tc_prod(_1585428, _1585428)))), c_Product__Type_OPair(_1585428, _1585428)))), _1585430)), c_fequal), _1585432), _1585434)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585428, _1585428)), hAPP(hAPP(c_Product__Type_OPair(_1585428, _1585428), _1585432), _1585434)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585428, _1585428), tc_HOL_Obool)), _1585430), c_Relation_OId(_1585428)))))], (41060 ^ _782464) ^ [_1585849, _1585851, _1585853, _1585855] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585849, _1585849)), hAPP(hAPP(c_Product__Type_OPair(_1585849, _1585849), _1585853), _1585855)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool)), _1585851), c_Relation_OId(_1585849)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585849, tc_fun(_1585849, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585849, tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool), tc_fun(_1585849, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585849, tc_fun(tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool), tc_fun(_1585849, tc_HOL_Obool)), _1585849), c_COMBC(_1585849, tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585849, tc_prod(_1585849, _1585849)), tc_fun(_1585849, tc_fun(tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool), tc_HOL_Obool)), _1585849), hAPP(c_COMBB(tc_prod(_1585849, _1585849), tc_fun(tc_fun(tc_prod(_1585849, _1585849), tc_HOL_Obool), tc_HOL_Obool), _1585849), c_member(tc_prod(_1585849, _1585849)))), c_Product__Type_OPair(_1585849, _1585849)))), _1585851)), c_fequal), _1585853), _1585855)))], (41066 ^ _782464) ^ [_1586276, _1586278, _1586280] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586276, _1586276)), _1586278), _1586280)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586276, _1586276)), _1586278), c_Transitive__Closure_Ortrancl(_1586276, _1586280))))], (41072 ^ _782464) ^ [_1586401, _1586403, _1586405] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586401, _1586401)), hAPP(hAPP(c_Product__Type_OPair(_1586401, _1586401), _1586403), _1586403)), c_Transitive__Closure_Ortrancl(_1586401, _1586405))))], (41074 ^ _782464) ^ [_1586450, _1586452] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586450, _1586450)), hAPP(hAPP(c_Product__Type_OPair(_1586450, _1586450), _1586452), _1586452)), c_Relation_OId(_1586450))))], (41076 ^ _782464) ^ [_1586496, _1586498, _1586500, _1586502] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586496, _1586496)), hAPP(hAPP(c_Product__Type_OPair(_1586496, _1586496), _1586498), _1586500)), c_Transitive__Closure_Otrancl(_1586496, _1586502))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586496, _1586496)), hAPP(hAPP(c_Product__Type_OPair(_1586496, _1586496), _1586498), _1586500)), c_Transitive__Closure_Ortrancl(_1586496, _1586502))))], (41082 ^ _782464) ^ [_1586665, _1586667] : [-(c_Transitive__Closure_Otrancl(_1586665, c_Transitive__Closure_Ortrancl(_1586665, _1586667)) = c_Transitive__Closure_Ortrancl(_1586665, _1586667))], (41084 ^ _782464) ^ [_1586699, _1586701] : [-(c_Transitive__Closure_Ortrancl(_1586699, c_Transitive__Closure_Otrancl(_1586699, _1586701)) = c_Transitive__Closure_Ortrancl(_1586699, _1586701))], (41086 ^ _782464) ^ [_1586733, _1586735] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586733, _1586733), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1586733, _1586735)), c_Relation_OId(_1586733)) = c_Transitive__Closure_Ortrancl(_1586733, _1586735))], (41088 ^ _782464) ^ [_1586780, _1586782] : [-(c_Transitive__Closure_Otrancl(_1586780, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586780, _1586780), tc_HOL_Obool)), _1586782), c_Relation_OId(_1586780))) = c_Transitive__Closure_Ortrancl(_1586780, _1586782))], (41090 ^ _782464) ^ [_1586827, _1586829] : [-(c_Transitive__Closure_Otrancl(_1586827, _1586829) = hAPP(hAPP(c_Relation_Orel__comp(_1586827, _1586827, _1586827), _1586829), c_Transitive__Closure_Ortrancl(_1586827, _1586829)))], (41092 ^ _782464) ^ [_1586868, _1586870] : [-(c_Transitive__Closure_Otrancl(_1586868, _1586870) = hAPP(hAPP(c_Relation_Orel__comp(_1586868, _1586868, _1586868), c_Transitive__Closure_Ortrancl(_1586868, _1586870)), _1586870))], (41094 ^ _782464) ^ [_1586909, _1586911, _1586913] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1586909, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1586909, _1586909, _1586911), _1586913)), _1586913)), -(hAPP(c_Relation_OImage(_1586909, _1586909, c_Transitive__Closure_Ortrancl(_1586909, _1586911)), _1586913) = _1586913)], (41100 ^ _782464) ^ [_1587042, _1587044, _1587046] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587042, _1587042), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587042, _1587042), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587042, _1587044)), c_Transitive__Closure_Ortrancl(_1587042, _1587046))), c_Transitive__Closure_Ortrancl(_1587042, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587042, _1587042), tc_HOL_Obool)), _1587044), _1587046)))))], (41102 ^ _782464) ^ [_1587119, _1587121, _1587123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587119, _1587119), tc_HOL_Obool)), _1587121), _1587123)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587119, _1587119), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587119, _1587121)), c_Transitive__Closure_Ortrancl(_1587119, _1587123))))], (41108 ^ _782464) ^ [_1587262, _1587264, _1587266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587262, _1587262), tc_HOL_Obool)), _1587264), _1587266)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587262, _1587262), tc_HOL_Obool)), _1587266), c_Transitive__Closure_Ortrancl(_1587262, _1587264))), -(c_Transitive__Closure_Ortrancl(_1587262, _1587266) = c_Transitive__Closure_Ortrancl(_1587262, _1587264))], (41118 ^ _782464) ^ [_1587465, _1587467, _1587469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587465, _1587465), tc_HOL_Obool)), _1587467), c_Transitive__Closure_Ortrancl(_1587465, _1587469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587465, _1587465), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587465, _1587467)), c_Transitive__Closure_Ortrancl(_1587465, _1587469))))], (41124 ^ _782464) ^ [_1587614, _1587616, _1587618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587614, _1587614), tc_HOL_Obool)), c_Relation_OId(_1587614)), _1587616)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587614, _1587614), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1587614, _1587614, _1587614), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1587614, _1587614), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587614, _1587618)), _1587616)), _1587618)), _1587616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587614, _1587614), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587614, _1587618)), _1587616)))], (41134 ^ _782464) ^ [_1587889, _1587891] : [-(hAPP(c_Relation_ODomain(_1587889, _1587889), c_Transitive__Closure_Ortrancl(_1587889, _1587891)) = c_Orderings_Otop__class_Otop(tc_fun(_1587889, tc_HOL_Obool)))], (41136 ^ _782464) ^ [_1587928, _1587930] : [-(hAPP(c_Relation_ORange(_1587928, _1587928), c_Transitive__Closure_Ortrancl(_1587928, _1587930)) = c_Orderings_Otop__class_Otop(tc_fun(_1587928, tc_HOL_Obool)))], (41138 ^ _782464) ^ [_1587967] : [-(c_Transitive__Closure_Ortrancl(_1587967, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1587967, _1587967), tc_HOL_Obool))) = c_Relation_OId(_1587967))], (41140 ^ _782464) ^ [_1588003, _1588005] : [-(c_Transitive__Closure_Ortrancl(_1588003, _1588005) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588003, _1588003), tc_HOL_Obool)), c_Relation_OId(_1588003)), hAPP(hAPP(c_Relation_Orel__comp(_1588003, _1588003, _1588003), c_Transitive__Closure_Ortrancl(_1588003, _1588005)), _1588005)))], (41142 ^ _782464) ^ [_1588060, _1588062, _1588064, _1588066] : [41143 ^ _782464 : [(41144 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588060, _1588060)), _1588062), c_Transitive__Closure_Ortrancl(_1588060, _1588064)))], (41146 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588060, _1588060)), _1588062), c_Transitive__Closure_Ortrancl(_1588060, _1588066)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588060, _1588060)), _1588062), c_Transitive__Closure_Ortrancl(_1588060, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588060, _1588060), tc_HOL_Obool)), _1588064), _1588066)))))], (41150 ^ _782464) ^ [_1588285, _1588287] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588285, _1588285, _1588285), c_Transitive__Closure_Ortrancl(_1588285, _1588287)), c_Transitive__Closure_Ortrancl(_1588285, _1588287)) = c_Transitive__Closure_Ortrancl(_1588285, _1588287))], (41152 ^ _782464) ^ [_1588329, _1588331] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588329, _1588329, _1588329), _1588331), c_Transitive__Closure_Ortrancl(_1588329, _1588331)) = hAPP(hAPP(c_Relation_Orel__comp(_1588329, _1588329, _1588329), c_Transitive__Closure_Ortrancl(_1588329, _1588331)), _1588331))], (41154 ^ _782464) ^ [_1588380, _1588382] : [-(c_Transitive__Closure_Ortrancl(_1588380, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588380, _1588380), tc_HOL_Obool)), _1588382), c_Relation_OId(_1588380))) = c_Transitive__Closure_Ortrancl(_1588380, _1588382))], (41156 ^ _782464) ^ [_1588427, _1588429, _1588431] : [-(c_Transitive__Closure_Ortrancl(_1588427, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588427, _1588427), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588427, _1588429)), c_Transitive__Closure_Ortrancl(_1588427, _1588431))) = c_Transitive__Closure_Ortrancl(_1588427, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588427, _1588427), tc_HOL_Obool)), _1588429), _1588431)))], (41158 ^ _782464) ^ [_1588494, _1588496] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588494, _1588494), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588494, _1588496)), c_Relation_OId(_1588494)) = c_Transitive__Closure_Ortrancl(_1588494, _1588496))], (41160 ^ _782464) ^ [_1588541, _1588543] : [-(c_Transitive__Closure_Ortrancl(_1588541, c_Transitive__Closure_Ortrancl(_1588541, _1588543)) = c_Transitive__Closure_Ortrancl(_1588541, _1588543))], (41162 ^ _782464) ^ [_1588575, _1588577, _1588579, _1588581, _1588583] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588575, _1588575)), hAPP(hAPP(c_Product__Type_OPair(_1588575, _1588575), _1588577), _1588579)), c_Transitive__Closure_Ortrancl(_1588575, _1588581))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588575, _1588575)), hAPP(hAPP(c_Product__Type_OPair(_1588575, _1588575), _1588579), _1588583)), c_Transitive__Closure_Ortrancl(_1588575, _1588581))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588575, _1588575)), hAPP(hAPP(c_Product__Type_OPair(_1588575, _1588575), _1588577), _1588583)), c_Transitive__Closure_Ortrancl(_1588575, _1588581))))], (41172 ^ _782464) ^ [_1588848, _1588850, _1588852, _1588854, _1588856] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588848, _1588848)), hAPP(hAPP(c_Product__Type_OPair(_1588848, _1588848), _1588850), _1588852)), c_Transitive__Closure_Ortrancl(_1588848, _1588854))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588848, _1588848)), hAPP(hAPP(c_Product__Type_OPair(_1588848, _1588848), _1588852), _1588856)), _1588854)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588848, _1588848)), hAPP(hAPP(c_Product__Type_OPair(_1588848, _1588848), _1588850), _1588856)), c_Transitive__Closure_Ortrancl(_1588848, _1588854))))], (41182 ^ _782464) ^ [_1589115, _1589117, _1589119, _1589121, _1589123] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589115, _1589115)), hAPP(hAPP(c_Product__Type_OPair(_1589115, _1589115), _1589117), _1589119)), _1589121)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589115, _1589115)), hAPP(hAPP(c_Product__Type_OPair(_1589115, _1589115), _1589119), _1589123)), c_Transitive__Closure_Ortrancl(_1589115, _1589121))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589115, _1589115)), hAPP(hAPP(c_Product__Type_OPair(_1589115, _1589115), _1589117), _1589123)), c_Transitive__Closure_Ortrancl(_1589115, _1589121))))], (41192 ^ _782464) ^ [_1589382, _1589384] : [-(c_Transitive__Closure_Ortrancl(_1589382, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1589382, _1589382), tc_HOL_Obool)), _1589384), c_Relation_OId(_1589382))) = c_Transitive__Closure_Ortrancl(_1589382, _1589384))], (41194 ^ _782464) ^ [_1589429, _1589431] : [-(c_Relation_Orefl__on(_1589429, c_Orderings_Otop__class_Otop(tc_fun(_1589429, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1589429, _1589431)))], (41196 ^ _782464) ^ [_1589463, _1589465] : [-(hAPP(c_Relation_OImage(_1589463, _1589463, c_Relation_OId(_1589463)), _1589465) = _1589465)], (41198 ^ _782464) ^ [_1589497, _1589499, _1589501] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589497, _1589499, _1589499), _1589501), c_Relation_OId(_1589499)) = _1589501)], (41200 ^ _782464) ^ [_1589536, _1589538, _1589540] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589536, _1589536, _1589538), c_Relation_OId(_1589536)), _1589540) = _1589540)], (41202 ^ _782464) ^ [_1589593, _1589595, _1589597] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589593, _1589593)), hAPP(hAPP(c_Product__Type_OPair(_1589593, _1589593), _1589595), _1589597)), c_Relation_OId(_1589593))), -(_1589595 = _1589597)], (41208 ^ _782464) ^ [_1589710, _1589712, _1589714] : [_1589712 = _1589714, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589710, _1589710)), hAPP(hAPP(c_Product__Type_OPair(_1589710, _1589710), _1589712), _1589714)), c_Relation_OId(_1589710))))], (41214 ^ _782464) ^ [_1589833, _1589835, _1589837, _1589839, _1589841] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589833, _1589833)), hAPP(hAPP(c_Product__Type_OPair(_1589833, _1589833), _1589835), _1589837)), c_Transitive__Closure_Ortrancl(_1589833, _1589839))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589833, _1589833)), hAPP(hAPP(c_Product__Type_OPair(_1589833, _1589833), _1589837), _1589841)), c_Transitive__Closure_Otrancl(_1589833, _1589839))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589833, _1589833)), hAPP(hAPP(c_Product__Type_OPair(_1589833, _1589833), _1589835), _1589841)), c_Transitive__Closure_Otrancl(_1589833, _1589839))))], (41224 ^ _782464) ^ [_1590106, _1590108, _1590110, _1590112, _1590114] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590106, _1590106)), hAPP(hAPP(c_Product__Type_OPair(_1590106, _1590106), _1590108), _1590110)), c_Transitive__Closure_Otrancl(_1590106, _1590112))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590106, _1590106)), hAPP(hAPP(c_Product__Type_OPair(_1590106, _1590106), _1590110), _1590114)), c_Transitive__Closure_Ortrancl(_1590106, _1590112))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590106, _1590106)), hAPP(hAPP(c_Product__Type_OPair(_1590106, _1590106), _1590108), _1590114)), c_Transitive__Closure_Otrancl(_1590106, _1590112))))], (41234 ^ _782464) ^ [_1590379, _1590381, _1590383, _1590385, _1590387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590379, _1590379)), hAPP(hAPP(c_Product__Type_OPair(_1590379, _1590379), _1590381), _1590383)), c_Transitive__Closure_Ortrancl(_1590379, _1590385))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590379, _1590379)), hAPP(hAPP(c_Product__Type_OPair(_1590379, _1590379), _1590383), _1590387)), _1590385)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590379, _1590379)), hAPP(hAPP(c_Product__Type_OPair(_1590379, _1590379), _1590381), _1590387)), c_Transitive__Closure_Otrancl(_1590379, _1590385))))], (41244 ^ _782464) ^ [_1590646, _1590648, _1590650, _1590652] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590646, _1590646)), hAPP(hAPP(c_Product__Type_OPair(_1590646, _1590646), _1590648), _1590650)), c_Transitive__Closure_Ortrancl(_1590646, _1590652))), -(_1590648 = _1590650), 41251 ^ _782464 : [(41252 ^ _782464) ^ [] : [_1590648 = _1590650], (41254 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590646, _1590646)), hAPP(hAPP(c_Product__Type_OPair(_1590646, _1590646), _1590648), _1590650)), c_Transitive__Closure_Otrancl(_1590646, _1590652))))]]], (41256 ^ _782464) ^ [_1590908, _1590910, _1590912, _1590914, _1590916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590908, _1590908)), hAPP(hAPP(c_Product__Type_OPair(_1590908, _1590908), _1590910), _1590912)), _1590914)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590908, _1590908)), hAPP(hAPP(c_Product__Type_OPair(_1590908, _1590908), _1590912), _1590916)), c_Transitive__Closure_Ortrancl(_1590908, _1590914))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590908, _1590908)), hAPP(hAPP(c_Product__Type_OPair(_1590908, _1590908), _1590910), _1590916)), c_Transitive__Closure_Otrancl(_1590908, _1590914))))], (41266 ^ _782464) ^ [_1591196, _1591198, _1591200, _1591202] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591196, _1591196)), hAPP(hAPP(c_Product__Type_OPair(_1591196, _1591196), _1591198), _1591200)), c_Transitive__Closure_Ortrancl(_1591196, _1591202))), -(_1591198 = _1591200), 41273 ^ _782464 : [(41274 ^ _782464) ^ [] : [_1591198 = _1591200], (41276 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591196, _1591196)), hAPP(hAPP(c_Product__Type_OPair(_1591196, _1591196), _1591198), _1591200)), c_Transitive__Closure_Otrancl(_1591196, _1591202))))]]], (41278 ^ _782464) ^ [_1591454, _1591456, _1591458, _1591460] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591454, _1591454)), hAPP(hAPP(c_Product__Type_OPair(_1591454, _1591454), _1591456), _1591458)), c_Transitive__Closure_Ortrancl(_1591454, _1591460)))), 41279 ^ _782464 : [(41280 ^ _782464) ^ [] : [_1591456 = _1591458], (41282 ^ _782464) ^ [] : [-(_1591456 = _1591458), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591454, _1591454)), hAPP(hAPP(c_Product__Type_OPair(_1591454, _1591454), _1591456), _1591458)), c_Transitive__Closure_Otrancl(_1591454, _1591460)))]]], (41290 ^ _782464) ^ [_1591720] : [-(hAPP(c_Relation_ODomain(_1591720, _1591720), c_Relation_OId(_1591720)) = c_Orderings_Otop__class_Otop(tc_fun(_1591720, tc_HOL_Obool)))], (41292 ^ _782464) ^ [_1591756] : [-(hAPP(c_Relation_ORange(_1591756, _1591756), c_Relation_OId(_1591756)) = c_Orderings_Otop__class_Otop(tc_fun(_1591756, tc_HOL_Obool)))], (41294 ^ _782464) ^ [_1591792] : [-(c_Relation_Orefl__on(_1591792, c_Orderings_Otop__class_Otop(tc_fun(_1591792, tc_HOL_Obool)), c_Relation_OId(_1591792)))], (41296 ^ _782464) ^ [] : [-(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))))], (41298 ^ _782464) ^ [_1591840, _1591842, _1591844, _1591846] : [-(hBOOL(hAPP(hAPP(c_member(_1591840), _1591842), hAPP(c_Relation_ODomain(_1591840, _1591840), _1591844)))), 41301 ^ _782464 : [(41302 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591840, _1591840)), hAPP(hAPP(c_Product__Type_OPair(_1591840, _1591840), _1591842), _1591846)), c_Transitive__Closure_Ortrancl(_1591840, _1591844))), -(_1591842 = _1591846)], (41308 ^ _782464) ^ [] : [_1591842 = _1591846, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591840, _1591840)), hAPP(hAPP(c_Product__Type_OPair(_1591840, _1591840), _1591842), _1591846)), c_Transitive__Closure_Ortrancl(_1591840, _1591844))))]]], (41314 ^ _782464) ^ [_1592136, _1592138, _1592140, _1592142] : [hBOOL(hAPP(hAPP(c_member(_1592136), _1592138), c_Wellfounded_Oacc(_1592136, _1592140))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1592136, _1592136)), hAPP(hAPP(c_Product__Type_OPair(_1592136, _1592136), _1592142), _1592138)), c_Transitive__Closure_Ortrancl(_1592136, _1592140))), -(hBOOL(hAPP(hAPP(c_member(_1592136), _1592142), c_Wellfounded_Oacc(_1592136, _1592140))))], (41324 ^ _782464) ^ [_1592357, _1592359, _1592361, _1592363] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592357, _1592357)), hAPP(hAPP(c_Product__Type_OPair(_1592357, _1592357), _1592359), _1592361)), c_Transitive__Closure_Ortrancl(_1592357, _1592363))), hBOOL(hAPP(hAPP(c_member(_1592357), _1592361), c_Wellfounded_Oacc(_1592357, _1592363))), -(hBOOL(hAPP(hAPP(c_member(_1592357), _1592359), c_Wellfounded_Oacc(_1592357, _1592363))))], (41334 ^ _782464) ^ [_1592599, _1592601, _1592603, _1592605] : [c_Wellfounded_Owf(_1592599, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1592599, _1592599)), hAPP(hAPP(c_Product__Type_OPair(_1592599, _1592599), _1592601), _1592603)), _1592605)), 41337 ^ _782464 : [(41338 ^ _782464) ^ [] : [-(c_Wellfounded_Owf(_1592599, _1592605))], (41340 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592599, _1592599)), hAPP(hAPP(c_Product__Type_OPair(_1592599, _1592599), _1592603), _1592601)), c_Transitive__Closure_Ortrancl(_1592599, _1592605)))]]], (41342 ^ _782464) ^ [_1592794, _1592796, _1592798, _1592800] : [-(c_Wellfounded_Owf(_1592794, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1592794, _1592794)), hAPP(hAPP(c_Product__Type_OPair(_1592794, _1592794), _1592796), _1592798)), _1592800))), c_Wellfounded_Owf(_1592794, _1592800), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592794, _1592794)), hAPP(hAPP(c_Product__Type_OPair(_1592794, _1592794), _1592798), _1592796)), c_Transitive__Closure_Ortrancl(_1592794, _1592800))))], (41352 ^ _782464) ^ [_1593041, _1593043, _1593045, _1593047] : [c_Wellfounded_Oacyclic(_1593041, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593041, _1593041)), hAPP(hAPP(c_Product__Type_OPair(_1593041, _1593041), _1593043), _1593045)), _1593047)), 41355 ^ _782464 : [(41356 ^ _782464) ^ [] : [-(c_Wellfounded_Oacyclic(_1593041, _1593047))], (41358 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593041, _1593041)), hAPP(hAPP(c_Product__Type_OPair(_1593041, _1593041), _1593045), _1593043)), c_Transitive__Closure_Ortrancl(_1593041, _1593047)))]]], (41360 ^ _782464) ^ [_1593236, _1593238, _1593240, _1593242] : [-(c_Wellfounded_Oacyclic(_1593236, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593236, _1593236)), hAPP(hAPP(c_Product__Type_OPair(_1593236, _1593236), _1593238), _1593240)), _1593242))), c_Wellfounded_Oacyclic(_1593236, _1593242), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593236, _1593236)), hAPP(hAPP(c_Product__Type_OPair(_1593236, _1593236), _1593240), _1593238)), c_Transitive__Closure_Ortrancl(_1593236, _1593242))))], (41370 ^ _782464) ^ [_1593462, _1593464] : [-(c_Relation_Orefl__on(_1593462, c_Orderings_Otop__class_Otop(tc_fun(_1593462, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593462, _1593462), tc_HOL_Obool)), _1593464), c_Relation_OId(_1593462))))], (41372 ^ _782464) ^ [_1593509] : [-(c_Relation_OId(_1593509) = hAPP(c_Set_OCollect(tc_prod(_1593509, _1593509)), hAPP(hAPP(c_COMBB(tc_fun(_1593509, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1593509, _1593509)), c_HOL_OEx(_1593509)), hAPP(hAPP(c_COMBC(tc_prod(_1593509, _1593509), tc_fun(_1593509, tc_prod(_1593509, _1593509)), tc_fun(_1593509, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593509, _1593509), tc_HOL_Obool), tc_fun(tc_fun(_1593509, tc_prod(_1593509, _1593509)), tc_fun(_1593509, tc_HOL_Obool)), tc_prod(_1593509, _1593509)), c_COMBB(tc_prod(_1593509, _1593509), tc_HOL_Obool, _1593509)), c_fequal)), hAPP(hAPP(c_COMBS(_1593509, _1593509, tc_prod(_1593509, _1593509)), c_Product__Type_OPair(_1593509, _1593509)), c_COMBI(_1593509))))))], (41374 ^ _782464) ^ [_1593638, _1593640] : [-(c_Relation_Oirrefl(_1593638, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1593638, _1593638), tc_HOL_Obool)), _1593640), c_Relation_OId(_1593638))))], (41376 ^ _782464) ^ [_1593694, _1593696] : [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), _1593694), _1593696)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1593694), _1593696)))], (41382 ^ _782464) ^ [_1593799, _1593801] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1593799), _1593801)), -(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), _1593799), _1593801)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (41388 ^ _782464) ^ [_1593910, _1593912, _1593914, _1593916, _1593918] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593910, _1593910)), hAPP(hAPP(c_Product__Type_OPair(_1593910, _1593910), _1593912), _1593914)), c_Transitive__Closure_Ortrancl(_1593910, _1593916))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1593910, _1593910), tc_HOL_Obool)), _1593916), hAPP(hAPP(c_Product__Type_OSigma(_1593910, _1593910), _1593918), hAPP(c_COMBK(tc_fun(_1593910, tc_HOL_Obool), _1593910), _1593918)))), -(_1593912 = _1593914), -(hBOOL(hAPP(hAPP(c_member(_1593910), _1593912), _1593918)))], (41402 ^ _782464) ^ [_1594184, _1594186, _1594188] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594184, _1594184), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1594184, _1594184), _1594186)), c_Transitive__Closure_Ortrancl(_1594184, _1594186)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1594184, _1594184), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594184, _1594184)), hAPP(hAPP(c_Product__Type_OPair(_1594184, _1594184), _1594188), _1594188)), c_Transitive__Closure_Otrancl(_1594184, _1594186)))], (41408 ^ _782464) ^ [_1594370, _1594372, _1594374, _1594376, _1594378] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594370, _1594370)), hAPP(hAPP(c_Product__Type_OPair(_1594370, _1594370), hAPP(_1594372, hAPP(c_Nat_OSuc, 41409 ^ [_1594370, _1594372, _1594374, _1594376, _1594378]))), hAPP(_1594372, 41409 ^ [_1594370, _1594372, _1594374, _1594376, _1594378]))), c_Transitive__Closure_Ortrancl(_1594370, _1594374))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594370, _1594370)), hAPP(hAPP(c_Product__Type_OPair(_1594370, _1594370), hAPP(_1594372, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1594376), _1594378))), hAPP(_1594372, _1594376))), c_Transitive__Closure_Ortrancl(_1594370, _1594374))))], (41415 ^ _782464) ^ [_1594663, _1594665] : [-(c_Transitive__Closure_Ortrancl(_1594663, hAPP(c_Relation_Oconverse(_1594663, _1594663), _1594665)) = hAPP(c_Relation_Oconverse(_1594663, _1594663), c_Transitive__Closure_Ortrancl(_1594663, _1594665)))], (41417 ^ _782464) ^ [_1594706] : [-(hAPP(c_Relation_Oconverse(_1594706, _1594706), c_Relation_OId(_1594706)) = c_Relation_OId(_1594706))], (41419 ^ _782464) ^ [_1594754, _1594756] : [c_Wellfounded_Oacyclic(_1594754, hAPP(c_Relation_Oconverse(_1594754, _1594754), _1594756)), -(c_Wellfounded_Oacyclic(_1594754, _1594756))], (41425 ^ _782464) ^ [_1594839, _1594841] : [c_Wellfounded_Oacyclic(_1594839, _1594841), -(c_Wellfounded_Oacyclic(_1594839, hAPP(c_Relation_Oconverse(_1594839, _1594839), _1594841)))], (41431 ^ _782464) ^ [_1594930, _1594932, _1594934, _1594936, _1594938] : [-(hAPP(c_Relation_Oconverse(_1594930, _1594932), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594934, tc_fun(tc_prod(_1594930, _1594932), tc_HOL_Obool)), _1594936), _1594938)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594934, tc_fun(tc_prod(_1594932, _1594930), tc_HOL_Obool)), _1594936), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1594930, _1594932), tc_HOL_Obool), tc_fun(tc_prod(_1594932, _1594930), tc_HOL_Obool), _1594934), c_Relation_Oconverse(_1594930, _1594932)), _1594938)))], (41433 ^ _782464) ^ [_1595022, _1595024, _1595026, _1595028, _1595030] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595022, _1595024)), hAPP(hAPP(c_Product__Type_OPair(_1595022, _1595024), _1595026), _1595028)), hAPP(c_Relation_Oconverse(_1595024, _1595022), _1595030))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595024, _1595022)), hAPP(hAPP(c_Product__Type_OPair(_1595024, _1595022), _1595028), _1595026)), _1595030)))], (41439 ^ _782464) ^ [_1595193, _1595195, _1595197, _1595199, _1595201] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595193, _1595195)), hAPP(hAPP(c_Product__Type_OPair(_1595193, _1595195), _1595197), _1595199)), _1595201)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595195, _1595193)), hAPP(hAPP(c_Product__Type_OPair(_1595195, _1595193), _1595199), _1595197)), hAPP(c_Relation_Oconverse(_1595193, _1595195), _1595201))))], (41445 ^ _782464) ^ [_1595388, _1595390, _1595392, _1595394, _1595396] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595388, _1595390)), hAPP(hAPP(c_Product__Type_OPair(_1595388, _1595390), _1595392), _1595394)), hAPP(c_Relation_Oconverse(_1595390, _1595388), _1595396))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595390, _1595388)), hAPP(hAPP(c_Product__Type_OPair(_1595390, _1595388), _1595394), _1595392)), _1595396)))], (41451 ^ _782464) ^ [_1595555, _1595557, _1595559, _1595561, _1595563] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595557, _1595555)), hAPP(hAPP(c_Product__Type_OPair(_1595557, _1595555), _1595561), _1595559)), _1595563)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595555, _1595557)), hAPP(hAPP(c_Product__Type_OPair(_1595555, _1595557), _1595559), _1595561)), hAPP(c_Relation_Oconverse(_1595557, _1595555), _1595563))))], (41457 ^ _782464) ^ [_1595728, _1595730, _1595732, _1595734, _1595736] : [-(hAPP(c_Relation_Oconverse(_1595728, _1595730), hAPP(hAPP(c_Relation_Orel__comp(_1595728, _1595732, _1595730), _1595734), _1595736)) = hAPP(hAPP(c_Relation_Orel__comp(_1595730, _1595732, _1595728), hAPP(c_Relation_Oconverse(_1595732, _1595730), _1595736)), hAPP(c_Relation_Oconverse(_1595728, _1595732), _1595734)))], (41459 ^ _782464) ^ [_1595797, _1595799, _1595801, _1595803] : [-(hAPP(c_Relation_Oconverse(_1595797, _1595799), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595797, _1595799), tc_HOL_Obool)), _1595801), _1595803)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595799, _1595797), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1595797, _1595799), _1595801)), hAPP(c_Relation_Oconverse(_1595797, _1595799), _1595803)))], (41461 ^ _782464) ^ [_1595872, _1595874] : [-(hAPP(c_Relation_Oconverse(_1595872, _1595872), c_Relation_OId__on(_1595872, _1595874)) = c_Relation_OId__on(_1595872, _1595874))], (41463 ^ _782464) ^ [_1595909, _1595911, _1595913, _1595915] : [-(hAPP(c_Relation_Oconverse(_1595909, _1595909), hAPP(hAPP(c_Relation_Oinv__image(_1595911, _1595909), _1595913), _1595915)) = hAPP(hAPP(c_Relation_Oinv__image(_1595911, _1595909), hAPP(c_Relation_Oconverse(_1595911, _1595911), _1595913)), _1595915))], (41465 ^ _782464) ^ [_1595968, _1595970, _1595972] : [-(hAPP(c_Relation_Oconverse(_1595968, _1595970), hAPP(c_Relation_Oconverse(_1595970, _1595968), _1595972)) = _1595972)], (41467 ^ _782464) ^ [_1596007, _1596009, _1596011, _1596013] : [-(hAPP(c_Relation_Oconverse(_1596007, _1596009), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1596007, _1596009), tc_HOL_Obool)), _1596011), _1596013)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1596009, _1596007), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1596007, _1596009), _1596011)), hAPP(c_Relation_Oconverse(_1596007, _1596009), _1596013)))], (41469 ^ _782464) ^ [_1596100, _1596102, _1596104] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596100, _1596102)), hAPP(c_Relation_Oconverse(_1596102, _1596100), _1596104))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596102, _1596100)), _1596104)))], (41475 ^ _782464) ^ [_1596215, _1596217, _1596219] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596217, _1596215)), _1596219)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596215, _1596217)), hAPP(c_Relation_Oconverse(_1596217, _1596215), _1596219))))], (41481 ^ _782464) ^ [_1596336, _1596338] : [-(hAPP(c_Relation_OField(_1596336), hAPP(c_Relation_Oconverse(_1596336, _1596336), _1596338)) = hAPP(c_Relation_OField(_1596336), _1596338))], (41483 ^ _782464) ^ [_1596395, _1596397, _1596399] : [c_Relation_Orefl__on(_1596395, _1596397, hAPP(c_Relation_Oconverse(_1596395, _1596395), _1596399)), -(c_Relation_Orefl__on(_1596395, _1596397, _1596399))], (41489 ^ _782464) ^ [_1596486, _1596488, _1596490] : [c_Relation_Orefl__on(_1596486, _1596488, _1596490), -(c_Relation_Orefl__on(_1596486, _1596488, hAPP(c_Relation_Oconverse(_1596486, _1596486), _1596490)))], (41495 ^ _782464) ^ [_1596583, _1596585, _1596587, _1596589, _1596591] : [-(hAPP(c_Relation_Oconverse(_1596583, _1596585), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596587, tc_fun(tc_prod(_1596583, _1596585), tc_HOL_Obool)), _1596589), _1596591)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596587, tc_fun(tc_prod(_1596585, _1596583), tc_HOL_Obool)), _1596589), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1596583, _1596585), tc_HOL_Obool), tc_fun(tc_prod(_1596585, _1596583), tc_HOL_Obool), _1596587), c_Relation_Oconverse(_1596583, _1596585)), _1596591)))], (41497 ^ _782464) ^ [_1596675, _1596677] : [-(c_Transitive__Closure_Otrancl(_1596675, hAPP(c_Relation_Oconverse(_1596675, _1596675), _1596677)) = hAPP(c_Relation_Oconverse(_1596675, _1596675), c_Transitive__Closure_Otrancl(_1596675, _1596677)))], (41499 ^ _782464) ^ [_1596718, _1596720] : [c_Wellfounded_Owf(_1596718, hAPP(c_Relation_Oconverse(_1596718, _1596718), _1596720)), -(c_Wellfounded_Owf(_1596718, hAPP(c_Relation_Oconverse(_1596718, _1596718), c_Transitive__Closure_Otrancl(_1596718, _1596720))))], (41505 ^ _782464) ^ [_1596825, _1596827, _1596829] : [c_Equiv__Relations_Oequiv(_1596825, _1596827, _1596829), -(hAPP(hAPP(c_Relation_Orel__comp(_1596825, _1596825, _1596825), hAPP(c_Relation_Oconverse(_1596825, _1596825), _1596829)), _1596829) = _1596829)], (41511 ^ _782464) ^ [_1596938, _1596940, _1596942] : [-(hAPP(c_Relation_ORange(_1596938, _1596940), _1596942) = hAPP(c_Relation_ODomain(_1596940, _1596938), hAPP(c_Relation_Oconverse(_1596938, _1596940), _1596942)))], (41513 ^ _782464) ^ [_1596983, _1596985, _1596987] : [-(hAPP(c_Relation_ODomain(_1596983, _1596985), hAPP(c_Relation_Oconverse(_1596985, _1596983), _1596987)) = hAPP(c_Relation_ORange(_1596985, _1596983), _1596987))], (41515 ^ _782464) ^ [_1597028, _1597030, _1597032] : [-(hAPP(c_Relation_ORange(_1597028, _1597030), hAPP(c_Relation_Oconverse(_1597030, _1597028), _1597032)) = hAPP(c_Relation_ODomain(_1597030, _1597028), _1597032))], (41517 ^ _782464) ^ [_1597073, _1597075, _1597077, _1597079] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597073, _1597073)), hAPP(hAPP(c_Product__Type_OPair(_1597073, _1597073), _1597075), _1597077)), c_Transitive__Closure_Ortrancl(_1597073, _1597079))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597073, _1597073)), hAPP(hAPP(c_Product__Type_OPair(_1597073, _1597073), _1597077), _1597075)), c_Transitive__Closure_Ortrancl(_1597073, hAPP(c_Relation_Oconverse(_1597073, _1597073), _1597079)))))], (41523 ^ _782464) ^ [_1597254, _1597256, _1597258, _1597260] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597254, _1597254)), hAPP(hAPP(c_Product__Type_OPair(_1597254, _1597254), _1597256), _1597258)), c_Transitive__Closure_Ortrancl(_1597254, hAPP(c_Relation_Oconverse(_1597254, _1597254), _1597260)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597254, _1597254)), hAPP(hAPP(c_Product__Type_OPair(_1597254, _1597254), _1597258), _1597256)), c_Transitive__Closure_Ortrancl(_1597254, _1597260))))], (41529 ^ _782464) ^ [_1597435, _1597437, _1597439, _1597441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597435, _1597435)), hAPP(hAPP(c_Product__Type_OPair(_1597435, _1597435), _1597437), _1597439)), hAPP(c_Relation_Oconverse(_1597435, _1597435), c_Transitive__Closure_Otrancl(_1597435, _1597441)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597435, _1597435)), hAPP(hAPP(c_Product__Type_OPair(_1597435, _1597435), _1597437), _1597439)), c_Transitive__Closure_Otrancl(_1597435, hAPP(c_Relation_Oconverse(_1597435, _1597435), _1597441)))))], (41535 ^ _782464) ^ [_1597628, _1597630, _1597632, _1597634] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597628, _1597628)), hAPP(hAPP(c_Product__Type_OPair(_1597628, _1597628), _1597630), _1597632)), c_Transitive__Closure_Otrancl(_1597628, hAPP(c_Relation_Oconverse(_1597628, _1597628), _1597634)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597628, _1597628)), hAPP(hAPP(c_Product__Type_OPair(_1597628, _1597628), _1597630), _1597632)), hAPP(c_Relation_Oconverse(_1597628, _1597628), c_Transitive__Closure_Otrancl(_1597628, _1597634)))))], (41541 ^ _782464) ^ [_1597845, _1597847, _1597849, _1597851, _1597853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597845, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1597847, _1597845, _1597849), _1597851)), _1597853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597847, tc_HOL_Obool)), _1597851), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1597847, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1597845, _1597847, hAPP(c_Relation_Oconverse(_1597847, _1597845), _1597849)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1597845, tc_HOL_Obool)), _1597853))))))], (41547 ^ _782464) ^ [_1598036, _1598038, _1598040, _1598042, _1598044] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598038, tc_HOL_Obool)), _1598042), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598038, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598036, _1598038, hAPP(c_Relation_Oconverse(_1598038, _1598036), _1598040)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598036, tc_HOL_Obool)), _1598044))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598036, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598038, _1598036, _1598040), _1598042)), _1598044)))], (41553 ^ _782464) ^ [_1598233, _1598235, _1598237] : [c_Relation_Orefl__on(_1598233, _1598235, _1598237), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598233, _1598233), tc_HOL_Obool)), _1598237), hAPP(hAPP(c_Relation_Orel__comp(_1598233, _1598233, _1598233), hAPP(c_Relation_Oconverse(_1598233, _1598233), _1598237)), _1598237))))], (41559 ^ _782464) ^ [_1598372, _1598374, _1598376] : [hAPP(hAPP(c_Relation_Orel__comp(_1598372, _1598372, _1598372), hAPP(c_Relation_Oconverse(_1598372, _1598372), _1598374)), _1598374) = _1598374, hAPP(c_Relation_ODomain(_1598372, _1598372), _1598374) = _1598376, -(c_Equiv__Relations_Oequiv(_1598372, _1598376, _1598374))], (41569 ^ _782464) ^ [_1598551, _1598553] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1598551, _1598551)), _1598553)), c_Wellfounded_Oacyclic(_1598551, _1598553), -(c_Wellfounded_Owf(_1598551, hAPP(c_Relation_Oconverse(_1598551, _1598551), _1598553)))], (41579 ^ _782464) ^ [_1598706, _1598708, _1598710] : [-(hAPP(c_Relation_Oconverse(_1598706, _1598708), _1598710) = hAPP(c_Set_OCollect(tc_prod(_1598708, _1598706)), hAPP(c_Product__Type_Oprod_Oprod__case(_1598708, _1598706, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1598708, tc_fun(tc_prod(_1598706, _1598708), tc_HOL_Obool), tc_fun(_1598706, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598706, tc_fun(tc_fun(tc_prod(_1598706, _1598708), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598706, _1598708), tc_HOL_Obool), tc_fun(_1598706, tc_HOL_Obool)), _1598708), c_COMBC(_1598706, tc_fun(tc_prod(_1598706, _1598708), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598706, tc_prod(_1598706, _1598708)), tc_fun(_1598706, tc_fun(tc_fun(tc_prod(_1598706, _1598708), tc_HOL_Obool), tc_HOL_Obool)), _1598708), hAPP(c_COMBB(tc_prod(_1598706, _1598708), tc_fun(tc_fun(tc_prod(_1598706, _1598708), tc_HOL_Obool), tc_HOL_Obool), _1598706), c_member(tc_prod(_1598706, _1598708)))), hAPP(c_COMBC(_1598706, _1598708, tc_prod(_1598706, _1598708)), c_Product__Type_OPair(_1598706, _1598708))))), _1598710))))], (41581 ^ _782464) ^ [_1598882, _1598884, _1598886, _1598888, _1598890, _1598892] : [c_Relation_Osingle__valued(_1598882, _1598884, hAPP(c_Relation_Oconverse(_1598884, _1598882), _1598886)), -(_1598888 = c_Orderings_Obot__class_Obot(tc_fun(_1598890, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1598884, _1598882, _1598886), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598890, tc_fun(_1598884, tc_HOL_Obool)), _1598888), _1598892)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598890, tc_fun(_1598882, tc_HOL_Obool)), _1598888), hAPP(hAPP(c_COMBB(tc_fun(_1598884, tc_HOL_Obool), tc_fun(_1598882, tc_HOL_Obool), _1598890), c_Relation_OImage(_1598884, _1598882, _1598886)), _1598892)))], (41591 ^ _782464) ^ [_1599126, _1599128, _1599130] : [c_Relation_Ototal__on(_1599126, _1599128, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599126, _1599126), tc_HOL_Obool)), _1599130), c_Relation_OId(_1599126))), -(c_Relation_Ototal__on(_1599126, _1599128, _1599130))], (41597 ^ _782464) ^ [_1599237, _1599239, _1599241] : [c_Relation_Ototal__on(_1599237, _1599239, _1599241), -(c_Relation_Ototal__on(_1599237, _1599239, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599237, _1599237), tc_HOL_Obool)), _1599241), c_Relation_OId(_1599237))))], (41603 ^ _782464) ^ [_1599354] : [-(c_Relation_Osingle__valued(_1599354, _1599354, c_Relation_OId(_1599354)))], (41605 ^ _782464) ^ [_1599380, _1599382, _1599384, _1599386, _1599388] : [c_Relation_Osingle__valued(_1599380, _1599382, _1599384), c_Relation_Osingle__valued(_1599382, _1599386, _1599388), -(c_Relation_Osingle__valued(_1599380, _1599386, hAPP(hAPP(c_Relation_Orel__comp(_1599380, _1599382, _1599386), _1599384), _1599388)))], (41615 ^ _782464) ^ [_1599547, _1599549, _1599551, _1599553] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1599547, _1599549), tc_HOL_Obool)), _1599551), _1599553)), c_Relation_Osingle__valued(_1599547, _1599549, _1599553), -(c_Relation_Osingle__valued(_1599547, _1599549, _1599551))], (41625 ^ _782464) ^ [_1599714, _1599716] : [-(c_Relation_Osingle__valued(_1599714, _1599714, c_Relation_OId__on(_1599714, _1599716)))], (41627 ^ _782464) ^ [_1599743, _1599745] : [-(c_Relation_Ototal__on(_1599743, c_Orderings_Obot__class_Obot(tc_fun(_1599743, tc_HOL_Obool)), _1599745))], (41629 ^ _782464) ^ [_1599792, _1599794, _1599796] : [c_Relation_Ototal__on(_1599792, _1599794, hAPP(c_Relation_Oconverse(_1599792, _1599792), _1599796)), -(c_Relation_Ototal__on(_1599792, _1599794, _1599796))], (41635 ^ _782464) ^ [_1599883, _1599885, _1599887] : [c_Relation_Ototal__on(_1599883, _1599885, _1599887), -(c_Relation_Ototal__on(_1599883, _1599885, hAPP(c_Relation_Oconverse(_1599883, _1599883), _1599887)))], (41655 ^ _782464) ^ [_1600372, _1600374, _1600376] : [41658 ^ _782464 : [(41659 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600372, _1600374)), hAPP(hAPP(c_Product__Type_OPair(_1600372, _1600374), 41656 ^ [_1600372, _1600374, _1600376]), 41657 ^ [_1600372, _1600374, _1600376])), _1600376)))], (41662 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600372, _1600374)), hAPP(hAPP(c_Product__Type_OPair(_1600372, _1600374), 41656 ^ [_1600372, _1600374, _1600376]), 41660 ^ [_1600372, _1600374, _1600376])), _1600376)))], (41664 ^ _782464) ^ [] : [41657 ^ [_1600372, _1600374, _1600376] = 41660 ^ [_1600372, _1600374, _1600376]]], -(c_Relation_Osingle__valued(_1600372, _1600374, _1600376))], (41641 ^ _782464) ^ [_1599998, _1600000, _1600002] : [c_Relation_Osingle__valued(_1599998, _1600000, _1600002), 41644 ^ _782464 : [(41645 ^ _782464) ^ [_1600119, _1600121] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599998, _1600000)), hAPP(hAPP(c_Product__Type_OPair(_1599998, _1600000), _1600121), _1600119)), _1600002)), 41648 ^ _782464 : [(41649 ^ _782464) ^ [_1600245] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599998, _1600000)), hAPP(hAPP(c_Product__Type_OPair(_1599998, _1600000), _1600121), _1600245)), _1600002)), -(_1600119 = _1600245)]]]]], (41668 ^ _782464) ^ [_1600742, _1600744, _1600746, _1600748, _1600750, _1600752] : [c_Relation_Osingle__valued(_1600742, _1600744, _1600746), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600742, _1600744)), hAPP(hAPP(c_Product__Type_OPair(_1600742, _1600744), _1600748), _1600750)), _1600746)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600742, _1600744)), hAPP(hAPP(c_Product__Type_OPair(_1600742, _1600744), _1600748), _1600752)), _1600746)), -(_1600750 = _1600752)], (41704 ^ _782464) ^ [_1601532, _1601534, _1601536] : [41706 ^ _782464 : [(41707 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601532), 41705 ^ [_1601532, _1601534, _1601536]), _1601534)))], (41710 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601532), 41708 ^ [_1601532, _1601534, _1601536]), _1601534)))], (41712 ^ _782464) ^ [] : [41705 ^ [_1601532, _1601534, _1601536] = 41708 ^ [_1601532, _1601534, _1601536]], (41714 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601532, _1601532)), hAPP(hAPP(c_Product__Type_OPair(_1601532, _1601532), 41705 ^ [_1601532, _1601534, _1601536]), 41708 ^ [_1601532, _1601534, _1601536])), _1601536))], (41716 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601532, _1601532)), hAPP(hAPP(c_Product__Type_OPair(_1601532, _1601532), 41708 ^ [_1601532, _1601534, _1601536]), 41705 ^ [_1601532, _1601534, _1601536])), _1601536))]], -(c_Relation_Ototal__on(_1601532, _1601534, _1601536))], (41682 ^ _782464) ^ [_1601043, _1601045, _1601047] : [c_Relation_Ototal__on(_1601043, _1601045, _1601047), 41685 ^ _782464 : [(41686 ^ _782464) ^ [_1601187] : [hBOOL(hAPP(hAPP(c_member(_1601043), _1601187), _1601045)), 41689 ^ _782464 : [(41690 ^ _782464) ^ [_1601327] : [hBOOL(hAPP(hAPP(c_member(_1601043), _1601327), _1601045)), -(_1601187 = _1601327), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601043, _1601043)), hAPP(hAPP(c_Product__Type_OPair(_1601043, _1601043), _1601187), _1601327)), _1601047))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601043, _1601043)), hAPP(hAPP(c_Product__Type_OPair(_1601043, _1601043), _1601327), _1601187)), _1601047)))]]]]], (41720 ^ _782464) ^ [_1602114, _1602116, _1602118, _1602120, _1602122] : [c_Relation_Osingle__valued(_1602114, _1602114, _1602116), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602114, _1602114)), hAPP(hAPP(c_Product__Type_OPair(_1602114, _1602114), _1602118), _1602120)), c_Transitive__Closure_Ortrancl(_1602114, _1602116))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602114, _1602114)), hAPP(hAPP(c_Product__Type_OPair(_1602114, _1602114), _1602118), _1602122)), c_Transitive__Closure_Ortrancl(_1602114, _1602116))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602114, _1602114)), hAPP(hAPP(c_Product__Type_OPair(_1602114, _1602114), _1602120), _1602122)), c_Transitive__Closure_Ortrancl(_1602114, _1602116)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602114, _1602114)), hAPP(hAPP(c_Product__Type_OPair(_1602114, _1602114), _1602122), _1602120)), c_Transitive__Closure_Ortrancl(_1602114, _1602116))))], (41738 ^ _782464) ^ [_1602504, _1602506, _1602508, _1602510, _1602512] : [c_Relation_Osingle__valued(_1602504, _1602506, hAPP(c_Relation_Oconverse(_1602506, _1602504), _1602508)), -(hAPP(c_Relation_OImage(_1602506, _1602504, _1602508), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602506, tc_HOL_Obool)), _1602510), _1602512)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602504, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1602506, _1602504, _1602508), _1602510)), hAPP(c_Relation_OImage(_1602506, _1602504, _1602508), _1602512)))], (41744 ^ _782464) ^ [_1602687, _1602689, _1602691] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602687, _1602687)), _1602689), c_Transitive__Closure_Ortrancl(_1602687, _1602691))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602687, _1602687)), _1602689), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1602687, _1602687), 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(_1602687, _1602687), tc_HOL_Obool), tc_fun(tc_prod(_1602687, _1602687), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1602687, _1602687), tc_HOL_Obool)), _1602691)))))], (41750 ^ _782464) ^ [_1602894, _1602896] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602894, _1602894)), hAPP(hAPP(c_Product__Type_OPair(_1602894, _1602894), 41751 ^ [_1602894, _1602896]), 41751 ^ [_1602894, _1602896])), c_Transitive__Closure_Otrancl(_1602894, _1602896)))), -(c_Wellfounded_Oacyclic(_1602894, _1602896))], (41757 ^ _782464) ^ [_1602966, _1602968, _1602970] : [c_Relation_Osingle__valued(_1602966, _1602966, _1602968), -(c_Relation_Osingle__valued(_1602966, _1602966, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602966, _1602966), tc_HOL_Obool), _1602970), _1602968)))], (41763 ^ _782464) ^ [_1603073, _1603075, _1603077] : [c_Wellfounded_Owf(_1603073, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603073, _1603073), tc_HOL_Obool), _1603075), _1603077)), -(c_Wellfounded_Owf(_1603073, _1603077))], (41769 ^ _782464) ^ [_1603176, _1603178, _1603180, _1603182] : [-(hAPP(hAPP(c_Nat_Ocompow(_1603176, _1603176), _1603178), hAPP(hAPP(c_Nat_Ocompow(_1603176, _1603176), _1603180), _1603182)) = hAPP(hAPP(c_Nat_Ocompow(_1603176, _1603176), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1603180), _1603178)), _1603182))], (41771 ^ _782464) ^ [_1603238, _1603240, _1603242, _1603244] : [-(hAPP(_1603238, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603240, _1603240), _1603242), _1603238), _1603244)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603240, _1603240), _1603242), _1603238), hAPP(_1603238, _1603244)))], (41773 ^ _782464) ^ [_1603297, _1603299, _1603301, _1603303] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1603297, _1603299), tc_fun(_1603297, _1603299)), _1603301), c_Fun_Ocomp(_1603299, _1603299, _1603297, _1603303)) = c_Fun_Ocomp(_1603299, _1603299, _1603297, hAPP(hAPP(c_Nat_Ocompow(_1603299, _1603299), _1603301), _1603303)))], (41775 ^ _782464) ^ [_1603360, _1603362] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603360, _1603360), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1603362) = _1603362)], (41777 ^ _782464) ^ [_1603397, _1603399, _1603401] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1603397, _1603397, _1603397), _1603399), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603397, _1603397), tc_HOL_Obool), _1603401), _1603399)) = hAPP(hAPP(c_Relation_Orel__comp(_1603397, _1603397, _1603397), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603397, _1603397), tc_HOL_Obool), _1603401), _1603399)), _1603399))], (41779 ^ _782464) ^ [_1603468, _1603470, _1603472, _1603474] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603468, _1603468)), _1603470), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603468, _1603468), tc_HOL_Obool), _1603472), _1603474))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603468, _1603468)), _1603470), c_Transitive__Closure_Ortrancl(_1603468, _1603474))))], (41785 ^ _782464) ^ [_1603637, _1603639, _1603641] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603637, _1603637)), _1603639), c_Transitive__Closure_Ortrancl(_1603637, _1603641))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603637, _1603637)), _1603639), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603637, _1603637), tc_HOL_Obool), 41788 ^ [_1603637, _1603639, _1603641]), _1603641))))], (41792 ^ _782464) ^ [_1603796, _1603798, _1603800] : [41793 ^ _782464 : [(41794 ^ _782464) ^ [_1603872] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603796, _1603796)), _1603798), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603796, _1603796), tc_HOL_Obool), _1603872), _1603800)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603796, _1603796)), _1603798), c_Transitive__Closure_Ortrancl(_1603796, _1603800))))], (41798 ^ _782464) ^ [_1603960, _1603962, _1603964] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603960, _1603960), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1603962)), _1603964) = hAPP(hAPP(c_Relation_Orel__comp(_1603960, _1603960, _1603960), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603960, _1603960), tc_HOL_Obool), _1603962), _1603964)), _1603964))], (41800 ^ _782464) ^ [_1604024, _1604026, _1604028, _1604030] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604024, _1604024), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1604026), _1604028)), _1604030) = hAPP(hAPP(c_Relation_Orel__comp(_1604024, _1604024, _1604024), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604024, _1604024), tc_HOL_Obool), _1604026), _1604030)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604024, _1604024), tc_HOL_Obool), _1604028), _1604030)))], (41802 ^ _782464) ^ [_1604105, _1604107] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604105, _1604105), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604107) = c_Relation_OId(_1604105))], (41804 ^ _782464) ^ [_1604144, _1604146, _1604148] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604144, _1604144)), hAPP(hAPP(c_Product__Type_OPair(_1604144, _1604144), _1604146), _1604146)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604144, _1604144), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604148))))], (41806 ^ _782464) ^ [_1604202, _1604204, _1604206, _1604208] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604202, _1604202)), hAPP(hAPP(c_Product__Type_OPair(_1604202, _1604202), _1604204), _1604206)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604202, _1604202), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604208))), -(_1604204 = _1604206)], (41812 ^ _782464) ^ [_1604345, _1604347, _1604349, _1604351, _1604353, _1604355] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604345, _1604345)), hAPP(hAPP(c_Product__Type_OPair(_1604345, _1604345), _1604347), _1604349)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604345, _1604345), tc_HOL_Obool), _1604351), _1604353))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604345, _1604345)), hAPP(hAPP(c_Product__Type_OPair(_1604345, _1604345), _1604349), _1604355)), _1604353)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604345, _1604345)), hAPP(hAPP(c_Product__Type_OPair(_1604345, _1604345), _1604347), _1604355)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604345, _1604345), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604351)), _1604353))))], (41822 ^ _782464) ^ [_1604658, _1604660, _1604662, _1604664, _1604666, _1604668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604658, _1604658)), hAPP(hAPP(c_Product__Type_OPair(_1604658, _1604658), _1604660), _1604662)), _1604664)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604658, _1604658)), hAPP(hAPP(c_Product__Type_OPair(_1604658, _1604658), _1604662), _1604666)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604658, _1604658), tc_HOL_Obool), _1604668), _1604664))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604658, _1604658)), hAPP(hAPP(c_Product__Type_OPair(_1604658, _1604658), _1604660), _1604666)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604658, _1604658), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604668)), _1604664))))], (41832 ^ _782464) ^ [_1604971, _1604973, _1604975] : [-(hAPP(hAPP(c_Nat_Ocompow(_1604971, _1604971), hAPP(c_Nat_OSuc, _1604973)), _1604975) = hAPP(c_Fun_Ocomp(_1604971, _1604971, _1604971, _1604975), hAPP(hAPP(c_Nat_Ocompow(_1604971, _1604971), _1604973), _1604975)))], (41834 ^ _782464) ^ [_1605027, _1605029, _1605031, _1605033] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605027, _1605027), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1605029), _1605031)), _1605033) = hAPP(c_Fun_Ocomp(_1605027, _1605027, _1605027, hAPP(hAPP(c_Nat_Ocompow(_1605027, _1605027), _1605029), _1605033)), hAPP(hAPP(c_Nat_Ocompow(_1605027, _1605027), _1605031), _1605033)))], (41836 ^ _782464) ^ [_1605097, _1605099] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605097, _1605097), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605099) = c_Fun_Oid(_1605097))], (41838 ^ _782464) ^ [_1605151, _1605153, _1605155] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605151, _1605151)), _1605153), c_Transitive__Closure_Otrancl(_1605151, _1605155))), 41842 ^ _782464 : [(41843 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41841 ^ [_1605151, _1605153, _1605155])))], (41845 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605151, _1605151)), _1605153), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605151, _1605151), tc_HOL_Obool), 41841 ^ [_1605151, _1605153, _1605155]), _1605155))))]]], (41847 ^ _782464) ^ [_1605349, _1605351, _1605353] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605349, _1605349)), _1605351), c_Transitive__Closure_Otrancl(_1605349, _1605353)))), 41848 ^ _782464 : [(41849 ^ _782464) ^ [_1605428] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605428)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1605349, _1605349)), _1605351), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605349, _1605349), tc_HOL_Obool), _1605428), _1605353)))]]], (41857 ^ _782464) ^ [_1605599, _1605601] : [-(c_Transitive__Closure_Ortrancl(_1605599, _1605601) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1605599, _1605599), 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(_1605599, _1605599), tc_HOL_Obool), tc_fun(tc_prod(_1605599, _1605599), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1605599, _1605599), tc_HOL_Obool)), _1605601)))], (41859 ^ _782464) ^ [_1605670] : [-(c_Nat_Ofunpow(_1605670) = c_Nat_Ocompow(_1605670, _1605670))], (41861 ^ _782464) ^ [_1605698, _1605700, _1605702, _1605704, _1605706] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605698, _1605698)), hAPP(hAPP(c_Product__Type_OPair(_1605698, _1605698), _1605700), _1605702)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605698, _1605698), tc_HOL_Obool), _1605704), _1605706))), 41866 ^ _782464 : [(41867 ^ _782464) ^ [] : [-(_1605704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41869 ^ _782464) ^ [] : [-(_1605700 = _1605702)]], 41872 ^ _782464 : [(41873 ^ _782464) ^ [] : [-(_1605704 = hAPP(c_Nat_OSuc, 41871 ^ [_1605698, _1605700, _1605702, _1605704, _1605706]))], (41875 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605698, _1605698)), hAPP(hAPP(c_Product__Type_OPair(_1605698, _1605698), _1605700), 41870 ^ [_1605698, _1605700, _1605702, _1605704, _1605706])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605698, _1605698), tc_HOL_Obool), 41871 ^ [_1605698, _1605700, _1605702, _1605704, _1605706]), _1605706))))], (41877 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605698, _1605698)), hAPP(hAPP(c_Product__Type_OPair(_1605698, _1605698), 41870 ^ [_1605698, _1605700, _1605702, _1605704, _1605706]), _1605702)), _1605706)))]]], (41879 ^ _782464) ^ [_1606140, _1606142, _1606144, _1606146, _1606148] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606140, _1606140)), hAPP(hAPP(c_Product__Type_OPair(_1606140, _1606140), _1606142), _1606144)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606140, _1606140), tc_HOL_Obool), _1606146), _1606148))), 41884 ^ _782464 : [(41885 ^ _782464) ^ [] : [-(_1606146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41887 ^ _782464) ^ [] : [-(_1606142 = _1606144)]], 41890 ^ _782464 : [(41891 ^ _782464) ^ [] : [-(_1606146 = hAPP(c_Nat_OSuc, 41889 ^ [_1606140, _1606142, _1606144, _1606146, _1606148]))], (41893 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606140, _1606140)), hAPP(hAPP(c_Product__Type_OPair(_1606140, _1606140), _1606142), 41888 ^ [_1606140, _1606142, _1606144, _1606146, _1606148])), _1606148)))], (41895 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606140, _1606140)), hAPP(hAPP(c_Product__Type_OPair(_1606140, _1606140), 41888 ^ [_1606140, _1606142, _1606144, _1606146, _1606148]), _1606144)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606140, _1606140), tc_HOL_Obool), 41889 ^ [_1606140, _1606142, _1606144, _1606146, _1606148]), _1606148))))]]], (41897 ^ _782464) ^ [_1606582, _1606584, _1606586, _1606588, _1606590] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606582, _1606582)), hAPP(hAPP(c_Product__Type_OPair(_1606582, _1606582), _1606584), _1606586)), c_Transitive__Closure_Ortrancl(_1606582, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1606582, _1606582), tc_HOL_Obool)), _1606588), _1606590)))), 41903 ^ _782464 : [(41904 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606582, _1606582)), hAPP(hAPP(c_Product__Type_OPair(_1606582, _1606582), 41902 ^ [_1606582, _1606584, _1606586, _1606588, _1606590]), _1606586)), c_Transitive__Closure_Ortrancl(_1606582, _1606588))))], (41907 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606582, _1606582)), hAPP(hAPP(c_Product__Type_OPair(_1606582, _1606582), 41905 ^ [_1606582, _1606584, _1606586, _1606588, _1606590]), 41902 ^ [_1606582, _1606584, _1606586, _1606588, _1606590])), _1606590)))], (41909 ^ _782464) ^ [] : [41905 ^ [_1606582, _1606584, _1606586, _1606588, _1606590] = 41902 ^ [_1606582, _1606584, _1606586, _1606588, _1606590]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606582, _1606582)), hAPP(hAPP(c_Product__Type_OPair(_1606582, _1606582), _1606584), _1606586)), c_Transitive__Closure_Ortrancl(_1606582, _1606588))))], (41913 ^ _782464) ^ [_1607141, _1607143, _1607145, _1607147, _1607149] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607141, _1607141)), hAPP(hAPP(c_Product__Type_OPair(_1607141, _1607141), _1607143), _1607145)), c_Transitive__Closure_Ortrancl(_1607141, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607141, _1607141), tc_HOL_Obool)), _1607147), _1607149)))), 41919 ^ _782464 : [(41920 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607141, _1607141)), hAPP(hAPP(c_Product__Type_OPair(_1607141, _1607141), _1607143), 41918 ^ [_1607141, _1607143, _1607145, _1607147, _1607149])), c_Transitive__Closure_Ortrancl(_1607141, _1607147))))], (41923 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607141, _1607141)), hAPP(hAPP(c_Product__Type_OPair(_1607141, _1607141), 41918 ^ [_1607141, _1607143, _1607145, _1607147, _1607149]), 41921 ^ [_1607141, _1607143, _1607145, _1607147, _1607149])), _1607149)))], (41925 ^ _782464) ^ [] : [41918 ^ [_1607141, _1607143, _1607145, _1607147, _1607149] = 41921 ^ [_1607141, _1607143, _1607145, _1607147, _1607149]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607141, _1607141)), hAPP(hAPP(c_Product__Type_OPair(_1607141, _1607141), _1607143), _1607145)), c_Transitive__Closure_Ortrancl(_1607141, _1607147))))], (41929 ^ _782464) ^ [_1607700, _1607702, _1607704, _1607706, _1607708] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607700, _1607700)), hAPP(hAPP(c_Product__Type_OPair(_1607700, _1607700), _1607702), _1607704)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607700, _1607700), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1607706)), _1607708))), 41933 ^ _782464 : [(41934 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607700, _1607700)), hAPP(hAPP(c_Product__Type_OPair(_1607700, _1607700), _1607702), 41932 ^ [_1607700, _1607702, _1607704, _1607706, _1607708])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607700, _1607700), tc_HOL_Obool), _1607706), _1607708))))], (41936 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607700, _1607700)), hAPP(hAPP(c_Product__Type_OPair(_1607700, _1607700), 41932 ^ [_1607700, _1607702, _1607704, _1607706, _1607708]), _1607704)), _1607708)))]]], (41938 ^ _782464) ^ [_1608012, _1608014, _1608016, _1608018, _1608020] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608012, _1608012)), hAPP(hAPP(c_Product__Type_OPair(_1608012, _1608012), _1608014), _1608016)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608012, _1608012), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608018)), _1608020))), 41942 ^ _782464 : [(41943 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608012, _1608012)), hAPP(hAPP(c_Product__Type_OPair(_1608012, _1608012), _1608014), 41941 ^ [_1608012, _1608014, _1608016, _1608018, _1608020])), _1608020)))], (41945 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608012, _1608012)), hAPP(hAPP(c_Product__Type_OPair(_1608012, _1608012), 41941 ^ [_1608012, _1608014, _1608016, _1608018, _1608020]), _1608016)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608012, _1608012), tc_HOL_Obool), _1608018), _1608020))))]]], (41947 ^ _782464) ^ [_1608320, _1608322, _1608324, _1608326, _1608328] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608320, _1608320)), hAPP(hAPP(c_Product__Type_OPair(_1608320, _1608320), _1608322), _1608324)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608320, _1608320), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608326)), _1608328))), 41951 ^ _782464 : [(41952 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608320, _1608320)), hAPP(hAPP(c_Product__Type_OPair(_1608320, _1608320), _1608322), 41950 ^ [_1608320, _1608322, _1608324, _1608326, _1608328])), _1608328)))], (41954 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608320, _1608320)), hAPP(hAPP(c_Product__Type_OPair(_1608320, _1608320), 41950 ^ [_1608320, _1608322, _1608324, _1608326, _1608328]), _1608324)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608320, _1608320), tc_HOL_Obool), _1608326), _1608328))))]]], (41956 ^ _782464) ^ [_1608632, _1608634, _1608636, _1608638] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608632, _1608632)), hAPP(hAPP(c_Product__Type_OPair(_1608632, _1608632), _1608634), _1608636)), c_Transitive__Closure_Otrancl(_1608632, _1608638))), 41960 ^ _782464 : [(41961 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608632, _1608632)), hAPP(hAPP(c_Product__Type_OPair(_1608632, _1608632), _1608634), 41959 ^ [_1608632, _1608634, _1608636, _1608638])), c_Transitive__Closure_Ortrancl(_1608632, _1608638))))], (41963 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608632, _1608632)), hAPP(hAPP(c_Product__Type_OPair(_1608632, _1608632), 41959 ^ [_1608632, _1608634, _1608636, _1608638]), _1608636)), _1608638)))]]], (41965 ^ _782464) ^ [_1608892, _1608894, _1608896, _1608898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608892, _1608892)), hAPP(hAPP(c_Product__Type_OPair(_1608892, _1608892), _1608894), _1608896)), c_Transitive__Closure_Otrancl(_1608892, _1608898))), 41969 ^ _782464 : [(41970 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608892, _1608892)), hAPP(hAPP(c_Product__Type_OPair(_1608892, _1608892), _1608894), 41968 ^ [_1608892, _1608894, _1608896, _1608898])), _1608898)))], (41972 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608892, _1608892)), hAPP(hAPP(c_Product__Type_OPair(_1608892, _1608892), 41968 ^ [_1608892, _1608894, _1608896, _1608898]), _1608896)), c_Transitive__Closure_Ortrancl(_1608892, _1608898))))]]], (41974 ^ _782464) ^ [_1609152, _1609154] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609152, _1609152)), _1609154), c_Relation_OId(_1609152))), -(_1609154 = hAPP(hAPP(c_Product__Type_OPair(_1609152, _1609152), 41977 ^ [_1609152, _1609154]), 41977 ^ [_1609152, _1609154]))], (41981 ^ _782464) ^ [_1609294, _1609296, _1609298] : [class_Orderings_Olinorder(_1609294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609294), _1609296)), -(hBOOL(hAPP(hAPP(c_member(_1609294), _1609298), _1609296))), -(c_Big__Operators_Olattice_OSup__fin(_1609294, c_Orderings_Oord__class_Omax(_1609294), hAPP(hAPP(c_Set_Oinsert(_1609294), _1609298), _1609296)) = hAPP(hAPP(c_Finite__Set_Ofold(_1609294, _1609294, c_Orderings_Oord__class_Omax(_1609294)), _1609298), _1609296))], (41995 ^ _782464) ^ [_1609514, _1609516, _1609518, _1609520, _1609522, _1609524] : [c_Finite__Set_Ofolding(_1609514, _1609516, _1609518, _1609520), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609514), _1609522)), -(hAPP(hAPP(_1609520, _1609522), _1609524) = hAPP(hAPP(c_Finite__Set_Ofold(_1609514, _1609516, _1609518), _1609524), _1609522))], (42005 ^ _782464) ^ [_1609703, _1609705, _1609707, _1609709] : [-(hAPP(c_Finite__Set_Ofold__image(_1609703, _1609705, _1609707), _1609709) = c_Finite__Set_Ofold(_1609705, _1609703, hAPP(hAPP(c_COMBB(_1609703, tc_fun(_1609703, _1609703), _1609705), _1609707), _1609709)))], (42007 ^ _782464) ^ [_1609756, _1609758, _1609760, _1609762] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1609756, _1609758, _1609760), _1609762), c_Orderings_Obot__class_Obot(tc_fun(_1609756, tc_HOL_Obool))) = _1609762)], (42009 ^ _782464) ^ [_1609800, _1609802, _1609804, _1609806, _1609808] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1609800, _1609802, _1609804), _1609806), _1609808) = c_HOL_OThe(_1609802, c_Finite__Set_Ofold__graph(_1609800, _1609802, _1609804, _1609806, _1609808)))], (42011 ^ _782464) ^ [_1609850, _1609852, _1609854] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1609850), _1609852)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609850, tc_HOL_Obool)), _1609852), _1609854) = hAPP(hAPP(c_Finite__Set_Ofold(_1609850, tc_fun(_1609850, tc_HOL_Obool), c_Set_Oinsert(_1609850)), _1609854), _1609852))], (42017 ^ _782464) ^ [_1609989, _1609991, _1609993, _1609995] : [class_Lattices_Osemilattice__sup(_1609989), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609989), _1609991)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1609989, _1609989, c_Lattices_Osemilattice__sup__class_Osup(_1609989)), _1609993), hAPP(hAPP(c_Set_Oinsert(_1609989), _1609995), _1609991)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1609989), _1609995), hAPP(hAPP(c_Finite__Set_Ofold(_1609989, _1609989, c_Lattices_Osemilattice__sup__class_Osup(_1609989)), _1609993), _1609991)))], (42027 ^ _782464) ^ [_1610212, _1610214, _1610216, _1610218] : [class_Lattices_Osemilattice__inf(_1610212), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610212), _1610214)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610212, _1610212, c_Lattices_Osemilattice__inf__class_Oinf(_1610212)), _1610216), hAPP(hAPP(c_Set_Oinsert(_1610212), _1610218), _1610214)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1610212), _1610218), hAPP(hAPP(c_Finite__Set_Ofold(_1610212, _1610212, c_Lattices_Osemilattice__inf__class_Oinf(_1610212)), _1610216), _1610214)))], (42037 ^ _782464) ^ [_1610435, _1610437, _1610439, _1610441] : [class_Orderings_Olinorder(_1610435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610435), _1610437)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610435, _1610435, c_Orderings_Oord__class_Omin(_1610435)), _1610439), hAPP(hAPP(c_Set_Oinsert(_1610435), _1610441), _1610437)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1610435), _1610441), hAPP(hAPP(c_Finite__Set_Ofold(_1610435, _1610435, c_Orderings_Oord__class_Omin(_1610435)), _1610439), _1610437)))], (42047 ^ _782464) ^ [_1610658, _1610660, _1610662, _1610664] : [class_Orderings_Olinorder(_1610658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610658), _1610660)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610658, _1610658, c_Orderings_Oord__class_Omax(_1610658)), _1610662), hAPP(hAPP(c_Set_Oinsert(_1610658), _1610664), _1610660)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1610658), _1610664), hAPP(hAPP(c_Finite__Set_Ofold(_1610658, _1610658, c_Orderings_Oord__class_Omax(_1610658)), _1610662), _1610660)))], (42057 ^ _782464) ^ [_1610881, _1610883, _1610885] : [class_Complete__Lattice_Ocomplete__lattice(_1610881), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610881), _1610883)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1610881), _1610885), c_Complete__Lattice_OSup__class_OSup(_1610881, _1610883)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610881, _1610881, c_Lattices_Osemilattice__sup__class_Osup(_1610881)), _1610885), _1610883))], (42067 ^ _782464) ^ [_1611066, _1611068, _1611070] : [class_Complete__Lattice_Ocomplete__lattice(_1611066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611066), _1611068)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1611066), _1611070), c_Complete__Lattice_OInf__class_OInf(_1611066, _1611068)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611066, _1611066, c_Lattices_Osemilattice__inf__class_Oinf(_1611066)), _1611070), _1611068))], (42077 ^ _782464) ^ [_1611251, _1611253, _1611255, _1611257, _1611259, _1611261] : [c_Finite__Set_Ofun__left__comm__idem(_1611251, _1611253, _1611255), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611251), _1611257)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1611251, _1611253, _1611255), _1611259), hAPP(hAPP(c_Set_Oinsert(_1611251), _1611261), _1611257)) = hAPP(hAPP(_1611255, _1611261), hAPP(hAPP(c_Finite__Set_Ofold(_1611251, _1611253, _1611255), _1611259), _1611257)))], (42087 ^ _782464) ^ [_1611474, _1611476, _1611478, _1611480, _1611482, _1611484] : [c_Finite__Set_Ofun__left__comm__idem(_1611474, _1611476, _1611478), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611474), _1611480)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1611474, _1611476, _1611478), _1611482), hAPP(hAPP(c_Set_Oinsert(_1611474), _1611484), _1611480)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611474, _1611476, _1611478), hAPP(hAPP(_1611478, _1611484), _1611482)), _1611480))], (42097 ^ _782464) ^ [_1611697, _1611699, _1611701, _1611703, _1611705] : [class_Complete__Lattice_Ocomplete__lattice(_1611697), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611699), _1611701)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1611697), _1611703), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611699, _1611697), _1611701), _1611705)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611699, _1611697, hAPP(hAPP(c_COMBB(_1611697, tc_fun(_1611697, _1611697), _1611699), c_Lattices_Osemilattice__sup__class_Osup(_1611697)), _1611705)), _1611703), _1611701))], (42107 ^ _782464) ^ [_1611928, _1611930, _1611932, _1611934, _1611936] : [class_Complete__Lattice_Ocomplete__lattice(_1611928), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611930), _1611932)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1611928), _1611934), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611930, _1611928), _1611932), _1611936)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611930, _1611928, hAPP(hAPP(c_COMBB(_1611928, tc_fun(_1611928, _1611928), _1611930), c_Lattices_Osemilattice__inf__class_Oinf(_1611928)), _1611936)), _1611934), _1611932))], (42117 ^ _782464) ^ [_1612159, _1612161, _1612163, _1612165, _1612167] : [c_Finite__Set_Ofolding__one__idem(_1612159, _1612161, _1612163), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612159), _1612165)), -(hAPP(_1612163, hAPP(hAPP(c_Set_Oinsert(_1612159), _1612167), _1612165)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612159, _1612159, _1612161), _1612167), _1612165))], (42127 ^ _782464) ^ [_1612352, _1612354, _1612356, _1612358] : [class_Lattices_Osemilattice__sup(_1612352), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612352), _1612354)), hBOOL(hAPP(hAPP(c_member(_1612352), _1612356), _1612354)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612352), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1612352), _1612356), _1612358)), hAPP(hAPP(c_Finite__Set_Ofold(_1612352, _1612352, c_Lattices_Osemilattice__sup__class_Osup(_1612352)), _1612358), _1612354))))], (42141 ^ _782464) ^ [_1612619, _1612621, _1612623, _1612625] : [class_Lattices_Osemilattice__inf(_1612619), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612619), _1612621)), hBOOL(hAPP(hAPP(c_member(_1612619), _1612623), _1612621)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612619), hAPP(hAPP(c_Finite__Set_Ofold(_1612619, _1612619, c_Lattices_Osemilattice__inf__class_Oinf(_1612619)), _1612625), _1612621)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1612619), _1612623), _1612625))))], (42155 ^ _782464) ^ [_1612886, _1612888, _1612890, _1612892] : [class_Orderings_Olinorder(_1612886), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612886), _1612888)), hBOOL(hAPP(hAPP(c_member(_1612886), _1612890), _1612888)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612886), hAPP(hAPP(c_Finite__Set_Ofold(_1612886, _1612886, c_Orderings_Oord__class_Omin(_1612886)), _1612892), _1612888)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1612886), _1612890), _1612892))))], (42169 ^ _782464) ^ [_1613153, _1613155, _1613157, _1613159] : [class_Orderings_Olinorder(_1613153), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613153), _1613155)), hBOOL(hAPP(hAPP(c_member(_1613153), _1613157), _1613155)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613153), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1613153), _1613157), _1613159)), hAPP(hAPP(c_Finite__Set_Ofold(_1613153, _1613153, c_Orderings_Oord__class_Omax(_1613153)), _1613159), _1613155))))], (42183 ^ _782464) ^ [_1613420, _1613422] : [class_Complete__Lattice_Ocomplete__lattice(_1613420), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613420), _1613422)), -(c_Complete__Lattice_OSup__class_OSup(_1613420, _1613422) = hAPP(hAPP(c_Finite__Set_Ofold(_1613420, _1613420, c_Lattices_Osemilattice__sup__class_Osup(_1613420)), c_Orderings_Obot__class_Obot(_1613420)), _1613422))], (42193 ^ _782464) ^ [_1613589, _1613591] : [class_Complete__Lattice_Ocomplete__lattice(_1613589), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613589), _1613591)), -(c_Complete__Lattice_OInf__class_OInf(_1613589, _1613591) = hAPP(hAPP(c_Finite__Set_Ofold(_1613589, _1613589, c_Lattices_Osemilattice__inf__class_Oinf(_1613589)), c_Orderings_Otop__class_Otop(_1613589)), _1613591))], (42203 ^ _782464) ^ [_1613758, _1613760, _1613762] : [class_Lattices_Oab__semigroup__idem__mult(_1613758), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613758), _1613760)), -(hAPP(c_Finite__Set_Ofold1(_1613758, c_Groups_Otimes__class_Otimes(_1613758)), hAPP(hAPP(c_Set_Oinsert(_1613758), _1613762), _1613760)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613758, _1613758, c_Groups_Otimes__class_Otimes(_1613758)), _1613762), _1613760))], (42213 ^ _782464) ^ [_1613953, _1613955, _1613957] : [class_Lattices_Olattice(_1613953), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613953), _1613955)), -(c_Big__Operators_Olattice__class_OSup__fin(_1613953, hAPP(hAPP(c_Set_Oinsert(_1613953), _1613957), _1613955)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613953, _1613953, c_Lattices_Osemilattice__sup__class_Osup(_1613953)), _1613957), _1613955))], (42223 ^ _782464) ^ [_1614138, _1614140, _1614142] : [class_Lattices_Olattice(_1614138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614138), _1614140)), -(c_Big__Operators_Olattice__class_OInf__fin(_1614138, hAPP(hAPP(c_Set_Oinsert(_1614138), _1614142), _1614140)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614138, _1614138, c_Lattices_Osemilattice__inf__class_Oinf(_1614138)), _1614142), _1614140))], (42233 ^ _782464) ^ [_1614323, _1614325, _1614327] : [class_Orderings_Olinorder(_1614323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614323), _1614325)), -(c_Big__Operators_Olinorder__class_OMin(_1614323, hAPP(hAPP(c_Set_Oinsert(_1614323), _1614327), _1614325)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614323, _1614323, c_Orderings_Oord__class_Omin(_1614323)), _1614327), _1614325))], (42243 ^ _782464) ^ [_1614508, _1614510, _1614512] : [class_Orderings_Olinorder(_1614508), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614508), _1614510)), -(c_Big__Operators_Olinorder__class_OMax(_1614508, hAPP(hAPP(c_Set_Oinsert(_1614508), _1614512), _1614510)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614508, _1614508, c_Orderings_Oord__class_Omax(_1614508)), _1614512), _1614510))], (42253 ^ _782464) ^ [_1614693, _1614695, _1614697] : [class_Orderings_Olinorder(_1614693), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614693), _1614695)), -(c_Big__Operators_Olattice_OInf__fin(_1614693, c_Orderings_Oord__class_Omin(_1614693), hAPP(hAPP(c_Set_Oinsert(_1614693), _1614697), _1614695)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614693, _1614693, c_Orderings_Oord__class_Omin(_1614693)), _1614697), _1614695))], (42263 ^ _782464) ^ [_1614884, _1614886, _1614888] : [class_Orderings_Olinorder(_1614884), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614884), _1614886)), -(c_Big__Operators_Olattice_OSup__fin(_1614884, c_Orderings_Oord__class_Omax(_1614884), hAPP(hAPP(c_Set_Oinsert(_1614884), _1614888), _1614886)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614884, _1614884, c_Orderings_Oord__class_Omax(_1614884)), _1614888), _1614886))], (42273 ^ _782464) ^ [_1615075, _1615077, _1615079] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1615075), _1615077)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615075, tc_HOL_Obool)), _1615079), _1615077) = hAPP(hAPP(c_Finite__Set_Ofold(_1615075, tc_fun(_1615075, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1615075, tc_HOL_Obool), tc_fun(tc_fun(_1615075, tc_HOL_Obool), tc_fun(_1615075, tc_HOL_Obool)), _1615075), hAPP(c_COMBC(tc_fun(_1615075, tc_HOL_Obool), tc_fun(_1615075, tc_HOL_Obool), tc_fun(_1615075, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1615075, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1615075, tc_fun(_1615075, tc_HOL_Obool), tc_fun(_1615075, tc_HOL_Obool)), c_Set_Oinsert(_1615075)), c_Orderings_Obot__class_Obot(tc_fun(_1615075, tc_HOL_Obool))))), _1615079), _1615077))], (42279 ^ _782464) ^ [_1615342, _1615344, _1615346, _1615348, _1615350] : [c_Finite__Set_Ofolding__one(_1615342, _1615344, _1615346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615342), _1615348)), -(hBOOL(hAPP(hAPP(c_member(_1615342), _1615350), _1615348))), -(hAPP(_1615346, hAPP(hAPP(c_Set_Oinsert(_1615342), _1615350), _1615348)) = hAPP(hAPP(c_Finite__Set_Ofold(_1615342, _1615342, _1615344), _1615350), _1615348))], (42293 ^ _782464) ^ [_1615564, _1615566, _1615568, _1615570] : [class_Complete__Lattice_Ocomplete__lattice(_1615564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615566), _1615568)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615566, _1615564), _1615568), _1615570) = hAPP(hAPP(c_Finite__Set_Ofold(_1615566, _1615564, hAPP(hAPP(c_COMBB(_1615564, tc_fun(_1615564, _1615564), _1615566), c_Lattices_Osemilattice__sup__class_Osup(_1615564)), _1615570)), c_Orderings_Obot__class_Obot(_1615564)), _1615568))], (42303 ^ _782464) ^ [_1615779, _1615781, _1615783, _1615785] : [class_Complete__Lattice_Ocomplete__lattice(_1615779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615781), _1615783)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615781, _1615779), _1615783), _1615785) = hAPP(hAPP(c_Finite__Set_Ofold(_1615781, _1615779, hAPP(hAPP(c_COMBB(_1615779, tc_fun(_1615779, _1615779), _1615781), c_Lattices_Osemilattice__inf__class_Oinf(_1615779)), _1615785)), c_Orderings_Otop__class_Otop(_1615779)), _1615783))], (42313 ^ _782464) ^ [_1615994, _1615996, _1615998] : [class_Groups_Oab__semigroup__mult(_1615994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615994), _1615996)), -(hBOOL(hAPP(hAPP(c_member(_1615994), _1615998), _1615996))), -(hAPP(c_Finite__Set_Ofold1(_1615994, c_Groups_Otimes__class_Otimes(_1615994)), hAPP(hAPP(c_Set_Oinsert(_1615994), _1615998), _1615996)) = hAPP(hAPP(c_Finite__Set_Ofold(_1615994, _1615994, c_Groups_Otimes__class_Otimes(_1615994)), _1615998), _1615996))], (42327 ^ _782464) ^ [_1616218, _1616220, _1616222] : [class_Lattices_Olattice(_1616218), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616218), _1616220)), -(hBOOL(hAPP(hAPP(c_member(_1616218), _1616222), _1616220))), -(c_Big__Operators_Olattice__class_OSup__fin(_1616218, hAPP(hAPP(c_Set_Oinsert(_1616218), _1616222), _1616220)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616218, _1616218, c_Lattices_Osemilattice__sup__class_Osup(_1616218)), _1616222), _1616220))], (42341 ^ _782464) ^ [_1616432, _1616434, _1616436] : [class_Lattices_Olattice(_1616432), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616432), _1616434)), -(hBOOL(hAPP(hAPP(c_member(_1616432), _1616436), _1616434))), -(c_Big__Operators_Olattice__class_OInf__fin(_1616432, hAPP(hAPP(c_Set_Oinsert(_1616432), _1616436), _1616434)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616432, _1616432, c_Lattices_Osemilattice__inf__class_Oinf(_1616432)), _1616436), _1616434))], (42355 ^ _782464) ^ [_1616646, _1616648, _1616650] : [class_Orderings_Olinorder(_1616646), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616646), _1616648)), -(hBOOL(hAPP(hAPP(c_member(_1616646), _1616650), _1616648))), -(c_Big__Operators_Olinorder__class_OMin(_1616646, hAPP(hAPP(c_Set_Oinsert(_1616646), _1616650), _1616648)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616646, _1616646, c_Orderings_Oord__class_Omin(_1616646)), _1616650), _1616648))], (42369 ^ _782464) ^ [_1616860, _1616862, _1616864] : [class_Orderings_Olinorder(_1616860), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616860), _1616862)), -(hBOOL(hAPP(hAPP(c_member(_1616860), _1616864), _1616862))), -(c_Big__Operators_Olinorder__class_OMax(_1616860, hAPP(hAPP(c_Set_Oinsert(_1616860), _1616864), _1616862)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616860, _1616860, c_Orderings_Oord__class_Omax(_1616860)), _1616864), _1616862))], (42383 ^ _782464) ^ [_1617074, _1617076, _1617078] : [class_Orderings_Olinorder(_1617074), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617074), _1617076)), -(hBOOL(hAPP(hAPP(c_member(_1617074), _1617078), _1617076))), -(c_Big__Operators_Olattice_OInf__fin(_1617074, c_Orderings_Oord__class_Omin(_1617074), hAPP(hAPP(c_Set_Oinsert(_1617074), _1617078), _1617076)) = hAPP(hAPP(c_Finite__Set_Ofold(_1617074, _1617074, c_Orderings_Oord__class_Omin(_1617074)), _1617078), _1617076))], (42397 ^ _782464) ^ [_1617294, _1617296, _1617298, _1617300, _1617302, _1617304] : [c_Finite__Set_Ofun__left__comm(_1617294, _1617296, _1617298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617294), _1617300)), hBOOL(hAPP(hAPP(c_member(_1617294), _1617302), _1617300)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617294, _1617296, _1617298), _1617304), _1617300) = hAPP(hAPP(_1617298, _1617302), hAPP(hAPP(c_Finite__Set_Ofold(_1617294, _1617296, _1617298), _1617304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1617294, tc_HOL_Obool)), _1617300), hAPP(hAPP(c_Set_Oinsert(_1617294), _1617302), c_Orderings_Obot__class_Obot(tc_fun(_1617294, tc_HOL_Obool)))))))], (42411 ^ _782464) ^ [_1617623, _1617625, _1617627, _1617629, _1617631, _1617633] : [c_Finite__Set_Ofun__left__comm(_1617623, _1617625, _1617627), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617623), _1617629)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617623, _1617625, _1617627), _1617631), hAPP(hAPP(c_Set_Oinsert(_1617623), _1617633), _1617629)) = hAPP(hAPP(_1617627, _1617633), hAPP(hAPP(c_Finite__Set_Ofold(_1617623, _1617625, _1617627), _1617631), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1617623, tc_HOL_Obool)), _1617629), hAPP(hAPP(c_Set_Oinsert(_1617623), _1617633), c_Orderings_Obot__class_Obot(tc_fun(_1617623, tc_HOL_Obool)))))))], (42421 ^ _782464) ^ [_1617894, _1617896, _1617898, _1617900, _1617902] : [c_Finite__Set_Ofun__left__comm(_1617894, _1617896, _1617898), -(hAPP(c_Fun_Ocomp(_1617896, _1617896, _1617896, hAPP(_1617898, _1617900)), hAPP(_1617898, _1617902)) = hAPP(c_Fun_Ocomp(_1617896, _1617896, _1617896, hAPP(_1617898, _1617902)), hAPP(_1617898, _1617900)))], (42427 ^ _782464) ^ [_1618035, _1618037, _1618039, _1618041, _1618043] : [c_Finite__Set_Ofun__left__comm(_1618035, _1618037, _1618039), -(c_Finite__Set_Ofun__left__comm(_1618041, _1618037, hAPP(hAPP(c_COMBB(_1618035, tc_fun(_1618037, _1618037), _1618041), _1618039), _1618043)))], (42433 ^ _782464) ^ [_1618148] : [class_Groups_Oab__semigroup__mult(_1618148), -(c_Finite__Set_Ofun__left__comm(_1618148, _1618148, c_Groups_Otimes__class_Otimes(_1618148)))], (42439 ^ _782464) ^ [_1618227, _1618229, _1618231, _1618233, _1618235, _1618237] : [c_Finite__Set_Ofun__left__comm(_1618227, _1618229, _1618231), -(hAPP(hAPP(_1618231, _1618233), hAPP(hAPP(_1618231, _1618235), _1618237)) = hAPP(hAPP(_1618231, _1618235), hAPP(hAPP(_1618231, _1618233), _1618237)))], (42445 ^ _782464) ^ [_1618362, _1618364, _1618366, _1618368, _1618370, _1618372, _1618374] : [c_Finite__Set_Ofun__left__comm(_1618362, _1618364, _1618366), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618362, _1618364, _1618366, _1618368, _1618370), _1618372)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618362, _1618364, _1618366, _1618368, _1618370), _1618374)), -(_1618374 = _1618372)], (42459 ^ _782464) ^ [_1618607, _1618609, _1618611, _1618613, _1618615, _1618617] : [c_Finite__Set_Ofun__left__comm(_1618607, _1618609, _1618611), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618607), _1618613)), -(hAPP(hAPP(_1618611, _1618615), hAPP(hAPP(c_Finite__Set_Ofold(_1618607, _1618609, _1618611), _1618617), _1618613)) = hAPP(hAPP(c_Finite__Set_Ofold(_1618607, _1618609, _1618611), hAPP(hAPP(_1618611, _1618615), _1618617)), _1618613))], (42469 ^ _782464) ^ [_1618826, _1618828, _1618830, _1618832, _1618834, _1618836] : [c_Finite__Set_Ofun__left__comm(_1618826, _1618828, _1618830), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618826, _1618828, _1618830, _1618832, _1618834), _1618836)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618826, _1618828, _1618830), _1618832), _1618834) = _1618836)], (42479 ^ _782464) ^ [_1619009, _1619011, _1619013, _1619015, _1619017] : [c_Finite__Set_Ofun__left__comm(_1619009, _1619011, _1619013), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619009), _1619015)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619009, _1619011, _1619013, _1619017, _1619015), hAPP(hAPP(c_Finite__Set_Ofold(_1619009, _1619011, _1619013), _1619017), _1619015))))], (42489 ^ _782464) ^ [_1619196, _1619198, _1619200, _1619202, _1619204, _1619206] : [c_Finite__Set_Ofun__left__comm(_1619196, _1619198, _1619200), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619196), _1619202)), -(hBOOL(hAPP(hAPP(c_member(_1619196), _1619204), _1619202))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619196, _1619198, _1619200), _1619206), hAPP(hAPP(c_Set_Oinsert(_1619196), _1619204), _1619202)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619196, _1619198, _1619200), hAPP(hAPP(_1619200, _1619204), _1619206)), _1619202))], (42503 ^ _782464) ^ [_1619448, _1619450, _1619452, _1619454, _1619456, _1619458] : [c_Finite__Set_Ofun__left__comm(_1619448, _1619450, _1619452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619448), _1619454)), -(hBOOL(hAPP(hAPP(c_member(_1619448), _1619456), _1619454))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619448, _1619450, _1619452), _1619458), hAPP(hAPP(c_Set_Oinsert(_1619448), _1619456), _1619454)) = hAPP(hAPP(_1619452, _1619456), hAPP(hAPP(c_Finite__Set_Ofold(_1619448, _1619450, _1619452), _1619458), _1619454)))], (42517 ^ _782464) ^ [_1619700, _1619702, _1619704, _1619706, _1619708, _1619710, _1619712] : [c_Finite__Set_Ofun__left__comm(_1619700, _1619702, _1619704), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619700, _1619702, _1619704, _1619706, _1619708), _1619710)), hBOOL(hAPP(hAPP(c_member(_1619700), _1619712), _1619708)), 42529 ^ _782464 : [(42530 ^ _782464) ^ [] : [-(_1619710 = hAPP(hAPP(_1619704, _1619712), 42528 ^ [_1619700, _1619702, _1619704, _1619706, _1619708, _1619710, _1619712]))], (42532 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619700, _1619702, _1619704, _1619706, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1619700, tc_HOL_Obool)), _1619708), hAPP(hAPP(c_Set_Oinsert(_1619700), _1619712), c_Orderings_Obot__class_Obot(tc_fun(_1619700, tc_HOL_Obool))))), 42528 ^ [_1619700, _1619702, _1619704, _1619706, _1619708, _1619710, _1619712])))]]], (42534 ^ _782464) ^ [_1620084, _1620086, _1620088, _1620090, _1620092, _1620094, _1620096] : [c_Finite__Set_Ofun__left__comm(_1620084, _1620086, _1620088), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1620084, _1620086, _1620088, _1620090, hAPP(hAPP(c_Set_Oinsert(_1620084), _1620092), _1620094)), _1620096)), -(hBOOL(hAPP(hAPP(c_member(_1620084), _1620092), _1620094))), 42546 ^ _782464 : [(42547 ^ _782464) ^ [] : [-(_1620096 = hAPP(hAPP(_1620088, _1620092), 42545 ^ [_1620084, _1620086, _1620088, _1620090, _1620092, _1620094, _1620096]))], (42549 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1620084, _1620086, _1620088, _1620090, _1620094), 42545 ^ [_1620084, _1620086, _1620088, _1620090, _1620092, _1620094, _1620096])))]]], (42551 ^ _782464) ^ [_1620410, _1620412, _1620414, _1620416] : [class_Orderings_Olinorder(_1620410), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620410), _1620412)), 42561 ^ _782464 : [(42562 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620410), 42560 ^ [_1620410, _1620412, _1620414, _1620416]), _1620412)))], (42564 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620410), 42560 ^ [_1620410, _1620412, _1620414, _1620416]), _1620414))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620410), hAPP(hAPP(c_Finite__Set_Ofold(_1620410, _1620410, c_Orderings_Oord__class_Omax(_1620410)), _1620416), _1620412)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1620410), _1620414), _1620416))))], (42568 ^ _782464) ^ [_1620774, _1620776, _1620778, _1620780] : [class_Orderings_Olinorder(_1620774), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620774), _1620776)), 42578 ^ _782464 : [(42579 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620774), 42577 ^ [_1620774, _1620776, _1620778, _1620780]), _1620776)))], (42581 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620774), _1620778), 42577 ^ [_1620774, _1620776, _1620778, _1620780]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620774), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1620774), _1620778), _1620780)), hAPP(hAPP(c_Finite__Set_Ofold(_1620774, _1620774, c_Orderings_Oord__class_Omin(_1620774)), _1620780), _1620776))))], (42585 ^ _782464) ^ [_1621138, _1621140, _1621142, _1621144] : [class_Lattices_Osemilattice__inf(_1621138), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621138), _1621140)), 42595 ^ _782464 : [(42596 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621138), 42594 ^ [_1621138, _1621140, _1621142, _1621144]), _1621140)))], (42598 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621138), _1621142), 42594 ^ [_1621138, _1621140, _1621142, _1621144]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621138), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1621138), _1621142), _1621144)), hAPP(hAPP(c_Finite__Set_Ofold(_1621138, _1621138, c_Lattices_Osemilattice__inf__class_Oinf(_1621138)), _1621144), _1621140))))], (42602 ^ _782464) ^ [_1621502, _1621504, _1621506, _1621508] : [class_Lattices_Osemilattice__sup(_1621502), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621502), _1621504)), 42612 ^ _782464 : [(42613 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621502), 42611 ^ [_1621502, _1621504, _1621506, _1621508]), _1621504)))], (42615 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621502), 42611 ^ [_1621502, _1621504, _1621506, _1621508]), _1621506))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621502), hAPP(hAPP(c_Finite__Set_Ofold(_1621502, _1621502, c_Lattices_Osemilattice__sup__class_Osup(_1621502)), _1621508), _1621504)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1621502), _1621506), _1621508))))], (42619 ^ _782464) ^ [_1621866, _1621868, _1621870] : [class_Divides_Osemiring__div(_1621866), -(_1621868 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1621866), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1621866), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1621866), _1621868), _1621870)), _1621870)), c_Divides_Odiv__class_Omod(_1621866, _1621868, _1621870)))], (42642 ^ _782464) ^ [_1622533, _1622535] : [-(c_Wellfounded_Owf(_1622533, _1622535)), 42645 ^ _782464 : [(42646 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622533), 42644 ^ [_1622533, _1622535]), 42643 ^ [_1622533, _1622535])))], (42648 ^ _782464) ^ [_1622753] : [hBOOL(hAPP(hAPP(c_member(_1622533), _1622753), 42643 ^ [_1622533, _1622535])), 42652 ^ _782464 : [(42653 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622533, _1622533)), hAPP(hAPP(c_Product__Type_OPair(_1622533, _1622533), 42651 ^ [_1622533, _1622535, _1622753]), _1622753)), _1622535)))], (42655 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622533), 42651 ^ [_1622533, _1622535, _1622753]), 42643 ^ [_1622533, _1622535])))]]]]], (42625 ^ _782464) ^ [_1622014, _1622016] : [c_Wellfounded_Owf(_1622014, _1622016), 42628 ^ _782464 : [(42629 ^ _782464) ^ [_1622146] : [42630 ^ _782464 : [(42631 ^ _782464) ^ [_1622251] : [hBOOL(hAPP(hAPP(c_member(_1622014), _1622251), _1622146))]], 42633 ^ _782464 : [(42634 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622014), 42632 ^ [_1622014, _1622016, _1622146]), _1622146)))], (42636 ^ _782464) ^ [_1622373] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1622014, _1622014)), hAPP(hAPP(c_Product__Type_OPair(_1622014, _1622014), _1622373), 42632 ^ [_1622014, _1622016, _1622146])), _1622016)), hBOOL(hAPP(hAPP(c_member(_1622014), _1622373), _1622146))]]]]], (42659 ^ _782464) ^ [_1623009, _1623011, _1623013, _1623015, _1623017, _1623019, _1623021, _1623023] : [c_Finite__Set_Ofolding__image__simple__idem(_1623009, _1623011, _1623013, _1623015, _1623017, _1623019), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623011), _1623021)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623011), _1623023)), -(hAPP(_1623019, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1623011, tc_HOL_Obool)), _1623021), _1623023)) = hAPP(hAPP(_1623013, hAPP(_1623019, _1623021)), hAPP(_1623019, _1623023)))], (42673 ^ _782464) ^ [_1623302, _1623304] : [-(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)))), _1623302)) = 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)))), _1623304))), 42675 ^ _782464 : [(42676 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42674 ^ [_1623302, _1623304])))], (42678 ^ _782464) ^ [] : [42679 ^ _782464 : [(42680 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1623302, 42674 ^ [_1623302, _1623304])))], (42682 ^ _782464) ^ [] : [hBOOL(hAPP(_1623304, 42674 ^ [_1623302, _1623304]))]], 42683 ^ _782464 : [(42684 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1623304, 42674 ^ [_1623302, _1623304])))], (42686 ^ _782464) ^ [] : [hBOOL(hAPP(_1623302, 42674 ^ [_1623302, _1623304]))]]]]], (42690 ^ _782464) ^ [_1623623, _1623625, _1623627, _1623629, _1623631, _1623633, _1623635] : [c_Finite__Set_Ofolding__image__simple__idem(_1623623, _1623625, _1623627, _1623629, _1623631, _1623633), -(hAPP(hAPP(_1623627, _1623635), _1623635) = _1623635)], (42696 ^ _782464) ^ [_1623730, _1623732, _1623734, _1623736, _1623738, _1623740, _1623742, _1623744] : [c_Finite__Set_Ofolding__image__simple__idem(_1623730, _1623732, _1623734, _1623736, _1623738, _1623740), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623732), _1623742)), hBOOL(hAPP(hAPP(c_member(_1623732), _1623744), _1623742)), -(hAPP(hAPP(_1623734, hAPP(_1623738, _1623744)), hAPP(_1623740, _1623742)) = hAPP(_1623740, _1623742))], (42710 ^ _782464) ^ [_1624007, _1624009, _1624011, _1624013, _1624015, _1624017, _1624019, _1624021] : [c_Finite__Set_Ofolding__image__simple__idem(_1624007, _1624009, _1624011, _1624013, _1624015, _1624017), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624009), _1624019)), -(hAPP(_1624017, hAPP(hAPP(c_Set_Oinsert(_1624009), _1624021), _1624019)) = hAPP(hAPP(_1624011, hAPP(_1624015, _1624021)), hAPP(_1624017, _1624019)))], (42720 ^ _782464) ^ [_1624222, _1624224, _1624226, _1624228, _1624230, _1624232, _1624234, _1624236] : [c_Finite__Set_Ofolding__image__simple__idem(_1624222, _1624224, _1624226, _1624228, _1624230, _1624232), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624224), _1624234)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624224, tc_HOL_Obool)), _1624236), _1624234)), -(hAPP(hAPP(_1624226, hAPP(_1624232, _1624236)), hAPP(_1624232, _1624234)) = hAPP(_1624232, _1624234))], (42734 ^ _782464) ^ [_1624505, _1624507, _1624509, _1624511, _1624513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624505, tc_HOL_Obool)), _1624507), _1624509)), 42740 ^ _782464 : [(42741 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624505), 42739 ^ [_1624505, _1624507, _1624509, _1624511, _1624513]), _1624507)))], (42743 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1624511, 42739 ^ [_1624505, _1624507, _1624509, _1624511, _1624513])))], (42745 ^ _782464) ^ [] : [hBOOL(hAPP(_1624513, 42739 ^ [_1624505, _1624507, _1624509, _1624511, _1624513]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624505, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624505, tc_HOL_Obool)), _1624507), hAPP(c_Set_OCollect(_1624505), _1624511))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624505, tc_HOL_Obool)), _1624509), hAPP(c_Set_OCollect(_1624505), _1624513)))))], (42749 ^ _782464) ^ [_1624905, _1624907, _1624909, _1624911] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624905, _1624907)), _1624909), hAPP(c_Relation_Oconverse(_1624907, _1624905), _1624911))), 42754 ^ _782464 : [(42755 ^ _782464) ^ [] : [-(_1624909 = hAPP(hAPP(c_Product__Type_OPair(_1624905, _1624907), 42753 ^ [_1624905, _1624907, _1624909, _1624911]), 42752 ^ [_1624905, _1624907, _1624909, _1624911]))], (42757 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624907, _1624905)), hAPP(hAPP(c_Product__Type_OPair(_1624907, _1624905), 42752 ^ [_1624905, _1624907, _1624909, _1624911]), 42753 ^ [_1624905, _1624907, _1624909, _1624911])), _1624911)))]]], (42759 ^ _782464) ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625158, _1625160)), _1625162), hAPP(hAPP(c_Relation_Orel__comp(_1625158, _1625164, _1625160), _1625166), _1625168))), 42765 ^ _782464 : [(42766 ^ _782464) ^ [] : [-(_1625162 = hAPP(hAPP(c_Product__Type_OPair(_1625158, _1625160), 42762 ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168]), 42764 ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168]))], (42768 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625158, _1625164)), hAPP(hAPP(c_Product__Type_OPair(_1625158, _1625164), 42762 ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168]), 42763 ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168])), _1625166)))], (42770 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625164, _1625160)), hAPP(hAPP(c_Product__Type_OPair(_1625164, _1625160), 42763 ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168]), 42764 ^ [_1625158, _1625160, _1625162, _1625164, _1625166, _1625168])), _1625168)))]]], (42772 ^ _782464) ^ [_1625536, _1625538, _1625540] : [-(c_Nitpick_Oplus__frac(_1625536, _1625538, _1625540) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1625536), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1625536), _1625538), hAPP(c_Nitpick_Odenom(_1625536), _1625540))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1625536), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1625536), tc_Int_Oint), c_Nitpick_Ofrac(_1625536)), 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(_1625536), _1625538))), 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(_1625536), _1625538))))), 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(_1625536), _1625540))), 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(_1625536), _1625540)))))), c_COMBI(tc_Int_Oint))))], (42774 ^ _782464) ^ [_1625667, _1625669, _1625671] : [-(c_Nitpick_Otimes__frac(_1625667, _1625669, _1625671) = hAPP(hAPP(c_Nitpick_Ofrac(_1625667), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1625667), _1625669)), hAPP(c_Nitpick_Onum(_1625667), _1625671))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1625667), _1625669)), hAPP(c_Nitpick_Odenom(_1625667), _1625671))))], (42776 ^ _782464) ^ [_1625738, _1625740, _1625742] : [-(c_Nitpick_Oof__frac(_1625740, _1625738, _1625742) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1625738), hAPP(c_Int_Oring__1__class_Oof__int(_1625738), hAPP(c_Nitpick_Onum(_1625740), _1625742))), hAPP(c_Int_Oring__1__class_Oof__int(_1625738), hAPP(c_Nitpick_Odenom(_1625740), _1625742)))), class_Rings_Oinverse(_1625738), class_Rings_Oring__1(_1625738)], (42786 ^ _782464) ^ [_1625931, _1625933] : [-(c_Nitpick_Oinverse__frac(_1625931, _1625933) = hAPP(hAPP(c_Nitpick_Ofrac(_1625931), hAPP(c_Nitpick_Odenom(_1625931), _1625933)), hAPP(c_Nitpick_Onum(_1625931), _1625933)))], (42788 ^ _782464) ^ [_1625977, _1625979] : [-(c_Nitpick_Ouminus__frac(_1625977, _1625979) = c_Nitpick_OAbs__Frac(_1625977, 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(_1625977), _1625979))), hAPP(c_Nitpick_Odenom(_1625977), _1625979))))], (42790 ^ _782464) ^ [_1626045, _1626047, _1626049] : [c_Nitpick_Oless__frac(_1626045, _1626047, _1626049), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626045), c_Nitpick_Oplus__frac(_1626045, _1626047, c_Nitpick_Ouminus__frac(_1626045, _1626049)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42796 ^ _782464) ^ [_1626156, _1626158, _1626160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626156), c_Nitpick_Oplus__frac(_1626156, _1626158, c_Nitpick_Ouminus__frac(_1626156, _1626160)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1626156, _1626158, _1626160))], (42802 ^ _782464) ^ [_1626291, _1626293, _1626295] : [c_Nitpick_Oless__eq__frac(_1626291, _1626293, _1626295), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626291), c_Nitpick_Oplus__frac(_1626291, _1626293, c_Nitpick_Ouminus__frac(_1626291, _1626295)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42808 ^ _782464) ^ [_1626402, _1626404, _1626406] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626402), c_Nitpick_Oplus__frac(_1626402, _1626404, c_Nitpick_Ouminus__frac(_1626402, _1626406)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1626402, _1626404, _1626406))], (42814 ^ _782464) ^ [_1626519] : [-(c_Nitpick_Onum(_1626519) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1626519, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1626519)))], (42816 ^ _782464) ^ [_1626554] : [-(c_Nitpick_Odenom(_1626554) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1626554, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1626554)))], (42818 ^ _782464) ^ [_1626589, _1626591, _1626593, _1626595] : [class_Rings_Olinordered__semidom(_1626589), 42824 ^ _782464 : [(42825 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626591), 42823 ^ [_1626589, _1626591, _1626593, _1626595]), _1626593)))], (42827 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1626589), c_Groups_Ozero__class_Ozero(_1626589)), hAPP(_1626595, 42823 ^ [_1626589, _1626591, _1626593, _1626595])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1626589), c_Groups_Ozero__class_Ozero(_1626589)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1626591, _1626589), _1626595), _1626593))))], (42831 ^ _782464) ^ [_1626885, _1626887, _1626889] : [-(c_Product__Type_Ointernal__split(_1626885, _1626887, _1626889) = c_Product__Type_Oprod_Oprod__case(_1626885, _1626887, _1626889))], (42833 ^ _782464) ^ [_1626920, _1626922, _1626924, _1626926, _1626928, _1626930] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1626920, _1626922, _1626924), _1626926), hAPP(hAPP(c_Product__Type_OPair(_1626920, _1626922), _1626928), _1626930)) = hAPP(hAPP(_1626926, _1626928), _1626930))], (42835 ^ _782464) ^ [_1626978, _1626980, _1626982, _1626984] : [class_Rings_Olinordered__semidom(_1626978), 42841 ^ _782464 : [(42842 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626980), 42840 ^ [_1626978, _1626980, _1626982, _1626984]), _1626982)))], (42844 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626978), c_Groups_Ozero__class_Ozero(_1626978)), hAPP(_1626984, 42840 ^ [_1626978, _1626980, _1626982, _1626984])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626978), c_Groups_Ozero__class_Ozero(_1626978)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1626980, _1626978), _1626984), _1626982))))], (42848 ^ _782464) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42850 ^ _782464) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42852 ^ _782464) ^ [_1627310, _1627312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 42853 ^ [_1627310, _1627312]), hAPP(_1627310, 42853 ^ [_1627310, _1627312]))), -(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)), _1627310)), _1627312)))))], (42859 ^ _782464) ^ [_1627470, _1627472] : [-(c_List_Olenlex(_1627470, _1627472) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1627470)), tc_List_Olist(_1627470)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1627470), c_Wellfounded_Oless__than, c_List_Olex(_1627470, _1627472))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627470), tc_List_Olist(_1627470), tc_prod(tc_Nat_Onat, tc_List_Olist(_1627470))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1627470), tc_prod(tc_Nat_Onat, tc_List_Olist(_1627470))), tc_List_Olist(_1627470)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1627470))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627470)))), c_COMBI(tc_List_Olist(_1627470)))))], (42861 ^ _782464) ^ [_1627578, _1627580, _1627582, _1627584, _1627586] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627578), tc_List_Olist(_1627578))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627578), tc_List_Olist(_1627578)), _1627580), _1627582)), hAPP(c_List_Olexn(_1627578, _1627584), _1627586))), 42864 ^ _782464 : [(42865 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627578)), _1627580) = _1627586)], (42867 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627578)), _1627582) = _1627586)]]], (42869 ^ _782464) ^ [_1627780, _1627782, _1627784] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627780)), _1627782) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627780)), _1627784)), _1627782 = _1627784], (42875 ^ _782464) ^ [_1627872, _1627874] : [-(c_List_Olenlex(_1627872, _1627874) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1627872), tc_List_Olist(_1627872), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627872), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627872), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), tc_List_Olist(_1627872)), c_COMBS(tc_List_Olist(_1627872), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1627872)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627872)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627872), tc_fun(tc_List_Olist(_1627872), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1627872), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), tc_List_Olist(_1627872)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1627872))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1627872)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1627872))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627872)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627872), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627872), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), tc_List_Olist(_1627872)), c_COMBS(tc_List_Olist(_1627872), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1627872)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627872)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627872), tc_fun(tc_List_Olist(_1627872), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1627872), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), tc_List_Olist(_1627872)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1627872))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1627872)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1627872))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627872)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627872), tc_fun(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627872), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627872), tc_HOL_Obool)), tc_List_Olist(_1627872)), c_COMBC(tc_List_Olist(_1627872), tc_fun(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627872), tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872))), tc_fun(tc_List_Olist(_1627872), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1627872)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1627872)), c_member(tc_prod(tc_List_Olist(_1627872), tc_List_Olist(_1627872))))), c_Product__Type_OPair(tc_List_Olist(_1627872), tc_List_Olist(_1627872))))), c_List_Olex(_1627872, _1627874)))))))], (42877 ^ _782464) ^ [_1628428, _1628430] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1628428))), c_Enum_Osublists(_1628428, _1628430)) = 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(_1628428)), _1628430)))], (42879 ^ _782464) ^ [_1628475, _1628477, _1628479] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628475)), c_List_Osublist(_1628475, _1628477, _1628479)) = 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(_1628475)), _1628477)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1628479)))))], (42881 ^ _782464) ^ [_1628541, _1628543, _1628545] : [-(hAPP(c_List_Olexn(_1628541, _1628543), hAPP(c_Nat_OSuc, _1628545)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1628541), tc_List_Olist(_1628541)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1628541, tc_List_Olist(_1628541)), tc_prod(_1628541, tc_List_Olist(_1628541))), tc_prod(tc_List_Olist(_1628541), tc_List_Olist(_1628541)), c_Product__Type_Omap__pair(tc_prod(_1628541, tc_List_Olist(_1628541)), tc_List_Olist(_1628541), tc_prod(_1628541, tc_List_Olist(_1628541)), tc_List_Olist(_1628541), hAPP(c_Product__Type_Oprod_Oprod__case(_1628541, tc_List_Olist(_1628541), tc_List_Olist(_1628541)), c_List_Olist_OCons(_1628541)), hAPP(c_Product__Type_Oprod_Oprod__case(_1628541, tc_List_Olist(_1628541), tc_List_Olist(_1628541)), c_List_Olist_OCons(_1628541)))), c_Wellfounded_Olex__prod(_1628541, tc_List_Olist(_1628541), _1628543, hAPP(c_List_Olexn(_1628541, _1628543), _1628545)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1628541), tc_List_Olist(_1628541))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1628541), tc_List_Olist(_1628541), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628541), tc_fun(tc_List_Olist(_1628541), tc_HOL_Obool), tc_fun(tc_List_Olist(_1628541), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1628541), tc_HOL_Obool), tc_fun(tc_List_Olist(_1628541), tc_HOL_Obool)), tc_List_Olist(_1628541)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1628541))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1628541)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628541), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1628541)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1628541)))), hAPP(c_Nat_OSuc, _1628545))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628541), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1628541)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1628541)))), hAPP(c_Nat_OSuc, _1628545)))))))], (42883 ^ _782464) ^ [_1628853, _1628855, _1628857, _1628859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628853), tc_List_Olist(_1628853))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628853), tc_List_Olist(_1628853)), _1628855), _1628857)), c_List_Olex(_1628853, _1628859))), 42886 ^ _782464 : [(42887 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628853), tc_List_Olist(_1628853))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628853), tc_List_Olist(_1628853)), _1628855), _1628857)), c_List_Olexord(_1628853, _1628859))))], (42889 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628853)), _1628855) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628853)), _1628857))]]], (42891 ^ _782464) ^ [_1629104, _1629106, _1629108, _1629110] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629104), tc_List_Olist(_1629104))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629104), tc_List_Olist(_1629104)), _1629106), _1629108)), c_List_Olex(_1629104, _1629110)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629104), tc_List_Olist(_1629104))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629104), tc_List_Olist(_1629104)), _1629106), _1629108)), c_List_Olexord(_1629104, _1629110))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629104)), _1629106) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629104)), _1629108)], (42901 ^ _782464) ^ [_1629418, _1629420, _1629422, _1629424, _1629426, _1629428] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629418), tc_List_Olist(_1629418))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629418), tc_List_Olist(_1629418)), hAPP(hAPP(c_List_Olist_OCons(_1629418), _1629420), _1629422)), hAPP(hAPP(c_List_Olist_OCons(_1629418), _1629424), _1629426))), c_List_Olexord(_1629418, _1629428))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629418, _1629418)), hAPP(hAPP(c_Product__Type_OPair(_1629418, _1629418), _1629420), _1629424)), _1629428))), 42908 ^ _782464 : [(42909 ^ _782464) ^ [] : [-(_1629420 = _1629424)], (42911 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629418), tc_List_Olist(_1629418))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629418), tc_List_Olist(_1629418)), _1629422), _1629426)), c_List_Olexord(_1629418, _1629428))))]]], (42913 ^ _782464) ^ [_1629745, _1629747, _1629749, _1629751, _1629753, _1629755] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629745), tc_List_Olist(_1629745))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629745), tc_List_Olist(_1629745)), hAPP(hAPP(c_List_Olist_OCons(_1629745), _1629747), _1629749)), hAPP(hAPP(c_List_Olist_OCons(_1629745), _1629751), _1629753))), c_List_Olexord(_1629745, _1629755)))), 42914 ^ _782464 : [(42915 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629745, _1629745)), hAPP(hAPP(c_Product__Type_OPair(_1629745, _1629745), _1629747), _1629751)), _1629755))], (42917 ^ _782464) ^ [] : [_1629747 = _1629751, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629745), tc_List_Olist(_1629745))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629745), tc_List_Olist(_1629745)), _1629749), _1629753)), c_List_Olexord(_1629745, _1629755)))]]], (42925 ^ _782464) ^ [_1630118, _1630120, _1630122, _1630124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630118)), _1630120)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630118)), _1630122))), _1630120 = hAPP(hAPP(c_List_Olist_OCons(_1630118), _1630124), _1630122)], (42931 ^ _782464) ^ [_1630278, _1630280, _1630282, _1630284, _1630286] : [hAPP(hAPP(c_List_Olist_OCons(_1630278), _1630280), _1630282) = hAPP(hAPP(c_List_Olist_OCons(_1630278), _1630284), _1630286), 42934 ^ _782464 : [(42935 ^ _782464) ^ [] : [-(_1630280 = _1630284)], (42937 ^ _782464) ^ [] : [-(_1630282 = _1630286)]]], (42939 ^ _782464) ^ [_1630415, _1630417, _1630419, _1630421, _1630423] : [-(hAPP(hAPP(c_List_Olist_OCons(_1630415), _1630417), _1630419) = hAPP(hAPP(c_List_Olist_OCons(_1630415), _1630421), _1630423)), _1630417 = _1630421, _1630419 = _1630423], (42949 ^ _782464) ^ [_1630605, _1630607, _1630609] : [hAPP(hAPP(c_List_Olist_OCons(_1630605), _1630607), _1630609) = _1630609], (42951 ^ _782464) ^ [_1630655, _1630657, _1630659] : [_1630655 = hAPP(hAPP(c_List_Olist_OCons(_1630657), _1630659), _1630655)], (42953 ^ _782464) ^ [_1630690, _1630692, _1630694] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630690)), hAPP(hAPP(c_List_Olist_OCons(_1630690), _1630692), _1630694)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630690)), _1630694)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42955 ^ _782464) ^ [_1630772, _1630774, _1630776, _1630778, _1630780, _1630782] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630772), tc_List_Olist(_1630772))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630772), tc_List_Olist(_1630772)), hAPP(hAPP(c_List_Olist_OCons(_1630772), _1630774), _1630776)), hAPP(hAPP(c_List_Olist_OCons(_1630772), _1630778), _1630780))), c_List_Olex(_1630772, _1630782))), 42960 ^ _782464 : [(42961 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630772, _1630772)), hAPP(hAPP(c_Product__Type_OPair(_1630772, _1630772), _1630774), _1630778)), _1630782)))], (42963 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630772)), _1630776) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630772)), _1630780))]], 42964 ^ _782464 : [(42965 ^ _782464) ^ [] : [-(_1630774 = _1630778)], (42967 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630772), tc_List_Olist(_1630772))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630772), tc_List_Olist(_1630772)), _1630776), _1630780)), c_List_Olex(_1630772, _1630782))))]]], (42969 ^ _782464) ^ [_1631170, _1631172, _1631174, _1631176, _1631178, _1631180] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631170), tc_List_Olist(_1631170))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631170), tc_List_Olist(_1631170)), hAPP(hAPP(c_List_Olist_OCons(_1631170), _1631172), _1631174)), hAPP(hAPP(c_List_Olist_OCons(_1631170), _1631176), _1631178))), c_List_Olex(_1631170, _1631180)))), 42970 ^ _782464 : [(42971 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631170, _1631170)), hAPP(hAPP(c_Product__Type_OPair(_1631170, _1631170), _1631172), _1631176)), _1631180)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631170)), _1631174) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631170)), _1631178)], (42977 ^ _782464) ^ [] : [_1631172 = _1631176, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631170), tc_List_Olist(_1631170))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631170), tc_List_Olist(_1631170)), _1631174), _1631178)), c_List_Olex(_1631170, _1631180)))]]], (42985 ^ _782464) ^ [_1631626, _1631628, _1631630] : [-(c_List_Oset__Cons(_1631626, _1631628, _1631630) = hAPP(c_Set_OCollect(tc_List_Olist(_1631626)), hAPP(hAPP(c_COMBB(tc_fun(_1631626, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1631626)), c_HOL_OEx(_1631626)), hAPP(hAPP(c_COMBB(tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), tc_fun(_1631626, tc_HOL_Obool), tc_List_Olist(_1631626)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_HOL_Obool, _1631626), c_HOL_OEx(tc_List_Olist(_1631626)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631626), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631626, tc_fun(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), tc_fun(tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), tc_List_Olist(_1631626)), c_COMBS(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1631626, tc_fun(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), tc_List_Olist(_1631626)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631626), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), _1631626), c_COMBS(tc_List_Olist(_1631626), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1631626)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1631626), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1631626)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631626), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_List_Olist(_1631626))), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1631626), tc_List_Olist(_1631626)), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), tc_fun(tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_List_Olist(_1631626))), tc_fun(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool))), tc_List_Olist(_1631626)), c_COMBB(tc_fun(tc_List_Olist(_1631626), tc_List_Olist(_1631626)), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), _1631626)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631626), tc_List_Olist(_1631626)), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), tc_List_Olist(_1631626)), c_COMBB(tc_List_Olist(_1631626), tc_HOL_Obool, tc_List_Olist(_1631626))), c_fequal))), c_List_Olist_OCons(_1631626)))))), hAPP(hAPP(c_COMBC(_1631626, tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool)), _1631626), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1631626))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631626), c_fconj), hAPP(hAPP(c_COMBC(_1631626, tc_fun(_1631626, tc_HOL_Obool), tc_HOL_Obool), c_member(_1631626)), _1631628)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631626), tc_fun(tc_List_Olist(_1631626), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1631626))), _1631630)))))))], (42987 ^ _782464) ^ [_1632176, _1632178, _1632180, _1632182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1632176), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632178), _1632180))), -(hAPP(c_Random_Opick(_1632178, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632178)), _1632180), _1632182)), _1632176) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1632178), _1632180))], (42993 ^ _782464) ^ [_1632319, _1632321, _1632323, _1632325] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1632319), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632321), _1632323)))), -(hAPP(c_Random_Opick(_1632321, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632321)), _1632323), _1632325)), _1632319) = hAPP(c_Random_Opick(_1632321, _1632325), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1632319), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632321), _1632323))))], (42999 ^ _782464) ^ [_1632407, _1632409, _1632411] : [-(c_Random_Oselect__weight(_1632407, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632407)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1632407), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1632409)), _1632411)) = c_Random_Oselect__weight(_1632407, _1632411))], (43001 ^ _782464) ^ [_1632460, _1632462, _1632464, _1632466, _1632468, _1632470] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632460, _1632460)), hAPP(hAPP(c_Product__Type_OPair(_1632460, _1632460), _1632462), _1632464)), c_Transitive__Closure_Ortrancl(_1632460, _1632466))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632460), tc_List_Olist(_1632460))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632460), tc_List_Olist(_1632460)), _1632468), _1632470)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1632460), c_List_Olistrel1(_1632460, _1632466)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632460), tc_List_Olist(_1632460))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632460), tc_List_Olist(_1632460)), hAPP(hAPP(c_List_Olist_OCons(_1632460), _1632462), _1632468)), hAPP(hAPP(c_List_Olist_OCons(_1632460), _1632464), _1632470))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1632460), c_List_Olistrel1(_1632460, _1632466)))))], (43011 ^ _782464) ^ [_1632821, _1632823, _1632825, _1632827] : [hBOOL(hAPP(hAPP(c_member(_1632821), _1632823), c_Wellfounded_Oacc(_1632821, _1632825))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632821)), _1632827), c_Wellfounded_Oacc(tc_List_Olist(_1632821), c_List_Olistrel1(_1632821, _1632825)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632821)), hAPP(hAPP(c_List_Olist_OCons(_1632821), _1632823), _1632827)), c_Wellfounded_Oacc(tc_List_Olist(_1632821), c_List_Olistrel1(_1632821, _1632825)))))], (43021 ^ _782464) ^ [_1633062, _1633064] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1633062), tc_List_Olist(_1633062)), tc_HOL_Obool)), c_List_Olistrel1(_1633062, c_Transitive__Closure_Ortrancl(_1633062, _1633064))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633062), c_List_Olistrel1(_1633062, _1633064)))))], (43023 ^ _782464) ^ [_1633118, _1633120] : [-(c_List_Olistrel1(_1633118, hAPP(c_Relation_Oconverse(_1633118, _1633118), _1633120)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1633118), tc_List_Olist(_1633118)), c_List_Olistrel1(_1633118, _1633120)))], (43025 ^ _782464) ^ [_1633165, _1633167, _1633169] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633165, _1633165), tc_HOL_Obool)), _1633167), _1633169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1633165), tc_List_Olist(_1633165)), tc_HOL_Obool)), c_List_Olistrel1(_1633165, _1633167)), c_List_Olistrel1(_1633165, _1633169))))], (43031 ^ _782464) ^ [_1633316, _1633318, _1633320, _1633322, _1633324] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633316), tc_List_Olist(_1633316))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633316), tc_List_Olist(_1633316)), _1633318), _1633320)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633316), c_List_Olistrel1(_1633316, _1633322)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633316), tc_List_Olist(_1633316))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633316), tc_List_Olist(_1633316)), hAPP(hAPP(c_List_Olist_OCons(_1633316), _1633324), _1633318)), hAPP(hAPP(c_List_Olist_OCons(_1633316), _1633324), _1633320))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633316), c_List_Olistrel1(_1633316, _1633322)))))], (43037 ^ _782464) ^ [_1633571, _1633573, _1633575, _1633577, _1633579] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633571), tc_List_Olist(_1633571))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633571), tc_List_Olist(_1633571)), _1633573), _1633575)), c_List_Olistrel1(_1633571, _1633577))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633571), tc_List_Olist(_1633571))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633571), tc_List_Olist(_1633571)), hAPP(hAPP(c_List_Olist_OCons(_1633571), _1633579), _1633573)), hAPP(hAPP(c_List_Olist_OCons(_1633571), _1633579), _1633575))), c_List_Olistrel1(_1633571, _1633577))))], (43043 ^ _782464) ^ [_1633806, _1633808, _1633810, _1633812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633806), tc_List_Olist(_1633806))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633806), tc_List_Olist(_1633806)), _1633808), _1633810)), c_List_Olistrel1(_1633806, _1633812))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633806)), _1633808) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633806)), _1633810))], (43049 ^ _782464) ^ [_1633975, _1633977, _1633979, _1633981] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633975), tc_List_Olist(_1633975))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633975), tc_List_Olist(_1633975)), _1633977), _1633979)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633975), c_List_Olistrel1(_1633975, _1633981)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633975)), _1633977) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633975)), _1633979))], (43055 ^ _782464) ^ [_1634175, _1634177, _1634179, _1634181] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634175), tc_List_Olist(_1634175))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634175), tc_List_Olist(_1634175)), _1634177), _1634179)), c_List_Olistrel1(_1634175, hAPP(c_Relation_Oconverse(_1634175, _1634175), _1634181)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634175), tc_List_Olist(_1634175))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634175), tc_List_Olist(_1634175)), _1634177), _1634179)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1634175), tc_List_Olist(_1634175)), c_List_Olistrel1(_1634175, _1634181)))))], (43061 ^ _782464) ^ [_1634404, _1634406, _1634408, _1634410] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634404), tc_List_Olist(_1634404))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634404), tc_List_Olist(_1634404)), _1634406), _1634408)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1634404), tc_List_Olist(_1634404)), c_List_Olistrel1(_1634404, _1634410)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634404), tc_List_Olist(_1634404))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634404), tc_List_Olist(_1634404)), _1634406), _1634408)), c_List_Olistrel1(_1634404, hAPP(c_Relation_Oconverse(_1634404, _1634404), _1634410)))))], (43067 ^ _782464) ^ [_1634639, _1634641, _1634643, _1634645, _1634647] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634639, _1634639)), hAPP(hAPP(c_Product__Type_OPair(_1634639, _1634639), _1634641), _1634643)), _1634645)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634639), tc_List_Olist(_1634639))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634639), tc_List_Olist(_1634639)), hAPP(hAPP(c_List_Olist_OCons(_1634639), _1634641), _1634647)), hAPP(hAPP(c_List_Olist_OCons(_1634639), _1634643), _1634647))), c_List_Olistrel1(_1634639, _1634645))))], (43073 ^ _782464) ^ [_1634879, _1634881, _1634883, _1634885, _1634887, _1634889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634879), tc_List_Olist(_1634879))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634879), tc_List_Olist(_1634879)), hAPP(hAPP(c_List_Olist_OCons(_1634879), _1634881), _1634883)), hAPP(hAPP(c_List_Olist_OCons(_1634879), _1634885), _1634887))), c_List_Olistrel1(_1634879, _1634889))), 43078 ^ _782464 : [(43079 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634879, _1634879)), hAPP(hAPP(c_Product__Type_OPair(_1634879, _1634879), _1634881), _1634885)), _1634889)))], (43081 ^ _782464) ^ [] : [-(_1634883 = _1634887)]], 43082 ^ _782464 : [(43083 ^ _782464) ^ [] : [-(_1634881 = _1634885)], (43085 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634879), tc_List_Olist(_1634879))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634879), tc_List_Olist(_1634879)), _1634883), _1634887)), c_List_Olistrel1(_1634879, _1634889))))]]], (43087 ^ _782464) ^ [_1635249, _1635251, _1635253, _1635255, _1635257, _1635259] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635249), tc_List_Olist(_1635249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635249), tc_List_Olist(_1635249)), hAPP(hAPP(c_List_Olist_OCons(_1635249), _1635251), _1635253)), hAPP(hAPP(c_List_Olist_OCons(_1635249), _1635255), _1635257))), c_List_Olistrel1(_1635249, _1635259)))), 43088 ^ _782464 : [(43089 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635249, _1635249)), hAPP(hAPP(c_Product__Type_OPair(_1635249, _1635249), _1635251), _1635255)), _1635259)), _1635253 = _1635257], (43095 ^ _782464) ^ [] : [_1635251 = _1635255, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635249), tc_List_Olist(_1635249))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635249), tc_List_Olist(_1635249)), _1635253), _1635257)), c_List_Olistrel1(_1635249, _1635259)))]]], (43103 ^ _782464) ^ [_1635677, _1635679, _1635681, _1635683] : [-(c_List_Olist_Olist__size(_1635677, _1635679, hAPP(hAPP(c_List_Olist_OCons(_1635677), _1635681), _1635683)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1635679, _1635681)), c_List_Olist_Olist__size(_1635677, _1635679, _1635683))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43105 ^ _782464) ^ [_1635737, _1635739, _1635741, _1635743] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1635737), tc_List_Olist(_1635737), c_List_Olistrel(_1635737, _1635739)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1635737)), hAPP(hAPP(c_List_Olist_OCons(_1635737), _1635741), _1635743)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1635737), tc_HOL_Obool)))) = c_List_Oset__Cons(_1635737, hAPP(c_Relation_OImage(_1635737, _1635737, _1635739), hAPP(hAPP(c_Set_Oinsert(_1635737), _1635741), c_Orderings_Obot__class_Obot(tc_fun(_1635737, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1635737), tc_List_Olist(_1635737), c_List_Olistrel(_1635737, _1635739)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1635737)), _1635743), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1635737), tc_HOL_Obool))))))], (43107 ^ _782464) ^ [_1635860, _1635862, _1635864] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635860), tc_List_Olist(_1635860))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635860), tc_List_Olist(_1635860)), _1635862), _1635862)), c_List_Olistrel(_1635860, c_Transitive__Closure_Ortrancl(_1635860, _1635864)))))], (43109 ^ _782464) ^ [_1635920, _1635922, _1635924] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1635920, _1635920), tc_HOL_Obool)), _1635922), _1635924)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1635920), tc_List_Olist(_1635920)), tc_HOL_Obool)), c_List_Olistrel(_1635920, _1635922)), c_List_Olistrel(_1635920, _1635924))))], (43115 ^ _782464) ^ [_1636071, _1636073] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636071), tc_List_Olist(_1636071)), tc_HOL_Obool)), c_List_Olistrel(_1636071, _1636073)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636071), c_List_Olistrel1(_1636071, _1636073)))))], (43117 ^ _782464) ^ [_1636124, _1636126, _1636128, _1636130] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636124), tc_List_Olist(_1636124))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636124), tc_List_Olist(_1636124)), _1636126), _1636128)), c_List_Olistrel(_1636124, _1636130))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636124)), _1636126) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636124)), _1636128))], (43123 ^ _782464) ^ [_1636293, _1636295, _1636297, _1636299, _1636301] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636293), tc_List_Olist(_1636293))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636293), tc_List_Olist(_1636293)), _1636295), _1636297)), c_List_Olistrel(_1636293, c_Transitive__Closure_Ortrancl(_1636293, _1636299)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636293), tc_List_Olist(_1636293))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636293), tc_List_Olist(_1636293)), _1636297), _1636301)), c_List_Olistrel(_1636293, c_Transitive__Closure_Ortrancl(_1636293, _1636299)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636293), tc_List_Olist(_1636293))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636293), tc_List_Olist(_1636293)), _1636295), _1636301)), c_List_Olistrel(_1636293, c_Transitive__Closure_Ortrancl(_1636293, _1636299)))))], (43133 ^ _782464) ^ [_1636632, _1636634] : [-(c_List_Olistrel(_1636632, c_Transitive__Closure_Ortrancl(_1636632, _1636634)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636632), c_List_Olistrel1(_1636632, _1636634)))], (43135 ^ _782464) ^ [_1636671, _1636673, _1636675, _1636677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636671), tc_List_Olist(_1636671))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636671), tc_List_Olist(_1636671)), _1636673), _1636675)), c_List_Olistrel1(_1636671, _1636677))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636671), tc_List_Olist(_1636671))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636671), tc_List_Olist(_1636671)), _1636673), _1636675)), c_List_Olistrel(_1636671, c_Transitive__Closure_Ortrancl(_1636671, _1636677)))))], (43141 ^ _782464) ^ [_1636878, _1636880, _1636882] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1636878, _1636878), tc_HOL_Obool)), _1636880), _1636882)), c_Relation_Orefl__on(_1636878, c_Orderings_Otop__class_Otop(tc_fun(_1636878, tc_HOL_Obool)), _1636882), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636878), tc_List_Olist(_1636878)), tc_HOL_Obool)), c_List_Olistrel1(_1636878, _1636880)), c_List_Olistrel(_1636878, _1636882))))], (43151 ^ _782464) ^ [_1637095, _1637097, _1637099, _1637101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637095), tc_List_Olist(_1637095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637095), tc_List_Olist(_1637095)), _1637097), _1637099)), c_List_Olistrel(_1637095, _1637101))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637095), tc_List_Olist(_1637095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637095), tc_List_Olist(_1637095)), _1637097), _1637099)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1637095), c_List_Olistrel1(_1637095, _1637101)))))], (43157 ^ _782464) ^ [_1637306, _1637308, _1637310, _1637312, _1637314, _1637316] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637306, _1637306)), hAPP(hAPP(c_Product__Type_OPair(_1637306, _1637306), _1637308), _1637310)), _1637312)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637306), tc_List_Olist(_1637306))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637306), tc_List_Olist(_1637306)), _1637314), _1637316)), c_List_Olistrel(_1637306, _1637312))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637306), tc_List_Olist(_1637306))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637306), tc_List_Olist(_1637306)), hAPP(hAPP(c_List_Olist_OCons(_1637306), _1637308), _1637314)), hAPP(hAPP(c_List_Olist_OCons(_1637306), _1637310), _1637316))), c_List_Olistrel(_1637306, _1637312))))], (43167 ^ _782464) ^ [_1637662, _1637664, _1637666, _1637668] : [c_List_Olistrelp(_1637662, hAPP(hAPP(c_COMBC(_1637662, tc_fun(tc_prod(_1637662, _1637662), tc_HOL_Obool), tc_fun(_1637662, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637662, tc_fun(tc_fun(tc_prod(_1637662, _1637662), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1637662, _1637662), tc_HOL_Obool), tc_fun(_1637662, tc_HOL_Obool)), _1637662), c_COMBC(_1637662, tc_fun(tc_prod(_1637662, _1637662), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637662, tc_prod(_1637662, _1637662)), tc_fun(_1637662, tc_fun(tc_fun(tc_prod(_1637662, _1637662), tc_HOL_Obool), tc_HOL_Obool)), _1637662), hAPP(c_COMBB(tc_prod(_1637662, _1637662), tc_fun(tc_fun(tc_prod(_1637662, _1637662), tc_HOL_Obool), tc_HOL_Obool), _1637662), c_member(tc_prod(_1637662, _1637662)))), c_Product__Type_OPair(_1637662, _1637662)))), _1637664), _1637666, _1637668), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637662), tc_List_Olist(_1637662))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637662), tc_List_Olist(_1637662)), _1637666), _1637668)), c_List_Olistrel(_1637662, _1637664))))], (43173 ^ _782464) ^ [_1638039, _1638041, _1638043, _1638045] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638039), tc_List_Olist(_1638039))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638039), tc_List_Olist(_1638039)), _1638043), _1638045)), c_List_Olistrel(_1638039, _1638041))), -(c_List_Olistrelp(_1638039, hAPP(hAPP(c_COMBC(_1638039, tc_fun(tc_prod(_1638039, _1638039), tc_HOL_Obool), tc_fun(_1638039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638039, tc_fun(tc_fun(tc_prod(_1638039, _1638039), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1638039, _1638039), tc_HOL_Obool), tc_fun(_1638039, tc_HOL_Obool)), _1638039), c_COMBC(_1638039, tc_fun(tc_prod(_1638039, _1638039), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638039, tc_prod(_1638039, _1638039)), tc_fun(_1638039, tc_fun(tc_fun(tc_prod(_1638039, _1638039), tc_HOL_Obool), tc_HOL_Obool)), _1638039), hAPP(c_COMBB(tc_prod(_1638039, _1638039), tc_fun(tc_fun(tc_prod(_1638039, _1638039), tc_HOL_Obool), tc_HOL_Obool), _1638039), c_member(tc_prod(_1638039, _1638039)))), c_Product__Type_OPair(_1638039, _1638039)))), _1638041), _1638043, _1638045))], (43179 ^ _782464) ^ [_1638422, _1638424, _1638426, _1638428, _1638430] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638422), tc_List_Olist(_1638422))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638422), tc_List_Olist(_1638422)), _1638424), hAPP(hAPP(c_List_Olist_OCons(_1638422), _1638426), _1638428))), c_List_Olistrel(_1638422, _1638430))), 43184 ^ _782464 : [(43185 ^ _782464) ^ [] : [-(_1638424 = hAPP(hAPP(c_List_Olist_OCons(_1638422), 43182 ^ [_1638422, _1638424, _1638426, _1638428, _1638430]), 43183 ^ [_1638422, _1638424, _1638426, _1638428, _1638430]))], (43187 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638422, _1638422)), hAPP(hAPP(c_Product__Type_OPair(_1638422, _1638422), 43182 ^ [_1638422, _1638424, _1638426, _1638428, _1638430]), _1638426)), _1638430)))], (43189 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638422), tc_List_Olist(_1638422))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638422), tc_List_Olist(_1638422)), 43183 ^ [_1638422, _1638424, _1638426, _1638428, _1638430]), _1638428)), c_List_Olistrel(_1638422, _1638430))))]]], (43191 ^ _782464) ^ [_1638811, _1638813, _1638815, _1638817, _1638819, _1638821] : [hBOOL(hAPP(hAPP(_1638811, _1638813), _1638815)), c_List_Olistrelp(_1638817, _1638811, _1638819, _1638821), -(c_List_Olistrelp(_1638817, _1638811, hAPP(hAPP(c_List_Olist_OCons(_1638817), _1638813), _1638819), hAPP(hAPP(c_List_Olist_OCons(_1638817), _1638815), _1638821)))], (43201 ^ _782464) ^ [_1639033, _1639035, _1639037, _1639039, _1639041, _1639043] : [c_List_Olistrelp(_1639033, _1639035, hAPP(hAPP(c_List_Olist_OCons(_1639033), _1639037), _1639039), hAPP(hAPP(c_List_Olist_OCons(_1639033), _1639041), _1639043)), 43204 ^ _782464 : [(43205 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1639035, _1639037), _1639041)))], (43207 ^ _782464) ^ [] : [-(c_List_Olistrelp(_1639033, _1639035, _1639039, _1639043))]]], (43209 ^ _782464) ^ [_1639190, _1639192, _1639194, _1639196, _1639198, _1639200] : [-(c_List_Olistrelp(_1639190, _1639192, hAPP(hAPP(c_List_Olist_OCons(_1639190), _1639194), _1639196), hAPP(hAPP(c_List_Olist_OCons(_1639190), _1639198), _1639200))), hBOOL(hAPP(hAPP(_1639192, _1639194), _1639198)), c_List_Olistrelp(_1639190, _1639192, _1639196, _1639200)], (43219 ^ _782464) ^ [_1639387, _1639389, _1639391, _1639393, _1639395] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639387), tc_List_Olist(_1639387))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639387), tc_List_Olist(_1639387)), hAPP(hAPP(c_List_Olist_OCons(_1639387), _1639389), _1639391)), _1639393)), c_List_Olistrel(_1639387, _1639395))), 43224 ^ _782464 : [(43225 ^ _782464) ^ [] : [-(_1639393 = hAPP(hAPP(c_List_Olist_OCons(_1639387), 43222 ^ [_1639387, _1639389, _1639391, _1639393, _1639395]), 43223 ^ [_1639387, _1639389, _1639391, _1639393, _1639395]))], (43227 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639387, _1639387)), hAPP(hAPP(c_Product__Type_OPair(_1639387, _1639387), _1639389), 43222 ^ [_1639387, _1639389, _1639391, _1639393, _1639395])), _1639395)))], (43229 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639387), tc_List_Olist(_1639387))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639387), tc_List_Olist(_1639387)), _1639391), 43223 ^ [_1639387, _1639389, _1639391, _1639393, _1639395])), c_List_Olistrel(_1639387, _1639395))))]]], (43231 ^ _782464) ^ [_1639776, _1639778, _1639780] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1639776, _1639776), tc_HOL_Obool)), _1639778), hAPP(hAPP(c_Product__Type_OSigma(_1639776, _1639776), _1639780), hAPP(c_COMBK(tc_fun(_1639776, tc_HOL_Obool), _1639776), _1639780)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1639776), tc_List_Olist(_1639776)), tc_HOL_Obool)), c_List_Olistrel(_1639776, _1639778)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1639776), tc_List_Olist(_1639776)), c_List_Olists(_1639776, _1639780)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1639776), tc_HOL_Obool), tc_List_Olist(_1639776)), c_List_Olists(_1639776, _1639780))))))], (43237 ^ _782464) ^ [_1640021] : [-(c_List_Olists(_1640021, c_Orderings_Otop__class_Otop(tc_fun(_1640021, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1640021), tc_HOL_Obool)))], (43239 ^ _782464) ^ [_1640059, _1640061, _1640063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640059, tc_HOL_Obool)), _1640061), _1640063)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1640059), tc_HOL_Obool)), c_List_Olists(_1640059, _1640061)), c_List_Olists(_1640059, _1640063))))], (43245 ^ _782464) ^ [_1640194, _1640196, _1640198] : [c_Equiv__Relations_Oequiv(_1640194, _1640196, _1640198), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1640194), c_List_Olists(_1640194, _1640196), c_List_Olistrel(_1640194, _1640198)))], (43251 ^ _782464) ^ [_1640293, _1640295, _1640297] : [c_Relation_Orefl__on(_1640293, _1640295, _1640297), -(c_Relation_Orefl__on(tc_List_Olist(_1640293), c_List_Olists(_1640293, _1640295), c_List_Olistrel(_1640293, _1640297)))], (43257 ^ _782464) ^ [_1640413, _1640415, _1640417, _1640419] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640413)), hAPP(hAPP(c_List_Olist_OCons(_1640413), _1640415), _1640417)), c_List_Olists(_1640413, _1640419))), 43260 ^ _782464 : [(43261 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1640413), _1640415), _1640419)))], (43263 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640413)), _1640417), c_List_Olists(_1640413, _1640419))))]]], (43265 ^ _782464) ^ [_1640594, _1640596, _1640598, _1640600] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640594)), hAPP(hAPP(c_List_Olist_OCons(_1640594), _1640596), _1640598)), c_List_Olists(_1640594, _1640600)))), hBOOL(hAPP(hAPP(c_member(_1640594), _1640596), _1640600)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640594)), _1640598), c_List_Olists(_1640594, _1640600)))], (43275 ^ _782464) ^ [_1640811, _1640813, _1640815] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640811)), _1640813), c_Wellfounded_Oacc(tc_List_Olist(_1640811), c_List_Olistrel1(_1640811, _1640815)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640811)), _1640813), c_List_Olists(_1640811, c_Wellfounded_Oacc(_1640811, _1640815)))))], (43281 ^ _782464) ^ [_1640954, _1640956, _1640958] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640954)), _1640956), c_List_Olists(_1640954, c_Wellfounded_Oacc(_1640954, _1640958)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640954)), _1640956), c_Wellfounded_Oacc(tc_List_Olist(_1640954), c_List_Olistrel1(_1640954, _1640958)))))], (43287 ^ _782464) ^ [_1641118, _1641120, _1641122, _1641124] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641118), tc_List_Olist(_1641118))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641118), tc_List_Olist(_1641118)), _1641120), _1641122)), c_List_Olistrel(_1641118, _1641124))), 43290 ^ _782464 : [(43291 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641118)), _1641120) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641118)), _1641122))], (43293 ^ _782464) ^ [_1641347] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641347), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641118)), _1641120))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641118, _1641118)), hAPP(hAPP(c_Product__Type_OPair(_1641118, _1641118), hAPP(hAPP(c_List_Onth(_1641118), _1641120), _1641347)), hAPP(hAPP(c_List_Onth(_1641118), _1641122), _1641347))), _1641124)))]]], (43299 ^ _782464) ^ [_1641526, _1641528, _1641530, _1641532] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641526), tc_List_Olist(_1641526))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641526), tc_List_Olist(_1641526)), _1641528), _1641530)), c_List_Olistrel(_1641526, _1641532)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641526)), _1641528) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641526)), _1641530), 43305 ^ _782464 : [(43306 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43304 ^ [_1641526, _1641528, _1641530, _1641532]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641526)), _1641528))))], (43308 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1641526, _1641526)), hAPP(hAPP(c_Product__Type_OPair(_1641526, _1641526), hAPP(hAPP(c_List_Onth(_1641526), _1641528), 43304 ^ [_1641526, _1641528, _1641530, _1641532])), hAPP(hAPP(c_List_Onth(_1641526), _1641530), 43304 ^ [_1641526, _1641528, _1641530, _1641532]))), _1641532))]]], (43312 ^ _782464) ^ [_1641969, _1641971, _1641973] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641969, _1641969)), hAPP(hAPP(c_Product__Type_OPair(_1641969, _1641969), 43313 ^ [_1641969, _1641971, _1641973]), 43313 ^ [_1641969, _1641971, _1641973])), _1641971))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641969), tc_List_Olist(_1641969))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641969), tc_List_Olist(_1641969)), _1641973), _1641973)), c_List_Olexord(_1641969, _1641971)))], (43319 ^ _782464) ^ [_1642144, _1642146, _1642148] : [-(hAPP(hAPP(c_List_Onth(_1642144), hAPP(hAPP(c_List_Olist_OCons(_1642144), _1642146), _1642148)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1642146)], (43321 ^ _782464) ^ [_1642187, _1642189, _1642191, _1642193] : [-(hAPP(hAPP(c_List_Onth(_1642187), hAPP(hAPP(c_List_Olist_OCons(_1642187), _1642189), _1642191)), hAPP(c_Nat_OSuc, _1642193)) = hAPP(hAPP(c_List_Onth(_1642187), _1642191), _1642193))], (43323 ^ _782464) ^ [_1642261, _1642263, _1642265] : [_1642261 = _1642263, 43326 ^ _782464 : [(43327 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642265)), _1642261) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642265)), _1642263))], (43329 ^ _782464) ^ [_1642409] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642409), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642265)), _1642261))), -(hAPP(hAPP(c_List_Onth(_1642265), _1642261), _1642409) = hAPP(hAPP(c_List_Onth(_1642265), _1642263), _1642409))]]], (43335 ^ _782464) ^ [_1642548, _1642550, _1642552] : [-(_1642548 = _1642550), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642552)), _1642548) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642552)), _1642550), 43341 ^ _782464 : [(43342 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43340 ^ [_1642548, _1642550, _1642552]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642552)), _1642548))))], (43344 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Onth(_1642552), _1642548), 43340 ^ [_1642548, _1642550, _1642552]) = hAPP(hAPP(c_List_Onth(_1642552), _1642550), 43340 ^ [_1642548, _1642550, _1642552])]]], (43348 ^ _782464) ^ [_1642872] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1642872)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1642872), tc_HOL_Obool))))], (43350 ^ _782464) ^ [_1642908, _1642910, _1642912, _1642914] : [-(hAPP(hAPP(c_List_Onth(_1642908), hAPP(hAPP(c_List_Olist_OCons(_1642908), _1642910), _1642912)), _1642914) = c_Nat_Onat_Onat__case(_1642908, _1642910, hAPP(c_List_Onth(_1642908), _1642912), _1642914))], (43352 ^ _782464) ^ [_1642978, _1642980, _1642982, _1642984] : [_1642978 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1642980), hAPP(hAPP(c_List_Olist_OCons(_1642980), _1642982), _1642984)), _1642978) = _1642982)], (43358 ^ _782464) ^ [_1643085, _1643087, _1643089, _1643091] : [-(_1643085 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1643087), hAPP(hAPP(c_List_Olist_OCons(_1643087), _1643089), _1643091)), _1643085) = hAPP(hAPP(c_List_Onth(_1643087), _1643091), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643085), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43364 ^ _782464) ^ [_1643172, _1643174, _1643176, _1643178] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643172) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1643174), hAPP(hAPP(c_List_Olist_OCons(_1643174), _1643176), _1643178)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643172)) = _1643176)], (43370 ^ _782464) ^ [_1643291, _1643293, _1643295, _1643297] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643291) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1643293), hAPP(hAPP(c_List_Olist_OCons(_1643293), _1643295), _1643297)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643291)) = hAPP(hAPP(c_List_Onth(_1643293), _1643297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643291)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43376 ^ _782464) ^ [_1643393, _1643395, _1643397, _1643399] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643393), tc_List_Olist(_1643393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643393), tc_List_Olist(_1643393)), _1643395), _1643397)), c_List_Olexord(_1643393, _1643399))), 43381 ^ _782464 : [(43382 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643393)), _1643395)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643393)), _1643397))))], (43384 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1643393), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643393)), _1643395)), _1643397) = _1643395)]], 43386 ^ _782464 : [(43387 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43385 ^ [_1643393, _1643395, _1643397, _1643399]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643393)), _1643395)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643393)), _1643397)))))], (43389 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1643393), 43385 ^ [_1643393, _1643395, _1643397, _1643399]), _1643395) = hAPP(hAPP(c_List_Otake(_1643393), 43385 ^ [_1643393, _1643395, _1643397, _1643399]), _1643397))], (43391 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643393, _1643393)), hAPP(hAPP(c_Product__Type_OPair(_1643393, _1643393), hAPP(hAPP(c_List_Onth(_1643393), _1643395), 43385 ^ [_1643393, _1643395, _1643397, _1643399])), hAPP(hAPP(c_List_Onth(_1643393), _1643397), 43385 ^ [_1643393, _1643395, _1643397, _1643399]))), _1643399)))]]], (43393 ^ _782464) ^ [_1643933, _1643935, _1643937, _1643939] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643933), tc_List_Olist(_1643933))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643933), tc_List_Olist(_1643933)), _1643935), _1643937)), c_List_Olexord(_1643933, _1643939)))), 43394 ^ _782464 : [(43395 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643933)), _1643935)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643933)), _1643937))), hAPP(hAPP(c_List_Otake(_1643933), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643933)), _1643935)), _1643937) = _1643935], (43401 ^ _782464) ^ [_1644240] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644240), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643933)), _1643935)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643933)), _1643937)))), hAPP(hAPP(c_List_Otake(_1643933), _1644240), _1643935) = hAPP(hAPP(c_List_Otake(_1643933), _1644240), _1643937), hBOOL(hAPP(hAPP(c_member(tc_prod(_1643933, _1643933)), hAPP(hAPP(c_Product__Type_OPair(_1643933, _1643933), hAPP(hAPP(c_List_Onth(_1643933), _1643935), _1644240)), hAPP(hAPP(c_List_Onth(_1643933), _1643937), _1644240))), _1643939))]]], (43413 ^ _782464) ^ [_1644594, _1644596, _1644598, _1644600] : [43416 ^ _782464 : [(43417 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644594, _1644594)), hAPP(hAPP(c_Product__Type_OPair(_1644594, _1644594), 43414 ^ [_1644594, _1644596, _1644598, _1644600]), 43415 ^ [_1644594, _1644596, _1644598, _1644600])), _1644596))], (43419 ^ _782464) ^ [] : [43414 ^ [_1644594, _1644596, _1644598, _1644600] = 43415 ^ [_1644594, _1644596, _1644598, _1644600]], (43421 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644594, _1644594)), hAPP(hAPP(c_Product__Type_OPair(_1644594, _1644594), 43415 ^ [_1644594, _1644596, _1644598, _1644600]), 43414 ^ [_1644594, _1644596, _1644598, _1644600])), _1644596))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644594), tc_List_Olist(_1644594))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644594), tc_List_Olist(_1644594)), _1644598), _1644600)), c_List_Olexord(_1644594, _1644596)))), -(_1644598 = _1644600), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644594), tc_List_Olist(_1644594))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644594), tc_List_Olist(_1644594)), _1644600), _1644598)), c_List_Olexord(_1644594, _1644596))))], (43433 ^ _782464) ^ [_1645141, _1645143, _1645145] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645141)), _1645143)), _1645145)), -(hAPP(hAPP(c_List_Otake(_1645141), _1645145), _1645143) = _1645143)], (43439 ^ _782464) ^ [_1645260, _1645262, _1645264, _1645266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645260), _1645262)), -(hAPP(hAPP(c_List_Onth(_1645264), hAPP(hAPP(c_List_Otake(_1645264), _1645262), _1645266)), _1645260) = hAPP(hAPP(c_List_Onth(_1645264), _1645266), _1645260))], (43445 ^ _782464) ^ [_1645399, _1645401, _1645403] : [-(c_List_Osublist(_1645399, _1645401, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1645403)) = hAPP(hAPP(c_List_Otake(_1645399), _1645403), _1645401))], (43447 ^ _782464) ^ [_1645441, _1645443, _1645445, _1645447] : [-(hAPP(hAPP(c_List_Otake(_1645441), _1645443), hAPP(hAPP(c_List_Otake(_1645441), _1645445), _1645447)) = hAPP(hAPP(c_List_Otake(_1645441), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1645443), _1645445)), _1645447))], (43449 ^ _782464) ^ [_1645500, _1645502, _1645504] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645500)), hAPP(hAPP(c_List_Otake(_1645500), _1645502), _1645504)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645500)), _1645504)), _1645502))], (43451 ^ _782464) ^ [_1645555, _1645557, _1645559, _1645561] : [-(hAPP(hAPP(c_List_Otake(_1645555), hAPP(c_Nat_OSuc, _1645557)), hAPP(hAPP(c_List_Olist_OCons(_1645555), _1645559), _1645561)) = hAPP(hAPP(c_List_Olist_OCons(_1645555), _1645559), hAPP(hAPP(c_List_Otake(_1645555), _1645557), _1645561)))], (43453 ^ _782464) ^ [_1645619, _1645621, _1645623] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1645619), _1645621)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1645619)), hAPP(c_Set_OCollect(tc_List_Olist(_1645619)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1645619), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1645619)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645619), tc_fun(_1645619, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1645619, tc_HOL_Obool), tc_fun(tc_fun(_1645619, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1645619)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1645619, tc_HOL_Obool))), c_List_Oset(_1645619))), _1645621))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645619), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1645619)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1645619)))), _1645623))))))], (43459 ^ _782464) ^ [_1645922, _1645924, _1645926] : [-(hAPP(c_List_Oset(_1645922), c_List_Osublist(_1645922, _1645924, _1645926)) = hAPP(c_Set_OCollect(_1645922), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1645922), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1645922, 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)), _1645922), 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)), _1645922), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1645922, tc_fun(tc_Nat_Onat, _1645922), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645922, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1645922), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1645922), c_COMBB(_1645922, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1645922), _1645924))))), 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(_1645922)), _1645924)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1645926))))))], (43461 ^ _782464) ^ [_1646066, _1646068] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1646066), hAPP(c_List_Oset(_1646066), _1646068))))], (43463 ^ _782464) ^ [_1646100, _1646102, _1646104] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646100, tc_HOL_Obool)), hAPP(c_List_Oset(_1646100), hAPP(hAPP(c_List_Otake(_1646100), _1646102), _1646104))), hAPP(c_List_Oset(_1646100), _1646104))))], (43465 ^ _782464) ^ [_1646155, _1646157, _1646159, _1646161] : [hBOOL(hAPP(hAPP(c_member(_1646155), _1646157), hAPP(c_List_Oset(_1646155), hAPP(hAPP(c_List_Otake(_1646155), _1646159), _1646161)))), -(hBOOL(hAPP(hAPP(c_member(_1646155), _1646157), hAPP(c_List_Oset(_1646155), _1646161))))], (43471 ^ _782464) ^ [_1646300, _1646302, _1646304] : [-(hAPP(c_List_Oset(_1646300), hAPP(hAPP(c_List_Olist_OCons(_1646300), _1646302), _1646304)) = hAPP(hAPP(c_Set_Oinsert(_1646300), _1646302), hAPP(c_List_Oset(_1646300), _1646304)))], (43473 ^ _782464) ^ [_1646353, _1646355, _1646357, _1646359] : [hBOOL(hAPP(hAPP(c_member(_1646353), _1646355), hAPP(c_List_Oset(_1646353), hAPP(hAPP(c_List_Olist_OCons(_1646353), _1646357), _1646359)))), -(_1646355 = _1646357), -(hBOOL(hAPP(hAPP(c_member(_1646353), _1646355), hAPP(c_List_Oset(_1646353), _1646359))))], (43483 ^ _782464) ^ [_1646510, _1646512, _1646514, _1646516] : [-(hBOOL(hAPP(hAPP(c_member(_1646510), _1646512), hAPP(c_List_Oset(_1646510), _1646514)))), hBOOL(hAPP(hAPP(c_member(_1646510), _1646512), hAPP(c_List_Oset(_1646510), c_List_Osublist(_1646510, _1646514, _1646516))))], (43489 ^ _782464) ^ [_1646634, _1646636, _1646638, _1646640] : [hBOOL(hAPP(hAPP(c_member(_1646634), _1646636), hAPP(c_List_Oset(_1646634), c_List_Osublist(_1646634, _1646638, _1646640)))), -(hBOOL(hAPP(hAPP(c_member(_1646634), _1646636), hAPP(c_List_Oset(_1646634), _1646638))))], (43495 ^ _782464) ^ [_1646771, _1646773] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1646771), tc_fun(_1646771, tc_HOL_Obool), c_List_Oset(_1646771)), hAPP(c_List_Oset(tc_List_Olist(_1646771)), c_Enum_Osublists(_1646771, _1646773))) = hAPP(c_Set_OPow(_1646771), hAPP(c_List_Oset(_1646771), _1646773)))], (43497 ^ _782464) ^ [_1646830, _1646832, _1646834] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646830, tc_HOL_Obool)), hAPP(c_List_Oset(_1646830), _1646832)), hAPP(c_List_Oset(_1646830), hAPP(hAPP(c_List_Olist_OCons(_1646830), _1646834), _1646832)))))], (43499 ^ _782464) ^ [_1646885, _1646887, _1646889] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646885, tc_HOL_Obool)), hAPP(c_List_Oset(_1646885), c_List_Osublist(_1646885, _1646887, _1646889))), hAPP(c_List_Oset(_1646885), _1646887))))], (43501 ^ _782464) ^ [_1646936, _1646938] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1646936), hAPP(c_List_Oset(_1646936), _1646938))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646936)), _1646938))))], (43503 ^ _782464) ^ [_1647001, _1647003, _1647005] : [43505 ^ _782464 : [(43506 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1647001), 43504 ^ [_1647001, _1647003, _1647005]), hAPP(c_List_Oset(_1647001), _1647003))))], (43508 ^ _782464) ^ [] : [hBOOL(hAPP(_1647005, 43504 ^ [_1647001, _1647003, _1647005]))]], 43509 ^ _782464 : [(43510 ^ _782464) ^ [_1647185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647185), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647001)), _1647003))), -(hBOOL(hAPP(_1647005, hAPP(hAPP(c_List_Onth(_1647001), _1647003), _1647185))))]]], (43516 ^ _782464) ^ [_1647312, _1647314, _1647316] : [43518 ^ _782464 : [(43519 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43517 ^ [_1647312, _1647314, _1647316]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647312)), _1647314))))], (43521 ^ _782464) ^ [] : [hBOOL(hAPP(_1647316, hAPP(hAPP(c_List_Onth(_1647312), _1647314), 43517 ^ [_1647312, _1647314, _1647316])))]], 43522 ^ _782464 : [(43523 ^ _782464) ^ [_1647514] : [hBOOL(hAPP(hAPP(c_member(_1647312), _1647514), hAPP(c_List_Oset(_1647312), _1647314))), -(hBOOL(hAPP(_1647316, _1647514)))]]], (43529 ^ _782464) ^ [_1647631, _1647633, _1647635, _1647637] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647631), _1647633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1647635, tc_HOL_Obool)), hAPP(c_List_Oset(_1647635), hAPP(hAPP(c_List_Otake(_1647635), _1647631), _1647637))), hAPP(c_List_Oset(_1647635), hAPP(hAPP(c_List_Otake(_1647635), _1647633), _1647637)))))], (43535 ^ _782464) ^ [_1647794, _1647796, _1647798, _1647800, _1647802] : [hBOOL(hAPP(hAPP(c_member(_1647794), _1647796), hAPP(c_List_Oset(_1647794), _1647798))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647800), hAPP(_1647802, _1647796))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647800), c_List_Olist_Olist__size(_1647794, _1647802, _1647798))))], (43545 ^ _782464) ^ [_1647993, _1647995, _1647997, _1647999, _1648001] : [hBOOL(hAPP(hAPP(c_member(_1647993), _1647995), hAPP(c_List_Oset(_1647993), _1647997))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647999), hAPP(_1648001, _1647995))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647999), c_List_Olist_Olist__size(_1647993, _1648001, _1647997))))], (43565 ^ _782464) ^ [_1648437, _1648439, _1648441] : [43567 ^ _782464 : [(43568 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1648437), 43566 ^ [_1648437, _1648439, _1648441]), hAPP(c_List_Oset(_1648437), _1648439))))], (43570 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648437), 43566 ^ [_1648437, _1648439, _1648441]), _1648441))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648437)), _1648439), c_List_Olists(_1648437, _1648441))))], (43555 ^ _782464) ^ [_1648210, _1648212, _1648214] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648210)), _1648212), c_List_Olists(_1648210, _1648214))), 43558 ^ _782464 : [(43559 ^ _782464) ^ [_1648318] : [hBOOL(hAPP(hAPP(c_member(_1648210), _1648318), hAPP(c_List_Oset(_1648210), _1648212))), -(hBOOL(hAPP(hAPP(c_member(_1648210), _1648318), _1648214)))]]], (43574 ^ _782464) ^ [_1648657, _1648659, _1648661] : [hBOOL(hAPP(hAPP(c_member(_1648657), _1648659), hAPP(c_List_Oset(_1648657), _1648661))), -(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(_1648657)), _1648661))))], (43580 ^ _782464) ^ [_1648796, _1648798, _1648800] : [hBOOL(hAPP(hAPP(c_member(_1648796), _1648798), hAPP(c_List_Oset(_1648796), _1648800))), 43584 ^ _782464 : [(43585 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43583 ^ [_1648796, _1648798, _1648800]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648796)), _1648800))))], (43587 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1648796), _1648800), 43583 ^ [_1648796, _1648798, _1648800]) = _1648798)]]], (43589 ^ _782464) ^ [_1648984, _1648986, _1648988] : [-(hBOOL(hAPP(hAPP(c_member(_1648984), _1648986), hAPP(c_List_Oset(_1648984), _1648988)))), 43590 ^ _782464 : [(43591 ^ _782464) ^ [_1649058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648984)), _1648988))), hAPP(hAPP(c_List_Onth(_1648984), _1648988), _1649058) = _1648986]]], (43599 ^ _782464) ^ [_1649220, _1649222, _1649224] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649220), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649222)), _1649224))), -(hBOOL(hAPP(hAPP(c_member(_1649222), hAPP(hAPP(c_List_Onth(_1649222), _1649224), _1649220)), hAPP(c_List_Oset(_1649222), _1649224))))], (43605 ^ _782464) ^ [_1649363, _1649365] : [-(c_List_Olists(_1649363, _1649365) = hAPP(c_Set_OCollect(tc_List_Olist(_1649363)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649363), tc_fun(_1649363, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649363, tc_HOL_Obool), tc_fun(tc_fun(_1649363, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649363)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649363, tc_HOL_Obool))), c_List_Oset(_1649363))), _1649365)))], (43607 ^ _782464) ^ [_1649441, _1649443] : [-(hAPP(c_List_Oset(_1649441), _1649443) = hAPP(c_Set_OCollect(_1649441), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1649441), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1649441, 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)), _1649441), 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)), _1649441), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1649441, tc_fun(tc_Nat_Onat, _1649441), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649441, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1649441), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1649441), c_COMBB(_1649441, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1649441), _1649443))))), 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(_1649441)), _1649443))))))], (43609 ^ _782464) ^ [_1649567, _1649569, _1649571] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1649567), _1649569)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1649567)), hAPP(c_Set_OCollect(tc_List_Olist(_1649567)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1649567), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1649567)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649567), tc_fun(_1649567, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649567, tc_HOL_Obool), tc_fun(tc_fun(_1649567, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649567)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649567, tc_HOL_Obool))), c_List_Oset(_1649567))), _1649569))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649567), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1649567)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1649567)))), _1649571))))))], (43615 ^ _782464) ^ [_1649891, _1649893, _1649895, _1649897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649891), tc_List_Olist(_1649891))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649891), tc_List_Olist(_1649891)), _1649893), _1649895)), c_List_Olistrel(_1649891, _1649897))), 43618 ^ _782464 : [(43619 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649891)), _1649893) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649891)), _1649895))], (43621 ^ _782464) ^ [_1650227] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649891, _1649891)), _1650227), hAPP(c_List_Oset(tc_prod(_1649891, _1649891)), hAPP(hAPP(c_List_Ozip(_1649891, _1649891), _1649893), _1649895)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1649891, _1649891, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1649891, tc_fun(tc_prod(_1649891, _1649891), tc_HOL_Obool), tc_fun(_1649891, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649891, tc_fun(tc_fun(tc_prod(_1649891, _1649891), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1649891, _1649891), tc_HOL_Obool), tc_fun(_1649891, tc_HOL_Obool)), _1649891), c_COMBC(_1649891, tc_fun(tc_prod(_1649891, _1649891), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649891, tc_prod(_1649891, _1649891)), tc_fun(_1649891, tc_fun(tc_fun(tc_prod(_1649891, _1649891), tc_HOL_Obool), tc_HOL_Obool)), _1649891), hAPP(c_COMBB(tc_prod(_1649891, _1649891), tc_fun(tc_fun(tc_prod(_1649891, _1649891), tc_HOL_Obool), tc_HOL_Obool), _1649891), c_member(tc_prod(_1649891, _1649891)))), c_Product__Type_OPair(_1649891, _1649891)))), _1649897)), _1650227)))]]], (43627 ^ _782464) ^ [_1650620, _1650622, _1650624, _1650626] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650620), tc_List_Olist(_1650620))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650620), tc_List_Olist(_1650620)), _1650622), _1650624)), c_List_Olistrel(_1650620, _1650626)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650620)), _1650622) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650620)), _1650624), 43633 ^ _782464 : [(43634 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650620, _1650620)), 43632 ^ [_1650620, _1650622, _1650624, _1650626]), hAPP(c_List_Oset(tc_prod(_1650620, _1650620)), hAPP(hAPP(c_List_Ozip(_1650620, _1650620), _1650622), _1650624)))))], (43636 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1650620, _1650620, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1650620, tc_fun(tc_prod(_1650620, _1650620), tc_HOL_Obool), tc_fun(_1650620, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650620, tc_fun(tc_fun(tc_prod(_1650620, _1650620), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650620, _1650620), tc_HOL_Obool), tc_fun(_1650620, tc_HOL_Obool)), _1650620), c_COMBC(_1650620, tc_fun(tc_prod(_1650620, _1650620), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650620, tc_prod(_1650620, _1650620)), tc_fun(_1650620, tc_fun(tc_fun(tc_prod(_1650620, _1650620), tc_HOL_Obool), tc_HOL_Obool)), _1650620), hAPP(c_COMBB(tc_prod(_1650620, _1650620), tc_fun(tc_fun(tc_prod(_1650620, _1650620), tc_HOL_Obool), tc_HOL_Obool), _1650620), c_member(tc_prod(_1650620, _1650620)))), c_Product__Type_OPair(_1650620, _1650620)))), _1650626)), 43632 ^ [_1650620, _1650622, _1650624, _1650626]))]]], (43640 ^ _782464) ^ [_1651358, _1651360, _1651362] : [-(hAPP(c_List_Oset(tc_List_Olist(_1651358)), c_Enum_On__lists(_1651358, _1651360, _1651362)) = hAPP(c_Set_OCollect(tc_List_Olist(_1651358)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1651358), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1651358)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651358), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1651358)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1651358)))), _1651360))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651358), tc_fun(_1651358, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1651358, tc_HOL_Obool), tc_fun(tc_fun(_1651358, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1651358)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1651358, tc_HOL_Obool))), c_List_Oset(_1651358))), hAPP(c_List_Oset(_1651358), _1651362)))))], (43642 ^ _782464) ^ [_1651503, _1651505, _1651507, _1651509] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1651503, _1651505))), hAPP(hAPP(c_List_Ozip(_1651503, _1651505), _1651507), _1651509)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651503)), _1651507)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651505)), _1651509)))], (43644 ^ _782464) ^ [_1651571, _1651573, _1651575, _1651577, _1651579] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1651571, _1651573)), _1651575), hAPP(hAPP(c_List_Ozip(_1651571, _1651573), _1651577), _1651579)) = hAPP(hAPP(c_List_Ozip(_1651571, _1651573), hAPP(hAPP(c_List_Otake(_1651571), _1651575), _1651577)), hAPP(hAPP(c_List_Otake(_1651573), _1651575), _1651579)))], (43646 ^ _782464) ^ [_1651647, _1651649, _1651651, _1651653, _1651655, _1651657] : [-(hAPP(hAPP(c_List_Ozip(_1651647, _1651649), hAPP(hAPP(c_List_Olist_OCons(_1651647), _1651651), _1651653)), hAPP(hAPP(c_List_Olist_OCons(_1651649), _1651655), _1651657)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1651647, _1651649)), hAPP(hAPP(c_Product__Type_OPair(_1651647, _1651649), _1651651), _1651655)), hAPP(hAPP(c_List_Ozip(_1651647, _1651649), _1651653), _1651657)))], (43648 ^ _782464) ^ [_1651752, _1651754, _1651756] : [_1651752 = _1651754, 43651 ^ _782464 : [(43652 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651756)), _1651752) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651756)), _1651754))], (43654 ^ _782464) ^ [_1651908] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651756, _1651756)), _1651908), hAPP(c_List_Oset(tc_prod(_1651756, _1651756)), hAPP(hAPP(c_List_Ozip(_1651756, _1651756), _1651752), _1651754)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1651756, _1651756, tc_HOL_Obool), c_fequal), _1651908)))]]], (43660 ^ _782464) ^ [_1652063, _1652065, _1652067] : [-(_1652063 = _1652065), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652067)), _1652063) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652067)), _1652065), 43666 ^ _782464 : [(43667 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652067, _1652067)), 43665 ^ [_1652063, _1652065, _1652067]), hAPP(c_List_Oset(tc_prod(_1652067, _1652067)), hAPP(hAPP(c_List_Ozip(_1652067, _1652067), _1652063), _1652065)))))], (43669 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1652067, _1652067, tc_HOL_Obool), c_fequal), 43665 ^ [_1652063, _1652065, _1652067]))]]], (43673 ^ _782464) ^ [_1652398, _1652400, _1652402, _1652404] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652398, _1652398)), hAPP(hAPP(c_Product__Type_OPair(_1652398, _1652398), _1652400), _1652402)), hAPP(c_List_Oset(tc_prod(_1652398, _1652398)), hAPP(hAPP(c_List_Ozip(_1652398, _1652398), _1652404), _1652404)))), 43676 ^ _782464 : [(43677 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652398), _1652400), hAPP(c_List_Oset(_1652398), _1652404))))], (43679 ^ _782464) ^ [] : [-(_1652400 = _1652402)]]], (43681 ^ _782464) ^ [_1652597, _1652599, _1652601, _1652603] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652597, _1652597)), hAPP(hAPP(c_Product__Type_OPair(_1652597, _1652597), _1652599), _1652601)), hAPP(c_List_Oset(tc_prod(_1652597, _1652597)), hAPP(hAPP(c_List_Ozip(_1652597, _1652597), _1652603), _1652603))))), hBOOL(hAPP(hAPP(c_member(_1652597), _1652599), hAPP(c_List_Oset(_1652597), _1652603))), _1652599 = _1652601], (43691 ^ _782464) ^ [_1652832, _1652834, _1652836, _1652838, _1652840, _1652842] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652832, _1652834)), hAPP(hAPP(c_Product__Type_OPair(_1652832, _1652834), _1652836), _1652838)), hAPP(c_List_Oset(tc_prod(_1652832, _1652834)), hAPP(hAPP(c_List_Ozip(_1652832, _1652834), _1652840), _1652842)))), -(hBOOL(hAPP(hAPP(c_member(_1652832), _1652836), hAPP(c_List_Oset(_1652832), _1652840))))], (43697 ^ _782464) ^ [_1653013, _1653015, _1653017, _1653019, _1653021, _1653023] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653013, _1653015)), hAPP(hAPP(c_Product__Type_OPair(_1653013, _1653015), _1653017), _1653019)), hAPP(c_List_Oset(tc_prod(_1653013, _1653015)), hAPP(hAPP(c_List_Ozip(_1653013, _1653015), _1653021), _1653023)))), -(hBOOL(hAPP(hAPP(c_member(_1653015), _1653019), hAPP(c_List_Oset(_1653015), _1653023))))], (43703 ^ _782464) ^ [_1653194, _1653196, _1653198, _1653200, _1653202, _1653204] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653194, _1653196)), hAPP(hAPP(c_Product__Type_OPair(_1653194, _1653196), _1653198), _1653200)), hAPP(c_List_Oset(tc_prod(_1653194, _1653196)), hAPP(hAPP(c_List_Ozip(_1653194, _1653196), _1653202), _1653204)))), 43706 ^ _782464 : [(43707 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653194), _1653198), hAPP(c_List_Oset(_1653194), _1653202))))], (43709 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653196), _1653200), hAPP(c_List_Oset(_1653196), _1653204))))]]], (43711 ^ _782464) ^ [_1653429, _1653431, _1653433, _1653435, _1653437] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653429), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653431)), _1653433))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653429), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653435)), _1653437))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1653431, _1653435)), hAPP(hAPP(c_List_Ozip(_1653431, _1653435), _1653433), _1653437)), _1653429) = hAPP(hAPP(c_Product__Type_OPair(_1653431, _1653435), hAPP(hAPP(c_List_Onth(_1653431), _1653433), _1653429)), hAPP(hAPP(c_List_Onth(_1653435), _1653437), _1653429)))], (43721 ^ _782464) ^ [_1653708, _1653710, _1653712, _1653714] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653708)), _1653710), hAPP(c_List_Oset(tc_List_Olist(_1653708)), c_Enum_On__lists(_1653708, _1653712, _1653714)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653708)), _1653710) = _1653712)], (43727 ^ _782464) ^ [_1653843, _1653845, _1653847] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1653843))), c_Enum_On__lists(_1653843, _1653845, _1653847)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653843)), _1653847)), _1653845))], (43729 ^ _782464) ^ [_1653896, _1653898, _1653900, _1653902] : [-(hAPP(c_List_Oset(tc_prod(_1653896, _1653898)), hAPP(hAPP(c_List_Ozip(_1653896, _1653898), _1653900), _1653902)) = hAPP(c_Set_OCollect(tc_prod(_1653896, _1653898)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1653896, _1653898)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1653896, _1653898), 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(_1653896, _1653898)), 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(_1653896, _1653898)), 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(_1653896, _1653898), tc_fun(tc_Nat_Onat, tc_prod(_1653896, _1653898)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1653896, _1653898), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1653896, _1653898)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1653896, _1653898)), c_COMBB(tc_prod(_1653896, _1653898), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1653898, tc_prod(_1653896, _1653898)), hAPP(hAPP(c_COMBB(_1653896, tc_fun(_1653898, tc_prod(_1653896, _1653898)), tc_Nat_Onat), c_Product__Type_OPair(_1653896, _1653898)), hAPP(c_List_Onth(_1653896), _1653900))), hAPP(c_List_Onth(_1653898), _1653902)))))), 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(_1653896)), _1653900)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653898)), _1653902)))))))], (43731 ^ _782464) ^ [_1654121, _1654123, _1654125, _1654127] : [-(hAPP(c_List_Oset(tc_prod(_1654121, _1654123)), c_Enum_Oproduct(_1654121, _1654123, _1654125, _1654127)) = hAPP(hAPP(c_Product__Type_OSigma(_1654121, _1654123), hAPP(c_List_Oset(_1654121), _1654125)), hAPP(c_COMBK(tc_fun(_1654123, tc_HOL_Obool), _1654121), hAPP(c_List_Oset(_1654123), _1654127))))], (43733 ^ _782464) ^ [_1654191, _1654193] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1654191, _1654193) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1654191), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1654193), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43735 ^ _782464) ^ [_1654238, _1654240] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654238, _1654240)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1654238, _1654240))], (43737 ^ _782464) ^ [_1654273, _1654275] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1654273, _1654275) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654273, _1654275)))], (43739 ^ _782464) ^ [_1654308, _1654310] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1654308), _1654310) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654308, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1654310), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43741 ^ _782464) ^ [_1654351, _1654353] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1654351, _1654353) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1654351), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1654353)))], (43743 ^ _782464) ^ [_1654404] : [c_List_Onat__list(_1654404), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1654404)))], (43749 ^ _782464) ^ [_1654477] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1654477)), -(c_List_Onat__list(_1654477))], (43755 ^ _782464) ^ [_1654556, _1654558] : [class_Groups_Ocomm__monoid__add(_1654556), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654556), _1654558) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1654556), hAPP(c_List_Onth(_1654556), _1654558)), 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(_1654556)), _1654558))))], (43771 ^ _782464) ^ [_1654869] : [43773 ^ _782464 : [(43774 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43772 ^ [_1654869]), hAPP(c_List_Oset(tc_Nat_Onat), _1654869))))], (43776 ^ _782464) ^ [] : [43772 ^ [_1654869] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1654869) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43761 ^ _782464) ^ [_1654701] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1654701) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43764 ^ _782464 : [(43765 ^ _782464) ^ [_1654776] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1654776), hAPP(c_List_Oset(tc_Nat_Onat), _1654701))), -(_1654776 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43780 ^ _782464) ^ [_1655025, _1655027, _1655029] : [class_Groups_Omonoid__add(_1655025), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1655025), hAPP(hAPP(c_List_Olist_OCons(_1655025), _1655027), _1655029)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1655025), _1655027), hAPP(c_List_Omonoid__add__class_Olistsum(_1655025), _1655029)))], (43786 ^ _782464) ^ [_1655154, _1655156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655154), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1655156))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1655156), _1655154)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1655156))))], (43792 ^ _782464) ^ [_1655275, _1655277, _1655279, _1655281] : [43794 ^ _782464 : [(43795 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655275), 43793 ^ [_1655275, _1655277, _1655279, _1655281]), hAPP(c_List_Oset(_1655275), _1655277))))], (43797 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1655279, 43793 ^ [_1655275, _1655277, _1655279, _1655281])), hAPP(_1655281, 43793 ^ [_1655275, _1655277, _1655279, _1655281])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1655275, _1655279, _1655277)), c_List_Olist_Olist__size(_1655275, _1655281, _1655277))))], (43801 ^ _782464) ^ [_1655525, _1655527, _1655529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655525), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655527)), _1655529))), -(c_List_Obutlast(_1655527, hAPP(hAPP(c_List_Otake(_1655527), _1655525), _1655529)) = hAPP(hAPP(c_List_Otake(_1655527), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655525), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1655529))], (43807 ^ _782464) ^ [_1655678, _1655680, _1655682] : [hBOOL(hAPP(hAPP(c_member(_1655678), _1655680), hAPP(c_List_Oset(_1655678), c_List_Obutlast(_1655678, _1655682)))), -(hBOOL(hAPP(hAPP(c_member(_1655678), _1655680), hAPP(c_List_Oset(_1655678), _1655682))))], (43813 ^ _782464) ^ [_1655811, _1655813, _1655815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655811), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655813)), _1655815))), -(hAPP(hAPP(c_List_Otake(_1655813), _1655811), c_List_Obutlast(_1655813, _1655815)) = hAPP(hAPP(c_List_Otake(_1655813), _1655811), _1655815))], (43819 ^ _782464) ^ [_1655952, _1655954] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655952)), c_List_Obutlast(_1655952, _1655954)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655952)), _1655954)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43821 ^ _782464) ^ [_1656000, _1656002] : [-(c_List_Obutlast(_1656000, _1656002) = hAPP(hAPP(c_List_Otake(_1656000), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656000)), _1656002)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1656002))], (43823 ^ _782464) ^ [_1656049, _1656051, _1656053] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656049), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1656051))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1656051), _1656049), _1656053)) = 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), _1656051)), _1656053)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1656051), _1656049)))], (43829 ^ _782464) ^ [_1656210, _1656212, _1656214, _1656216] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656210), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656212)), _1656214))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656210), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656212)), _1656216))), 43839 ^ _782464 : [(43840 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43838 ^ [_1656210, _1656212, _1656214, _1656216]), _1656210)))], (43842 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Onth(_1656212), _1656214), 43838 ^ [_1656210, _1656212, _1656214, _1656216]) = hAPP(hAPP(c_List_Onth(_1656212), _1656216), 43838 ^ [_1656210, _1656212, _1656214, _1656216])]], -(hAPP(hAPP(c_List_Otake(_1656212), _1656210), _1656214) = hAPP(hAPP(c_List_Otake(_1656212), _1656210), _1656216))], (43846 ^ _782464) ^ [_1656627, _1656629, _1656631, _1656633] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656627)), _1656629)), _1656631)), -(hAPP(hAPP(c_List_Olist__update(_1656627, _1656629), _1656631), _1656633) = _1656629)], (43852 ^ _782464) ^ [_1656746, _1656748, _1656750, _1656752, _1656754] : [-(_1656746 = _1656748), -(hAPP(hAPP(c_List_Onth(_1656750), hAPP(hAPP(c_List_Olist__update(_1656750, _1656752), _1656746), _1656754)), _1656748) = hAPP(hAPP(c_List_Onth(_1656750), _1656752), _1656748))], (43858 ^ _782464) ^ [_1656813, _1656815, _1656817] : [-(hAPP(hAPP(c_List_Olist__update(_1656813, _1656815), _1656817), hAPP(hAPP(c_List_Onth(_1656813), _1656815), _1656817)) = _1656815)], (43860 ^ _782464) ^ [_1656857, _1656859, _1656861, _1656863] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656857)), hAPP(hAPP(c_List_Olist__update(_1656857, _1656859), _1656861), _1656863)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656857)), _1656859))], (43862 ^ _782464) ^ [_1656909, _1656911, _1656913, _1656915, _1656917] : [-(hAPP(hAPP(c_List_Olist__update(_1656909, hAPP(hAPP(c_List_Olist_OCons(_1656909), _1656911), _1656913)), _1656915), _1656917) = c_Nat_Onat_Onat__case(tc_List_Olist(_1656909), hAPP(hAPP(c_List_Olist_OCons(_1656909), _1656917), _1656913), hAPP(hAPP(c_COMBB(tc_List_Olist(_1656909), tc_List_Olist(_1656909), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1656909), _1656911)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1656909, tc_List_Olist(_1656909)), c_List_Olist__update(_1656909, _1656913)), _1656917)), _1656915))], (43864 ^ _782464) ^ [_1657006, _1657008, _1657010, _1657012] : [-(hAPP(hAPP(c_List_Olist__update(_1657006, hAPP(hAPP(c_List_Olist_OCons(_1657006), _1657008), _1657010)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1657012) = hAPP(hAPP(c_List_Olist_OCons(_1657006), _1657012), _1657010))], (43866 ^ _782464) ^ [_1657060, _1657062, _1657064, _1657066, _1657068] : [-(hAPP(hAPP(c_List_Olist__update(_1657060, hAPP(hAPP(c_List_Olist_OCons(_1657060), _1657062), _1657064)), hAPP(c_Nat_OSuc, _1657066)), _1657068) = hAPP(hAPP(c_List_Olist_OCons(_1657060), _1657062), hAPP(hAPP(c_List_Olist__update(_1657060, _1657064), _1657066), _1657068)))], (43868 ^ _782464) ^ [_1657128, _1657130, _1657132, _1657134, _1657136] : [-(hAPP(hAPP(c_List_Olist__update(_1657128, hAPP(hAPP(c_List_Olist__update(_1657128, _1657130), _1657132), _1657134)), _1657132), _1657136) = hAPP(hAPP(c_List_Olist__update(_1657128, _1657130), _1657132), _1657136))], (43870 ^ _782464) ^ [_1657182, _1657184, _1657186, _1657188, _1657190, _1657192] : [-(_1657182 = _1657184), -(hAPP(hAPP(c_List_Olist__update(_1657186, hAPP(hAPP(c_List_Olist__update(_1657186, _1657188), _1657182), _1657190)), _1657184), _1657192) = hAPP(hAPP(c_List_Olist__update(_1657186, hAPP(hAPP(c_List_Olist__update(_1657186, _1657188), _1657184), _1657192)), _1657182), _1657190))], (43876 ^ _782464) ^ [_1657262, _1657264, _1657266, _1657268, _1657270, _1657272] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1657262, _1657264), hAPP(hAPP(c_List_Ozip(_1657262, _1657264), _1657266), _1657268)), _1657270), _1657272) = hAPP(hAPP(c_List_Ozip(_1657262, _1657264), hAPP(hAPP(c_List_Olist__update(_1657262, _1657266), _1657270), hAPP(c_Product__Type_Ofst(_1657262, _1657264), _1657272))), hAPP(hAPP(c_List_Olist__update(_1657264, _1657268), _1657270), hAPP(c_Product__Type_Osnd(_1657262, _1657264), _1657272))))], (43878 ^ _782464) ^ [_1657355, _1657357, _1657359, _1657361, _1657363, _1657365, _1657367] : [-(hAPP(hAPP(c_List_Ozip(_1657355, _1657357), hAPP(hAPP(c_List_Olist__update(_1657355, _1657359), _1657361), _1657363)), hAPP(hAPP(c_List_Olist__update(_1657357, _1657365), _1657361), _1657367)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1657355, _1657357), hAPP(hAPP(c_List_Ozip(_1657355, _1657357), _1657359), _1657365)), _1657361), hAPP(hAPP(c_Product__Type_OPair(_1657355, _1657357), _1657363), _1657367)))], (43880 ^ _782464) ^ [_1657447, _1657449, _1657451, _1657453, _1657455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657447, tc_HOL_Obool)), hAPP(c_List_Oset(_1657447), _1657449)), _1657451)), hBOOL(hAPP(hAPP(c_member(_1657447), _1657453), _1657451)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657447, tc_HOL_Obool)), hAPP(c_List_Oset(_1657447), hAPP(hAPP(c_List_Olist__update(_1657447, _1657449), _1657455), _1657453))), _1657451)))], (43890 ^ _782464) ^ [_1657680, _1657682, _1657684, _1657686] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657680, tc_HOL_Obool)), hAPP(c_List_Oset(_1657680), hAPP(hAPP(c_List_Olist__update(_1657680, _1657682), _1657684), _1657686))), hAPP(hAPP(c_Set_Oinsert(_1657680), _1657686), hAPP(c_List_Oset(_1657680), _1657682)))))], (43892 ^ _782464) ^ [_1657746, _1657748, _1657750, _1657752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657746), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657748)), _1657750))), -(hAPP(hAPP(c_List_Onth(_1657748), hAPP(hAPP(c_List_Olist__update(_1657748, _1657750), _1657746), _1657752)), _1657746) = _1657752)], (43898 ^ _782464) ^ [_1657885, _1657887, _1657889, _1657891] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657885), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657887)), _1657889))), 43901 ^ _782464 : [(43902 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1657887, _1657889), _1657885), _1657891) = _1657889, -(hAPP(hAPP(c_List_Onth(_1657887), _1657889), _1657885) = _1657891)], (43908 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Onth(_1657887), _1657889), _1657885) = _1657891, -(hAPP(hAPP(c_List_Olist__update(_1657887, _1657889), _1657885), _1657891) = _1657889)]]], (43914 ^ _782464) ^ [_1658179, _1658181, _1658183, _1658185, _1658187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658179), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658181)), _1658183))), 43917 ^ _782464 : [(43918 ^ _782464) ^ [] : [_1658179 = _1658185, -(hAPP(hAPP(c_List_Onth(_1658181), hAPP(hAPP(c_List_Olist__update(_1658181, _1658183), _1658179), _1658187)), _1658185) = _1658187)], (43924 ^ _782464) ^ [] : [-(_1658179 = _1658185), -(hAPP(hAPP(c_List_Onth(_1658181), hAPP(hAPP(c_List_Olist__update(_1658181, _1658183), _1658179), _1658187)), _1658185) = hAPP(hAPP(c_List_Onth(_1658181), _1658183), _1658185))]]], (43930 ^ _782464) ^ [_1658475, _1658477, _1658479, _1658481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658475), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658477)), _1658479))), -(hBOOL(hAPP(hAPP(c_member(_1658477), _1658481), hAPP(c_List_Oset(_1658477), hAPP(hAPP(c_List_Olist__update(_1658477, _1658479), _1658475), _1658481)))))], (43936 ^ _782464) ^ [_1658637, _1658639, _1658641, _1658643] : [_1658637 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658639)), _1658641)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1658639, hAPP(hAPP(c_List_Olist__update(_1658639, _1658641), _1658637), _1658643)) = c_List_Obutlast(_1658639, _1658641))], (43942 ^ _782464) ^ [_1658768, _1658770, _1658772, _1658774] : [-(_1658768 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658770)), _1658772)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1658770, hAPP(hAPP(c_List_Olist__update(_1658770, _1658772), _1658768), _1658774)) = hAPP(hAPP(c_List_Olist__update(_1658770, c_List_Obutlast(_1658770, _1658772)), _1658768), _1658774))], (43948 ^ _782464) ^ [_1658868, _1658870, _1658872, _1658874] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658868), tc_List_Olist(_1658868))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658868), tc_List_Olist(_1658868)), _1658870), _1658872)), c_List_Olistrel1(_1658868, _1658874))), 43953 ^ _782464 : [(43954 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658868, _1658868)), hAPP(hAPP(c_Product__Type_OPair(_1658868, _1658868), hAPP(hAPP(c_List_Onth(_1658868), _1658870), 43952 ^ [_1658868, _1658870, _1658872, _1658874])), 43951 ^ [_1658868, _1658870, _1658872, _1658874])), _1658874)))], (43956 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43952 ^ [_1658868, _1658870, _1658872, _1658874]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658868)), _1658870))))], (43958 ^ _782464) ^ [] : [-(_1658872 = hAPP(hAPP(c_List_Olist__update(_1658868, _1658870), 43952 ^ [_1658868, _1658870, _1658872, _1658874]), 43951 ^ [_1658868, _1658870, _1658872, _1658874]))]]], (43960 ^ _782464) ^ [_1659216, _1659218, _1659220, _1659222] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659216), tc_List_Olist(_1659216))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659216), tc_List_Olist(_1659216)), _1659218), _1659220)), c_List_Olistrel1(_1659216, _1659222)))), 43961 ^ _782464 : [(43962 ^ _782464) ^ [_1659349, _1659351] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1659216, _1659216)), hAPP(hAPP(c_Product__Type_OPair(_1659216, _1659216), hAPP(hAPP(c_List_Onth(_1659216), _1659218), _1659349)), _1659351)), _1659222)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659349), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659216)), _1659218))), _1659220 = hAPP(hAPP(c_List_Olist__update(_1659216, _1659218), _1659349), _1659351)]]], (43974 ^ _782464) ^ [_1659649, _1659651, _1659653, _1659655] : [hBOOL(hAPP(c_List_Odistinct(_1659649), _1659651)), -(hBOOL(hAPP(hAPP(c_member(_1659649), _1659653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659649, tc_HOL_Obool)), hAPP(c_List_Oset(_1659649), _1659651)), hAPP(hAPP(c_Set_Oinsert(_1659649), hAPP(hAPP(c_List_Onth(_1659649), _1659651), _1659655)), c_Orderings_Obot__class_Obot(tc_fun(_1659649, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1659649), hAPP(hAPP(c_List_Olist__update(_1659649, _1659651), _1659655), _1659653))))], (43984 ^ _782464) ^ [_1659867, _1659869, _1659871] : [hBOOL(hAPP(c_List_Odistinct(_1659867), _1659869)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1659867)), c_Enum_On__lists(_1659867, _1659871, _1659869))))], (43990 ^ _782464) ^ [_1659974, _1659976, _1659978, _1659980] : [hBOOL(hAPP(c_List_Odistinct(_1659974), _1659976)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1659974, _1659978)), hAPP(hAPP(c_List_Ozip(_1659974, _1659978), _1659976), _1659980))))], (43996 ^ _782464) ^ [_1660095, _1660097, _1660099, _1660101] : [hBOOL(hAPP(c_List_Odistinct(_1660095), _1660097)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1660099, _1660095)), hAPP(hAPP(c_List_Ozip(_1660099, _1660095), _1660101), _1660097))))], (44002 ^ _782464) ^ [_1660216, _1660218, _1660220] : [hBOOL(hAPP(c_List_Odistinct(_1660216), _1660218)), -(hBOOL(hAPP(c_List_Odistinct(_1660216), c_List_Osublist(_1660216, _1660218, _1660220))))], (44008 ^ _782464) ^ [_1660319, _1660321, _1660323, _1660325] : [hBOOL(hAPP(c_List_Odistinct(_1660319), _1660321)), hBOOL(hAPP(c_List_Odistinct(_1660323), _1660325)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1660319, _1660323)), c_Enum_Oproduct(_1660319, _1660323, _1660321, _1660325))))], (44018 ^ _782464) ^ [_1660496, _1660498] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1660496, _1660498))))], (44020 ^ _782464) ^ [_1660526, _1660528, _1660530] : [hBOOL(hAPP(c_List_Odistinct(_1660526), _1660528)), -(hBOOL(hAPP(c_List_Odistinct(_1660526), hAPP(hAPP(c_List_Otake(_1660526), _1660530), _1660528))))], (44026 ^ _782464) ^ [_1660655, _1660657, _1660659] : [hBOOL(hAPP(c_List_Odistinct(_1660655), hAPP(hAPP(c_List_Olist_OCons(_1660655), _1660657), _1660659))), 44029 ^ _782464 : [(44030 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1660655), _1660657), hAPP(c_List_Oset(_1660655), _1660659)))], (44032 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660655), _1660659)))]]], (44034 ^ _782464) ^ [_1660822, _1660824, _1660826] : [-(hBOOL(hAPP(c_List_Odistinct(_1660822), hAPP(hAPP(c_List_Olist_OCons(_1660822), _1660824), _1660826)))), -(hBOOL(hAPP(hAPP(c_member(_1660822), _1660824), hAPP(c_List_Oset(_1660822), _1660826)))), hBOOL(hAPP(c_List_Odistinct(_1660822), _1660826))], (44044 ^ _782464) ^ [_1661016, _1661018] : [hAPP(c_Finite__Set_Ocard(_1661016), hAPP(c_List_Oset(_1661016), _1661018)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661016)), _1661018), -(hBOOL(hAPP(c_List_Odistinct(_1661016), _1661018)))], (44050 ^ _782464) ^ [_1661135, _1661137] : [hBOOL(hAPP(c_List_Odistinct(_1661135), _1661137)), -(hAPP(c_Finite__Set_Ocard(_1661135), hAPP(c_List_Oset(_1661135), _1661137)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661135)), _1661137))], (44056 ^ _782464) ^ [_1661254, _1661256, _1661258, _1661260] : [hBOOL(hAPP(c_List_Odistinct(_1661254), _1661256)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661258), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661254)), _1661256))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661260), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661254)), _1661256))), 44067 ^ _782464 : [(44068 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Onth(_1661254), _1661256), _1661258) = hAPP(hAPP(c_List_Onth(_1661254), _1661256), _1661260), -(_1661258 = _1661260)], (44074 ^ _782464) ^ [] : [_1661258 = _1661260, -(hAPP(hAPP(c_List_Onth(_1661254), _1661256), _1661258) = hAPP(hAPP(c_List_Onth(_1661254), _1661256), _1661260))]]], (44098 ^ _782464) ^ [_1662164, _1662166] : [44100 ^ _782464 : [(44101 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44099 ^ [_1662164, _1662166]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662164)), _1662166))))], (44104 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44102 ^ [_1662164, _1662166]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662164)), _1662166))))], (44106 ^ _782464) ^ [] : [44099 ^ [_1662164, _1662166] = 44102 ^ [_1662164, _1662166]], (44108 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1662164), _1662166), 44099 ^ [_1662164, _1662166]) = hAPP(hAPP(c_List_Onth(_1662164), _1662166), 44102 ^ [_1662164, _1662166]))]], -(hBOOL(hAPP(c_List_Odistinct(_1662164), _1662166)))], (44080 ^ _782464) ^ [_1661704, _1661706] : [hBOOL(hAPP(c_List_Odistinct(_1661704), _1661706)), 44083 ^ _782464 : [(44084 ^ _782464) ^ [_1661836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661836), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661704)), _1661706))), 44087 ^ _782464 : [(44088 ^ _782464) ^ [_1661963] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661963), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661704)), _1661706))), -(_1661836 = _1661963), hAPP(hAPP(c_List_Onth(_1661704), _1661706), _1661836) = hAPP(hAPP(c_List_Onth(_1661704), _1661706), _1661963)]]]]], (44112 ^ _782464) ^ [_1662596, _1662598] : [class_Groups_Ocomm__monoid__add(_1662596), hBOOL(hAPP(c_List_Odistinct(_1662596), _1662598)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1662596), _1662598) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1662596, _1662596), c_COMBI(_1662596)), hAPP(c_List_Oset(_1662596), _1662598)))], (44122 ^ _782464) ^ [_1662782, _1662784] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1662782), _1662784)), -(c_Nitpick_Ocard_H(_1662782, _1662784) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662782)), c_Hilbert__Choice_OEps(tc_List_Olist(_1662782), hAPP(hAPP(c_COMBS(tc_List_Olist(_1662782), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1662782)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1662782), tc_fun(_1662782, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1662782, tc_HOL_Obool), tc_fun(tc_fun(_1662782, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1662782)), c_fequal), c_List_Oset(_1662782))), _1662784))), c_List_Odistinct(_1662782)))))], (44128 ^ _782464) ^ [_1663019, _1663021] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1663019), _1663021))), -(c_Nitpick_Ocard_H(_1663019, _1663021) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44134 ^ _782464) ^ [_1663064, _1663066, _1663068] : [hBOOL(hAPP(c_List_Odistinct(_1663064), _1663066)), -(hAPP(c_List_Oset(_1663064), c_List_Oremove1(_1663064, _1663068, _1663066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1663064, tc_HOL_Obool)), hAPP(c_List_Oset(_1663064), _1663066)), hAPP(hAPP(c_Set_Oinsert(_1663064), _1663068), c_Orderings_Obot__class_Obot(tc_fun(_1663064, tc_HOL_Obool)))))], (44140 ^ _782464) ^ [_1663227, _1663229, _1663231] : [hBOOL(hAPP(c_List_Odistinct(_1663227), _1663229)), -(hBOOL(hAPP(c_List_Odistinct(_1663227), c_List_Oremove1(_1663227, _1663231, _1663229))))], (44146 ^ _782464) ^ [_1663345, _1663347, _1663349, _1663351] : [_1663345 = _1663347, -(c_List_Oremove1(_1663349, _1663345, hAPP(hAPP(c_List_Olist_OCons(_1663349), _1663347), _1663351)) = _1663351)], (44152 ^ _782464) ^ [_1663444, _1663446, _1663448, _1663450] : [-(_1663444 = _1663446), -(c_List_Oremove1(_1663448, _1663444, hAPP(hAPP(c_List_Olist_OCons(_1663448), _1663446), _1663450)) = hAPP(hAPP(c_List_Olist_OCons(_1663448), _1663446), c_List_Oremove1(_1663448, _1663444, _1663450)))], (44158 ^ _782464) ^ [_1663510, _1663512, _1663514, _1663516] : [-(c_List_Oremove1(_1663510, _1663512, c_List_Oremove1(_1663510, _1663514, _1663516)) = c_List_Oremove1(_1663510, _1663514, c_List_Oremove1(_1663510, _1663512, _1663516)))], (44160 ^ _782464) ^ [_1663551, _1663553, _1663555] : [-(hBOOL(hAPP(hAPP(c_member(_1663551), _1663553), hAPP(c_List_Oset(_1663551), _1663555)))), -(c_List_Oremove1(_1663551, _1663553, _1663555) = _1663555)], (44166 ^ _782464) ^ [_1663604, _1663606, _1663608, _1663610] : [-(hBOOL(hAPP(hAPP(c_member(_1663604), _1663606), hAPP(c_List_Oset(_1663604), _1663608)))), hBOOL(hAPP(hAPP(c_member(_1663604), _1663606), hAPP(c_List_Oset(_1663604), c_List_Oremove1(_1663604, _1663610, _1663608))))], (44172 ^ _782464) ^ [_1663727, _1663729, _1663731, _1663733] : [-(_1663727 = _1663729), 44175 ^ _782464 : [(44176 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663731), _1663727), hAPP(c_List_Oset(_1663731), c_List_Oremove1(_1663731, _1663729, _1663733)))), -(hBOOL(hAPP(hAPP(c_member(_1663731), _1663727), hAPP(c_List_Oset(_1663731), _1663733))))], (44182 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663731), _1663727), hAPP(c_List_Oset(_1663731), _1663733))), -(hBOOL(hAPP(hAPP(c_member(_1663731), _1663727), hAPP(c_List_Oset(_1663731), c_List_Oremove1(_1663731, _1663729, _1663733)))))]]], (44188 ^ _782464) ^ [_1664028, _1664030, _1664032] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1664028, tc_HOL_Obool)), hAPP(c_List_Oset(_1664028), c_List_Oremove1(_1664028, _1664030, _1664032))), hAPP(c_List_Oset(_1664028), _1664032))))], (44190 ^ _782464) ^ [_1664091, _1664093, _1664095] : [hBOOL(hAPP(hAPP(c_member(_1664091), _1664093), hAPP(c_List_Oset(_1664091), _1664095))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664091)), c_List_Oremove1(_1664091, _1664093, _1664095)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664091)), _1664095)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44196 ^ _782464) ^ [_1664236, _1664238, _1664240] : [-(hBOOL(hAPP(hAPP(c_member(_1664236), _1664238), hAPP(c_List_Oset(_1664236), _1664240)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664236)), c_List_Oremove1(_1664236, _1664238, _1664240)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664236)), _1664240))], (44202 ^ _782464) ^ [_1664306, _1664308, _1664310] : [class_Orderings_Olinorder(_1664306), hBOOL(hAPP(c_Finite__Set_Ofinite(_1664306), _1664308)), -(c_List_Olinorder__class_Osorted__list__of__set(_1664306, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1664306, tc_HOL_Obool)), _1664308), hAPP(hAPP(c_Set_Oinsert(_1664306), _1664310), c_Orderings_Obot__class_Obot(tc_fun(_1664306, tc_HOL_Obool))))) = c_List_Oremove1(_1664306, _1664310, c_List_Olinorder__class_Osorted__list__of__set(_1664306, _1664308)))], (44212 ^ _782464) ^ [_1664528, _1664530, _1664532, _1664534] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664528) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1664530), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664528)), hAPP(hAPP(c_List_Olist_OCons(_1664530), _1664532), _1664534)) = c_List_Olist_ONil(_1664530))], (44218 ^ _782464) ^ [_1664651, _1664653, _1664655, _1664657] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664651) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1664653), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664651)), hAPP(hAPP(c_List_Olist_OCons(_1664653), _1664655), _1664657)) = hAPP(hAPP(c_List_Olist_OCons(_1664653), _1664655), hAPP(hAPP(c_List_Otake(_1664653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664651)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1664657)))], (44224 ^ _782464) ^ [_1664740, _1664742] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664740)), c_List_Olist_ONil(_1664740)), c_List_Olists(_1664740, _1664742))))], (44226 ^ _782464) ^ [_1664779, _1664781, _1664783] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664779), tc_List_Olist(_1664779))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664779), tc_List_Olist(_1664779)), _1664781), c_List_Olist_ONil(_1664779))), c_List_Olistrel(_1664779, _1664783))), -(_1664781 = c_List_Olist_ONil(_1664779))], (44232 ^ _782464) ^ [_1664926, _1664928, _1664930] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664926), tc_List_Olist(_1664926))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664926), tc_List_Olist(_1664926)), c_List_Olist_ONil(_1664926)), _1664928)), c_List_Olistrel(_1664926, _1664930))), -(_1664928 = c_List_Olist_ONil(_1664926))], (44238 ^ _782464) ^ [_1665073] : [-(hBOOL(hAPP(c_List_Odistinct(_1665073), c_List_Olist_ONil(_1665073))))], (44240 ^ _782464) ^ [_1665101, _1665103] : [-(_1665101 = c_List_Olist_ONil(_1665103)), hBOOL(hAPP(c_List_Odistinct(_1665103), _1665101)), -(hBOOL(hAPP(c_List_Odistinct(_1665103), c_List_Obutlast(_1665103, _1665101))))], (44250 ^ _782464) ^ [_1665252, _1665254] : [-(c_List_Oremove1(_1665252, _1665254, c_List_Olist_ONil(_1665252)) = c_List_Olist_ONil(_1665252))], (44252 ^ _782464) ^ [_1665285, _1665287, _1665289] : [-(hAPP(hAPP(c_List_Ozip(_1665285, _1665287), c_List_Olist_ONil(_1665285)), _1665289) = c_List_Olist_ONil(tc_prod(_1665285, _1665287)))], (44254 ^ _782464) ^ [_1665328, _1665330, _1665332] : [-(hAPP(hAPP(c_List_Ozip(_1665328, _1665330), _1665332), c_List_Olist_ONil(_1665330)) = c_List_Olist_ONil(tc_prod(_1665328, _1665330)))], (44256 ^ _782464) ^ [_1665371] : [class_Orderings_Olinorder(_1665371), -(c_List_Olinorder__class_Osorted__list__of__set(_1665371, c_Orderings_Obot__class_Obot(tc_fun(_1665371, tc_HOL_Obool))) = c_List_Olist_ONil(_1665371))], (44262 ^ _782464) ^ [_1665464, _1665466] : [-(c_List_Osublist(_1665464, c_List_Olist_ONil(_1665464), _1665466) = c_List_Olist_ONil(_1665464))], (44264 ^ _782464) ^ [_1665497, _1665499] : [-(c_List_Olistrelp(_1665497, _1665499, c_List_Olist_ONil(_1665497), c_List_Olist_ONil(_1665497)))], (44266 ^ _782464) ^ [_1665528, _1665530] : [-(c_List_Olistrelp(_1665528, _1665530, c_List_Olist_ONil(_1665528), c_List_Olist_ONil(_1665528)))], (44268 ^ _782464) ^ [_1665559, _1665561] : [-(c_List_Olist_Olist__size(_1665559, _1665561, c_List_Olist_ONil(_1665559)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44270 ^ _782464) ^ [_1665590, _1665592] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665590), _1665592)), -(c_List_Oupto(_1665592, _1665590) = c_List_Olist_ONil(tc_Int_Oint))], (44276 ^ _782464) ^ [_1665683, _1665685, _1665687] : [-(c_Enum_Oproduct(_1665683, _1665685, c_List_Olist_ONil(_1665683), _1665687) = c_List_Olist_ONil(tc_prod(_1665683, _1665685)))], (44278 ^ _782464) ^ [_1665737, _1665739, _1665741] : [c_List_Olist_ONil(_1665737) = hAPP(hAPP(c_List_Olist_OCons(_1665737), _1665739), _1665741)], (44280 ^ _782464) ^ [_1665789, _1665791, _1665793] : [hAPP(hAPP(c_List_Olist_OCons(_1665789), _1665791), _1665793) = c_List_Olist_ONil(_1665789)], (44282 ^ _782464) ^ [_1665826] : [-(c_Enum_Osublists(_1665826, c_List_Olist_ONil(_1665826)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1665826)), c_List_Olist_ONil(_1665826)), c_List_Olist_ONil(tc_List_Olist(_1665826))))], (44284 ^ _782464) ^ [_1665870, _1665872] : [-(hAPP(hAPP(c_List_Otake(_1665870), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1665872) = c_List_Olist_ONil(_1665870))], (44296 ^ _782464) ^ [_1666035, _1666037, _1666039] : [44297 ^ _782464 : [(44298 ^ _782464) ^ [] : [_1666037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44300 ^ _782464) ^ [] : [_1666039 = c_List_Olist_ONil(_1666035)]], -(hAPP(hAPP(c_List_Otake(_1666035), _1666037), _1666039) = c_List_Olist_ONil(_1666035))], (44286 ^ _782464) ^ [_1665923, _1665925, _1665927] : [hAPP(hAPP(c_List_Otake(_1665923), _1665925), _1665927) = c_List_Olist_ONil(_1665923), -(_1665925 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1665927 = c_List_Olist_ONil(_1665923))], (44304 ^ _782464) ^ [_1666178, _1666180] : [-(hAPP(hAPP(c_List_Otake(_1666178), _1666180), c_List_Olist_ONil(_1666178)) = c_List_Olist_ONil(_1666178))], (44306 ^ _782464) ^ [_1666224, _1666226] : [_1666224 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1666226, _1666224, c_List_Olist_ONil(_1666226)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666226)), c_List_Olist_ONil(_1666226)), c_List_Olist_ONil(tc_List_Olist(_1666226))))], (44312 ^ _782464) ^ [_1666339, _1666341] : [-(_1666339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1666341, _1666339, c_List_Olist_ONil(_1666341)) = c_List_Olist_ONil(tc_List_Olist(_1666341)))], (44318 ^ _782464) ^ [_1666387, _1666389] : [-(c_Enum_On__lists(_1666387, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1666389) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666387)), c_List_Olist_ONil(_1666387)), c_List_Olist_ONil(tc_List_Olist(_1666387))))], (44320 ^ _782464) ^ [_1666447, _1666449] : [hAPP(c_List_Oset(_1666447), _1666449) = c_Orderings_Obot__class_Obot(tc_fun(_1666447, tc_HOL_Obool)), -(_1666449 = c_List_Olist_ONil(_1666447))], (44326 ^ _782464) ^ [_1666544, _1666546] : [_1666546 = c_List_Olist_ONil(_1666544), -(hAPP(c_List_Oset(_1666544), _1666546) = c_Orderings_Obot__class_Obot(tc_fun(_1666544, tc_HOL_Obool)))], (44332 ^ _782464) ^ [_1666662, _1666664] : [c_Orderings_Obot__class_Obot(tc_fun(_1666662, tc_HOL_Obool)) = hAPP(c_List_Oset(_1666662), _1666664), -(_1666664 = c_List_Olist_ONil(_1666662))], (44338 ^ _782464) ^ [_1666759, _1666761] : [_1666761 = c_List_Olist_ONil(_1666759), -(c_Orderings_Obot__class_Obot(tc_fun(_1666759, tc_HOL_Obool)) = hAPP(c_List_Oset(_1666759), _1666761))], (44344 ^ _782464) ^ [_1666862] : [-(hAPP(c_List_Oset(_1666862), c_List_Olist_ONil(_1666862)) = c_Orderings_Obot__class_Obot(tc_fun(_1666862, tc_HOL_Obool)))], (44346 ^ _782464) ^ [_1666909, _1666911, _1666913] : [_1666909 = c_List_Olist_ONil(_1666911), -(c_List_Obutlast(_1666911, hAPP(hAPP(c_List_Olist_OCons(_1666911), _1666913), _1666909)) = c_List_Olist_ONil(_1666911))], (44352 ^ _782464) ^ [_1667012, _1667014, _1667016] : [-(_1667012 = c_List_Olist_ONil(_1667014)), -(c_List_Obutlast(_1667014, hAPP(hAPP(c_List_Olist_OCons(_1667014), _1667016), _1667012)) = hAPP(hAPP(c_List_Olist_OCons(_1667014), _1667016), c_List_Obutlast(_1667014, _1667012)))], (44358 ^ _782464) ^ [_1667091, _1667093] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667091)), _1667093) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1667093 = c_List_Olist_ONil(_1667091))], (44364 ^ _782464) ^ [_1667182, _1667184] : [_1667184 = c_List_Olist_ONil(_1667182), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667182)), _1667184) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44370 ^ _782464) ^ [_1667279] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667279)), c_List_Olist_ONil(_1667279)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44372 ^ _782464) ^ [_1667311] : [-(c_List_Obutlast(_1667311, c_List_Olist_ONil(_1667311)) = c_List_Olist_ONil(_1667311))], (44374 ^ _782464) ^ [_1667341] : [class_Groups_Omonoid__add(_1667341), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667341), c_List_Olist_ONil(_1667341)) = c_Groups_Ozero__class_Ozero(_1667341))], (44380 ^ _782464) ^ [_1667432, _1667434, _1667436] : [-(hAPP(hAPP(c_List_Olist__update(_1667432, c_List_Olist_ONil(_1667432)), _1667434), _1667436) = c_List_Olist_ONil(_1667432))], (44382 ^ _782464) ^ [_1667472, _1667474, _1667476] : [-(hAPP(hAPP(c_List_Olist__update(_1667472, c_List_Olist_ONil(_1667472)), _1667474), _1667476) = c_List_Olist_ONil(_1667472))], (44384 ^ _782464) ^ [_1667533, _1667535, _1667537, _1667539] : [hAPP(hAPP(c_List_Olist__update(_1667533, _1667535), _1667537), _1667539) = c_List_Olist_ONil(_1667533), -(_1667535 = c_List_Olist_ONil(_1667533))], (44390 ^ _782464) ^ [_1667636, _1667638, _1667640, _1667642] : [_1667638 = c_List_Olist_ONil(_1667636), -(hAPP(hAPP(c_List_Olist__update(_1667636, _1667638), _1667640), _1667642) = c_List_Olist_ONil(_1667636))], (44396 ^ _782464) ^ [_1667745, _1667747] : [-(c_List_Osublist(_1667745, _1667747, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1667745))], (44398 ^ _782464) ^ [_1667791, _1667793] : [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(_1667791)), _1667793))), _1667793 = c_List_Olist_ONil(_1667791)], (44404 ^ _782464) ^ [_1667885, _1667887] : [-(_1667887 = c_List_Olist_ONil(_1667885)), -(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(_1667885)), _1667887))))], (44410 ^ _782464) ^ [_1667934, _1667936, _1667938] : [-(hAPP(hAPP(c_List_Otake(_1667934), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1667934), _1667936), _1667938)) = hAPP(hAPP(c_List_Olist_OCons(_1667934), _1667936), c_List_Olist_ONil(_1667934)))], (44412 ^ _782464) ^ [_1668002, _1668004, _1668006] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668002), tc_List_Olist(_1668002))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668002), tc_List_Olist(_1668002)), c_List_Olist_ONil(_1668002)), _1668004)), c_List_Olistrel1(_1668002, _1668006)))], (44414 ^ _782464) ^ [_1668076, _1668078, _1668080] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668076), tc_List_Olist(_1668076))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668076), tc_List_Olist(_1668076)), _1668078), c_List_Olist_ONil(_1668076))), c_List_Olistrel1(_1668076, _1668080)))], (44416 ^ _782464) ^ [_1668135, _1668137] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668135), tc_List_Olist(_1668135))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668135), tc_List_Olist(_1668135)), c_List_Olist_ONil(_1668135)), c_List_Olist_ONil(_1668135))), c_List_Olistrel(_1668135, _1668137))))], (44418 ^ _782464) ^ [_1668209, _1668211, _1668213] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668209), tc_List_Olist(_1668209))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668209), tc_List_Olist(_1668209)), _1668211), c_List_Olist_ONil(_1668209))), c_List_Olexord(_1668209, _1668213)))], (44420 ^ _782464) ^ [_1668283, _1668285, _1668287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668283), tc_List_Olist(_1668283))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668283), tc_List_Olist(_1668283)), _1668285), c_List_Olist_ONil(_1668283))), c_List_Olex(_1668283, _1668287)))], (44422 ^ _782464) ^ [_1668357, _1668359, _1668361] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668357), tc_List_Olist(_1668357))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668357), tc_List_Olist(_1668357)), c_List_Olist_ONil(_1668357)), _1668359)), c_List_Olex(_1668357, _1668361)))], (44424 ^ _782464) ^ [_1668416, _1668418, _1668420, _1668422] : [-(hAPP(hAPP(c_List_Otake(_1668416), _1668418), hAPP(hAPP(c_List_Olist_OCons(_1668416), _1668420), _1668422)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1668416), c_List_Olist_ONil(_1668416), hAPP(hAPP(c_COMBB(tc_List_Olist(_1668416), tc_List_Olist(_1668416), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1668416), _1668420)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1668416), tc_List_Olist(_1668416)), c_List_Otake(_1668416)), _1668422)), _1668418))], (44426 ^ _782464) ^ [_1668514, _1668516] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1668514), _1668516)), -(c_List_Oupto(_1668514, _1668516) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1668514), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1668514), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1668516)))], (44432 ^ _782464) ^ [_1668631, _1668633] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1668631), _1668633))), -(c_List_Oupto(_1668631, _1668633) = c_List_Olist_ONil(tc_Int_Oint))], (44438 ^ _782464) ^ [_1668689, _1668691, _1668693] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668689)), -(c_List_Osublist(_1668691, hAPP(hAPP(c_List_Olist_OCons(_1668691), _1668693), c_List_Olist_ONil(_1668691)), _1668689) = hAPP(hAPP(c_List_Olist_OCons(_1668691), _1668693), c_List_Olist_ONil(_1668691)))], (44444 ^ _782464) ^ [_1668814, _1668816, _1668818] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668814))), -(c_List_Osublist(_1668816, hAPP(hAPP(c_List_Olist_OCons(_1668816), _1668818), c_List_Olist_ONil(_1668816)), _1668814) = c_List_Olist_ONil(_1668816))], (44450 ^ _782464) ^ [_1668872] : [-(c_List_Olists(_1668872, c_Orderings_Obot__class_Obot(tc_fun(_1668872, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1668872)), c_List_Olist_ONil(_1668872)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1668872), tc_HOL_Obool))))], (44452 ^ _782464) ^ [_1668937, _1668939, _1668941, _1668943] : [_1668937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1668939), _1668937), hAPP(hAPP(c_List_Olist_OCons(_1668939), _1668941), _1668943)) = c_List_Olist_ONil(_1668939))], (44458 ^ _782464) ^ [_1669048, _1669050, _1669052, _1669054] : [-(_1669048 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1669050), _1669048), hAPP(hAPP(c_List_Olist_OCons(_1669050), _1669052), _1669054)) = hAPP(hAPP(c_List_Olist_OCons(_1669050), _1669052), hAPP(hAPP(c_List_Otake(_1669050), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1669048), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1669054)))], (44464 ^ _782464) ^ [_1669137, _1669139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669137)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669139))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669137), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669139)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669137)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669137)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669139))))], (44470 ^ _782464) ^ [_1669296, _1669298] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669296)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669298)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669296), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669298)) = c_List_Olist_ONil(tc_Int_Oint))], (44476 ^ _782464) ^ [_1669354, _1669356] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1669354), tc_List_Olist(_1669354), c_List_Olistrel(_1669354, _1669356)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669354)), c_List_Olist_ONil(_1669354)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669354), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669354)), c_List_Olist_ONil(_1669354)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669354), tc_HOL_Obool))))], (44478 ^ _782464) ^ [_1669431, _1669433] : [-(c_List_Oset__Cons(_1669431, _1669433, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669431)), c_List_Olist_ONil(_1669431)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669431), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1669431, tc_List_Olist(_1669431), hAPP(hAPP(c_COMBC(_1669431, tc_List_Olist(_1669431), tc_List_Olist(_1669431)), c_List_Olist_OCons(_1669431)), c_List_Olist_ONil(_1669431))), _1669433))], (44480 ^ _782464) ^ [_1669506, _1669508] : [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), _1669506), _1669508))), 44483 ^ _782464 : [(44484 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1669506), _1669508)), -(c_List_Oupto(_1669506, _1669508) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1669506), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1669506), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1669508)))], (44490 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1669506), _1669508))), -(c_List_Oupto(_1669506, _1669508) = c_List_Olist_ONil(tc_Int_Oint))]]], (44496 ^ _782464) ^ [_1669756, _1669758, _1669760] : [-(_1669756 = c_List_Olist_ONil(_1669758)), -(hBOOL(hAPP(hAPP(c_member(_1669758), hAPP(c_Product__Type_Ofst(_1669758, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1669758, _1669756), _1669760))), hAPP(c_List_Oset(_1669758), _1669756))))], (44502 ^ _782464) ^ [_1669820] : [-(c_List_Olistset(_1669820, c_List_Olist_ONil(tc_fun(_1669820, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669820)), c_List_Olist_ONil(_1669820)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669820), tc_HOL_Obool))))], (44504 ^ _782464) ^ [_1669870, _1669872, _1669874, _1669876, _1669878] : [-(hAPP(hAPP(c_List_Ozip(_1669870, _1669872), _1669874), hAPP(hAPP(c_List_Olist_OCons(_1669872), _1669876), _1669878)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1669870, _1669872)), _1669870, c_List_Olist_ONil(tc_prod(_1669870, _1669872)), hAPP(hAPP(c_COMBC(_1669870, tc_fun(tc_List_Olist(_1669870), tc_List_Olist(tc_prod(_1669870, _1669872))), tc_fun(tc_List_Olist(_1669870), tc_List_Olist(tc_prod(_1669870, _1669872)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1669870, _1669872)), tc_List_Olist(tc_prod(_1669870, _1669872))), tc_fun(tc_fun(tc_List_Olist(_1669870), tc_List_Olist(tc_prod(_1669870, _1669872))), tc_fun(tc_List_Olist(_1669870), tc_List_Olist(tc_prod(_1669870, _1669872)))), _1669870), c_COMBB(tc_List_Olist(tc_prod(_1669870, _1669872)), tc_List_Olist(tc_prod(_1669870, _1669872)), tc_List_Olist(_1669870))), hAPP(hAPP(c_COMBB(tc_prod(_1669870, _1669872), tc_fun(tc_List_Olist(tc_prod(_1669870, _1669872)), tc_List_Olist(tc_prod(_1669870, _1669872))), _1669870), c_List_Olist_OCons(tc_prod(_1669870, _1669872))), hAPP(hAPP(c_COMBC(_1669870, _1669872, tc_prod(_1669870, _1669872)), c_Product__Type_OPair(_1669870, _1669872)), _1669876)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669870), tc_List_Olist(_1669872), tc_List_Olist(tc_prod(_1669870, _1669872))), c_List_Ozip(_1669870, _1669872)), _1669878))), _1669874))], (44506 ^ _782464) ^ [_1670097, _1670099, _1670101, _1670103, _1670105, _1670107] : [-(hAPP(c_List_Olist_Olist__case(_1670097, _1670099, _1670101, _1670103), hAPP(hAPP(c_List_Olist_OCons(_1670099), _1670105), _1670107)) = hAPP(hAPP(_1670103, _1670105), _1670107))], (44508 ^ _782464) ^ [_1670152, _1670154, _1670156, _1670158] : [-(hAPP(c_List_Olist_Olist__case(_1670152, _1670154, _1670156, _1670158), c_List_Olist_ONil(_1670154)) = _1670156)], (44510 ^ _782464) ^ [_1670191, _1670193, _1670195] : [-(c_List_Olistset(_1670191, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1670191, tc_HOL_Obool)), _1670193), _1670195)) = c_List_Oset__Cons(_1670191, _1670193, c_List_Olistset(_1670191, _1670195)))], (44512 ^ _782464) ^ [_1670239, _1670241, _1670243, _1670245, _1670247] : [-(hAPP(hAPP(c_List_Ozip(_1670239, _1670241), hAPP(hAPP(c_List_Olist_OCons(_1670239), _1670243), _1670245)), _1670247) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1670239, _1670241)), _1670241, c_List_Olist_ONil(tc_prod(_1670239, _1670241)), hAPP(hAPP(c_COMBC(_1670241, tc_fun(tc_List_Olist(_1670241), tc_List_Olist(tc_prod(_1670239, _1670241))), tc_fun(tc_List_Olist(_1670241), tc_List_Olist(tc_prod(_1670239, _1670241)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1670239, _1670241)), tc_List_Olist(tc_prod(_1670239, _1670241))), tc_fun(tc_fun(tc_List_Olist(_1670241), tc_List_Olist(tc_prod(_1670239, _1670241))), tc_fun(tc_List_Olist(_1670241), tc_List_Olist(tc_prod(_1670239, _1670241)))), _1670241), c_COMBB(tc_List_Olist(tc_prod(_1670239, _1670241)), tc_List_Olist(tc_prod(_1670239, _1670241)), tc_List_Olist(_1670241))), hAPP(hAPP(c_COMBB(tc_prod(_1670239, _1670241), tc_fun(tc_List_Olist(tc_prod(_1670239, _1670241)), tc_List_Olist(tc_prod(_1670239, _1670241))), _1670241), c_List_Olist_OCons(tc_prod(_1670239, _1670241))), hAPP(c_Product__Type_OPair(_1670239, _1670241), _1670243)))), hAPP(c_List_Ozip(_1670239, _1670241), _1670245))), _1670247))], (44514 ^ _782464) ^ [_1670440, _1670442, _1670444] : [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), _1670440), _1670442))), -(hBOOL(hAPP(hAPP(_1670444, _1670440), _1670442))), 44521 ^ _782464 : [(44522 ^ _782464) ^ [] : [-(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), 44519 ^ [_1670440, _1670442, _1670444]), 44520 ^ [_1670440, _1670442, _1670444]))))], (44530 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1670444, 44519 ^ [_1670440, _1670442, _1670444]), 44520 ^ [_1670440, _1670442, _1670444]))], (44524 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 44519 ^ [_1670440, _1670442, _1670444]), 44520 ^ [_1670440, _1670442, _1670444])), -(hBOOL(hAPP(hAPP(_1670444, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 44519 ^ [_1670440, _1670442, _1670444]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 44520 ^ [_1670440, _1670442, _1670444])))]]], (44534 ^ _782464) ^ [_1670949, _1670951, _1670953, _1670955, _1670957] : [_1670949 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1670951, _1670953, _1670955), _1670949), _1670957) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1670953), _1670951), c_List_Olist_ONil(_1670953)), _1670957))], (44540 ^ _782464) ^ [_1671072, _1671074, _1671076, _1671078, _1671080] : [-(_1671072 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1671074, _1671076, _1671078), _1671072), _1671080) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1671076), _1671074), tc_prod(_1671076, _1671074), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671076), _1671074), c_List_Olist_ONil(_1671076)), _1671080), hAPP(c_Product__Type_Oprod_Oprod__case(_1671076, _1671074, tc_prod(tc_List_Olist(_1671076), _1671074)), hAPP(hAPP(c_COMBC(_1671076, tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074)), tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1671076), _1671074), tc_prod(tc_List_Olist(_1671076), _1671074)), tc_fun(tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074)), tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074))), _1671076), c_COMBB(tc_prod(tc_List_Olist(_1671076), _1671074), tc_prod(tc_List_Olist(_1671076), _1671074), _1671074)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1671076), tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074))), tc_fun(tc_prod(tc_List_Olist(_1671076), _1671074), tc_prod(tc_List_Olist(_1671076), _1671074)), _1671076), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1671076), _1671074, tc_prod(tc_List_Olist(_1671076), _1671074))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1671076), tc_List_Olist(_1671076)), tc_fun(tc_List_Olist(_1671076), tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074))), _1671076), hAPP(c_COMBB(tc_List_Olist(_1671076), tc_fun(_1671074, tc_prod(tc_List_Olist(_1671076), _1671074)), tc_List_Olist(_1671076)), c_Product__Type_OPair(tc_List_Olist(_1671076), _1671074))), c_List_Olist_OCons(_1671076))))), hAPP(c_Lazy__Sequence_Oanamorph(_1671074, _1671076, _1671078), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1671072), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1671078, _1671080)))], (44546 ^ _782464) ^ [_1671366, _1671368, _1671370, _1671372] : [-(c_List_Osublist(_1671366, hAPP(hAPP(c_List_Olist_OCons(_1671366), _1671368), _1671370), _1671372) = hAPP(hAPP(c_List_Oappend(_1671366), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1671366)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1671372)), hAPP(hAPP(c_List_Olist_OCons(_1671366), _1671368), c_List_Olist_ONil(_1671366))), c_List_Olist_ONil(_1671366))), c_List_Osublist(_1671366, _1671370, 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)), _1671372)))))], (44548 ^ _782464) ^ [_1671480, _1671482, _1671484, _1671486, _1671488, _1671490] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671480), tc_List_Olist(_1671480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671480), tc_List_Olist(_1671480)), hAPP(hAPP(c_List_Oappend(_1671480), _1671482), hAPP(hAPP(c_List_Olist_OCons(_1671480), _1671484), c_List_Olist_ONil(_1671480)))), hAPP(hAPP(c_List_Oappend(_1671480), _1671486), hAPP(hAPP(c_List_Olist_OCons(_1671480), _1671488), c_List_Olist_ONil(_1671480))))), c_List_Olistrel1(_1671480, _1671490))), 44553 ^ _782464 : [(44554 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671480), tc_List_Olist(_1671480))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671480), tc_List_Olist(_1671480)), _1671482), _1671486)), c_List_Olistrel1(_1671480, _1671490))))], (44556 ^ _782464) ^ [] : [-(_1671484 = _1671488)]], 44557 ^ _782464 : [(44558 ^ _782464) ^ [] : [-(_1671482 = _1671486)], (44560 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1671480, _1671480)), hAPP(hAPP(c_Product__Type_OPair(_1671480, _1671480), _1671484), _1671488)), _1671490)))]]], (44562 ^ _782464) ^ [_1671890, _1671892, _1671894, _1671896, _1671898, _1671900] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671890), tc_List_Olist(_1671890))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671890), tc_List_Olist(_1671890)), hAPP(hAPP(c_List_Oappend(_1671890), _1671892), hAPP(hAPP(c_List_Olist_OCons(_1671890), _1671894), c_List_Olist_ONil(_1671890)))), hAPP(hAPP(c_List_Oappend(_1671890), _1671896), hAPP(hAPP(c_List_Olist_OCons(_1671890), _1671898), c_List_Olist_ONil(_1671890))))), c_List_Olistrel1(_1671890, _1671900)))), 44563 ^ _782464 : [(44564 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671890), tc_List_Olist(_1671890))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671890), tc_List_Olist(_1671890)), _1671892), _1671896)), c_List_Olistrel1(_1671890, _1671900))), _1671894 = _1671898], (44570 ^ _782464) ^ [] : [_1671892 = _1671896, hBOOL(hAPP(hAPP(c_member(tc_prod(_1671890, _1671890)), hAPP(hAPP(c_Product__Type_OPair(_1671890, _1671890), _1671894), _1671898)), _1671900))]]], (44578 ^ _782464) ^ [_1672382, _1672384, _1672386, _1672388, _1672390] : [hAPP(hAPP(c_List_Oappend(_1672382), _1672384), _1672386) = hAPP(hAPP(c_List_Olist_OCons(_1672382), _1672388), _1672390), 44583 ^ _782464 : [(44584 ^ _782464) ^ [] : [-(_1672384 = c_List_Olist_ONil(_1672382))], (44586 ^ _782464) ^ [] : [-(_1672386 = hAPP(hAPP(c_List_Olist_OCons(_1672382), _1672388), _1672390))]], 44588 ^ _782464 : [(44589 ^ _782464) ^ [] : [-(_1672384 = hAPP(hAPP(c_List_Olist_OCons(_1672382), _1672388), 44587 ^ [_1672382, _1672384, _1672386, _1672388, _1672390]))], (44591 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1672382), 44587 ^ [_1672382, _1672384, _1672386, _1672388, _1672390]), _1672386) = _1672390)]]], (44593 ^ _782464) ^ [_1672675, _1672677, _1672679, _1672681, _1672683] : [-(hAPP(hAPP(c_List_Oappend(_1672675), _1672677), _1672679) = hAPP(hAPP(c_List_Olist_OCons(_1672675), _1672681), _1672683)), 44594 ^ _782464 : [(44595 ^ _782464) ^ [] : [_1672677 = c_List_Olist_ONil(_1672675), _1672679 = hAPP(hAPP(c_List_Olist_OCons(_1672675), _1672681), _1672683)], (44601 ^ _782464) ^ [_1672858] : [_1672677 = hAPP(hAPP(c_List_Olist_OCons(_1672675), _1672681), _1672858), hAPP(hAPP(c_List_Oappend(_1672675), _1672858), _1672679) = _1672683]]], (44609 ^ _782464) ^ [_1673046, _1673048, _1673050, _1673052, _1673054] : [hAPP(hAPP(c_List_Olist_OCons(_1673046), _1673048), _1673050) = hAPP(hAPP(c_List_Oappend(_1673046), _1673052), _1673054), 44614 ^ _782464 : [(44615 ^ _782464) ^ [] : [-(_1673052 = c_List_Olist_ONil(_1673046))], (44617 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673046), _1673048), _1673050) = _1673054)]], 44619 ^ _782464 : [(44620 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673046), _1673048), 44618 ^ [_1673046, _1673048, _1673050, _1673052, _1673054]) = _1673052)], (44622 ^ _782464) ^ [] : [-(_1673050 = hAPP(hAPP(c_List_Oappend(_1673046), 44618 ^ [_1673046, _1673048, _1673050, _1673052, _1673054]), _1673054))]]], (44624 ^ _782464) ^ [_1673339, _1673341, _1673343, _1673345, _1673347] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673339), _1673341), _1673343) = hAPP(hAPP(c_List_Oappend(_1673339), _1673345), _1673347)), 44625 ^ _782464 : [(44626 ^ _782464) ^ [] : [_1673345 = c_List_Olist_ONil(_1673339), hAPP(hAPP(c_List_Olist_OCons(_1673339), _1673341), _1673343) = _1673347], (44632 ^ _782464) ^ [_1673522] : [hAPP(hAPP(c_List_Olist_OCons(_1673339), _1673341), _1673522) = _1673345, _1673343 = hAPP(hAPP(c_List_Oappend(_1673339), _1673522), _1673347)]]], (44640 ^ _782464) ^ [_1673710, _1673712, _1673714, _1673716, _1673718] : [hAPP(hAPP(c_List_Oappend(_1673710), _1673712), hAPP(hAPP(c_List_Olist_OCons(_1673710), _1673714), c_List_Olist_ONil(_1673710))) = hAPP(hAPP(c_List_Oappend(_1673710), _1673716), hAPP(hAPP(c_List_Olist_OCons(_1673710), _1673718), c_List_Olist_ONil(_1673710))), 44643 ^ _782464 : [(44644 ^ _782464) ^ [] : [-(_1673712 = _1673716)], (44646 ^ _782464) ^ [] : [-(_1673714 = _1673718)]]], (44648 ^ _782464) ^ [_1673887, _1673889, _1673891, _1673893, _1673895] : [-(hAPP(hAPP(c_List_Oappend(_1673887), _1673889), hAPP(hAPP(c_List_Olist_OCons(_1673887), _1673891), c_List_Olist_ONil(_1673887))) = hAPP(hAPP(c_List_Oappend(_1673887), _1673893), hAPP(hAPP(c_List_Olist_OCons(_1673887), _1673895), c_List_Olist_ONil(_1673887)))), _1673889 = _1673893, _1673891 = _1673895], (44658 ^ _782464) ^ [_1674102, _1674104, _1674106, _1674108] : [-(hAPP(hAPP(c_List_Oappend(_1674102), hAPP(hAPP(c_List_Olist_OCons(_1674102), _1674104), _1674106)), _1674108) = hAPP(hAPP(c_List_Olist_OCons(_1674102), _1674104), hAPP(hAPP(c_List_Oappend(_1674102), _1674106), _1674108)))], (44660 ^ _782464) ^ [_1674163, _1674165, _1674167, _1674169, _1674171, _1674173] : [hAPP(hAPP(c_List_Olist_OCons(_1674163), _1674165), _1674167) = _1674169, _1674171 = hAPP(hAPP(c_List_Oappend(_1674163), _1674167), _1674173), -(hAPP(hAPP(c_List_Olist_OCons(_1674163), _1674165), _1674171) = hAPP(hAPP(c_List_Oappend(_1674163), _1674169), _1674173))], (44670 ^ _782464) ^ [_1674393, _1674395, _1674397, _1674399] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674393)), hAPP(hAPP(c_List_Oappend(_1674393), _1674395), _1674397)), c_List_Olists(_1674393, _1674399))), 44673 ^ _782464 : [(44674 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674393)), _1674395), c_List_Olists(_1674393, _1674399))))], (44676 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674393)), _1674397), c_List_Olists(_1674393, _1674399))))]]], (44678 ^ _782464) ^ [_1674584, _1674586, _1674588, _1674590] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674584)), hAPP(hAPP(c_List_Oappend(_1674584), _1674586), _1674588)), c_List_Olists(_1674584, _1674590)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674584)), _1674586), c_List_Olists(_1674584, _1674590))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674584)), _1674588), c_List_Olists(_1674584, _1674590)))], (44688 ^ _782464) ^ [_1674811, _1674813, _1674815, _1674817, _1674819, _1674821] : [hAPP(hAPP(c_List_Oappend(_1674811), _1674813), _1674815) = _1674817, _1674819 = hAPP(hAPP(c_List_Oappend(_1674811), _1674815), _1674821), -(hAPP(hAPP(c_List_Oappend(_1674811), _1674813), _1674819) = hAPP(hAPP(c_List_Oappend(_1674811), _1674817), _1674821))], (44698 ^ _782464) ^ [_1675041, _1675043, _1675045, _1675047] : [hAPP(hAPP(c_List_Oappend(_1675041), _1675043), _1675045) = hAPP(hAPP(c_List_Oappend(_1675041), _1675047), _1675045), -(_1675043 = _1675047)], (44704 ^ _782464) ^ [_1675150, _1675152, _1675154, _1675156] : [_1675152 = _1675156, -(hAPP(hAPP(c_List_Oappend(_1675150), _1675152), _1675154) = hAPP(hAPP(c_List_Oappend(_1675150), _1675156), _1675154))], (44710 ^ _782464) ^ [_1675286, _1675288, _1675290, _1675292] : [hAPP(hAPP(c_List_Oappend(_1675286), _1675288), _1675290) = hAPP(hAPP(c_List_Oappend(_1675286), _1675288), _1675292), -(_1675290 = _1675292)], (44716 ^ _782464) ^ [_1675395, _1675397, _1675399, _1675401] : [_1675399 = _1675401, -(hAPP(hAPP(c_List_Oappend(_1675395), _1675397), _1675399) = hAPP(hAPP(c_List_Oappend(_1675395), _1675397), _1675401))], (44722 ^ _782464) ^ [_1675534, _1675536, _1675538, _1675540, _1675542] : [hAPP(hAPP(c_List_Oappend(_1675534), _1675536), _1675538) = hAPP(hAPP(c_List_Oappend(_1675534), _1675540), _1675542), 44728 ^ _782464 : [(44729 ^ _782464) ^ [] : [-(_1675536 = hAPP(hAPP(c_List_Oappend(_1675534), _1675540), 44725 ^ [_1675534, _1675536, _1675538, _1675540, _1675542]))], (44731 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1675534), 44725 ^ [_1675534, _1675536, _1675538, _1675540, _1675542]), _1675538) = _1675542)]], 44732 ^ _782464 : [(44733 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1675534), _1675536), 44725 ^ [_1675534, _1675536, _1675538, _1675540, _1675542]) = _1675540)], (44735 ^ _782464) ^ [] : [-(_1675538 = hAPP(hAPP(c_List_Oappend(_1675534), 44725 ^ [_1675534, _1675536, _1675538, _1675540, _1675542]), _1675542))]]], (44737 ^ _782464) ^ [_1675865, _1675867, _1675869, _1675871, _1675873] : [-(hAPP(hAPP(c_List_Oappend(_1675865), _1675867), _1675869) = hAPP(hAPP(c_List_Oappend(_1675865), _1675871), _1675873)), 44738 ^ _782464 : [(44739 ^ _782464) ^ [_1675977] : [_1675867 = hAPP(hAPP(c_List_Oappend(_1675865), _1675871), _1675977), hAPP(hAPP(c_List_Oappend(_1675865), _1675977), _1675869) = _1675873], (44745 ^ _782464) ^ [_1676089] : [hAPP(hAPP(c_List_Oappend(_1675865), _1675867), _1676089) = _1675871, _1675869 = hAPP(hAPP(c_List_Oappend(_1675865), _1676089), _1675873)]]], (44753 ^ _782464) ^ [_1676253, _1676255, _1676257, _1676259] : [-(hAPP(hAPP(c_List_Oappend(_1676253), hAPP(hAPP(c_List_Oappend(_1676253), _1676255), _1676257)), _1676259) = hAPP(hAPP(c_List_Oappend(_1676253), _1676255), hAPP(hAPP(c_List_Oappend(_1676253), _1676257), _1676259)))], (44755 ^ _782464) ^ [_1676314, _1676316, _1676318] : [-(hAPP(c_List_Oset(_1676314), hAPP(hAPP(c_List_Oappend(_1676314), _1676316), _1676318)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1676314, tc_HOL_Obool)), hAPP(c_List_Oset(_1676314), _1676316)), hAPP(c_List_Oset(_1676314), _1676318)))], (44757 ^ _782464) ^ [_1676375, _1676377, _1676379, _1676381, _1676383, _1676385] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676375)), _1676377) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676379)), _1676381), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676375)), _1676383) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676379)), _1676385), -(hAPP(hAPP(c_List_Ozip(_1676375, _1676379), hAPP(hAPP(c_List_Oappend(_1676375), _1676377), _1676383)), hAPP(hAPP(c_List_Oappend(_1676379), _1676381), _1676385)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1676375, _1676379)), hAPP(hAPP(c_List_Ozip(_1676375, _1676379), _1676377), _1676381)), hAPP(hAPP(c_List_Ozip(_1676375, _1676379), _1676383), _1676385)))], (44767 ^ _782464) ^ [_1676684, _1676686, _1676688] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676684)), hAPP(hAPP(c_List_Oappend(_1676684), _1676686), _1676688)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676684)), _1676686)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676684)), _1676688)))], (44769 ^ _782464) ^ [_1676746, _1676748, _1676750] : [class_Groups_Omonoid__add(_1676746), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676746), hAPP(hAPP(c_List_Oappend(_1676746), _1676748), _1676750)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676746), hAPP(c_List_Omonoid__add__class_Olistsum(_1676746), _1676748)), hAPP(c_List_Omonoid__add__class_Olistsum(_1676746), _1676750)))], (44775 ^ _782464) ^ [_1676897, _1676899, _1676901] : [_1676897 = c_List_Olist_ONil(_1676899), -(c_List_Obutlast(_1676899, hAPP(hAPP(c_List_Oappend(_1676899), _1676901), _1676897)) = c_List_Obutlast(_1676899, _1676901))], (44781 ^ _782464) ^ [_1677002, _1677004, _1677006] : [-(_1677002 = c_List_Olist_ONil(_1677004)), -(c_List_Obutlast(_1677004, hAPP(hAPP(c_List_Oappend(_1677004), _1677006), _1677002)) = hAPP(hAPP(c_List_Oappend(_1677004), _1677006), c_List_Obutlast(_1677004, _1677002)))], (44787 ^ _782464) ^ [_1677066, _1677068] : [-(hAPP(hAPP(c_List_Oappend(_1677066), c_List_Olist_ONil(_1677066)), _1677068) = _1677068)], (44789 ^ _782464) ^ [_1677119, _1677121, _1677123] : [c_List_Olist_ONil(_1677119) = hAPP(hAPP(c_List_Oappend(_1677119), _1677121), _1677123), 44792 ^ _782464 : [(44793 ^ _782464) ^ [] : [-(_1677121 = c_List_Olist_ONil(_1677119))], (44795 ^ _782464) ^ [] : [-(_1677123 = c_List_Olist_ONil(_1677119))]]], (44797 ^ _782464) ^ [_1677248, _1677250, _1677252] : [-(c_List_Olist_ONil(_1677248) = hAPP(hAPP(c_List_Oappend(_1677248), _1677250), _1677252)), _1677250 = c_List_Olist_ONil(_1677248), _1677252 = c_List_Olist_ONil(_1677248)], (44807 ^ _782464) ^ [_1677411, _1677413] : [-(hAPP(hAPP(c_List_Oappend(_1677411), _1677413), c_List_Olist_ONil(_1677411)) = _1677413)], (44809 ^ _782464) ^ [_1677464, _1677466, _1677468] : [_1677464 = hAPP(hAPP(c_List_Oappend(_1677466), _1677464), _1677468), -(_1677468 = c_List_Olist_ONil(_1677466))], (44815 ^ _782464) ^ [_1677559, _1677561, _1677563] : [_1677563 = c_List_Olist_ONil(_1677561), -(_1677559 = hAPP(hAPP(c_List_Oappend(_1677561), _1677559), _1677563))], (44821 ^ _782464) ^ [_1677678, _1677680, _1677682] : [_1677678 = hAPP(hAPP(c_List_Oappend(_1677680), _1677682), _1677678), -(_1677682 = c_List_Olist_ONil(_1677680))], (44827 ^ _782464) ^ [_1677773, _1677775, _1677777] : [_1677777 = c_List_Olist_ONil(_1677775), -(_1677773 = hAPP(hAPP(c_List_Oappend(_1677775), _1677777), _1677773))], (44833 ^ _782464) ^ [_1677892, _1677894, _1677896] : [hAPP(hAPP(c_List_Oappend(_1677892), _1677894), _1677896) = c_List_Olist_ONil(_1677892), 44836 ^ _782464 : [(44837 ^ _782464) ^ [] : [-(_1677894 = c_List_Olist_ONil(_1677892))], (44839 ^ _782464) ^ [] : [-(_1677896 = c_List_Olist_ONil(_1677892))]]], (44841 ^ _782464) ^ [_1678021, _1678023, _1678025] : [-(hAPP(hAPP(c_List_Oappend(_1678021), _1678023), _1678025) = c_List_Olist_ONil(_1678021)), _1678023 = c_List_Olist_ONil(_1678021), _1678025 = c_List_Olist_ONil(_1678021)], (44851 ^ _782464) ^ [_1678202, _1678204, _1678206] : [hAPP(hAPP(c_List_Oappend(_1678202), _1678204), _1678206) = _1678204, -(_1678206 = c_List_Olist_ONil(_1678202))], (44857 ^ _782464) ^ [_1678297, _1678299, _1678301] : [_1678301 = c_List_Olist_ONil(_1678297), -(hAPP(hAPP(c_List_Oappend(_1678297), _1678299), _1678301) = _1678299)], (44863 ^ _782464) ^ [_1678416, _1678418, _1678420] : [hAPP(hAPP(c_List_Oappend(_1678416), _1678418), _1678420) = _1678420, -(_1678418 = c_List_Olist_ONil(_1678416))], (44869 ^ _782464) ^ [_1678511, _1678513, _1678515] : [_1678513 = c_List_Olist_ONil(_1678511), -(hAPP(hAPP(c_List_Oappend(_1678511), _1678513), _1678515) = _1678515)], (44875 ^ _782464) ^ [_1678612, _1678614, _1678616] : [_1678612 = _1678614, -(_1678612 = hAPP(hAPP(c_List_Oappend(_1678616), c_List_Olist_ONil(_1678616)), _1678614))], (44881 ^ _782464) ^ [_1678711, _1678713, _1678715, _1678717] : [-(hAPP(hAPP(c_List_Onth(_1678711), hAPP(hAPP(c_List_Oappend(_1678711), _1678713), hAPP(hAPP(c_List_Olist_OCons(_1678711), _1678715), _1678717))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678711)), _1678713)) = _1678715)], (44883 ^ _782464) ^ [_1678771, _1678773, _1678775, _1678777] : [-(hAPP(hAPP(c_List_Onth(_1678771), hAPP(hAPP(c_List_Oappend(_1678771), _1678773), _1678775)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678771)), _1678773)), _1678777)) = hAPP(hAPP(c_List_Onth(_1678771), _1678775), _1678777))], (44885 ^ _782464) ^ [_1678837, _1678839, _1678841, _1678843] : [-(hAPP(hAPP(c_List_Otake(_1678837), _1678839), hAPP(hAPP(c_List_Oappend(_1678837), _1678841), _1678843)) = hAPP(hAPP(c_List_Oappend(_1678837), hAPP(hAPP(c_List_Otake(_1678837), _1678839), _1678841)), hAPP(hAPP(c_List_Otake(_1678837), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1678839), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678837)), _1678841))), _1678843)))], (44887 ^ _782464) ^ [_1678919, _1678921, _1678923, _1678925, _1678927] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678919), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678921)), _1678923))), -(hAPP(hAPP(c_List_Olist__update(_1678921, hAPP(hAPP(c_List_Oappend(_1678921), _1678923), _1678925)), _1678919), _1678927) = hAPP(hAPP(c_List_Oappend(_1678921), hAPP(hAPP(c_List_Olist__update(_1678921, _1678923), _1678919), _1678927)), _1678925))], (44893 ^ _782464) ^ [_1679094, _1679096, _1679098, _1679100, _1679102] : [-(hAPP(hAPP(c_List_Olist__update(_1679094, hAPP(hAPP(c_List_Oappend(_1679094), _1679096), hAPP(hAPP(c_List_Olist_OCons(_1679094), _1679098), _1679100))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679094)), _1679096)), _1679102) = hAPP(hAPP(c_List_Oappend(_1679094), _1679096), hAPP(hAPP(c_List_Olist_OCons(_1679094), _1679102), _1679100)))], (44895 ^ _782464) ^ [_1679188, _1679190, _1679192, _1679194] : [hBOOL(hAPP(hAPP(c_member(_1679188), _1679190), hAPP(c_List_Oset(_1679188), _1679192))), -(c_List_Oremove1(_1679188, _1679190, hAPP(hAPP(c_List_Oappend(_1679188), _1679192), _1679194)) = hAPP(hAPP(c_List_Oappend(_1679188), c_List_Oremove1(_1679188, _1679190, _1679192)), _1679194))], (44901 ^ _782464) ^ [_1679335, _1679337, _1679339, _1679341] : [-(hBOOL(hAPP(hAPP(c_member(_1679335), _1679337), hAPP(c_List_Oset(_1679335), _1679339)))), -(c_List_Oremove1(_1679335, _1679337, hAPP(hAPP(c_List_Oappend(_1679335), _1679339), _1679341)) = hAPP(hAPP(c_List_Oappend(_1679335), _1679339), c_List_Oremove1(_1679335, _1679337, _1679341)))], (44907 ^ _782464) ^ [_1679413, _1679415, _1679417, _1679419] : [44908 ^ _782464 : [(44909 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679413), _1679415), hAPP(c_List_Oset(_1679413), c_List_Obutlast(_1679413, _1679417))))], (44911 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679413), _1679415), hAPP(c_List_Oset(_1679413), c_List_Obutlast(_1679413, _1679419))))]], -(hBOOL(hAPP(hAPP(c_member(_1679413), _1679415), hAPP(c_List_Oset(_1679413), c_List_Obutlast(_1679413, hAPP(hAPP(c_List_Oappend(_1679413), _1679417), _1679419))))))], (44915 ^ _782464) ^ [_1679638, _1679640, _1679642] : [-(c_List_Obutlast(_1679638, hAPP(hAPP(c_List_Oappend(_1679638), _1679640), hAPP(hAPP(c_List_Olist_OCons(_1679638), _1679642), c_List_Olist_ONil(_1679638)))) = _1679640)], (44917 ^ _782464) ^ [_1679686, _1679688, _1679690, _1679692, _1679694, _1679696] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679686), tc_List_Olist(_1679686))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679686), tc_List_Olist(_1679686)), hAPP(hAPP(c_List_Oappend(_1679686), _1679688), _1679694)), hAPP(hAPP(c_List_Oappend(_1679686), _1679690), _1679696))), c_List_Olistrel1(_1679686, _1679692)))), 44918 ^ _782464 : [(44919 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679686), tc_List_Olist(_1679686))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679686), tc_List_Olist(_1679686)), _1679688), _1679690)), c_List_Olistrel1(_1679686, _1679692))), _1679694 = _1679696], (44925 ^ _782464) ^ [] : [_1679688 = _1679690, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679686), tc_List_Olist(_1679686))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679686), tc_List_Olist(_1679686)), _1679694), _1679696)), c_List_Olistrel1(_1679686, _1679692)))]]], (44933 ^ _782464) ^ [_1680134, _1680136, _1680138, _1680140, _1680142] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1680134), tc_List_Olist(_1680134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680134), tc_List_Olist(_1680134)), _1680136), _1680138)), c_List_Olexord(_1680134, _1680140))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1680134), tc_List_Olist(_1680134))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680134), tc_List_Olist(_1680134)), hAPP(hAPP(c_List_Oappend(_1680134), _1680142), _1680136)), hAPP(hAPP(c_List_Oappend(_1680134), _1680142), _1680138))), c_List_Olexord(_1680134, _1680140))))], (44939 ^ _782464) ^ [_1680387, _1680389, _1680391] : [hBOOL(hAPP(c_List_Odistinct(_1680387), hAPP(hAPP(c_List_Oappend(_1680387), _1680389), _1680391))), 44942 ^ _782464 : [(44943 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680387), _1680389)))], (44945 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680387), _1680391)))], (44947 ^ _782464) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680387, tc_HOL_Obool)), hAPP(c_List_Oset(_1680387), _1680389)), hAPP(c_List_Oset(_1680387), _1680391)) = c_Orderings_Obot__class_Obot(tc_fun(_1680387, tc_HOL_Obool)))]]], (44949 ^ _782464) ^ [_1680604, _1680606, _1680608] : [-(hBOOL(hAPP(c_List_Odistinct(_1680604), hAPP(hAPP(c_List_Oappend(_1680604), _1680606), _1680608)))), hBOOL(hAPP(c_List_Odistinct(_1680604), _1680606)), hBOOL(hAPP(c_List_Odistinct(_1680604), _1680608)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680604, tc_HOL_Obool)), hAPP(c_List_Oset(_1680604), _1680606)), hAPP(c_List_Oset(_1680604), _1680608)) = c_Orderings_Obot__class_Obot(tc_fun(_1680604, tc_HOL_Obool))], (44963 ^ _782464) ^ [_1680900, _1680902, _1680904, _1680906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680900), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680902)), _1680904))), -(hAPP(hAPP(c_List_Onth(_1680902), hAPP(hAPP(c_List_Oappend(_1680902), _1680904), _1680906)), _1680900) = hAPP(hAPP(c_List_Onth(_1680902), _1680904), _1680900))], (44969 ^ _782464) ^ [_1681047, _1681049, _1681051, _1681053] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681047), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681049)), _1681051)))), -(hAPP(hAPP(c_List_Onth(_1681049), hAPP(hAPP(c_List_Oappend(_1681049), _1681051), _1681053)), _1681047) = hAPP(hAPP(c_List_Onth(_1681049), _1681053), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681047), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681049)), _1681051))))], (44975 ^ _782464) ^ [_1681156, _1681158, _1681160, _1681162, _1681164] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681158)), _1681160))), -(hAPP(hAPP(c_List_Olist__update(_1681158, hAPP(hAPP(c_List_Oappend(_1681158), _1681160), _1681162)), _1681156), _1681164) = hAPP(hAPP(c_List_Oappend(_1681158), hAPP(hAPP(c_List_Olist__update(_1681158, _1681160), _1681156), _1681164)), _1681162))], (44981 ^ _782464) ^ [_1681325, _1681327, _1681329, _1681331, _1681333] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681327)), _1681329)))), -(hAPP(hAPP(c_List_Olist__update(_1681327, hAPP(hAPP(c_List_Oappend(_1681327), _1681329), _1681331)), _1681325), _1681333) = hAPP(hAPP(c_List_Oappend(_1681327), _1681329), hAPP(hAPP(c_List_Olist__update(_1681327, _1681331), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681325), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681327)), _1681329))), _1681333)))], (44987 ^ _782464) ^ [_1681428, _1681430, _1681432, _1681434] : [-(c_List_Osublist(_1681428, hAPP(hAPP(c_List_Oappend(_1681428), _1681430), _1681432), _1681434) = hAPP(hAPP(c_List_Oappend(_1681428), c_List_Osublist(_1681428, _1681430, _1681434)), c_List_Osublist(_1681428, _1681432, 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(_1681428)), _1681430)))), _1681434)))))], (44989 ^ _782464) ^ [_1681507, _1681509, _1681511, _1681513, _1681515, _1681517, _1681519, _1681521] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681507, _1681507)), hAPP(hAPP(c_Product__Type_OPair(_1681507, _1681507), _1681509), _1681511)), _1681513)), _1681515 = hAPP(hAPP(c_List_Oappend(_1681507), _1681517), hAPP(hAPP(c_List_Olist_OCons(_1681507), _1681509), _1681519)), _1681521 = hAPP(hAPP(c_List_Oappend(_1681507), _1681517), hAPP(hAPP(c_List_Olist_OCons(_1681507), _1681511), _1681519)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681507), tc_List_Olist(_1681507))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681507), tc_List_Olist(_1681507)), _1681515), _1681521)), c_List_Olistrel1(_1681507, _1681513))))], (45003 ^ _782464) ^ [_1681886, _1681888, _1681890, _1681892, _1681894, _1681896, _1681898] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681886, _1681886)), hAPP(hAPP(c_Product__Type_OPair(_1681886, _1681886), _1681888), _1681890)), _1681892)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681886), tc_List_Olist(_1681886))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681886), tc_List_Olist(_1681886)), hAPP(hAPP(c_List_Oappend(_1681886), _1681894), hAPP(hAPP(c_List_Olist_OCons(_1681886), _1681888), _1681896))), hAPP(hAPP(c_List_Oappend(_1681886), _1681894), hAPP(hAPP(c_List_Olist_OCons(_1681886), _1681890), _1681898)))), c_List_Olexord(_1681886, _1681892))))], (45009 ^ _782464) ^ [_1682135, _1682137, _1682139] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682135), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682137)), _1682139))), -(hAPP(hAPP(c_List_Otake(_1682137), hAPP(c_Nat_OSuc, _1682135)), _1682139) = hAPP(hAPP(c_List_Oappend(_1682137), hAPP(hAPP(c_List_Otake(_1682137), _1682135), _1682139)), hAPP(hAPP(c_List_Olist_OCons(_1682137), hAPP(hAPP(c_List_Onth(_1682137), _1682139), _1682135)), c_List_Olist_ONil(_1682137))))], (45015 ^ _782464) ^ [_1682328, _1682330, _1682332, _1682334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682328), tc_List_Olist(_1682328))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682328), tc_List_Olist(_1682328)), _1682330), _1682332)), c_List_Olistrel1(_1682328, _1682334))), 45020 ^ _782464 : [(45021 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682328, _1682328)), hAPP(hAPP(c_Product__Type_OPair(_1682328, _1682328), 45018 ^ [_1682328, _1682330, _1682332, _1682334]), 45019 ^ [_1682328, _1682330, _1682332, _1682334])), _1682334)))], (45025 ^ _782464) ^ [] : [-(_1682330 = hAPP(hAPP(c_List_Oappend(_1682328), 45022 ^ [_1682328, _1682330, _1682332, _1682334]), hAPP(hAPP(c_List_Olist_OCons(_1682328), 45018 ^ [_1682328, _1682330, _1682332, _1682334]), 45023 ^ [_1682328, _1682330, _1682332, _1682334])))], (45027 ^ _782464) ^ [] : [-(_1682332 = hAPP(hAPP(c_List_Oappend(_1682328), 45022 ^ [_1682328, _1682330, _1682332, _1682334]), hAPP(hAPP(c_List_Olist_OCons(_1682328), 45019 ^ [_1682328, _1682330, _1682332, _1682334]), 45023 ^ [_1682328, _1682330, _1682332, _1682334])))]]], (45029 ^ _782464) ^ [_1682733, _1682735, _1682737, _1682739, _1682741] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682733), tc_List_Olist(_1682733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682733), tc_List_Olist(_1682733)), hAPP(hAPP(c_List_Oappend(_1682733), _1682735), _1682737)), hAPP(hAPP(c_List_Oappend(_1682733), _1682735), _1682739))), c_List_Olexord(_1682733, _1682741))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682733, _1682733)), hAPP(hAPP(c_Product__Type_OPair(_1682733, _1682733), 45034 ^ [_1682733, _1682735, _1682737, _1682739, _1682741]), 45034 ^ [_1682733, _1682735, _1682737, _1682739, _1682741])), _1682741))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682733), tc_List_Olist(_1682733))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682733), tc_List_Olist(_1682733)), _1682737), _1682739)), c_List_Olexord(_1682733, _1682741))))], (45040 ^ _782464) ^ [_1683052, _1683054] : [-(hAPP(c_List_Orotate1(_1683052), _1683054) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1683052), _1683052, c_List_Olist_ONil(_1683052), hAPP(hAPP(c_COMBB(tc_List_Olist(_1683052), tc_fun(tc_List_Olist(_1683052), tc_List_Olist(_1683052)), _1683052), hAPP(c_COMBC(tc_List_Olist(_1683052), tc_List_Olist(_1683052), tc_List_Olist(_1683052)), c_List_Oappend(_1683052))), hAPP(hAPP(c_COMBC(_1683052, tc_List_Olist(_1683052), tc_List_Olist(_1683052)), c_List_Olist_OCons(_1683052)), c_List_Olist_ONil(_1683052)))), _1683054))], (45042 ^ _782464) ^ [_1683146, _1683148, _1683150, _1683152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683146), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683148)), _1683150))), -(hAPP(hAPP(c_List_Olist__update(_1683148, _1683150), _1683146), _1683152) = hAPP(hAPP(c_List_Oappend(_1683148), hAPP(hAPP(c_List_Otake(_1683148), _1683146), _1683150)), hAPP(hAPP(c_List_Olist_OCons(_1683148), _1683152), hAPP(hAPP(c_List_Odrop(_1683148), hAPP(c_Nat_OSuc, _1683146)), _1683150))))], (45048 ^ _782464) ^ [_1683339, _1683341, _1683343] : [-(hAPP(hAPP(c_List_Oappend(_1683339), hAPP(hAPP(c_List_Otake(_1683339), _1683341), _1683343)), hAPP(hAPP(c_List_Odrop(_1683339), _1683341), _1683343)) = _1683343)], (45050 ^ _782464) ^ [_1683390, _1683392, _1683394] : [-(hAPP(hAPP(c_List_Odrop(_1683390), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1683390), _1683392), _1683394)) = _1683394)], (45052 ^ _782464) ^ [_1683433, _1683435, _1683437, _1683439] : [-(hAPP(hAPP(c_List_Odrop(_1683433), hAPP(c_Nat_OSuc, _1683435)), hAPP(hAPP(c_List_Olist_OCons(_1683433), _1683437), _1683439)) = hAPP(hAPP(c_List_Odrop(_1683433), _1683435), _1683439))], (45054 ^ _782464) ^ [_1683489, _1683491, _1683493, _1683495, _1683497] : [hAPP(hAPP(c_List_Odrop(_1683489), _1683491), _1683493) = hAPP(hAPP(c_List_Olist_OCons(_1683489), _1683495), _1683497), -(hAPP(hAPP(c_List_Onth(_1683489), _1683493), _1683491) = _1683495)], (45060 ^ _782464) ^ [_1683620, _1683622, _1683624] : [hBOOL(hAPP(c_List_Odistinct(_1683620), _1683622)), -(hBOOL(hAPP(c_List_Odistinct(_1683620), hAPP(hAPP(c_List_Odrop(_1683620), _1683624), _1683622))))], (45066 ^ _782464) ^ [_1683746, _1683748] : [hBOOL(hAPP(c_List_Odistinct(_1683746), hAPP(c_List_Orotate1(_1683746), _1683748))), -(hBOOL(hAPP(c_List_Odistinct(_1683746), _1683748)))], (45072 ^ _782464) ^ [_1683845, _1683847] : [hBOOL(hAPP(c_List_Odistinct(_1683845), _1683847)), -(hBOOL(hAPP(c_List_Odistinct(_1683845), hAPP(c_List_Orotate1(_1683845), _1683847))))], (45078 ^ _782464) ^ [_1683950, _1683952, _1683954, _1683956, _1683958] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1683950, _1683952)), _1683954), hAPP(hAPP(c_List_Ozip(_1683950, _1683952), _1683956), _1683958)) = hAPP(hAPP(c_List_Ozip(_1683950, _1683952), hAPP(hAPP(c_List_Odrop(_1683950), _1683954), _1683956)), hAPP(hAPP(c_List_Odrop(_1683952), _1683954), _1683958)))], (45080 ^ _782464) ^ [_1684026, _1684028] : [-(hAPP(hAPP(c_List_Odrop(_1684026), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1684028) = _1684028)], (45082 ^ _782464) ^ [_1684059, _1684061, _1684063, _1684065] : [-(hAPP(hAPP(c_List_Odrop(_1684059), _1684061), hAPP(hAPP(c_List_Odrop(_1684059), _1684063), _1684065)) = hAPP(hAPP(c_List_Odrop(_1684059), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684061), _1684063)), _1684065))], (45084 ^ _782464) ^ [_1684118, _1684120, _1684122, _1684124] : [-(hAPP(hAPP(c_List_Odrop(_1684118), _1684120), hAPP(hAPP(c_List_Otake(_1684118), _1684122), _1684124)) = hAPP(hAPP(c_List_Otake(_1684118), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1684122), _1684120)), hAPP(hAPP(c_List_Odrop(_1684118), _1684120), _1684124)))], (45086 ^ _782464) ^ [_1684185, _1684187, _1684189, _1684191] : [-(hAPP(hAPP(c_List_Otake(_1684185), _1684187), hAPP(hAPP(c_List_Odrop(_1684185), _1684189), _1684191)) = hAPP(hAPP(c_List_Odrop(_1684185), _1684189), hAPP(hAPP(c_List_Otake(_1684185), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684187), _1684189)), _1684191)))], (45088 ^ _782464) ^ [_1684252, _1684254, _1684256, _1684258] : [hBOOL(hAPP(hAPP(c_member(_1684252), _1684254), hAPP(c_List_Oset(_1684252), hAPP(hAPP(c_List_Odrop(_1684252), _1684256), _1684258)))), -(hBOOL(hAPP(hAPP(c_member(_1684252), _1684254), hAPP(c_List_Oset(_1684252), _1684258))))], (45094 ^ _782464) ^ [_1684397, _1684399] : [-(hAPP(c_List_Oset(_1684397), hAPP(c_List_Orotate1(_1684397), _1684399)) = hAPP(c_List_Oset(_1684397), _1684399))], (45096 ^ _782464) ^ [_1684437, _1684439, _1684441] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684437, tc_HOL_Obool)), hAPP(c_List_Oset(_1684437), hAPP(hAPP(c_List_Odrop(_1684437), _1684439), _1684441))), hAPP(c_List_Oset(_1684437), _1684441))))], (45098 ^ _782464) ^ [_1684492, _1684494, _1684496] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684492)), hAPP(hAPP(c_List_Odrop(_1684492), _1684494), _1684496)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684492)), _1684496)), _1684494))], (45100 ^ _782464) ^ [_1684547, _1684549] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684547)), hAPP(c_List_Orotate1(_1684547), _1684549)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684547)), _1684549))], (45102 ^ _782464) ^ [_1684591, _1684593, _1684595] : [-(c_List_Obutlast(_1684591, hAPP(hAPP(c_List_Odrop(_1684591), _1684593), _1684595)) = hAPP(hAPP(c_List_Odrop(_1684591), _1684593), c_List_Obutlast(_1684591, _1684595)))], (45104 ^ _782464) ^ [_1684640, _1684642, _1684644] : [-(hAPP(hAPP(c_List_Odrop(_1684640), _1684642), c_List_Obutlast(_1684640, _1684644)) = c_List_Obutlast(_1684640, hAPP(hAPP(c_List_Odrop(_1684640), _1684642), _1684644)))], (45106 ^ _782464) ^ [_1684689, _1684691] : [-(hAPP(hAPP(c_List_Odrop(_1684689), _1684691), c_List_Olist_ONil(_1684689)) = c_List_Olist_ONil(_1684689))], (45108 ^ _782464) ^ [_1684741, _1684743] : [hAPP(c_List_Orotate1(_1684741), _1684743) = c_List_Olist_ONil(_1684741), -(_1684743 = c_List_Olist_ONil(_1684741))], (45114 ^ _782464) ^ [_1684832, _1684834] : [_1684834 = c_List_Olist_ONil(_1684832), -(hAPP(c_List_Orotate1(_1684832), _1684834) = c_List_Olist_ONil(_1684832))], (45120 ^ _782464) ^ [_1684929, _1684931, _1684933, _1684935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1684929), _1684931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684933, tc_HOL_Obool)), hAPP(c_List_Oset(_1684933), hAPP(hAPP(c_List_Odrop(_1684933), _1684931), _1684935))), hAPP(c_List_Oset(_1684933), hAPP(hAPP(c_List_Odrop(_1684933), _1684929), _1684935)))))], (45126 ^ _782464) ^ [_1685110, _1685112, _1685114] : [hAPP(hAPP(c_List_Odrop(_1685110), _1685112), _1685114) = c_List_Olist_ONil(_1685110), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685110)), _1685114)), _1685112)))], (45132 ^ _782464) ^ [_1685229, _1685231, _1685233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685229)), _1685233)), _1685231)), -(hAPP(hAPP(c_List_Odrop(_1685229), _1685231), _1685233) = c_List_Olist_ONil(_1685229))], (45138 ^ _782464) ^ [_1685354, _1685356, _1685358] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685354)), _1685356)), _1685358)), -(hAPP(hAPP(c_List_Odrop(_1685354), _1685358), _1685356) = c_List_Olist_ONil(_1685354))], (45144 ^ _782464) ^ [_1685477, _1685479, _1685481, _1685483] : [-(hAPP(hAPP(c_List_Odrop(_1685477), _1685479), hAPP(hAPP(c_List_Oappend(_1685477), _1685481), _1685483)) = hAPP(hAPP(c_List_Oappend(_1685477), hAPP(hAPP(c_List_Odrop(_1685477), _1685479), _1685481)), hAPP(hAPP(c_List_Odrop(_1685477), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1685479), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685477)), _1685481))), _1685483)))], (45146 ^ _782464) ^ [_1685580, _1685582, _1685584, _1685586] : [hAPP(hAPP(c_List_Oappend(_1685580), _1685582), _1685584) = _1685586, 45149 ^ _782464 : [(45150 ^ _782464) ^ [] : [-(_1685582 = hAPP(hAPP(c_List_Otake(_1685580), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685580)), _1685582)), _1685586))], (45152 ^ _782464) ^ [] : [-(_1685584 = hAPP(hAPP(c_List_Odrop(_1685580), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685580)), _1685582)), _1685586))]]], (45154 ^ _782464) ^ [_1685759, _1685761, _1685763, _1685765] : [-(hAPP(hAPP(c_List_Oappend(_1685759), _1685761), _1685763) = _1685765), _1685761 = hAPP(hAPP(c_List_Otake(_1685759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685759)), _1685761)), _1685765), _1685763 = hAPP(hAPP(c_List_Odrop(_1685759), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685759)), _1685761)), _1685765)], (45164 ^ _782464) ^ [_1685974, _1685976, _1685978, _1685980] : [-(hAPP(hAPP(c_List_Odrop(_1685974), _1685976), hAPP(hAPP(c_List_Olist_OCons(_1685974), _1685978), _1685980)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1685974), hAPP(hAPP(c_List_Olist_OCons(_1685974), _1685978), _1685980), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1685974), tc_List_Olist(_1685974)), c_List_Odrop(_1685974)), _1685980), _1685976))], (45166 ^ _782464) ^ [_1686065, _1686067, _1686069, _1686071] : [_1686065 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1686067), _1686065), hAPP(hAPP(c_List_Olist_OCons(_1686067), _1686069), _1686071)) = hAPP(hAPP(c_List_Olist_OCons(_1686067), _1686069), _1686071))], (45172 ^ _782464) ^ [_1686188, _1686190, _1686192, _1686194] : [-(_1686188 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1686190), _1686188), hAPP(hAPP(c_List_Olist_OCons(_1686190), _1686192), _1686194)) = hAPP(hAPP(c_List_Odrop(_1686190), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1686188), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1686194))], (45178 ^ _782464) ^ [_1686260, _1686262, _1686264, _1686266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686260), _1686262)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686264)), _1686266))), -(hAPP(hAPP(c_List_Onth(_1686264), hAPP(hAPP(c_List_Odrop(_1686264), _1686260), _1686266)), _1686262) = hAPP(hAPP(c_List_Onth(_1686264), _1686266), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686260), _1686262)))], (45184 ^ _782464) ^ [_1686461, _1686463, _1686465, _1686467, _1686469] : [hAPP(hAPP(c_List_Oappend(_1686461), _1686463), _1686465) = hAPP(hAPP(c_List_Oappend(_1686461), _1686467), _1686469), 45187 ^ _782464 : [(45188 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686463)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686467))), 45191 ^ _782464 : [(45192 ^ _782464) ^ [] : [-(_1686463 = hAPP(hAPP(c_List_Otake(_1686461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686463)), _1686467))], (45194 ^ _782464) ^ [] : [-(_1686465 = hAPP(hAPP(c_List_Oappend(_1686461), hAPP(hAPP(c_List_Odrop(_1686461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686463)), _1686467)), _1686469))]]], (45196 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686463)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686467)))), 45199 ^ _782464 : [(45200 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1686461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686467)), _1686463) = _1686467)], (45202 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1686461), hAPP(hAPP(c_List_Odrop(_1686461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686461)), _1686467)), _1686463)), _1686465) = _1686469)]]]]], (45204 ^ _782464) ^ [_1686974, _1686976, _1686978, _1686980, _1686982] : [-(hAPP(hAPP(c_List_Oappend(_1686974), _1686976), _1686978) = hAPP(hAPP(c_List_Oappend(_1686974), _1686980), _1686982)), 45207 ^ _782464 : [(45208 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686976)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686980))))], (45210 ^ _782464) ^ [] : [_1686976 = hAPP(hAPP(c_List_Otake(_1686974), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686976)), _1686980), _1686978 = hAPP(hAPP(c_List_Oappend(_1686974), hAPP(hAPP(c_List_Odrop(_1686974), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686976)), _1686980)), _1686982)]], 45215 ^ _782464 : [(45216 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686976)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686980)))], (45218 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Otake(_1686974), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686980)), _1686976) = _1686980, hAPP(hAPP(c_List_Oappend(_1686974), hAPP(hAPP(c_List_Odrop(_1686974), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686974)), _1686980)), _1686976)), _1686978) = _1686982]]], (45226 ^ _782464) ^ [_1687562, _1687564, _1687566] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687562), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687564)), _1687566))), -(hAPP(hAPP(c_List_Olist_OCons(_1687564), hAPP(hAPP(c_List_Onth(_1687564), _1687566), _1687562)), hAPP(hAPP(c_List_Odrop(_1687564), hAPP(c_Nat_OSuc, _1687562)), _1687566)) = hAPP(hAPP(c_List_Odrop(_1687564), _1687562), _1687566))], (45232 ^ _782464) ^ [_1687733, _1687735, _1687737, _1687739] : [-(hAPP(c_List_Orotate1(_1687733), c_List_Olist_ONil(_1687733)) = c_List_Olist_ONil(_1687733))], (45234 ^ _782464) ^ [_1687768, _1687770, _1687772, _1687774] : [-(hAPP(c_List_Orotate1(_1687770), hAPP(hAPP(c_List_Olist_OCons(_1687770), _1687772), _1687774)) = hAPP(hAPP(c_List_Oappend(_1687770), _1687774), hAPP(hAPP(c_List_Olist_OCons(_1687770), _1687772), c_List_Olist_ONil(_1687770))))], (45236 ^ _782464) ^ [_1687845, _1687847, _1687849, _1687851] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687845) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1687847), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687845)), hAPP(hAPP(c_List_Olist_OCons(_1687847), _1687849), _1687851)) = hAPP(hAPP(c_List_Olist_OCons(_1687847), _1687849), _1687851))], (45242 ^ _782464) ^ [_1687980, _1687982, _1687984, _1687986] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687980) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1687982), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687980)), hAPP(hAPP(c_List_Olist_OCons(_1687982), _1687984), _1687986)) = hAPP(hAPP(c_List_Odrop(_1687982), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687980)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1687986))], (45248 ^ _782464) ^ [_1688061, _1688063, _1688065, _1688067] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1688061), _1688063)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688065)), _1688067))), -(hAPP(hAPP(c_List_Otake(_1688065), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1688061), _1688063)), _1688067) = hAPP(hAPP(c_List_Oappend(_1688065), hAPP(hAPP(c_List_Otake(_1688065), _1688061), _1688067)), hAPP(hAPP(c_List_Otake(_1688065), _1688063), hAPP(hAPP(c_List_Odrop(_1688065), _1688061), _1688067))))], (45254 ^ _782464) ^ [_1688270, _1688272] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688270)), _1688272)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1688270), _1688272) = _1688272)], (45260 ^ _782464) ^ [_1688381, _1688383, _1688385, _1688387, _1688389] : [-(hAPP(hAPP(c_List_Ozip(_1688381, _1688383), _1688385), hAPP(hAPP(c_List_Oappend(_1688383), _1688387), _1688389)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1688381, _1688383)), hAPP(hAPP(c_List_Ozip(_1688381, _1688383), hAPP(hAPP(c_List_Otake(_1688381), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688383)), _1688387)), _1688385)), _1688387)), hAPP(hAPP(c_List_Ozip(_1688381, _1688383), hAPP(hAPP(c_List_Odrop(_1688381), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688383)), _1688387)), _1688385)), _1688389)))], (45262 ^ _782464) ^ [_1688488, _1688490, _1688492, _1688494, _1688496] : [-(hAPP(hAPP(c_List_Ozip(_1688488, _1688490), hAPP(hAPP(c_List_Oappend(_1688488), _1688492), _1688494)), _1688496) = hAPP(hAPP(c_List_Oappend(tc_prod(_1688488, _1688490)), hAPP(hAPP(c_List_Ozip(_1688488, _1688490), _1688492), hAPP(hAPP(c_List_Otake(_1688490), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688488)), _1688492)), _1688496))), hAPP(hAPP(c_List_Ozip(_1688488, _1688490), _1688494), hAPP(hAPP(c_List_Odrop(_1688490), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688488)), _1688492)), _1688496))))], (45264 ^ _782464) ^ [_1688595, _1688597, _1688599] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688595), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688597)), _1688599))), -(_1688599 = hAPP(hAPP(c_List_Oappend(_1688597), hAPP(hAPP(c_List_Otake(_1688597), _1688595), _1688599)), hAPP(hAPP(c_List_Olist_OCons(_1688597), hAPP(hAPP(c_List_Onth(_1688597), _1688599), _1688595)), hAPP(hAPP(c_List_Odrop(_1688597), hAPP(c_Nat_OSuc, _1688595)), _1688599))))], (45270 ^ _782464) ^ [_1688784, _1688786, _1688788] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688784), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688786)), _1688788))), -(hAPP(hAPP(c_List_Oappend(_1688786), hAPP(hAPP(c_List_Otake(_1688786), _1688784), _1688788)), hAPP(hAPP(c_List_Olist_OCons(_1688786), hAPP(c_List_Ohd(_1688786), hAPP(hAPP(c_List_Odrop(_1688786), _1688784), _1688788))), c_List_Olist_ONil(_1688786))) = hAPP(hAPP(c_List_Otake(_1688786), hAPP(c_Nat_OSuc, _1688784)), _1688788))], (45276 ^ _782464) ^ [_1688986, _1688988, _1688990] : [-(_1688986 = c_List_Olist_ONil(_1688988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688990), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688988)), _1688986))), -(hAPP(c_List_Ohd(_1688988), hAPP(hAPP(c_List_Odrop(_1688988), _1688990), _1688986)) = hAPP(hAPP(c_List_Onth(_1688988), _1688986), _1688990))], (45286 ^ _782464) ^ [_1689185, _1689187, _1689189] : [-(hAPP(c_List_Ohd(_1689185), hAPP(hAPP(c_List_Olist_OCons(_1689185), _1689187), _1689189)) = _1689187)], (45288 ^ _782464) ^ [_1689221, _1689223, _1689225] : [-(_1689221 = c_List_Olist_ONil(_1689223)), -(hAPP(c_List_Ohd(_1689223), hAPP(hAPP(c_List_Oappend(_1689223), _1689221), _1689225)) = hAPP(c_List_Ohd(_1689223), _1689221))], (45294 ^ _782464) ^ [_1689291, _1689293, _1689295] : [_1689291 = c_List_Olist_ONil(_1689293), -(hAPP(c_List_Ohd(_1689293), hAPP(hAPP(c_List_Oappend(_1689293), _1689291), _1689295)) = hAPP(c_List_Ohd(_1689293), _1689295))], (45300 ^ _782464) ^ [_1689404, _1689406, _1689408] : [-(_1689404 = c_List_Olist_ONil(_1689406)), -(hAPP(c_List_Ohd(_1689406), hAPP(hAPP(c_List_Oappend(_1689406), _1689404), _1689408)) = hAPP(c_List_Ohd(_1689406), _1689404))], (45306 ^ _782464) ^ [_1689460, _1689462] : [-(_1689460 = c_List_Olist_ONil(_1689462)), -(hBOOL(hAPP(hAPP(c_member(_1689462), hAPP(c_List_Ohd(_1689462), _1689460)), hAPP(c_List_Oset(_1689462), _1689460))))], (45312 ^ _782464) ^ [_1689511, _1689513] : [-(_1689511 = c_List_Olist_ONil(_1689513)), -(hAPP(c_List_Ohd(_1689513), _1689511) = hAPP(hAPP(c_List_Onth(_1689513), _1689511), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45318 ^ _782464) ^ [_1689558, _1689560] : [-(_1689558 = c_List_Olist_ONil(_1689560)), -(hAPP(c_List_Orotate1(_1689560), _1689558) = hAPP(hAPP(c_List_Oappend(_1689560), hAPP(c_List_Otl(_1689560), _1689558)), hAPP(hAPP(c_List_Olist_OCons(_1689560), hAPP(c_List_Ohd(_1689560), _1689558)), c_List_Olist_ONil(_1689560))))], (45324 ^ _782464) ^ [_1689625, _1689627, _1689629] : [-(_1689625 = c_List_Olist_ONil(_1689627)), -(hAPP(c_List_Ohd(_1689627), hAPP(c_List_Orotate(_1689627, _1689629), _1689625)) = hAPP(hAPP(c_List_Onth(_1689627), _1689625), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1689629, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689627)), _1689625))))], (45330 ^ _782464) ^ [_1689695, _1689697, _1689699] : [-(hAPP(hAPP(c_List_Odrop(_1689695), _1689697), hAPP(c_List_Otl(_1689695), _1689699)) = hAPP(c_List_Otl(_1689695), hAPP(hAPP(c_List_Odrop(_1689695), _1689697), _1689699)))], (45332 ^ _782464) ^ [_1689748, _1689750, _1689752] : [-(hAPP(c_List_Otl(_1689748), hAPP(hAPP(c_List_Odrop(_1689748), _1689750), _1689752)) = hAPP(hAPP(c_List_Odrop(_1689748), _1689750), hAPP(c_List_Otl(_1689748), _1689752)))], (45334 ^ _782464) ^ [_1689801, _1689803, _1689805] : [-(hAPP(c_List_Otl(_1689801), hAPP(hAPP(c_List_Olist_OCons(_1689801), _1689803), _1689805)) = _1689805)], (45336 ^ _782464) ^ [_1689841, _1689843] : [hBOOL(hAPP(c_List_Odistinct(_1689841), _1689843)), -(hBOOL(hAPP(c_List_Odistinct(_1689841), hAPP(c_List_Otl(_1689841), _1689843))))], (45342 ^ _782464) ^ [_1689962, _1689964, _1689966] : [hBOOL(hAPP(c_List_Odistinct(_1689962), hAPP(c_List_Orotate(_1689962, _1689964), _1689966))), -(hBOOL(hAPP(c_List_Odistinct(_1689962), _1689966)))], (45348 ^ _782464) ^ [_1690065, _1690067, _1690069] : [hBOOL(hAPP(c_List_Odistinct(_1690065), _1690069)), -(hBOOL(hAPP(c_List_Odistinct(_1690065), hAPP(c_List_Orotate(_1690065, _1690067), _1690069))))], (45354 ^ _782464) ^ [_1690174, _1690176, _1690178] : [-(c_List_Orotate(_1690174, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690176), _1690178)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1690174), tc_List_Olist(_1690174), tc_List_Olist(_1690174), c_List_Orotate(_1690174, _1690176)), c_List_Orotate(_1690174, _1690178)))], (45356 ^ _782464) ^ [_1690230] : [-(c_List_Orotate(_1690230, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1690230)))], (45358 ^ _782464) ^ [_1690260, _1690262, _1690264, _1690266] : [-(hAPP(c_List_Orotate(_1690260, _1690262), hAPP(c_List_Orotate(_1690260, _1690264), _1690266)) = hAPP(c_List_Orotate(_1690260, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690262), _1690264)), _1690266))], (45360 ^ _782464) ^ [_1690313, _1690315, _1690317] : [-(hAPP(c_List_Oset(_1690313), hAPP(c_List_Orotate(_1690313, _1690315), _1690317)) = hAPP(c_List_Oset(_1690313), _1690317))], (45362 ^ _782464) ^ [_1690356, _1690358, _1690360] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690356)), hAPP(c_List_Orotate(_1690356, _1690358), _1690360)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690356)), _1690360))], (45364 ^ _782464) ^ [_1690403] : [-(hAPP(c_List_Otl(_1690403), c_List_Olist_ONil(_1690403)) = c_List_Olist_ONil(_1690403))], (45366 ^ _782464) ^ [_1690453, _1690455, _1690457] : [hAPP(c_List_Orotate(_1690453, _1690455), _1690457) = c_List_Olist_ONil(_1690453), -(_1690457 = c_List_Olist_ONil(_1690453))], (45372 ^ _782464) ^ [_1690548, _1690550, _1690552] : [_1690552 = c_List_Olist_ONil(_1690548), -(hAPP(c_List_Orotate(_1690548, _1690550), _1690552) = c_List_Olist_ONil(_1690548))], (45378 ^ _782464) ^ [_1690649, _1690651] : [-(c_List_Orotate(_1690649, _1690651) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1690649), tc_List_Olist(_1690649)), _1690651), c_List_Orotate1(_1690649)))], (45380 ^ _782464) ^ [_1690692, _1690694, _1690696] : [-(hAPP(c_List_Orotate1(_1690692), hAPP(c_List_Orotate(_1690692, _1690694), _1690696)) = hAPP(c_List_Orotate(_1690692, _1690694), hAPP(c_List_Orotate1(_1690692), _1690696)))], (45382 ^ _782464) ^ [_1690737, _1690739, _1690741] : [-(_1690737 = c_List_Olist_ONil(_1690739)), -(hAPP(c_List_Otl(_1690739), hAPP(hAPP(c_List_Oappend(_1690739), _1690737), _1690741)) = hAPP(hAPP(c_List_Oappend(_1690739), hAPP(c_List_Otl(_1690739), _1690737)), _1690741))], (45388 ^ _782464) ^ [_1690803, _1690805, _1690807] : [-(hAPP(hAPP(c_List_Otake(_1690803), _1690805), hAPP(c_List_Otl(_1690803), _1690807)) = hAPP(c_List_Otl(_1690803), hAPP(hAPP(c_List_Otake(_1690803), hAPP(c_Nat_OSuc, _1690805)), _1690807)))], (45390 ^ _782464) ^ [_1690859, _1690861, _1690863] : [-(hAPP(c_List_Orotate(_1690859, _1690861), _1690863) = hAPP(c_List_Orotate(_1690859, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1690861, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690859)), _1690863))), _1690863))], (45392 ^ _782464) ^ [_1690909, _1690911, _1690913] : [-(hAPP(hAPP(c_List_Odrop(_1690909), hAPP(c_Nat_OSuc, _1690911)), _1690913) = hAPP(hAPP(c_List_Odrop(_1690909), _1690911), hAPP(c_List_Otl(_1690909), _1690913)))], (45394 ^ _782464) ^ [_1690960, _1690962, _1690964] : [-(hAPP(c_List_Orotate(_1690960, hAPP(c_Nat_OSuc, _1690962)), _1690964) = hAPP(c_List_Orotate1(_1690960), hAPP(c_List_Orotate(_1690960, _1690962), _1690964)))], (45396 ^ _782464) ^ [_1691007, _1691009, _1691011] : [-(hAPP(c_List_Otl(_1691007), hAPP(hAPP(c_List_Oappend(_1691007), _1691009), _1691011)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1691007), _1691007, hAPP(c_List_Otl(_1691007), _1691011), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1691007), tc_List_Olist(_1691007)), _1691007), hAPP(hAPP(c_COMBC(tc_List_Olist(_1691007), tc_List_Olist(_1691007), tc_List_Olist(_1691007)), c_List_Oappend(_1691007)), _1691011))), _1691009))], (45398 ^ _782464) ^ [_1691093, _1691095, _1691097] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691093, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691095)), _1691097)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1691095, _1691093), _1691097) = _1691097)], (45404 ^ _782464) ^ [_1691206, _1691208, _1691210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691206)), _1691208)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1691206, _1691210), _1691208) = _1691208)], (45410 ^ _782464) ^ [_1691321, _1691323] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691321)), hAPP(c_List_Otl(_1691321), _1691323)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691321)), _1691323)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45412 ^ _782464) ^ [_1691371, _1691373, _1691375] : [-(hAPP(c_List_Otl(_1691371), hAPP(hAPP(c_List_Otake(_1691371), _1691373), _1691375)) = hAPP(hAPP(c_List_Otake(_1691371), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1691373), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1691371), _1691375)))], (45414 ^ _782464) ^ [_1691426, _1691428, _1691430] : [-(_1691426 = c_List_Olist_ONil(_1691428)), -(hAPP(hAPP(c_List_Otake(_1691428), hAPP(c_Nat_OSuc, _1691430)), _1691426) = hAPP(hAPP(c_List_Olist_OCons(_1691428), hAPP(c_List_Ohd(_1691428), _1691426)), hAPP(hAPP(c_List_Otake(_1691428), _1691430), hAPP(c_List_Otl(_1691428), _1691426))))], (45420 ^ _782464) ^ [_1691503, _1691505, _1691507] : [-(hAPP(c_List_Orotate(_1691503, _1691505), _1691507) = hAPP(hAPP(c_List_Oappend(_1691503), hAPP(hAPP(c_List_Odrop(_1691503), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691505, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691503)), _1691507))), _1691507)), hAPP(hAPP(c_List_Otake(_1691503), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691505, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691503)), _1691507))), _1691507)))], (45422 ^ _782464) ^ [_1691582, _1691584] : [class_Lattices_Oab__semigroup__idem__mult(_1691582), -(_1691584 = c_List_Olist_ONil(_1691582)), -(hAPP(c_Finite__Set_Ofold1(_1691582, c_Groups_Otimes__class_Otimes(_1691582)), hAPP(c_List_Oset(_1691582), _1691584)) = hAPP(c_List_Ofoldl(_1691582, _1691582, c_Groups_Otimes__class_Otimes(_1691582), hAPP(c_List_Ohd(_1691582), _1691584)), hAPP(c_List_Otl(_1691582), _1691584)))], (45432 ^ _782464) ^ [_1691742, _1691744, _1691746, _1691748] : [45433 ^ _782464 : [(45434 ^ _782464) ^ [_1691839, _1691841] : [_1691742 = hAPP(hAPP(c_List_Olist_OCons(_1691744), _1691841), _1691839)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691744), tc_List_Olist(_1691744))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691744), tc_List_Olist(_1691744)), _1691746), hAPP(hAPP(c_List_Oappend(_1691744), _1691746), _1691742))), c_List_Olexord(_1691744, _1691748))))], (45438 ^ _782464) ^ [_1691938, _1691940, _1691942, _1691944] : [-(hAPP(c_List_Ofoldl(_1691938, _1691940, _1691942, _1691944), c_List_Olist_ONil(_1691940)) = _1691944)], (45440 ^ _782464) ^ [_1691977, _1691979, _1691981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1691977), _1691979)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1691977), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1691979), _1691981))))], (45446 ^ _782464) ^ [_1692092, _1692094, _1692096, _1692098] : [class_Groups_Osemigroup__add(_1692092), -(hAPP(c_List_Ofoldl(_1692092, _1692092, c_Groups_Oplus__class_Oplus(_1692092), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692092), _1692094), _1692096)), _1692098) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692092), _1692094), hAPP(c_List_Ofoldl(_1692092, _1692092, c_Groups_Oplus__class_Oplus(_1692092), _1692096), _1692098)))], (45452 ^ _782464) ^ [_1692243, _1692245, _1692247] : [class_Groups_Omonoid__add(_1692243), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692243), _1692245), hAPP(c_List_Ofoldl(_1692243, _1692243, c_Groups_Oplus__class_Oplus(_1692243), c_Groups_Ozero__class_Ozero(_1692243)), _1692247)) = hAPP(c_List_Ofoldl(_1692243, _1692243, c_Groups_Oplus__class_Oplus(_1692243), _1692245), _1692247))], (45458 ^ _782464) ^ [_1692380, _1692382, _1692384, _1692386, _1692388, _1692390] : [-(hAPP(c_List_Ofoldl(_1692380, _1692382, _1692384, _1692386), hAPP(hAPP(c_List_Olist_OCons(_1692382), _1692388), _1692390)) = hAPP(c_List_Ofoldl(_1692380, _1692382, _1692384, hAPP(hAPP(_1692384, _1692386), _1692388)), _1692390))], (45460 ^ _782464) ^ [_1692443, _1692445, _1692447, _1692449, _1692451, _1692453] : [-(hAPP(c_List_Ofoldl(_1692443, _1692445, _1692447, _1692449), hAPP(hAPP(c_List_Oappend(_1692445), _1692451), _1692453)) = hAPP(c_List_Ofoldl(_1692443, _1692445, _1692447, hAPP(c_List_Ofoldl(_1692443, _1692445, _1692447, _1692449), _1692451)), _1692453))], (45462 ^ _782464) ^ [_1692508] : [class_Groups_Omonoid__add(_1692508), -(c_List_Omonoid__add__class_Olistsum(_1692508) = c_List_Ofoldl(_1692508, _1692508, c_Groups_Oplus__class_Oplus(_1692508), c_Groups_Ozero__class_Ozero(_1692508)))], (45468 ^ _782464) ^ [_1692618, _1692620] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692618), _1692620) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45471 ^ _782464 : [(45472 ^ _782464) ^ [] : [-(_1692618 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45474 ^ _782464) ^ [_1692732] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1692732), hAPP(c_List_Oset(tc_Nat_Onat), _1692620))), -(_1692732 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45480 ^ _782464) ^ [_1692829, _1692831] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692829), _1692831) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1692829 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45486 ^ _782464 : [(45487 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45485 ^ [_1692829, _1692831]), hAPP(c_List_Oset(tc_Nat_Onat), _1692831))))], (45489 ^ _782464) ^ [] : [45485 ^ [_1692829, _1692831] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (45493 ^ _782464) ^ [_1693055, _1693057, _1693059, _1693061, _1693063] : [c_Finite__Set_Ofun__left__comm__idem(_1693055, _1693057, _1693059), -(hAPP(hAPP(c_Finite__Set_Ofold(_1693055, _1693057, _1693059), _1693061), hAPP(c_List_Oset(_1693055), _1693063)) = hAPP(c_List_Ofoldl(_1693057, _1693055, hAPP(c_COMBC(_1693055, _1693057, _1693057), _1693059), _1693061), _1693063))], (45499 ^ _782464) ^ [_1693200, _1693202] : [class_Complete__Lattice_Ocomplete__lattice(_1693200), -(c_Complete__Lattice_OSup__class_OSup(_1693200, hAPP(c_List_Oset(_1693200), _1693202)) = hAPP(c_List_Ofoldl(_1693200, _1693200, c_Lattices_Osemilattice__sup__class_Osup(_1693200), c_Orderings_Obot__class_Obot(_1693200)), _1693202))], (45505 ^ _782464) ^ [_1693315, _1693317] : [class_Complete__Lattice_Ocomplete__lattice(_1693315), -(c_Complete__Lattice_OInf__class_OInf(_1693315, hAPP(c_List_Oset(_1693315), _1693317)) = hAPP(c_List_Ofoldl(_1693315, _1693315, c_Lattices_Osemilattice__inf__class_Oinf(_1693315), c_Orderings_Otop__class_Otop(_1693315)), _1693317))], (45511 ^ _782464) ^ [_1693430, _1693432, _1693434] : [class_Lattices_Olattice(_1693430), -(c_Big__Operators_Olattice__class_OSup__fin(_1693430, hAPP(c_List_Oset(_1693430), hAPP(hAPP(c_List_Olist_OCons(_1693430), _1693432), _1693434))) = hAPP(c_List_Ofoldl(_1693430, _1693430, c_Lattices_Osemilattice__sup__class_Osup(_1693430), _1693432), _1693434))], (45517 ^ _782464) ^ [_1693559, _1693561, _1693563] : [class_Lattices_Olattice(_1693559), -(c_Big__Operators_Olattice__class_OInf__fin(_1693559, hAPP(c_List_Oset(_1693559), hAPP(hAPP(c_List_Olist_OCons(_1693559), _1693561), _1693563))) = hAPP(c_List_Ofoldl(_1693559, _1693559, c_Lattices_Osemilattice__inf__class_Oinf(_1693559), _1693561), _1693563))], (45523 ^ _782464) ^ [_1693688, _1693690, _1693692] : [class_Orderings_Olinorder(_1693688), -(c_Big__Operators_Olinorder__class_OMin(_1693688, hAPP(c_List_Oset(_1693688), hAPP(hAPP(c_List_Olist_OCons(_1693688), _1693690), _1693692))) = hAPP(c_List_Ofoldl(_1693688, _1693688, c_Orderings_Oord__class_Omin(_1693688), _1693690), _1693692))], (45529 ^ _782464) ^ [_1693817, _1693819, _1693821] : [class_Orderings_Olinorder(_1693817), -(c_Big__Operators_Olinorder__class_OMax(_1693817, hAPP(c_List_Oset(_1693817), hAPP(hAPP(c_List_Olist_OCons(_1693817), _1693819), _1693821))) = hAPP(c_List_Ofoldl(_1693817, _1693817, c_Orderings_Oord__class_Omax(_1693817), _1693819), _1693821))], (45535 ^ _782464) ^ [_1693946, _1693948, _1693950] : [class_Orderings_Olinorder(_1693946), -(c_Big__Operators_Olattice_OInf__fin(_1693946, c_Orderings_Oord__class_Omin(_1693946), hAPP(c_List_Oset(_1693946), hAPP(hAPP(c_List_Olist_OCons(_1693946), _1693948), _1693950))) = hAPP(c_List_Ofoldl(_1693946, _1693946, c_Orderings_Oord__class_Omin(_1693946), _1693948), _1693950))], (45541 ^ _782464) ^ [_1694081, _1694083, _1694085] : [class_Orderings_Olinorder(_1694081), -(c_Big__Operators_Olattice_OSup__fin(_1694081, c_Orderings_Oord__class_Omax(_1694081), hAPP(c_List_Oset(_1694081), hAPP(hAPP(c_List_Olist_OCons(_1694081), _1694083), _1694085))) = hAPP(c_List_Ofoldl(_1694081, _1694081, c_Orderings_Oord__class_Omax(_1694081), _1694083), _1694085))], (45547 ^ _782464) ^ [_1694216, _1694218, _1694220, _1694222] : [class_Complete__Lattice_Ocomplete__lattice(_1694216), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694218, _1694216), hAPP(c_List_Oset(_1694218), _1694220)), _1694222) = hAPP(c_List_Ofoldl(_1694216, _1694218, hAPP(c_COMBC(_1694218, _1694216, _1694216), hAPP(hAPP(c_COMBB(_1694216, tc_fun(_1694216, _1694216), _1694218), c_Lattices_Osemilattice__sup__class_Osup(_1694216)), _1694222)), c_Orderings_Obot__class_Obot(_1694216)), _1694220))], (45553 ^ _782464) ^ [_1694387, _1694389, _1694391, _1694393] : [class_Complete__Lattice_Ocomplete__lattice(_1694387), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1694389, _1694387), hAPP(c_List_Oset(_1694389), _1694391)), _1694393) = hAPP(c_List_Ofoldl(_1694387, _1694389, hAPP(c_COMBC(_1694389, _1694387, _1694387), hAPP(hAPP(c_COMBB(_1694387, tc_fun(_1694387, _1694387), _1694389), c_Lattices_Osemilattice__inf__class_Oinf(_1694387)), _1694393)), c_Orderings_Otop__class_Otop(_1694387)), _1694391))], (45559 ^ _782464) ^ [_1694558, _1694560] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1694558), hAPP(c_List_Oset(tc_Nat_Onat), _1694560))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1694558), 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)), _1694560))))], (45565 ^ _782464) ^ [_1694667, _1694669, _1694671] : [class_Orderings_Olinorder(_1694667), hBOOL(hAPP(c_Finite__Set_Ofinite(_1694667), _1694669)), -(c_List_Olinorder__class_Osorted__list__of__set(_1694667, hAPP(hAPP(c_Set_Oinsert(_1694667), _1694671), _1694669)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694667, _1694667, c_COMBI(_1694667)), _1694671), c_List_Olinorder__class_Osorted__list__of__set(_1694667, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1694667, tc_HOL_Obool)), _1694669), hAPP(hAPP(c_Set_Oinsert(_1694667), _1694671), c_Orderings_Obot__class_Obot(tc_fun(_1694667, tc_HOL_Obool)))))))], (45575 ^ _782464) ^ [_1694924, _1694926, _1694928] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694924), tc_List_Olist(_1694924))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694924), tc_List_Olist(_1694924)), c_List_Olist_ONil(_1694924)), _1694926)), c_List_Olexord(_1694924, _1694928))), -(_1694926 = hAPP(hAPP(c_List_Olist_OCons(_1694924), 45578 ^ [_1694924, _1694926, _1694928]), 45579 ^ [_1694924, _1694926, _1694928]))], (45583 ^ _782464) ^ [_1695107, _1695109, _1695111] : [45584 ^ _782464 : [(45585 ^ _782464) ^ [_1695196, _1695198] : [_1695109 = hAPP(hAPP(c_List_Olist_OCons(_1695107), _1695198), _1695196)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695107), tc_List_Olist(_1695107))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695107), tc_List_Olist(_1695107)), c_List_Olist_ONil(_1695107)), _1695109)), c_List_Olexord(_1695107, _1695111))))], (45589 ^ _782464) ^ [_1695291, _1695293, _1695295, _1695297] : [class_Orderings_Olinorder(_1695291), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695293, _1695291, _1695295), _1695297), c_List_Olist_ONil(_1695293)) = hAPP(hAPP(c_List_Olist_OCons(_1695293), _1695297), c_List_Olist_ONil(_1695293)))], (45595 ^ _782464) ^ [_1695414, _1695416, _1695418, _1695420, _1695422, _1695424] : [class_Orderings_Olinorder(_1695414), 45598 ^ _782464 : [(45599 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695414), hAPP(_1695416, _1695418)), hAPP(_1695416, _1695420))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695422, _1695414, _1695416), _1695418), hAPP(hAPP(c_List_Olist_OCons(_1695422), _1695420), _1695424)) = hAPP(hAPP(c_List_Olist_OCons(_1695422), _1695418), hAPP(hAPP(c_List_Olist_OCons(_1695422), _1695420), _1695424)))], (45605 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695414), hAPP(_1695416, _1695418)), hAPP(_1695416, _1695420)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695422, _1695414, _1695416), _1695418), hAPP(hAPP(c_List_Olist_OCons(_1695422), _1695420), _1695424)) = hAPP(hAPP(c_List_Olist_OCons(_1695422), _1695420), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695422, _1695414, _1695416), _1695418), _1695424)))]]], (45611 ^ _782464) ^ [_1695796, _1695798, _1695800] : [class_Orderings_Olinorder(_1695796), -(c_List_Oremove1(_1695796, _1695798, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695796, _1695796, c_COMBI(_1695796)), _1695798), _1695800)) = _1695800)], (45617 ^ _782464) ^ [_1695905, _1695907, _1695909, _1695911] : [class_Orderings_Olinorder(_1695905), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695905, _1695905, c_COMBI(_1695905)), _1695907), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695905, _1695905, c_COMBI(_1695905)), _1695909), _1695911)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695905, _1695905, c_COMBI(_1695905)), _1695909), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695905, _1695905, c_COMBI(_1695905)), _1695907), _1695911)))], (45623 ^ _782464) ^ [_1696080, _1696082, _1696084, _1696086, _1696088, _1696090] : [class_Orderings_Olinorder(_1696080), -(hAPP(_1696082, _1696084) = hAPP(_1696082, _1696086)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696088, _1696080, _1696082), _1696086), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696088, _1696080, _1696082), _1696084), _1696090)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696088, _1696080, _1696082), _1696084), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696088, _1696080, _1696082), _1696086), _1696090)))], (45633 ^ _782464) ^ [_1696270] : [class_Orderings_Olinorder(_1696270), -(c_Finite__Set_Ofun__left__comm(_1696270, tc_List_Olist(_1696270), c_List_Olinorder__class_Oinsort__key(_1696270, _1696270, c_COMBI(_1696270))))], (45639 ^ _782464) ^ [_1696361, _1696363, _1696365, _1696367, _1696369] : [class_Orderings_Olinorder(_1696361), -(hAPP(c_List_Oset(_1696363), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696363, _1696361, _1696365), _1696367), _1696369)) = hAPP(hAPP(c_Set_Oinsert(_1696363), _1696367), hAPP(c_List_Oset(_1696363), _1696369)))], (45645 ^ _782464) ^ [_1696498, _1696500, _1696502, _1696504, _1696506] : [class_Orderings_Olinorder(_1696498), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696500)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696500, _1696498, _1696502), _1696504), _1696506)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696500)), _1696506)))], (45651 ^ _782464) ^ [_1696633, _1696635, _1696637, _1696639, _1696641] : [class_Orderings_Olinorder(_1696633), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696635, _1696633, _1696637), _1696639), _1696641) = c_List_Olist_ONil(_1696635)], (45657 ^ _782464) ^ [_1696739, _1696741, _1696743, _1696745, _1696747] : [class_Orderings_Olinorder(_1696739), 45660 ^ _782464 : [(45661 ^ _782464) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1696741), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696741, _1696739, _1696743), _1696745), _1696747))), 45664 ^ _782464 : [(45665 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1696741), _1696745), hAPP(c_List_Oset(_1696741), _1696747)))], (45667 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696741), _1696747)))]]], (45669 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696741), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696741, _1696739, _1696743), _1696745), _1696747)))), -(hBOOL(hAPP(hAPP(c_member(_1696741), _1696745), hAPP(c_List_Oset(_1696741), _1696747)))), hBOOL(hAPP(c_List_Odistinct(_1696741), _1696747))]]], (45679 ^ _782464) ^ [_1697141, _1697143, _1697145, _1697147, _1697149] : [class_Orderings_Olinorder(_1697141), -(hBOOL(hAPP(hAPP(c_member(_1697141), hAPP(_1697143, _1697145)), hAPP(c_Set_Oimage(_1697147, _1697141, _1697143), hAPP(c_List_Oset(_1697147), _1697149))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697147, _1697141, _1697143, _1697145, _1697149) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697147, _1697141, _1697143), _1697145), _1697149))], (45689 ^ _782464) ^ [_1697313, _1697315, _1697317] : [class_Orderings_Olinorder(_1697313), -(hBOOL(hAPP(hAPP(c_member(_1697313), _1697315), hAPP(c_List_Oset(_1697313), _1697317)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697313, _1697313, c_COMBI(_1697313), _1697315, _1697317) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697313, _1697313, c_COMBI(_1697313)), _1697315), _1697317))], (45699 ^ _782464) ^ [_1697469, _1697471, _1697473, _1697475, _1697477] : [class_Orderings_Olinorder(_1697469), hBOOL(hAPP(c_List_Odistinct(_1697471), _1697473)), -(hBOOL(hAPP(c_List_Odistinct(_1697471), c_List_Olinorder__class_Oinsort__insert__key(_1697471, _1697469, _1697475, _1697477, _1697473))))], (45709 ^ _782464) ^ [_1697636, _1697638, _1697640] : [class_Orderings_Olinorder(_1697636), hBOOL(hAPP(hAPP(c_member(_1697636), _1697638), hAPP(c_List_Oset(_1697636), _1697640))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697636, _1697636, c_COMBI(_1697636), _1697638, _1697640) = _1697640)], (45719 ^ _782464) ^ [_1697807, _1697809, _1697811] : [class_Orderings_Olinorder(_1697807), -(hAPP(c_List_Oset(_1697807), c_List_Olinorder__class_Oinsort__insert__key(_1697807, _1697807, c_COMBI(_1697807), _1697809, _1697811)) = hAPP(hAPP(c_Set_Oinsert(_1697807), _1697809), hAPP(c_List_Oset(_1697807), _1697811)))], (45725 ^ _782464) ^ [_1697936, _1697938, _1697940, _1697942, _1697944] : [class_Orderings_Olinorder(_1697936), hBOOL(hAPP(hAPP(c_member(_1697936), hAPP(_1697938, _1697940)), hAPP(c_Set_Oimage(_1697942, _1697936, _1697938), hAPP(c_List_Oset(_1697942), _1697944)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697942, _1697936, _1697938, _1697940, _1697944) = _1697944)], (45735 ^ _782464) ^ [_1698130, _1698132, _1698134, _1698136] : [-(_1698130 = c_List_Olist_ONil(_1698132)), 45738 ^ _782464 : [(45739 ^ _782464) ^ [] : [_1698134 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698132)), _1698130)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1698132, hAPP(hAPP(c_List_Olist__update(_1698132, _1698130), _1698134), _1698136)) = _1698136)], (45745 ^ _782464) ^ [] : [-(_1698134 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698132)), _1698130)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1698132, hAPP(hAPP(c_List_Olist__update(_1698132, _1698130), _1698134), _1698136)) = c_List_Olast(_1698132, _1698130))]]], (45751 ^ _782464) ^ [_1698416, _1698418] : [-(_1698416 = c_List_Olist_ONil(_1698418)), -(c_List_Olast(_1698418, _1698416) = hAPP(hAPP(c_List_Onth(_1698418), _1698416), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698418)), _1698416)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (45757 ^ _782464) ^ [_1698478, _1698480, _1698482] : [_1698478 = c_List_Olist_ONil(_1698480), -(c_List_Olast(_1698480, hAPP(hAPP(c_List_Oappend(_1698480), _1698482), _1698478)) = c_List_Olast(_1698480, _1698482))], (45763 ^ _782464) ^ [_1698585, _1698587, _1698589] : [-(_1698585 = c_List_Olist_ONil(_1698587)), -(c_List_Olast(_1698587, hAPP(hAPP(c_List_Oappend(_1698587), _1698589), _1698585)) = c_List_Olast(_1698587, _1698585))], (45769 ^ _782464) ^ [_1698651, _1698653, _1698655] : [_1698651 = c_List_Olist_ONil(_1698653), -(c_List_Olast(_1698653, hAPP(hAPP(c_List_Oappend(_1698653), _1698655), _1698651)) = c_List_Olast(_1698653, _1698655))], (45775 ^ _782464) ^ [_1698756, _1698758, _1698760] : [-(_1698756 = c_List_Olist_ONil(_1698758)), -(c_List_Olast(_1698758, hAPP(hAPP(c_List_Oappend(_1698758), _1698760), _1698756)) = c_List_Olast(_1698758, _1698756))], (45781 ^ _782464) ^ [_1698812, _1698814, _1698816] : [_1698812 = c_List_Olist_ONil(_1698814), -(c_List_Olast(_1698814, hAPP(hAPP(c_List_Olist_OCons(_1698814), _1698816), _1698812)) = _1698816)], (45787 ^ _782464) ^ [_1698913, _1698915, _1698917] : [-(_1698913 = c_List_Olist_ONil(_1698915)), -(c_List_Olast(_1698915, hAPP(hAPP(c_List_Olist_OCons(_1698915), _1698917), _1698913)) = c_List_Olast(_1698915, _1698913))], (45793 ^ _782464) ^ [_1698979, _1698981, _1698983] : [_1698979 = c_List_Olist_ONil(_1698981), -(c_List_Olast(_1698981, hAPP(hAPP(c_List_Olist_OCons(_1698981), _1698983), _1698979)) = _1698983)], (45799 ^ _782464) ^ [_1699078, _1699080, _1699082] : [-(_1699078 = c_List_Olist_ONil(_1699080)), -(c_List_Olast(_1699080, hAPP(hAPP(c_List_Olist_OCons(_1699080), _1699082), _1699078)) = c_List_Olast(_1699080, _1699078))], (45805 ^ _782464) ^ [_1699130, _1699132] : [-(_1699130 = c_List_Olist_ONil(_1699132)), -(hBOOL(hAPP(hAPP(c_member(_1699132), c_List_Olast(_1699132, _1699130)), hAPP(c_List_Oset(_1699132), _1699130))))], (45811 ^ _782464) ^ [_1699183, _1699185, _1699187] : [-(c_List_Olast(_1699183, hAPP(hAPP(c_List_Oappend(_1699183), _1699185), hAPP(hAPP(c_List_Olist_OCons(_1699183), _1699187), c_List_Olist_ONil(_1699183)))) = _1699187)], (45813 ^ _782464) ^ [_1699231, _1699233, _1699235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699233)), _1699235))), -(c_List_Olast(_1699233, hAPP(hAPP(c_List_Odrop(_1699233), _1699231), _1699235)) = c_List_Olast(_1699233, _1699235))], (45819 ^ _782464) ^ [_1699358, _1699360] : [-(_1699358 = c_List_Olist_ONil(_1699360)), -(hAPP(hAPP(c_List_Oappend(_1699360), c_List_Obutlast(_1699360, _1699358)), hAPP(hAPP(c_List_Olist_OCons(_1699360), c_List_Olast(_1699360, _1699358)), c_List_Olist_ONil(_1699360))) = _1699358)], (45825 ^ _782464) ^ [_1699441, _1699443, _1699445, _1699447] : [hAPP(hAPP(c_List_Oappend(_1699441), _1699443), hAPP(hAPP(c_List_Olist_OCons(_1699441), _1699445), c_List_Olist_ONil(_1699441))) = _1699447, 45828 ^ _782464 : [(45829 ^ _782464) ^ [] : [_1699447 = c_List_Olist_ONil(_1699441)], (45831 ^ _782464) ^ [] : [-(c_List_Obutlast(_1699441, _1699447) = _1699443)], (45833 ^ _782464) ^ [] : [-(c_List_Olast(_1699441, _1699447) = _1699445)]]], (45835 ^ _782464) ^ [_1699630, _1699632, _1699634, _1699636] : [-(hAPP(hAPP(c_List_Oappend(_1699630), _1699632), hAPP(hAPP(c_List_Olist_OCons(_1699630), _1699634), c_List_Olist_ONil(_1699630))) = _1699636), -(_1699636 = c_List_Olist_ONil(_1699630)), c_List_Obutlast(_1699630, _1699636) = _1699632, c_List_Olast(_1699630, _1699636) = _1699634], (45849 ^ _782464) ^ [_1699898, _1699900, _1699902] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699898)), _1699900), c_List_Olists(_1699898, _1699902))), -(_1699900 = c_List_Olist_ONil(_1699898)), 45858 ^ _782464 : [(45859 ^ _782464) ^ [] : [-(_1699900 = hAPP(hAPP(c_List_Olist_OCons(_1699898), 45856 ^ [_1699898, _1699900, _1699902]), 45857 ^ [_1699898, _1699900, _1699902]))], (45861 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699898), 45856 ^ [_1699898, _1699900, _1699902]), _1699902)))], (45863 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699898)), 45857 ^ [_1699898, _1699900, _1699902]), c_List_Olists(_1699898, _1699902))))]]], (45865 ^ _782464) ^ [_1700181, _1700183, _1700185] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700181)), _1700183), c_List_Olists(_1700181, _1700185)))), 45866 ^ _782464 : [(45867 ^ _782464) ^ [] : [_1700183 = c_List_Olist_ONil(_1700181)], (45869 ^ _782464) ^ [_1700309, _1700311] : [_1700183 = hAPP(hAPP(c_List_Olist_OCons(_1700181), _1700311), _1700309), hBOOL(hAPP(hAPP(c_member(_1700181), _1700311), _1700185)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700181)), _1700309), c_List_Olists(_1700181, _1700185)))]]], (45881 ^ _782464) ^ [_1700543, _1700545] : [-(_1700543 = c_List_Olist_ONil(_1700545)), -(c_Random_Oselect__weight(_1700545, hAPP(hAPP(c_List_Omap(_1700545, tc_prod(tc_Code__Numeral_Ocode__numeral, _1700545)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1700545), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1700543)) = c_Random_Oselect(_1700545, _1700543))], (45887 ^ _782464) ^ [_1700605, _1700607, _1700609] : [c_Fun_Oinj__on(_1700605, _1700607, _1700609, c_Orderings_Otop__class_Otop(tc_fun(_1700605, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1700605), tc_List_Olist(_1700607), hAPP(c_List_Omap(_1700605, _1700607), _1700609), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1700605), tc_HOL_Obool))))], (45893 ^ _782464) ^ [_1700732, _1700734, _1700736, _1700738] : [-(_1700732 = c_List_Olist_ONil(_1700734)), -(c_List_Olast(_1700736, hAPP(hAPP(c_List_Omap(_1700734, _1700736), _1700738), _1700732)) = hAPP(_1700738, c_List_Olast(_1700734, _1700732)))], (45899 ^ _782464) ^ [_1700792, _1700794, _1700796, _1700798, _1700800] : [c_Fun_Oinj__on(_1700792, _1700794, _1700796, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1700792, tc_HOL_Obool)), hAPP(c_List_Oset(_1700792), _1700798)), hAPP(c_List_Oset(_1700792), _1700800))), 45902 ^ _782464 : [(45903 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Omap(_1700792, _1700794), _1700796), _1700798) = hAPP(hAPP(c_List_Omap(_1700792, _1700794), _1700796), _1700800), -(_1700798 = _1700800)], (45909 ^ _782464) ^ [] : [_1700798 = _1700800, -(hAPP(hAPP(c_List_Omap(_1700792, _1700794), _1700796), _1700798) = hAPP(hAPP(c_List_Omap(_1700792, _1700794), _1700796), _1700800))]]], (45915 ^ _782464) ^ [_1701117, _1701119, _1701121, _1701123, _1701125] : [hAPP(hAPP(c_List_Omap(_1701117, _1701119), _1701121), _1701123) = hAPP(hAPP(c_List_Omap(_1701117, _1701119), _1701121), _1701125), c_Fun_Oinj__on(_1701117, _1701119, _1701121, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1701117, tc_HOL_Obool)), hAPP(c_List_Oset(_1701117), _1701123)), hAPP(c_List_Oset(_1701117), _1701125))), -(_1701123 = _1701125)], (45925 ^ _782464) ^ [_1701340, _1701342, _1701344, _1701346, _1701348, _1701350, _1701352] : [-(hAPP(c_List_Ofoldl(_1701340, _1701342, _1701344, _1701346), hAPP(hAPP(c_List_Omap(_1701348, _1701342), _1701350), _1701352)) = hAPP(c_List_Ofoldl(_1701340, _1701348, hAPP(hAPP(c_COMBC(_1701340, tc_fun(_1701348, _1701342), tc_fun(_1701348, _1701340)), hAPP(hAPP(c_COMBB(tc_fun(_1701342, _1701340), tc_fun(tc_fun(_1701348, _1701342), tc_fun(_1701348, _1701340)), _1701340), c_COMBB(_1701342, _1701340, _1701348)), _1701344)), _1701350), _1701346), _1701352))], (45927 ^ _782464) ^ [_1701442, _1701444, _1701446, _1701448, _1701450] : [-(hAPP(c_List_Orotate(_1701442, _1701444), hAPP(hAPP(c_List_Omap(_1701446, _1701442), _1701448), _1701450)) = hAPP(hAPP(c_List_Omap(_1701446, _1701442), _1701448), hAPP(c_List_Orotate(_1701446, _1701444), _1701450)))], (45929 ^ _782464) ^ [_1701503, _1701505, _1701507, _1701509] : [-(hAPP(hAPP(c_List_Omap(_1701503, _1701505), _1701507), hAPP(c_List_Otl(_1701503), _1701509)) = hAPP(c_List_Otl(_1701505), hAPP(hAPP(c_List_Omap(_1701503, _1701505), _1701507), _1701509)))], (45931 ^ _782464) ^ [_1701581, _1701583, _1701585, _1701587] : [hAPP(hAPP(c_List_Omap(_1701581, _1701583), _1701585), _1701587) = c_List_Olist_ONil(_1701583), -(_1701587 = c_List_Olist_ONil(_1701581))], (45937 ^ _782464) ^ [_1701684, _1701686, _1701688, _1701690] : [_1701690 = c_List_Olist_ONil(_1701684), -(hAPP(hAPP(c_List_Omap(_1701684, _1701686), _1701688), _1701690) = c_List_Olist_ONil(_1701686))], (45943 ^ _782464) ^ [_1701793, _1701795, _1701797] : [-(hAPP(hAPP(c_List_Omap(_1701793, _1701795), _1701797), c_List_Olist_ONil(_1701793)) = c_List_Olist_ONil(_1701795))], (45945 ^ _782464) ^ [_1701854, _1701856, _1701858, _1701860] : [c_List_Olist_ONil(_1701854) = hAPP(hAPP(c_List_Omap(_1701856, _1701854), _1701858), _1701860), -(_1701860 = c_List_Olist_ONil(_1701856))], (45951 ^ _782464) ^ [_1701957, _1701959, _1701961, _1701963] : [_1701963 = c_List_Olist_ONil(_1701959), -(c_List_Olist_ONil(_1701957) = hAPP(hAPP(c_List_Omap(_1701959, _1701957), _1701961), _1701963))], (45957 ^ _782464) ^ [_1702066, _1702068, _1702070, _1702072, _1702074, _1702076] : [-(hAPP(hAPP(c_List_Omap(_1702066, _1702068), _1702070), hAPP(hAPP(c_List_Olist__update(_1702066, _1702072), _1702074), _1702076)) = hAPP(hAPP(c_List_Olist__update(_1702068, hAPP(hAPP(c_List_Omap(_1702066, _1702068), _1702070), _1702072)), _1702074), hAPP(_1702070, _1702076)))], (45959 ^ _782464) ^ [_1702138, _1702140, _1702142, _1702144, _1702146] : [class_Groups_Ocomm__monoid__add(_1702138), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702138), hAPP(hAPP(c_List_Omap(_1702140, _1702138), hAPP(hAPP(c_COMBS(_1702140, _1702138, _1702138), hAPP(hAPP(c_COMBB(_1702138, tc_fun(_1702138, _1702138), _1702140), c_Groups_Oplus__class_Oplus(_1702138)), _1702142)), _1702144)), _1702146)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1702138), hAPP(c_List_Omonoid__add__class_Olistsum(_1702138), hAPP(hAPP(c_List_Omap(_1702140, _1702138), _1702142), _1702146))), hAPP(c_List_Omonoid__add__class_Olistsum(_1702138), hAPP(hAPP(c_List_Omap(_1702140, _1702138), _1702144), _1702146))))], (45965 ^ _782464) ^ [_1702369, _1702371, _1702373] : [class_Groups_Omonoid__add(_1702369), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702369), hAPP(hAPP(c_List_Omap(_1702371, _1702369), hAPP(c_COMBK(_1702369, _1702371), c_Groups_Ozero__class_Ozero(_1702369))), _1702373)) = c_Groups_Ozero__class_Ozero(_1702369))], (45971 ^ _782464) ^ [_1702494, _1702496, _1702498, _1702500, _1702502] : [class_Rings_Osemiring__0(_1702494), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702494), hAPP(hAPP(c_List_Omap(_1702496, _1702494), hAPP(hAPP(c_COMBC(_1702496, _1702494, _1702494), hAPP(hAPP(c_COMBB(_1702494, tc_fun(_1702494, _1702494), _1702496), c_Groups_Otimes__class_Otimes(_1702494)), _1702498)), _1702500)), _1702502)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1702494), hAPP(c_List_Omonoid__add__class_Olistsum(_1702494), hAPP(hAPP(c_List_Omap(_1702496, _1702494), _1702498), _1702502))), _1702500))], (45977 ^ _782464) ^ [_1702697, _1702699, _1702701, _1702703, _1702705] : [class_Rings_Osemiring__0(_1702697), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702697), hAPP(hAPP(c_List_Omap(_1702699, _1702697), hAPP(hAPP(c_COMBB(_1702697, _1702697, _1702699), hAPP(c_Groups_Otimes__class_Otimes(_1702697), _1702701)), _1702703)), _1702705)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1702697), _1702701), hAPP(c_List_Omonoid__add__class_Olistsum(_1702697), hAPP(hAPP(c_List_Omap(_1702699, _1702697), _1702703), _1702705))))], (45983 ^ _782464) ^ [_1702880, _1702882, _1702884, _1702886, _1702888] : [class_Groups_Oab__group__add(_1702880), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702880), hAPP(hAPP(c_List_Omap(_1702882, _1702880), hAPP(hAPP(c_COMBS(_1702882, _1702880, _1702880), hAPP(hAPP(c_COMBB(_1702880, tc_fun(_1702880, _1702880), _1702882), c_Groups_Ominus__class_Ominus(_1702880)), _1702884)), _1702886)), _1702888)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1702880), hAPP(c_List_Omonoid__add__class_Olistsum(_1702880), hAPP(hAPP(c_List_Omap(_1702882, _1702880), _1702884), _1702888))), hAPP(c_List_Omonoid__add__class_Olistsum(_1702880), hAPP(hAPP(c_List_Omap(_1702882, _1702880), _1702886), _1702888))))], (45989 ^ _782464) ^ [_1703111, _1703113, _1703115, _1703117] : [-(hAPP(hAPP(c_List_Omap(_1703111, _1703113), _1703115), c_List_Obutlast(_1703111, _1703117)) = c_List_Obutlast(_1703113, hAPP(hAPP(c_List_Omap(_1703111, _1703113), _1703115), _1703117)))], (45991 ^ _782464) ^ [_1703164, _1703166, _1703168, _1703170, _1703172, _1703174, _1703176] : [hAPP(hAPP(c_List_Omap(_1703164, _1703166), _1703168), _1703170) = hAPP(hAPP(c_List_Omap(_1703172, _1703166), _1703174), _1703176), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703164)), _1703170) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703172)), _1703176))], (45997 ^ _782464) ^ [_1703315, _1703317, _1703319, _1703321] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703315)), hAPP(hAPP(c_List_Omap(_1703317, _1703315), _1703319), _1703321)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703317)), _1703321))], (46009 ^ _782464) ^ [_1703635, _1703637, _1703639, _1703641, _1703643] : [46011 ^ _782464 : [(46012 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703635), 46010 ^ [_1703635, _1703637, _1703639, _1703641, _1703643]), hAPP(c_List_Oset(_1703635), _1703641))))], (46014 ^ _782464) ^ [] : [hAPP(_1703639, 46010 ^ [_1703635, _1703637, _1703639, _1703641, _1703643]) = hAPP(_1703643, 46010 ^ [_1703635, _1703637, _1703639, _1703641, _1703643])]], -(hAPP(hAPP(c_List_Omap(_1703635, _1703637), _1703639), _1703641) = hAPP(hAPP(c_List_Omap(_1703635, _1703637), _1703643), _1703641))], (45999 ^ _782464) ^ [_1703391, _1703393, _1703395, _1703397, _1703399] : [hAPP(hAPP(c_List_Omap(_1703391, _1703393), _1703395), _1703397) = hAPP(hAPP(c_List_Omap(_1703391, _1703393), _1703399), _1703397), 46002 ^ _782464 : [(46003 ^ _782464) ^ [_1703514] : [hBOOL(hAPP(hAPP(c_member(_1703391), _1703514), hAPP(c_List_Oset(_1703391), _1703397))), -(hAPP(_1703395, _1703514) = hAPP(_1703399, _1703514))]]], (46018 ^ _782464) ^ [_1703892, _1703894, _1703896, _1703898, _1703900] : [-(hAPP(hAPP(c_List_Otake(_1703892), _1703894), hAPP(hAPP(c_List_Omap(_1703896, _1703892), _1703898), _1703900)) = hAPP(hAPP(c_List_Omap(_1703896, _1703892), _1703898), hAPP(hAPP(c_List_Otake(_1703896), _1703894), _1703900)))], (46020 ^ _782464) ^ [_1703957, _1703959, _1703961, _1703963, _1703965] : [hAPP(hAPP(c_List_Omap(_1703957, _1703959), _1703961), _1703963) = hAPP(hAPP(c_List_Omap(_1703957, _1703959), _1703961), _1703965), c_Fun_Oinj__on(_1703957, _1703959, _1703961, c_Orderings_Otop__class_Otop(tc_fun(_1703957, tc_HOL_Obool))), -(_1703963 = _1703965)], (46030 ^ _782464) ^ [_1704148, _1704150, _1704152, _1704154, _1704156] : [c_Fun_Oinj__on(_1704148, _1704150, _1704152, c_Orderings_Otop__class_Otop(tc_fun(_1704148, tc_HOL_Obool))), 46033 ^ _782464 : [(46034 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Omap(_1704148, _1704150), _1704152), _1704154) = hAPP(hAPP(c_List_Omap(_1704148, _1704150), _1704152), _1704156), -(_1704154 = _1704156)], (46040 ^ _782464) ^ [] : [_1704154 = _1704156, -(hAPP(hAPP(c_List_Omap(_1704148, _1704150), _1704152), _1704154) = hAPP(hAPP(c_List_Omap(_1704148, _1704150), _1704152), _1704156))]]], (46046 ^ _782464) ^ [_1704441, _1704443] : [-(hAPP(hAPP(c_List_Omap(_1704441, _1704441), c_COMBI(_1704441)), _1704443) = _1704443)], (46048 ^ _782464) ^ [_1704477, _1704479, _1704481, _1704483] : [-(hAPP(c_List_Oset(_1704477), hAPP(hAPP(c_List_Omap(_1704479, _1704477), _1704481), _1704483)) = hAPP(c_Set_Oimage(_1704479, _1704477, _1704481), hAPP(c_List_Oset(_1704479), _1704483)))], (46050 ^ _782464) ^ [_1704532, _1704534, _1704536, _1704538, _1704540] : [-(hAPP(hAPP(c_List_Omap(_1704532, _1704534), _1704536), hAPP(hAPP(c_List_Olist_OCons(_1704532), _1704538), _1704540)) = hAPP(hAPP(c_List_Olist_OCons(_1704534), hAPP(_1704536, _1704538)), hAPP(hAPP(c_List_Omap(_1704532, _1704534), _1704536), _1704540)))], (46052 ^ _782464) ^ [_1704600, _1704602] : [-(hAPP(hAPP(c_List_Ozip(_1704600, _1704600), _1704602), _1704602) = hAPP(hAPP(c_List_Omap(_1704600, tc_prod(_1704600, _1704600)), hAPP(hAPP(c_COMBS(_1704600, _1704600, tc_prod(_1704600, _1704600)), c_Product__Type_OPair(_1704600, _1704600)), c_COMBI(_1704600))), _1704602))], (46054 ^ _782464) ^ [_1704664, _1704666, _1704668, _1704670, _1704672, _1704674, _1704676, _1704678] : [-(hAPP(hAPP(c_List_Ozip(_1704664, _1704666), hAPP(hAPP(c_List_Omap(_1704668, _1704664), _1704670), _1704672)), hAPP(hAPP(c_List_Omap(_1704674, _1704666), _1704676), _1704678)) = hAPP(hAPP(c_List_Omap(tc_prod(_1704668, _1704674), tc_prod(_1704664, _1704666)), hAPP(c_Product__Type_Oprod_Oprod__case(_1704668, _1704674, tc_prod(_1704664, _1704666)), hAPP(hAPP(c_COMBC(_1704668, tc_fun(_1704674, _1704666), tc_fun(_1704674, tc_prod(_1704664, _1704666))), hAPP(hAPP(c_COMBB(tc_fun(_1704666, tc_prod(_1704664, _1704666)), tc_fun(tc_fun(_1704674, _1704666), tc_fun(_1704674, tc_prod(_1704664, _1704666))), _1704668), c_COMBB(_1704666, tc_prod(_1704664, _1704666), _1704674)), hAPP(hAPP(c_COMBB(_1704664, tc_fun(_1704666, tc_prod(_1704664, _1704666)), _1704668), c_Product__Type_OPair(_1704664, _1704666)), _1704670))), _1704676))), hAPP(hAPP(c_List_Ozip(_1704668, _1704674), _1704672), _1704678)))], (46056 ^ _782464) ^ [_1704835, _1704837, _1704839, _1704841, _1704843, _1704845] : [-(hAPP(hAPP(c_List_Ozip(_1704835, _1704837), hAPP(hAPP(c_List_Omap(_1704839, _1704835), _1704841), _1704843)), _1704845) = hAPP(hAPP(c_List_Omap(tc_prod(_1704839, _1704837), tc_prod(_1704835, _1704837)), hAPP(c_Product__Type_Oprod_Oprod__case(_1704839, _1704837, tc_prod(_1704835, _1704837)), hAPP(hAPP(c_COMBB(_1704835, tc_fun(_1704837, tc_prod(_1704835, _1704837)), _1704839), c_Product__Type_OPair(_1704835, _1704837)), _1704841))), hAPP(hAPP(c_List_Ozip(_1704839, _1704837), _1704843), _1704845)))], (46058 ^ _782464) ^ [_1704939, _1704941, _1704943, _1704945, _1704947, _1704949, _1704951, _1704953] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1704939, _1704941), _1704943), _1704945), hAPP(hAPP(c_List_Ozip(_1704939, _1704941), hAPP(hAPP(c_List_Omap(_1704947, _1704939), _1704949), _1704951)), _1704953)) = hAPP(hAPP(c_List_Omap(tc_prod(_1704947, _1704941), _1704943), hAPP(c_Product__Type_Oprod_Oprod__case(_1704947, _1704941, _1704943), hAPP(hAPP(c_COMBB(tc_fun(_1704941, tc_prod(_1704939, _1704941)), tc_fun(_1704941, _1704943), _1704947), hAPP(c_COMBB(tc_prod(_1704939, _1704941), _1704943, _1704941), _1704945)), hAPP(hAPP(c_COMBB(_1704939, tc_fun(_1704941, tc_prod(_1704939, _1704941)), _1704947), c_Product__Type_OPair(_1704939, _1704941)), _1704949)))), hAPP(hAPP(c_List_Ozip(_1704947, _1704941), _1704951), _1704953)))], (46060 ^ _782464) ^ [_1705082, _1705084, _1705086, _1705088, _1705090, _1705092, _1705094, _1705096] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1705082, _1705084), _1705086), _1705088), hAPP(hAPP(c_List_Ozip(_1705082, _1705084), _1705090), hAPP(hAPP(c_List_Omap(_1705092, _1705084), _1705094), _1705096))) = hAPP(hAPP(c_List_Omap(tc_prod(_1705082, _1705092), _1705086), hAPP(c_Product__Type_Oprod_Oprod__case(_1705082, _1705092, _1705086), hAPP(hAPP(c_COMBB(tc_fun(_1705092, tc_prod(_1705082, _1705084)), tc_fun(_1705092, _1705086), _1705082), hAPP(c_COMBB(tc_prod(_1705082, _1705084), _1705086, _1705092), _1705088)), hAPP(hAPP(c_COMBC(_1705082, tc_fun(_1705092, _1705084), tc_fun(_1705092, tc_prod(_1705082, _1705084))), hAPP(hAPP(c_COMBB(tc_fun(_1705084, tc_prod(_1705082, _1705084)), tc_fun(tc_fun(_1705092, _1705084), tc_fun(_1705092, tc_prod(_1705082, _1705084))), _1705082), c_COMBB(_1705084, tc_prod(_1705082, _1705084), _1705092)), c_Product__Type_OPair(_1705082, _1705084))), _1705094)))), hAPP(hAPP(c_List_Ozip(_1705082, _1705092), _1705090), _1705096)))], (46062 ^ _782464) ^ [_1705263, _1705265, _1705267, _1705269, _1705271, _1705273] : [-(hAPP(hAPP(c_List_Ozip(_1705263, _1705265), _1705267), hAPP(hAPP(c_List_Omap(_1705269, _1705265), _1705271), _1705273)) = hAPP(hAPP(c_List_Omap(tc_prod(_1705263, _1705269), tc_prod(_1705263, _1705265)), hAPP(c_Product__Type_Oprod_Oprod__case(_1705263, _1705269, tc_prod(_1705263, _1705265)), hAPP(hAPP(c_COMBC(_1705263, tc_fun(_1705269, _1705265), tc_fun(_1705269, tc_prod(_1705263, _1705265))), hAPP(hAPP(c_COMBB(tc_fun(_1705265, tc_prod(_1705263, _1705265)), tc_fun(tc_fun(_1705269, _1705265), tc_fun(_1705269, tc_prod(_1705263, _1705265))), _1705263), c_COMBB(_1705265, tc_prod(_1705263, _1705265), _1705269)), c_Product__Type_OPair(_1705263, _1705265))), _1705271))), hAPP(hAPP(c_List_Ozip(_1705263, _1705269), _1705267), _1705273)))], (46064 ^ _782464) ^ [_1705405, _1705407, _1705409, _1705411, _1705413] : [-(hAPP(hAPP(c_List_Omap(_1705405, _1705407), _1705409), hAPP(hAPP(c_List_Oappend(_1705405), _1705411), _1705413)) = hAPP(hAPP(c_List_Oappend(_1705407), hAPP(hAPP(c_List_Omap(_1705405, _1705407), _1705409), _1705411)), hAPP(hAPP(c_List_Omap(_1705405, _1705407), _1705409), _1705413)))], (46066 ^ _782464) ^ [_1705475, _1705477, _1705479, _1705481] : [-(_1705475 = c_List_Olist_ONil(_1705477)), -(hAPP(c_List_Ohd(_1705479), hAPP(hAPP(c_List_Omap(_1705477, _1705479), _1705481), _1705475)) = hAPP(_1705481, hAPP(c_List_Ohd(_1705477), _1705475)))], (46072 ^ _782464) ^ [_1705539, _1705541, _1705543, _1705545, _1705547] : [-(hAPP(hAPP(c_List_Odrop(_1705539), _1705541), hAPP(hAPP(c_List_Omap(_1705543, _1705539), _1705545), _1705547)) = hAPP(hAPP(c_List_Omap(_1705543, _1705539), _1705545), hAPP(hAPP(c_List_Odrop(_1705543), _1705541), _1705547)))], (46074 ^ _782464) ^ [_1705604, _1705606, _1705608, _1705610, _1705612] : [-(c_List_Olist_Olist__size(_1705604, _1705606, hAPP(hAPP(c_List_Omap(_1705608, _1705604), _1705610), _1705612)) = c_List_Olist_Olist__size(_1705608, hAPP(c_Fun_Ocomp(_1705604, tc_Nat_Onat, _1705608, _1705606), _1705610), _1705612))], (46076 ^ _782464) ^ [_1705660, _1705662, _1705664, _1705666, _1705668] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1705660), tc_List_Olist(_1705662), tc_List_Olist(_1705664), hAPP(c_List_Omap(_1705660, _1705662), _1705666)), hAPP(c_List_Omap(_1705664, _1705660), _1705668)) = hAPP(c_List_Omap(_1705664, _1705662), hAPP(c_Fun_Ocomp(_1705660, _1705662, _1705664, _1705666), _1705668)))], (46078 ^ _782464) ^ [_1705731, _1705733, _1705735, _1705737, _1705739] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1705731), tc_List_Olist(_1705733), tc_List_Olist(_1705735), hAPP(c_List_Omap(_1705731, _1705733), _1705737)), hAPP(c_List_Omap(_1705735, _1705731), _1705739)) = hAPP(c_List_Omap(_1705735, _1705733), hAPP(c_Fun_Ocomp(_1705731, _1705733, _1705735, _1705737), _1705739)))], (46080 ^ _782464) ^ [_1705802, _1705804, _1705806, _1705808, _1705810, _1705812] : [-(hAPP(hAPP(c_List_Omap(_1705802, _1705804), _1705806), hAPP(hAPP(c_List_Omap(_1705808, _1705802), _1705810), _1705812)) = hAPP(hAPP(c_List_Omap(_1705808, _1705804), hAPP(c_Fun_Ocomp(_1705802, _1705804, _1705808, _1705806), _1705810)), _1705812))], (46082 ^ _782464) ^ [_1705870, _1705872, _1705874, _1705876, _1705878, _1705880] : [-(hAPP(hAPP(c_List_Omap(_1705870, _1705872), _1705874), hAPP(hAPP(c_List_Omap(_1705876, _1705870), _1705878), _1705880)) = hAPP(hAPP(c_List_Omap(_1705876, _1705872), hAPP(c_Fun_Ocomp(_1705870, _1705872, _1705876, _1705874), _1705878)), _1705880))], (46084 ^ _782464) ^ [_1705938] : [-(hAPP(c_List_Omap(_1705938, _1705938), c_COMBI(_1705938)) = c_Fun_Oid(tc_List_Olist(_1705938)))], (46086 ^ _782464) ^ [_1705973] : [-(hAPP(c_List_Omap(_1705973, _1705973), c_Fun_Oid(_1705973)) = c_Fun_Oid(tc_List_Olist(_1705973)))], (46088 ^ _782464) ^ [_1706008, _1706010, _1706012, _1706014, _1706016] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1706008), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1706010)), _1706012))), -(hAPP(hAPP(c_List_Onth(_1706014), hAPP(hAPP(c_List_Omap(_1706010, _1706014), _1706016), _1706012)), _1706008) = hAPP(_1706016, hAPP(hAPP(c_List_Onth(_1706010), _1706012), _1706008)))], (46094 ^ _782464) ^ [_1706167, _1706169, _1706171, _1706173, _1706175, _1706177] : [-(hBOOL(hAPP(hAPP(c_member(_1706167), _1706169), hAPP(c_List_Oset(_1706167), _1706171)))), -(hAPP(hAPP(c_List_Omap(_1706167, _1706173), c_Fun_Ofun__upd(_1706167, _1706173, _1706175, _1706169, _1706177)), _1706171) = hAPP(hAPP(c_List_Omap(_1706167, _1706173), _1706175), _1706171))], (46100 ^ _782464) ^ [_1706268, _1706270, _1706272, _1706274] : [hBOOL(hAPP(c_List_Odistinct(_1706268), hAPP(hAPP(c_List_Omap(_1706270, _1706268), _1706272), _1706274))), 46103 ^ _782464 : [(46104 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1706270), _1706274)))], (46106 ^ _782464) ^ [] : [-(c_Fun_Oinj__on(_1706270, _1706268, _1706272, hAPP(c_List_Oset(_1706270), _1706274)))]]], (46108 ^ _782464) ^ [_1706419, _1706421, _1706423, _1706425] : [-(hBOOL(hAPP(c_List_Odistinct(_1706419), hAPP(hAPP(c_List_Omap(_1706421, _1706419), _1706423), _1706425)))), hBOOL(hAPP(c_List_Odistinct(_1706421), _1706425)), c_Fun_Oinj__on(_1706421, _1706419, _1706423, hAPP(c_List_Oset(_1706421), _1706425))], (46118 ^ _782464) ^ [_1706606, _1706608] : [class_Groups_Oordered__ab__group__add__abs(_1706606), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706606), hAPP(c_Groups_Oabs__class_Oabs(_1706606), hAPP(c_List_Omonoid__add__class_Olistsum(_1706606), _1706608))), hAPP(c_List_Omonoid__add__class_Olistsum(_1706606), hAPP(hAPP(c_List_Omap(_1706606, _1706606), c_Groups_Oabs__class_Oabs(_1706606)), _1706608)))))], (46124 ^ _782464) ^ [_1706747, _1706749, _1706751, _1706753] : [class_Groups_Oab__group__add(_1706747), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1706747), hAPP(c_List_Omonoid__add__class_Olistsum(_1706747), hAPP(hAPP(c_List_Omap(_1706749, _1706747), _1706751), _1706753))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1706747), hAPP(hAPP(c_List_Omap(_1706749, _1706747), hAPP(c_Fun_Ocomp(_1706747, _1706747, _1706749, c_Groups_Ouminus__class_Ouminus(_1706747)), _1706751)), _1706753)))], (46130 ^ _782464) ^ [_1706930, _1706932, _1706934] : [c_Fun_Oinj__on(tc_List_Olist(_1706930), tc_List_Olist(_1706932), hAPP(c_List_Omap(_1706930, _1706932), _1706934), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1706930), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1706930, _1706932, _1706934, c_Orderings_Otop__class_Otop(tc_fun(_1706930, tc_HOL_Obool))))], (46136 ^ _782464) ^ [_1707057, _1707059, _1707061] : [c_Fun_Oinj__on(_1707057, _1707059, _1707061, c_Orderings_Otop__class_Otop(tc_fun(_1707057, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1707057), tc_List_Olist(_1707059), hAPP(c_List_Omap(_1707057, _1707059), _1707061), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1707057), tc_HOL_Obool))))], (46142 ^ _782464) ^ [_1707190, _1707192, _1707194] : [c_Fun_Oinj__on(tc_List_Olist(_1707190), tc_List_Olist(_1707192), hAPP(c_List_Omap(_1707190, _1707192), _1707194), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1707190), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1707190, _1707192, _1707194, c_Orderings_Otop__class_Otop(tc_fun(_1707190, tc_HOL_Obool))))], (46148 ^ _782464) ^ [_1707321, _1707323, _1707325, _1707327] : [class_Groups_Ocomm__monoid__add(_1707321), hBOOL(hAPP(c_List_Odistinct(_1707323), _1707325)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707321), hAPP(hAPP(c_List_Omap(_1707323, _1707321), _1707327), _1707325)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1707323, _1707321), _1707327), hAPP(c_List_Oset(_1707323), _1707325)))], (46158 ^ _782464) ^ [_1707520, _1707522, _1707524, _1707526] : [class_Rings_Osemiring__1(_1707520), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707520), hAPP(hAPP(c_List_Omap(_1707522, _1707520), hAPP(c_COMBK(_1707520, _1707522), _1707524)), _1707526)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1707520), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1707520), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707522)), _1707526))), _1707524))], (46164 ^ _782464) ^ [_1707679, _1707681, _1707683, _1707685, _1707687] : [-(c_Enum_Oproduct(_1707679, _1707681, hAPP(hAPP(c_List_Olist_OCons(_1707679), _1707683), _1707685), _1707687) = hAPP(hAPP(c_List_Oappend(tc_prod(_1707679, _1707681)), hAPP(hAPP(c_List_Omap(_1707681, tc_prod(_1707679, _1707681)), hAPP(c_Product__Type_OPair(_1707679, _1707681), _1707683)), _1707687)), c_Enum_Oproduct(_1707679, _1707681, _1707685, _1707687)))], (46166 ^ _782464) ^ [_1707757, _1707759, _1707761, _1707763, _1707765] : [class_Groups_Ocomm__monoid__add(_1707757), hBOOL(hAPP(hAPP(c_member(_1707759), _1707761), hAPP(c_List_Oset(_1707759), _1707763))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707757), hAPP(hAPP(c_List_Omap(_1707759, _1707757), _1707765), _1707763)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1707757), hAPP(_1707765, _1707761)), hAPP(c_List_Omonoid__add__class_Olistsum(_1707757), hAPP(hAPP(c_List_Omap(_1707759, _1707757), _1707765), c_List_Oremove1(_1707759, _1707761, _1707763)))))], (46176 ^ _782464) ^ [_1708006, _1708008, _1708010, _1708012] : [c_Fun_Oinj__on(_1708006, _1708008, _1708010, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1708006, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1708006), tc_fun(_1708006, tc_HOL_Obool), c_List_Oset(_1708006)), _1708012))), -(c_Fun_Oinj__on(tc_List_Olist(_1708006), tc_List_Olist(_1708008), hAPP(c_List_Omap(_1708006, _1708008), _1708010), _1708012))], (46182 ^ _782464) ^ [_1708155, _1708157, _1708159, _1708161] : [class_Groups_Ocomm__monoid__add(_1708155), 46185 ^ _782464 : [(46186 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1708157), _1708159)), -(c_Nitpick_Osetsum_H(_1708157, _1708155, _1708161, _1708159) = hAPP(c_List_Omonoid__add__class_Olistsum(_1708155), hAPP(hAPP(c_List_Omap(_1708157, _1708155), _1708161), c_Hilbert__Choice_OEps(tc_List_Olist(_1708157), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708157), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708157)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708157), tc_fun(_1708157, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1708157, tc_HOL_Obool), tc_fun(tc_fun(_1708157, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1708157)), c_fequal), c_List_Oset(_1708157))), _1708159))), c_List_Odistinct(_1708157))))))], (46192 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1708157), _1708159))), -(c_Nitpick_Osetsum_H(_1708157, _1708155, _1708161, _1708159) = c_Groups_Ozero__class_Ozero(_1708155))]]], (46198 ^ _782464) ^ [_1708543, _1708545, _1708547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708543), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708545)), _1708547))), -(hAPP(c_Random_Opick(_1708545, hAPP(hAPP(c_List_Omap(_1708545, tc_prod(tc_Code__Numeral_Ocode__numeral, _1708545)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1708545), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1708547)), hAPP(c_Code__Numeral_Oof__nat, _1708543)) = hAPP(hAPP(c_List_Onth(_1708545), _1708547), _1708543))], (46204 ^ _782464) ^ [_1708716, _1708718, _1708720] : [-(c_Enum_Osublists(_1708716, hAPP(hAPP(c_List_Olist_OCons(_1708716), _1708718), _1708720)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1708716)), tc_List_Olist(tc_List_Olist(_1708716))), c_Enum_Osublists(_1708716, _1708720)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1708716)), tc_List_Olist(tc_List_Olist(_1708716)), tc_List_Olist(tc_List_Olist(_1708716))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1708716)), tc_fun(tc_List_Olist(tc_List_Olist(_1708716)), tc_List_Olist(tc_List_Olist(_1708716))), tc_List_Olist(tc_List_Olist(_1708716))), c_List_Oappend(tc_List_Olist(_1708716))), hAPP(c_List_Omap(tc_List_Olist(_1708716), tc_List_Olist(_1708716)), hAPP(c_List_Olist_OCons(_1708716), _1708718)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1708716))))))], (46206 ^ _782464) ^ [_1708865, _1708867] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1708865)), hAPP(c_Code__Numeral_Oof__nat, _1708867))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708865), _1708867)))], (46212 ^ _782464) ^ [_1708970, _1708972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708970), _1708972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1708970)), hAPP(c_Code__Numeral_Oof__nat, _1708972))))], (46218 ^ _782464) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46220 ^ _782464) ^ [_1709114, _1709116] : [hAPP(c_Code__Numeral_Oof__nat, _1709114) = hAPP(c_Code__Numeral_Oof__nat, _1709116), -(_1709114 = _1709116)], (46226 ^ _782464) ^ [_1709199, _1709201] : [_1709199 = _1709201, -(hAPP(c_Code__Numeral_Oof__nat, _1709199) = hAPP(c_Code__Numeral_Oof__nat, _1709201))], (46232 ^ _782464) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (46234 ^ _782464) ^ [_1709308, _1709310] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1709308)), hAPP(c_Code__Numeral_Oof__nat, _1709310)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1709308), _1709310)))], (46236 ^ _782464) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (46238 ^ _782464) ^ [_1709372, _1709374] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709372), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709374), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 46245 ^ _782464 : [(46246 ^ _782464) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1709372) = hAPP(c_Code__Numeral_Oof__nat, _1709374), -(_1709372 = _1709374)], (46252 ^ _782464) ^ [] : [_1709372 = _1709374, -(hAPP(c_Code__Numeral_Oof__nat, _1709372) = hAPP(c_Code__Numeral_Oof__nat, _1709374))]]], (46258 ^ _782464) ^ [_1709669, _1709671, _1709673, _1709675] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709669)), _1709671) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709673)), _1709675), -(hAPP(hAPP(c_List_Omap(tc_prod(_1709669, _1709673), _1709669), c_Product__Type_Ofst(_1709669, _1709673)), hAPP(hAPP(c_List_Ozip(_1709669, _1709673), _1709671), _1709675)) = _1709671)], (46264 ^ _782464) ^ [_1709826, _1709828, _1709830, _1709832] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709826)), _1709828) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709830)), _1709832), -(hAPP(hAPP(c_List_Omap(tc_prod(_1709826, _1709830), _1709830), c_Product__Type_Osnd(_1709826, _1709830)), hAPP(hAPP(c_List_Ozip(_1709826, _1709830), _1709828), _1709832)) = _1709832)], (46270 ^ _782464) ^ [] : [-(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))], (46272 ^ _782464) ^ [_1710001, _1710003, _1710005] : [-(hAPP(hAPP(c_List_Ozip(_1710001, _1710003), hAPP(hAPP(c_List_Omap(tc_prod(_1710001, _1710003), _1710001), c_Product__Type_Ofst(_1710001, _1710003)), _1710005)), hAPP(hAPP(c_List_Omap(tc_prod(_1710001, _1710003), _1710003), c_Product__Type_Osnd(_1710001, _1710003)), _1710005)) = _1710005)], (46274 ^ _782464) ^ [_1710067, _1710069] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710067)), hAPP(c_Code__Numeral_Oof__nat, _1710069)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710067), _1710069)))], (46276 ^ _782464) ^ [_1710128, _1710130] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710128)), hAPP(c_Code__Numeral_Oof__nat, _1710130))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710128), _1710130)))], (46282 ^ _782464) ^ [_1710233, _1710235] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710233), _1710235)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710233)), hAPP(c_Code__Numeral_Oof__nat, _1710235))))], (46288 ^ _782464) ^ [_1710344, _1710346] : [hBOOL(hAPP(c_List_Odistinct(_1710344), _1710346)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1710344, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710344), tc_fun(_1710344, tc_HOL_Obool)), c_List_Oset(_1710344)), c_Enum_Osublists(_1710344, _1710346)))))], (46294 ^ _782464) ^ [_1710481, _1710483, _1710485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1710481), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710483), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1710483)), _1710485)))), -(hBOOL(hAPP(hAPP(c_member(_1710483), hAPP(c_Random_Opick(_1710483, _1710485), _1710481)), hAPP(c_List_Oset(_1710483), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710483), _1710483), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1710483)), _1710485)))))], (46300 ^ _782464) ^ [_1710672, _1710674, _1710676, _1710678, _1710680] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710672)), _1710674) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710676)), _1710678), 46303 ^ _782464 : [(46304 ^ _782464) ^ [] : [hAPP(hAPP(c_List_Ozip(_1710672, _1710676), _1710674), _1710678) = _1710680, 46307 ^ _782464 : [(46308 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710672, _1710676), _1710672), c_Product__Type_Ofst(_1710672, _1710676)), _1710680) = _1710674)], (46310 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710672, _1710676), _1710676), c_Product__Type_Osnd(_1710672, _1710676)), _1710680) = _1710678)]]], (46312 ^ _782464) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1710672, _1710676), _1710674), _1710678) = _1710680), hAPP(hAPP(c_List_Omap(tc_prod(_1710672, _1710676), _1710672), c_Product__Type_Ofst(_1710672, _1710676)), _1710680) = _1710674, hAPP(hAPP(c_List_Omap(tc_prod(_1710672, _1710676), _1710676), c_Product__Type_Osnd(_1710672, _1710676)), _1710680) = _1710678]]], (46322 ^ _782464) ^ [_1711120, _1711122, _1711124] : [-(c_List_Olist_Olist__size(_1711120, _1711122, _1711124) = 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(_1711120, tc_Nat_Onat), _1711122), _1711124))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711120)), _1711124)))], (46324 ^ _782464) ^ [_1711182] : [-(_1711182 = 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)), _1711182)))], (46330 ^ _782464) ^ [_1711214] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1711214)), _1711214 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46336 ^ _782464) ^ [_1711296, _1711298, _1711300, _1711302] : [class_Groups_Ocomm__monoid__add(_1711296), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711296), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1711296), _1711298), c_List_Oupto(_1711300, _1711302))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1711296), _1711298), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1711300, _1711302))))], (46342 ^ _782464) ^ [_1711439, _1711441, _1711443, _1711445] : [class_Groups_Ocomm__monoid__add(_1711439), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1711439), _1711441), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1711443, _1711445))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1711439), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1711439), _1711441), c_List_Oupto(_1711443, _1711445))))], (46348 ^ _782464) ^ [_1711582, _1711584, _1711586] : [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, _1711582), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1711582)), _1711584)))), -(hBOOL(hAPP(hAPP(c_member(_1711582), hAPP(c_Product__Type_Ofst(_1711582, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1711582, _1711584), _1711586))), hAPP(c_List_Oset(_1711582), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1711582), _1711582), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1711582)), _1711584)))))], (46354 ^ _782464) ^ [_1711779, _1711781] : [-(c_Random_Oselect__weight(_1711779, _1711781) = 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(_1711779, 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, _1711779), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1711779)), _1711781)))), hAPP(hAPP(c_COMBB(_1711779, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1711779, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1711779, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1711779, _1711781))))], (46356 ^ _782464) ^ [_1711863, _1711865] : [-(c_Random_Oselect(_1711863, _1711865) = 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(_1711863, 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(_1711863)), _1711865)))), hAPP(hAPP(c_COMBB(_1711863, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1711863, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1711863, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1711863, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1711863), _1711865)), c_Code__Numeral_Onat__of))))], (46358 ^ _782464) ^ [_1711951, _1711953] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1711951)), hAPP(c_Code__Numeral_Oof__nat, _1711953)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1711951), _1711953)))], (46360 ^ _782464) ^ [_1711997] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1711997)) = _1711997)], (46362 ^ _782464) ^ [_1712026] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1712026)) = _1712026)], (46364 ^ _782464) ^ [_1712055] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1712055)) = _1712055)], (46366 ^ _782464) ^ [_1712084, _1712086] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1712084), _1712086) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712084)), hAPP(c_Code__Numeral_Onat__of, _1712086))))], (46368 ^ _782464) ^ [_1712145, _1712147] : [hAPP(c_Code__Numeral_Onat__of, _1712145) = hAPP(c_Code__Numeral_Onat__of, _1712147), -(_1712145 = _1712147)], (46374 ^ _782464) ^ [_1712230, _1712232] : [_1712230 = _1712232, -(hAPP(c_Code__Numeral_Onat__of, _1712230) = hAPP(c_Code__Numeral_Onat__of, _1712232))], (46380 ^ _782464) ^ [_1712336, _1712338] : [hAPP(c_Code__Numeral_Onat__of, _1712336) = hAPP(c_Code__Numeral_Onat__of, _1712338), -(_1712336 = _1712338)], (46386 ^ _782464) ^ [_1712421, _1712423] : [_1712421 = _1712423, -(hAPP(c_Code__Numeral_Onat__of, _1712421) = hAPP(c_Code__Numeral_Onat__of, _1712423))], (46392 ^ _782464) ^ [] : [-(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))))], (46394 ^ _782464) ^ [_1712545, _1712547] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1712545), _1712547)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712545)), hAPP(c_Code__Numeral_Onat__of, _1712547))))], (46400 ^ _782464) ^ [_1712650, _1712652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712650)), hAPP(c_Code__Numeral_Onat__of, _1712652))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1712650), _1712652)))], (46406 ^ _782464) ^ [_1712761] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712761)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (46408 ^ _782464) ^ [_1712792] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1712792)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712792))], (46410 ^ _782464) ^ [] : [-(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))], (46412 ^ _782464) ^ [_1712857, _1712859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1712857), _1712859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712857)), hAPP(c_Code__Numeral_Onat__of, _1712859))))], (46418 ^ _782464) ^ [_1712962, _1712964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712962)), hAPP(c_Code__Numeral_Onat__of, _1712964))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1712962), _1712964)))], (46424 ^ _782464) ^ [_1713073] : [-(hAPP(c_Code__Numeral_Onat__of, _1713073) = c_Code__Numeral_Onat__of__aux(_1713073, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46426 ^ _782464) ^ [_1713102, _1713104] : [-(c_Code__Numeral_Onat__of__aux(_1713102, _1713104) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713102)), _1713104))], (46428 ^ _782464) ^ [_1713139] : [-(c_Code__Numeral_OSuc__code__numeral(_1713139) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1713139))))], (46430 ^ _782464) ^ [_1713173, _1713175] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1713173), _1713175) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713173)), hAPP(c_Code__Numeral_Onat__of, _1713175))))], (46432 ^ _782464) ^ [_1713219] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1713219), 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, _1713219)) = _1713219)], (46438 ^ _782464) ^ [_1713316, _1713318] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1713316), _1713318) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713316)), hAPP(c_Code__Numeral_Onat__of, _1713318))))], (46440 ^ _782464) ^ [_1713362, _1713364] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1713362), _1713364) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713362)), hAPP(c_Code__Numeral_Onat__of, _1713364))))], (46442 ^ _782464) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (46444 ^ _782464) ^ [_1713426, _1713428] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1713426), _1713428) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1713426), _1713428))], (46446 ^ _782464) ^ [_1713463, _1713465] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1713463, _1713465) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1713463), hAPP(c_Code__Numeral_Onat__of, _1713465))))], (46448 ^ _782464) ^ [_1713501] : [-(_1713501 = 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, _1713501)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1713501))))], (46454 ^ _782464) ^ [_1713552, _1713554, _1713556, _1713558, _1713560] : [class_Groups_Omonoid__add(_1713552), class_Groups_Oordered__ab__semigroup__add(_1713552), 46464 ^ _782464 : [(46465 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713554), 46463 ^ [_1713552, _1713554, _1713556, _1713558, _1713560]), hAPP(c_List_Oset(_1713554), _1713556))))], (46467 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713552), hAPP(_1713558, 46463 ^ [_1713552, _1713554, _1713556, _1713558, _1713560])), hAPP(_1713560, 46463 ^ [_1713552, _1713554, _1713556, _1713558, _1713560])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713552), hAPP(c_List_Omonoid__add__class_Olistsum(_1713552), hAPP(hAPP(c_List_Omap(_1713554, _1713552), _1713558), _1713556))), hAPP(c_List_Omonoid__add__class_Olistsum(_1713552), hAPP(hAPP(c_List_Omap(_1713554, _1713552), _1713560), _1713556)))))], (46471 ^ _782464) ^ [_1713976, _1713978] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1713976), _1713978) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1713976, 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)))), _1713978))))], (46473 ^ _782464) ^ [_1714014, _1714016, _1714018, _1714020, _1714022] : [c_List_Opartition(_1714014, _1714016, _1714018) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1714014), tc_List_Olist(_1714014)), _1714020), _1714022), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1714014, tc_HOL_Obool)), hAPP(c_List_Oset(_1714014), _1714020)), hAPP(c_List_Oset(_1714014), _1714022)) = hAPP(c_List_Oset(_1714014), _1714018))], (46479 ^ _782464) ^ [_1714183, _1714185, _1714187, _1714189] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1714183)), _1714185), c_List_Olists(_1714183, _1714187))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1714183)), _1714185), c_List_Olists(_1714183, _1714189))), -(hBOOL(hAPP(c_List_Olistsp(_1714183, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714183, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1714183, tc_fun(_1714183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714183)), _1714187)), hAPP(hAPP(c_COMBC(_1714183, tc_fun(_1714183, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714183)), _1714189))), _1714185)))], (46489 ^ _782464) ^ [_1714460, _1714462] : [-(hBOOL(hAPP(c_List_Olistsp(_1714460, _1714462), c_List_Olist_ONil(_1714460))))], (46491 ^ _782464) ^ [_1714492, _1714494] : [-(hBOOL(hAPP(c_List_Olistsp(_1714492, _1714494), c_List_Olist_ONil(_1714492))))], (46503 ^ _782464) ^ [_1714740, _1714742, _1714744] : [46505 ^ _782464 : [(46506 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1714740), 46504 ^ [_1714740, _1714742, _1714744]), hAPP(c_List_Oset(_1714740), _1714744))))], (46508 ^ _782464) ^ [] : [hBOOL(hAPP(_1714742, 46504 ^ [_1714740, _1714742, _1714744]))]], -(hBOOL(hAPP(c_List_Olistsp(_1714740, _1714742), _1714744)))], (46493 ^ _782464) ^ [_1714542, _1714544, _1714546] : [hBOOL(hAPP(c_List_Olistsp(_1714542, _1714544), _1714546)), 46496 ^ _782464 : [(46497 ^ _782464) ^ [_1714631] : [hBOOL(hAPP(hAPP(c_member(_1714542), _1714631), hAPP(c_List_Oset(_1714542), _1714546))), -(hBOOL(hAPP(_1714544, _1714631)))]]], (46512 ^ _782464) ^ [_1714930, _1714932, _1714934, _1714936] : [hBOOL(hAPP(c_List_Olistsp(_1714930, _1714932), _1714934)), hBOOL(hAPP(c_List_Olistsp(_1714930, _1714936), _1714934)), -(hBOOL(hAPP(c_List_Olistsp(_1714930, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714930, tc_HOL_Obool)), _1714932), _1714936)), _1714934)))], (46522 ^ _782464) ^ [_1715119, _1715121, _1715123] : [-(c_List_Olistsp(_1715119, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715119, tc_HOL_Obool)), _1715121), _1715123)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1715119), tc_HOL_Obool)), c_List_Olistsp(_1715119, _1715121)), c_List_Olistsp(_1715119, _1715123)))], (46524 ^ _782464) ^ [_1715200, _1715202, _1715204, _1715206] : [hBOOL(hAPP(c_List_Olistsp(_1715200, hAPP(hAPP(c_COMBS(_1715200, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715200), c_fconj), _1715202)), _1715204)), _1715206)), 46527 ^ _782464 : [(46528 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715200, _1715202), _1715206)))], (46530 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715200, _1715204), _1715206)))]]], (46532 ^ _782464) ^ [_1715373, _1715375, _1715377, _1715379] : [-(hBOOL(hAPP(c_List_Olistsp(_1715373, hAPP(hAPP(c_COMBS(_1715373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715373), c_fconj), _1715375)), _1715377)), _1715379))), hBOOL(hAPP(c_List_Olistsp(_1715373, _1715375), _1715379)), hBOOL(hAPP(c_List_Olistsp(_1715373, _1715377), _1715379))], (46542 ^ _782464) ^ [_1715603, _1715605, _1715607, _1715609] : [hBOOL(hAPP(c_List_Olistsp(_1715603, _1715605), hAPP(hAPP(c_List_Olist_OCons(_1715603), _1715607), _1715609))), 46545 ^ _782464 : [(46546 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1715605, _1715607)))], (46548 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715603, _1715605), _1715609)))]]], (46550 ^ _782464) ^ [_1715746, _1715748, _1715750, _1715752] : [-(hBOOL(hAPP(c_List_Olistsp(_1715746, _1715748), hAPP(hAPP(c_List_Olist_OCons(_1715746), _1715750), _1715752)))), hBOOL(hAPP(_1715748, _1715750)), hBOOL(hAPP(c_List_Olistsp(_1715746, _1715748), _1715752))], (46560 ^ _782464) ^ [_1715946, _1715948, _1715950, _1715952] : [hBOOL(hAPP(c_List_Olistsp(_1715946, _1715948), hAPP(hAPP(c_List_Oappend(_1715946), _1715950), _1715952))), 46563 ^ _782464 : [(46564 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715946, _1715948), _1715950)))], (46566 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715946, _1715948), _1715952)))]]], (46568 ^ _782464) ^ [_1716095, _1716097, _1716099, _1716101] : [-(hBOOL(hAPP(c_List_Olistsp(_1716095, _1716097), hAPP(hAPP(c_List_Oappend(_1716095), _1716099), _1716101)))), hBOOL(hAPP(c_List_Olistsp(_1716095, _1716097), _1716099)), hBOOL(hAPP(c_List_Olistsp(_1716095, _1716097), _1716101))], (46578 ^ _782464) ^ [_1716280, _1716282, _1716284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1716280, tc_HOL_Obool)), _1716282), _1716284)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1716280), tc_HOL_Obool)), c_List_Olistsp(_1716280, _1716282)), c_List_Olistsp(_1716280, _1716284))))], (46584 ^ _782464) ^ [_1716415, _1716417, _1716419, _1716421, _1716423] : [c_List_Opartition(_1716415, _1716417, _1716419) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716415), tc_List_Olist(_1716415)), _1716421), _1716423), 46587 ^ _782464 : [(46588 ^ _782464) ^ [_1716568] : [hBOOL(hAPP(hAPP(c_member(_1716415), _1716568), hAPP(c_List_Oset(_1716415), _1716421))), -(hBOOL(hAPP(_1716417, _1716568)))], (46594 ^ _782464) ^ [_1716677] : [hBOOL(hAPP(hAPP(c_member(_1716415), _1716677), hAPP(c_List_Oset(_1716415), _1716423))), hBOOL(hAPP(_1716417, _1716677))]]], (46600 ^ _782464) ^ [_1716797, _1716799] : [-(c_List_Opartition(_1716797, _1716799, c_List_Olist_ONil(_1716797)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716797), tc_List_Olist(_1716797)), c_List_Olist_ONil(_1716797)), c_List_Olist_ONil(_1716797)))], (46602 ^ _782464) ^ [_1716863, _1716865, _1716867] : [hBOOL(hAPP(c_List_Olistsp(_1716863, hAPP(hAPP(c_COMBC(_1716863, tc_fun(_1716863, tc_HOL_Obool), tc_HOL_Obool), c_member(_1716863)), _1716865)), _1716867)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1716863)), _1716867), c_List_Olists(_1716863, _1716865))))], (46608 ^ _782464) ^ [_1717002, _1717004, _1717006] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1717002)), _1717006), c_List_Olists(_1717002, _1717004))), -(hBOOL(hAPP(c_List_Olistsp(_1717002, hAPP(hAPP(c_COMBC(_1717002, tc_fun(_1717002, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717002)), _1717004)), _1717006)))], (46614 ^ _782464) ^ [_1717147, _1717149, _1717151, _1717153] : [-(c_List_Opartition(_1717147, _1717149, hAPP(hAPP(c_List_Olist_OCons(_1717147), _1717151), _1717153)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1717147), tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1717147), tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717147), tc_fun(tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), tc_fun(tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), tc_List_Olist(_1717147)), c_COMBS(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), tc_fun(tc_List_Olist(_1717147), tc_fun(tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), tc_List_Olist(_1717147)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_fun(tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), tc_List_Olist(_1717147)), hAPP(c_If(tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), hAPP(_1717149, _1717151)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1717147), tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), tc_List_Olist(_1717147)), c_Product__Type_OPair(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), hAPP(c_List_Olist_OCons(_1717147), _1717151))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717147), tc_fun(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147))), tc_fun(tc_fun(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_fun(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), tc_List_Olist(_1717147)), c_COMBB(tc_List_Olist(_1717147), tc_prod(tc_List_Olist(_1717147), tc_List_Olist(_1717147)), tc_List_Olist(_1717147))), c_Product__Type_OPair(tc_List_Olist(_1717147), tc_List_Olist(_1717147)))), hAPP(c_List_Olist_OCons(_1717147), _1717151)))), c_List_Opartition(_1717147, _1717149, _1717153)))], (46616 ^ _782464) ^ [_1717566, _1717568, _1717570] : [-(c_List_Olistsp(_1717566, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717566, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1717566, tc_fun(_1717566, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717566)), _1717568)), hAPP(hAPP(c_COMBC(_1717566, tc_fun(_1717566, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717566)), _1717570))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1717566), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717566), tc_fun(tc_List_Olist(_1717566), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1717566))), c_List_Olists(_1717566, _1717568))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717566), tc_fun(tc_List_Olist(_1717566), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1717566))), c_List_Olists(_1717566, _1717570))))], (46618 ^ _782464) ^ [_1717722, _1717724, _1717726, _1717728, _1717730] : [c_List_Olist__all2(_1717722, _1717724, _1717726, _1717728, _1717730), 46621 ^ _782464 : [(46622 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717722)), _1717728) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717724)), _1717730))], (46624 ^ _782464) ^ [_1717888] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717722, _1717724)), _1717888), hAPP(c_List_Oset(tc_prod(_1717722, _1717724)), hAPP(hAPP(c_List_Ozip(_1717722, _1717724), _1717728), _1717730)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1717722, _1717724, tc_HOL_Obool), _1717726), _1717888)))]]], (46630 ^ _782464) ^ [_1718047, _1718049, _1718051, _1718053, _1718055] : [-(c_List_Olist__all2(_1718047, _1718049, _1718051, _1718053, _1718055)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718047)), _1718053) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718049)), _1718055), 46636 ^ _782464 : [(46637 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718047, _1718049)), 46635 ^ [_1718047, _1718049, _1718051, _1718053, _1718055]), hAPP(c_List_Oset(tc_prod(_1718047, _1718049)), hAPP(hAPP(c_List_Ozip(_1718047, _1718049), _1718053), _1718055)))))], (46639 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1718047, _1718049, tc_HOL_Obool), _1718051), 46635 ^ [_1718047, _1718049, _1718051, _1718053, _1718055]))]]], (46643 ^ _782464) ^ [_1718388, _1718390, _1718392, _1718394] : [46645 ^ _782464 : [(46646 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46644 ^ [_1718388, _1718390, _1718392, _1718394]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718388)), _1718390))))], (46648 ^ _782464) ^ [] : [hBOOL(hAPP(_1718392, hAPP(hAPP(c_List_Onth(_1718388), _1718390), 46644 ^ [_1718388, _1718390, _1718392, _1718394])))]], hBOOL(hAPP(hAPP(c_member(_1718388), _1718394), hAPP(c_List_Oset(_1718388), _1718390))), -(hBOOL(hAPP(_1718392, _1718394)))], (46656 ^ _782464) ^ [_1718714, _1718716, _1718718, _1718720, _1718722, _1718724, _1718726] : [c_List_Olist__all2(_1718714, _1718716, _1718718, hAPP(hAPP(c_List_Omap(_1718720, _1718714), _1718722), _1718724), _1718726), -(c_List_Olist__all2(_1718720, _1718716, hAPP(hAPP(c_COMBB(_1718714, tc_fun(_1718716, tc_HOL_Obool), _1718720), _1718718), _1718722), _1718724, _1718726))], (46662 ^ _782464) ^ [_1718853, _1718855, _1718857, _1718859, _1718861, _1718863, _1718865] : [c_List_Olist__all2(_1718859, _1718855, hAPP(hAPP(c_COMBB(_1718853, tc_fun(_1718855, tc_HOL_Obool), _1718859), _1718857), _1718861), _1718863, _1718865), -(c_List_Olist__all2(_1718853, _1718855, _1718857, hAPP(hAPP(c_List_Omap(_1718859, _1718853), _1718861), _1718863), _1718865))], (46668 ^ _782464) ^ [_1719028, _1719030, _1719032, _1719034, _1719036, _1719038, _1719040] : [c_List_Olist__all2(_1719028, _1719030, _1719032, _1719034, hAPP(hAPP(c_List_Omap(_1719036, _1719030), _1719038), _1719040)), -(c_List_Olist__all2(_1719028, _1719036, hAPP(hAPP(c_COMBC(_1719028, tc_fun(_1719036, _1719030), tc_fun(_1719036, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719030, tc_HOL_Obool), tc_fun(tc_fun(_1719036, _1719030), tc_fun(_1719036, tc_HOL_Obool)), _1719028), c_COMBB(_1719030, tc_HOL_Obool, _1719036)), _1719032)), _1719038), _1719034, _1719040))], (46674 ^ _782464) ^ [_1719225, _1719227, _1719229, _1719231, _1719233, _1719235, _1719237] : [c_List_Olist__all2(_1719225, _1719233, hAPP(hAPP(c_COMBC(_1719225, tc_fun(_1719233, _1719227), tc_fun(_1719233, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719227, tc_HOL_Obool), tc_fun(tc_fun(_1719233, _1719227), tc_fun(_1719233, tc_HOL_Obool)), _1719225), c_COMBB(_1719227, tc_HOL_Obool, _1719233)), _1719229)), _1719235), _1719231, _1719237), -(c_List_Olist__all2(_1719225, _1719227, _1719229, _1719231, hAPP(hAPP(c_List_Omap(_1719233, _1719227), _1719235), _1719237)))], (46680 ^ _782464) ^ [_1719428, _1719430, _1719432, _1719434, _1719436, _1719438, _1719440] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719428)), _1719430) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719432)), _1719434), 46683 ^ _782464 : [(46684 ^ _782464) ^ [] : [c_List_Olist__all2(_1719428, _1719432, _1719436, hAPP(hAPP(c_List_Oappend(_1719428), _1719430), _1719438), hAPP(hAPP(c_List_Oappend(_1719432), _1719434), _1719440)), 46687 ^ _782464 : [(46688 ^ _782464) ^ [] : [-(c_List_Olist__all2(_1719428, _1719432, _1719436, _1719430, _1719434))], (46690 ^ _782464) ^ [] : [-(c_List_Olist__all2(_1719428, _1719432, _1719436, _1719438, _1719440))]]], (46692 ^ _782464) ^ [] : [-(c_List_Olist__all2(_1719428, _1719432, _1719436, hAPP(hAPP(c_List_Oappend(_1719428), _1719430), _1719438), hAPP(hAPP(c_List_Oappend(_1719432), _1719434), _1719440))), c_List_Olist__all2(_1719428, _1719432, _1719436, _1719430, _1719434), c_List_Olist__all2(_1719428, _1719432, _1719436, _1719438, _1719440)]]], (46702 ^ _782464) ^ [_1719850, _1719852, _1719854, _1719856, _1719858, _1719860, _1719862] : [c_List_Olist__all2(_1719850, _1719852, _1719854, _1719856, _1719858), c_List_Olist__all2(_1719850, _1719852, _1719854, _1719860, _1719862), -(c_List_Olist__all2(_1719850, _1719852, _1719854, hAPP(hAPP(c_List_Oappend(_1719850), _1719856), _1719860), hAPP(hAPP(c_List_Oappend(_1719852), _1719858), _1719862)))], (46712 ^ _782464) ^ [_1720049, _1720051, _1720053, _1720055, _1720057, _1720059] : [c_List_Olist__all2(_1720049, _1720051, _1720053, _1720055, _1720057), -(c_List_Olist__all2(_1720049, _1720051, _1720053, hAPP(hAPP(c_List_Odrop(_1720049), _1720059), _1720055), hAPP(hAPP(c_List_Odrop(_1720051), _1720059), _1720057)))], (46718 ^ _782464) ^ [_1720208, _1720210, _1720212, _1720214, _1720216, _1720218, _1720220] : [c_List_Olist__all2(_1720208, _1720210, _1720212, hAPP(hAPP(c_List_Olist_OCons(_1720208), _1720214), _1720216), hAPP(hAPP(c_List_Olist_OCons(_1720210), _1720218), _1720220)), 46721 ^ _782464 : [(46722 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1720212, _1720214), _1720218)))], (46724 ^ _782464) ^ [] : [-(c_List_Olist__all2(_1720208, _1720210, _1720212, _1720216, _1720220))]]], (46726 ^ _782464) ^ [_1720371, _1720373, _1720375, _1720377, _1720379, _1720381, _1720383] : [-(c_List_Olist__all2(_1720371, _1720373, _1720375, hAPP(hAPP(c_List_Olist_OCons(_1720371), _1720377), _1720379), hAPP(hAPP(c_List_Olist_OCons(_1720373), _1720381), _1720383))), hBOOL(hAPP(hAPP(_1720375, _1720377), _1720381)), c_List_Olist__all2(_1720371, _1720373, _1720375, _1720379, _1720383)], (46736 ^ _782464) ^ [_1720594, _1720596, _1720598] : [_1720594 = _1720596, -(c_List_Olist__all2(_1720598, _1720598, c_fequal, _1720594, _1720596))], (46742 ^ _782464) ^ [_1720675, _1720677, _1720679] : [c_List_Olist__all2(_1720679, _1720679, c_fequal, _1720675, _1720677), -(_1720675 = _1720677)], (46748 ^ _782464) ^ [_1720762, _1720764, _1720766, _1720768, _1720770, _1720772] : [c_List_Olist__all2(_1720762, _1720764, _1720766, _1720768, _1720770), -(c_List_Olist__all2(_1720762, _1720764, _1720766, hAPP(hAPP(c_List_Otake(_1720762), _1720772), _1720768), hAPP(hAPP(c_List_Otake(_1720764), _1720772), _1720770)))], (46754 ^ _782464) ^ [_1720891, _1720893, _1720895, _1720897, _1720899] : [c_List_Olist__all2(_1720891, _1720893, _1720895, _1720897, _1720899), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720891)), _1720897) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720893)), _1720899))], (46760 ^ _782464) ^ [_1721029, _1721031, _1721033, _1721035] : [c_List_Olist__all2(_1721029, _1721031, _1721033, c_List_Olist_ONil(_1721029), _1721035), -(_1721035 = c_List_Olist_ONil(_1721031))], (46766 ^ _782464) ^ [_1721120, _1721122, _1721124, _1721126] : [_1721126 = c_List_Olist_ONil(_1721122), -(c_List_Olist__all2(_1721120, _1721122, _1721124, c_List_Olist_ONil(_1721120), _1721126))], (46772 ^ _782464) ^ [_1721238, _1721240, _1721242, _1721244] : [c_List_Olist__all2(_1721238, _1721240, _1721242, _1721244, c_List_Olist_ONil(_1721240)), -(_1721244 = c_List_Olist_ONil(_1721238))], (46778 ^ _782464) ^ [_1721329, _1721331, _1721333, _1721335] : [_1721335 = c_List_Olist_ONil(_1721329), -(c_List_Olist__all2(_1721329, _1721331, _1721333, _1721335, c_List_Olist_ONil(_1721331)))], (46784 ^ _782464) ^ [_1721426, _1721428, _1721430, _1721432, _1721434, _1721436] : [c_List_Olist__all2(_1721426, _1721428, _1721430, _1721432, _1721434), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721436), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721428)), _1721434))), -(hBOOL(hAPP(hAPP(_1721430, hAPP(hAPP(c_List_Onth(_1721426), _1721432), _1721436)), hAPP(hAPP(c_List_Onth(_1721428), _1721434), _1721436))))], (46794 ^ _782464) ^ [_1721643, _1721645, _1721647, _1721649, _1721651, _1721653] : [c_List_Olist__all2(_1721643, _1721645, _1721647, _1721649, _1721651), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721653), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721643)), _1721649))), -(hBOOL(hAPP(hAPP(_1721647, hAPP(hAPP(c_List_Onth(_1721643), _1721649), _1721653)), hAPP(hAPP(c_List_Onth(_1721645), _1721651), _1721653))))], (46804 ^ _782464) ^ [_1721884, _1721886, _1721888, _1721890, _1721892] : [c_List_Olist__all2(_1721884, _1721886, _1721888, _1721890, _1721892), 46807 ^ _782464 : [(46808 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721884)), _1721890) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721886)), _1721892))], (46810 ^ _782464) ^ [_1722047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722047), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721884)), _1721890))), -(hBOOL(hAPP(hAPP(_1721888, hAPP(hAPP(c_List_Onth(_1721884), _1721890), _1722047)), hAPP(hAPP(c_List_Onth(_1721886), _1721892), _1722047))))]]], (46816 ^ _782464) ^ [_1722200, _1722202, _1722204, _1722206, _1722208] : [-(c_List_Olist__all2(_1722200, _1722202, _1722204, _1722206, _1722208)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722200)), _1722206) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722202)), _1722208), 46822 ^ _782464 : [(46823 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46821 ^ [_1722200, _1722202, _1722204, _1722206, _1722208]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722200)), _1722206))))], (46825 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1722204, hAPP(hAPP(c_List_Onth(_1722200), _1722206), 46821 ^ [_1722200, _1722202, _1722204, _1722206, _1722208])), hAPP(hAPP(c_List_Onth(_1722202), _1722208), 46821 ^ [_1722200, _1722202, _1722204, _1722206, _1722208])))]]], (46829 ^ _782464) ^ [_1722560, _1722562, _1722564, _1722566, _1722568, _1722570, _1722572, _1722574] : [c_List_Olist__all2(_1722560, _1722562, _1722564, _1722566, _1722568), hBOOL(hAPP(hAPP(_1722564, _1722570), _1722572)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722574), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722562)), _1722568))), -(c_List_Olist__all2(_1722560, _1722562, _1722564, hAPP(hAPP(c_List_Olist__update(_1722560, _1722566), _1722574), _1722570), hAPP(hAPP(c_List_Olist__update(_1722562, _1722568), _1722574), _1722572)))], (46843 ^ _782464) ^ [_1722859, _1722861, _1722863, _1722865, _1722867, _1722869, _1722871, _1722873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722859), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722861)), _1722863))), c_List_Olist__all2(_1722861, _1722865, _1722867, _1722863, _1722869), hBOOL(hAPP(hAPP(_1722867, _1722871), _1722873)), -(c_List_Olist__all2(_1722861, _1722865, _1722867, hAPP(hAPP(c_List_Olist__update(_1722861, _1722863), _1722859), _1722871), hAPP(hAPP(c_List_Olist__update(_1722865, _1722869), _1722859), _1722873)))], (46857 ^ _782464) ^ [_1723158, _1723160, _1723162, _1723164, _1723166] : [46859 ^ _782464 : [(46860 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1723158, _1723160)), 46858 ^ [_1723158, _1723160, _1723162, _1723164, _1723166]), hAPP(c_List_Oset(tc_prod(_1723158, _1723160)), hAPP(hAPP(c_List_Ozip(_1723158, _1723160), _1723162), _1723164)))))], (46862 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1723158, _1723160, tc_HOL_Obool), _1723166), 46858 ^ [_1723158, _1723160, _1723162, _1723164, _1723166]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723158)), _1723162) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723160)), _1723164), -(c_List_Olist__all2(_1723158, _1723160, _1723166, _1723162, _1723164))], (46870 ^ _782464) ^ [_1723497, _1723499, _1723501, _1723503, _1723505] : [c_Finite__Set_Ofun__left__comm(_1723497, _1723499, _1723501), -(hAPP(hAPP(c_Finite__Set_Ofold(_1723497, _1723499, _1723501), _1723503), hAPP(c_List_Oset(_1723497), _1723505)) = hAPP(c_List_Ofoldl(_1723499, _1723497, hAPP(c_COMBC(_1723497, _1723499, _1723499), _1723501), _1723503), c_List_Oremdups(_1723497, _1723505)))], (46876 ^ _782464) ^ [_1723648, _1723650] : [-(hBOOL(hAPP(c_List_Odistinct(_1723648), c_List_Oremdups(_1723648, _1723650))))], (46878 ^ _782464) ^ [_1723680, _1723682] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723680)), c_List_Oremdups(_1723680, _1723682))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723680)), _1723682))))], (46880 ^ _782464) ^ [_1723742, _1723744] : [c_List_Oremdups(_1723742, _1723744) = c_List_Olist_ONil(_1723742), -(_1723744 = c_List_Olist_ONil(_1723742))], (46886 ^ _782464) ^ [_1723829, _1723831] : [_1723831 = c_List_Olist_ONil(_1723829), -(c_List_Oremdups(_1723829, _1723831) = c_List_Olist_ONil(_1723829))], (46892 ^ _782464) ^ [_1723937, _1723939] : [c_List_Olist_ONil(_1723937) = c_List_Oremdups(_1723937, _1723939), -(_1723939 = c_List_Olist_ONil(_1723937))], (46898 ^ _782464) ^ [_1724024, _1724026] : [_1724026 = c_List_Olist_ONil(_1724024), -(c_List_Olist_ONil(_1724024) = c_List_Oremdups(_1724024, _1724026))], (46904 ^ _782464) ^ [_1724117] : [-(c_List_Oremdups(_1724117, c_List_Olist_ONil(_1724117)) = c_List_Olist_ONil(_1724117))], (46906 ^ _782464) ^ [_1724162, _1724164] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724162)), c_List_Oremdups(_1724162, _1724164)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724162)), _1724164), -(c_List_Oremdups(_1724162, _1724164) = _1724164)], (46912 ^ _782464) ^ [_1724275, _1724277] : [c_List_Oremdups(_1724275, _1724277) = _1724277, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724275)), c_List_Oremdups(_1724275, _1724277)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724275)), _1724277))], (46918 ^ _782464) ^ [_1724394, _1724396] : [-(hAPP(c_List_Oset(_1724394), c_List_Oremdups(_1724394, _1724396)) = hAPP(c_List_Oset(_1724394), _1724396))], (46920 ^ _782464) ^ [_1724432, _1724434] : [-(c_List_Oremdups(_1724432, c_List_Oremdups(_1724432, _1724434)) = c_List_Oremdups(_1724432, _1724434))], (46922 ^ _782464) ^ [_1724466, _1724468] : [hBOOL(hAPP(c_List_Odistinct(_1724466), _1724468)), -(c_List_Oremdups(_1724466, _1724468) = _1724468)], (46928 ^ _782464) ^ [_1724572, _1724574] : [c_List_Oremdups(_1724572, _1724574) = _1724574, -(hBOOL(hAPP(c_List_Odistinct(_1724572), _1724574)))], (46934 ^ _782464) ^ [_1724659, _1724661] : [hBOOL(hAPP(c_List_Odistinct(_1724659), _1724661)), -(c_List_Oremdups(_1724659, _1724661) = _1724661)], (46940 ^ _782464) ^ [_1724752, _1724754, _1724756, _1724758] : [-(c_List_Oremdups(_1724752, hAPP(hAPP(c_List_Omap(_1724754, _1724752), _1724756), c_List_Oremdups(_1724754, _1724758))) = c_List_Oremdups(_1724752, hAPP(hAPP(c_List_Omap(_1724754, _1724752), _1724756), _1724758)))], (46942 ^ _782464) ^ [_1724808, _1724810, _1724812] : [hBOOL(hAPP(c_List_Odistinct(_1724808), _1724810)), -(c_List_Oremove1(_1724808, _1724812, c_List_Oremdups(_1724808, _1724810)) = c_List_Oremdups(_1724808, c_List_Oremove1(_1724808, _1724812, _1724810)))], (46948 ^ _782464) ^ [_1724935, _1724937, _1724939] : [hBOOL(hAPP(hAPP(c_member(_1724935), _1724937), hAPP(c_List_Oset(_1724935), _1724939))), -(c_List_Oremdups(_1724935, hAPP(hAPP(c_List_Olist_OCons(_1724935), _1724937), _1724939)) = c_List_Oremdups(_1724935, _1724939))], (46954 ^ _782464) ^ [_1725060, _1725062, _1725064] : [-(hBOOL(hAPP(hAPP(c_member(_1725060), _1725062), hAPP(c_List_Oset(_1725060), _1725064)))), -(c_List_Oremdups(_1725060, hAPP(hAPP(c_List_Olist_OCons(_1725060), _1725062), _1725064)) = hAPP(hAPP(c_List_Olist_OCons(_1725060), _1725062), c_List_Oremdups(_1725060, _1725064)))], (46960 ^ _782464) ^ [_1725134, _1725136] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725134)), c_List_Oremdups(_1725134, _1725136)) = hAPP(c_Finite__Set_Ocard(_1725134), hAPP(c_List_Oset(_1725134), _1725136)))], (46962 ^ _782464) ^ [_1725179, _1725181] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725179)), c_List_Oremdups(_1725179, c_List_Oconcat(_1725179, _1725181))) = hAPP(c_Finite__Set_Ocard(_1725179), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1725179), tc_fun(_1725179, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1725179)), _1725181)), c_List_Oset(_1725179))))], (46964 ^ _782464) ^ [_1725245, _1725247] : [class_Orderings_Olinorder(_1725245), -(c_List_Olinorder__class_Osorted__list__of__set(_1725245, hAPP(c_List_Oset(_1725245), _1725247)) = c_List_Olinorder__class_Osort__key(_1725245, _1725245, c_COMBI(_1725245), c_List_Oremdups(_1725245, _1725247)))], (46970 ^ _782464) ^ [_1725356] : [-(c_List_Oconcat(_1725356, c_List_Olist_ONil(tc_List_Olist(_1725356))) = c_List_Olist_ONil(_1725356))], (46972 ^ _782464) ^ [_1725388, _1725390] : [-(c_List_Oconcat(_1725388, _1725390) = hAPP(c_List_Ofoldl(tc_List_Olist(_1725388), tc_List_Olist(_1725388), c_List_Oappend(_1725388), c_List_Olist_ONil(_1725388)), _1725390))], (46974 ^ _782464) ^ [_1725432, _1725434, _1725436] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1725432), tc_List_Olist(_1725432), c_List_Oappend(_1725432), _1725434), _1725436) = hAPP(hAPP(c_List_Oappend(_1725432), _1725434), c_List_Oconcat(_1725432, _1725436)))], (46976 ^ _782464) ^ [_1725484, _1725486, _1725488, _1725490] : [class_Orderings_Olinorder(_1725484), 46979 ^ _782464 : [(46980 ^ _782464) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725486), c_List_Olinorder__class_Osort__key(_1725486, _1725484, _1725488, _1725490))), -(hBOOL(hAPP(c_List_Odistinct(_1725486), _1725490)))], (46986 ^ _782464) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725486), _1725490)), -(hBOOL(hAPP(c_List_Odistinct(_1725486), c_List_Olinorder__class_Osort__key(_1725486, _1725484, _1725488, _1725490))))]]], (46992 ^ _782464) ^ [_1725740, _1725742, _1725744, _1725746] : [class_Orderings_Olinorder(_1725740), -(hAPP(c_List_Oset(_1725742), c_List_Olinorder__class_Osort__key(_1725742, _1725740, _1725744, _1725746)) = hAPP(c_List_Oset(_1725742), _1725746))], (46998 ^ _782464) ^ [_1725849, _1725851, _1725853, _1725855] : [class_Orderings_Olinorder(_1725849), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725851)), c_List_Olinorder__class_Osort__key(_1725851, _1725849, _1725853, _1725855)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725851)), _1725855))], (47004 ^ _782464) ^ [_1725966, _1725968, _1725970] : [class_Orderings_Olinorder(_1725966), -(c_List_Olinorder__class_Osort__key(_1725968, _1725966, _1725970, c_List_Olist_ONil(_1725968)) = c_List_Olist_ONil(_1725968))], (47010 ^ _782464) ^ [_1726061, _1726063, _1726065] : [-(c_List_Oconcat(_1726061, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1726061)), _1726063), _1726065)) = hAPP(hAPP(c_List_Oappend(_1726061), _1726063), c_List_Oconcat(_1726061, _1726065)))], (47022 ^ _782464) ^ [_1726333, _1726335] : [47024 ^ _782464 : [(47025 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726333)), 47023 ^ [_1726333, _1726335]), hAPP(c_List_Oset(tc_List_Olist(_1726333)), _1726335))))], (47027 ^ _782464) ^ [] : [47023 ^ [_1726333, _1726335] = c_List_Olist_ONil(_1726333)]], -(c_List_Oconcat(_1726333, _1726335) = c_List_Olist_ONil(_1726333))], (47012 ^ _782464) ^ [_1726127, _1726129] : [c_List_Oconcat(_1726127, _1726129) = c_List_Olist_ONil(_1726127), 47015 ^ _782464 : [(47016 ^ _782464) ^ [_1726218] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726127)), _1726218), hAPP(c_List_Oset(tc_List_Olist(_1726127)), _1726129))), -(_1726218 = c_List_Olist_ONil(_1726127))]]], (47041 ^ _782464) ^ [_1726745, _1726747] : [47043 ^ _782464 : [(47044 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726745)), 47042 ^ [_1726745, _1726747]), hAPP(c_List_Oset(tc_List_Olist(_1726745)), _1726747))))], (47046 ^ _782464) ^ [] : [47042 ^ [_1726745, _1726747] = c_List_Olist_ONil(_1726745)]], -(c_List_Olist_ONil(_1726745) = c_List_Oconcat(_1726745, _1726747))], (47031 ^ _782464) ^ [_1726539, _1726541] : [c_List_Olist_ONil(_1726539) = c_List_Oconcat(_1726539, _1726541), 47034 ^ _782464 : [(47035 ^ _782464) ^ [_1726630] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726539)), _1726630), hAPP(c_List_Oset(tc_List_Olist(_1726539)), _1726541))), -(_1726630 = c_List_Olist_ONil(_1726539))]]], (47050 ^ _782464) ^ [_1726936, _1726938, _1726940, _1726942] : [-(hAPP(hAPP(c_List_Omap(_1726936, _1726938), _1726940), c_List_Oconcat(_1726936, _1726942)) = c_List_Oconcat(_1726938, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1726936), tc_List_Olist(_1726938)), hAPP(c_List_Omap(_1726936, _1726938), _1726940)), _1726942)))], (47052 ^ _782464) ^ [_1726999, _1727001] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726999)), c_List_Oconcat(_1726999, _1727001)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1726999), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1726999))), _1727001)))], (47054 ^ _782464) ^ [_1727052, _1727054] : [-(hAPP(c_List_Oset(_1727052), c_List_Oconcat(_1727052, _1727054)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1727052), tc_fun(_1727052, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1727052)), _1727054)), c_List_Oset(_1727052)))], (47056 ^ _782464) ^ [_1727108, _1727110, _1727112, _1727114, _1727116] : [class_Orderings_Olinorder(_1727108), -(c_List_Olinorder__class_Osort__key(_1727110, _1727108, _1727112, hAPP(hAPP(c_List_Olist_OCons(_1727110), _1727114), _1727116)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727110, _1727108, _1727112), _1727114), c_List_Olinorder__class_Osort__key(_1727110, _1727108, _1727112, _1727116)))], (47062 ^ _782464) ^ [_1727245, _1727247, _1727249] : [-(c_List_Oconcat(_1727245, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1727245)), _1727247), _1727249)) = hAPP(hAPP(c_List_Oappend(_1727245), c_List_Oconcat(_1727245, _1727247)), c_List_Oconcat(_1727245, _1727249)))], (47064 ^ _782464) ^ [_1727299, _1727301] : [class_Orderings_Olinorder(_1727299), -(c_List_Olinorder__class_Osort__key(_1727299, _1727299, c_COMBI(_1727299), _1727301) = hAPP(c_List_Ofoldl(tc_List_Olist(_1727299), _1727299, hAPP(c_COMBC(_1727299, tc_List_Olist(_1727299), tc_List_Olist(_1727299)), c_List_Olinorder__class_Oinsort__key(_1727299, _1727299, c_COMBI(_1727299))), c_List_Olist_ONil(_1727299)), _1727301))], (47070 ^ _782464) ^ [_1727446, _1727448, _1727450] : [47072 ^ _782464 : [(47073 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1727446), tc_List_Olist(_1727446))), 47071 ^ [_1727446, _1727448, _1727450]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1727446), tc_List_Olist(_1727446))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1727446), tc_List_Olist(_1727446)), _1727448), _1727450)))))], (47075 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1727446), tc_List_Olist(_1727446), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1727446), tc_fun(tc_List_Olist(_1727446), tc_Nat_Onat), tc_fun(tc_List_Olist(_1727446), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1727446), tc_Nat_Onat), tc_fun(tc_List_Olist(_1727446), tc_HOL_Obool)), tc_List_Olist(_1727446)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1727446))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1727446)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1727446))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1727446)))), 47071 ^ [_1727446, _1727448, _1727450]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1727446))), _1727448) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1727446))), _1727450), 47080 ^ _782464 : [(47081 ^ _782464) ^ [] : [c_List_Oconcat(_1727446, _1727448) = c_List_Oconcat(_1727446, _1727450), -(_1727448 = _1727450)], (47087 ^ _782464) ^ [] : [_1727448 = _1727450, -(c_List_Oconcat(_1727446, _1727448) = c_List_Oconcat(_1727446, _1727450))]]], (47093 ^ _782464) ^ [_1728173, _1728175, _1728177] : [c_List_Oconcat(_1728173, _1728175) = c_List_Oconcat(_1728173, _1728177), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728173))), _1728175) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728173))), _1728177), 47103 ^ _782464 : [(47104 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1728173), tc_List_Olist(_1728173))), 47102 ^ [_1728173, _1728175, _1728177]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1728173), tc_List_Olist(_1728173))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1728173), tc_List_Olist(_1728173)), _1728175), _1728177)))))], (47106 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1728173), tc_List_Olist(_1728173), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728173), tc_fun(tc_List_Olist(_1728173), tc_Nat_Onat), tc_fun(tc_List_Olist(_1728173), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1728173), tc_Nat_Onat), tc_fun(tc_List_Olist(_1728173), tc_HOL_Obool)), tc_List_Olist(_1728173)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1728173))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1728173)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1728173))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1728173)))), 47102 ^ [_1728173, _1728175, _1728177]))]], -(_1728175 = _1728177)], (47110 ^ _782464) ^ [_1728814, _1728816, _1728818, _1728820] : [-(c_List_Oconcat(_1728814, hAPP(hAPP(c_List_Omap(_1728816, tc_List_Olist(_1728814)), hAPP(hAPP(c_COMBC(_1728816, tc_List_Olist(_1728814), tc_List_Olist(_1728814)), hAPP(hAPP(c_COMBB(_1728814, tc_fun(tc_List_Olist(_1728814), tc_List_Olist(_1728814)), _1728816), c_List_Olist_OCons(_1728814)), _1728818)), c_List_Olist_ONil(_1728814))), _1728820)) = hAPP(hAPP(c_List_Omap(_1728816, _1728814), _1728818), _1728820))], (47112 ^ _782464) ^ [_1728901, _1728903, _1728905] : [-(c_Enum_On__lists(_1728901, hAPP(c_Nat_OSuc, _1728903), _1728905) = c_List_Oconcat(tc_List_Olist(_1728901), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728901), tc_List_Olist(tc_List_Olist(_1728901))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728901), tc_List_Olist(_1728901), tc_List_Olist(tc_List_Olist(_1728901))), hAPP(hAPP(c_COMBB(tc_fun(_1728901, tc_List_Olist(_1728901)), tc_fun(tc_List_Olist(_1728901), tc_List_Olist(tc_List_Olist(_1728901))), tc_List_Olist(_1728901)), c_List_Omap(_1728901, tc_List_Olist(_1728901))), hAPP(c_COMBC(_1728901, tc_List_Olist(_1728901), tc_List_Olist(_1728901)), c_List_Olist_OCons(_1728901)))), _1728905)), c_Enum_On__lists(_1728901, _1728903, _1728905))))], (47114 ^ _782464) ^ [_1729021, _1729023, _1729025, _1729027] : [-(c_List_Otranspose(_1729021, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729021)), hAPP(hAPP(c_List_Olist_OCons(_1729021), _1729023), _1729025)), _1729027)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729021)), hAPP(hAPP(c_List_Olist_OCons(_1729021), _1729023), c_List_Oconcat(_1729021, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729021), tc_List_Olist(_1729021)), c_List_Olist_Olist__case(tc_List_Olist(_1729021), _1729021, c_List_Olist_ONil(_1729021), hAPP(hAPP(c_COMBB(tc_List_Olist(_1729021), tc_fun(tc_List_Olist(_1729021), tc_List_Olist(_1729021)), _1729021), c_COMBK(tc_List_Olist(_1729021), tc_List_Olist(_1729021))), hAPP(hAPP(c_COMBC(_1729021, tc_List_Olist(_1729021), tc_List_Olist(_1729021)), c_List_Olist_OCons(_1729021)), c_List_Olist_ONil(_1729021))))), _1729027)))), c_List_Otranspose(_1729021, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1729021)), _1729025), c_List_Oconcat(tc_List_Olist(_1729021), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729021), tc_List_Olist(tc_List_Olist(_1729021))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1729021)), _1729021, c_List_Olist_ONil(tc_List_Olist(_1729021)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1729021), tc_List_Olist(tc_List_Olist(_1729021))), _1729021), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729021), tc_List_Olist(tc_List_Olist(_1729021)), tc_List_Olist(tc_List_Olist(_1729021))), c_List_Olist_OCons(tc_List_Olist(_1729021))), c_List_Olist_ONil(tc_List_Olist(_1729021)))))), _1729027))))))], (47116 ^ _782464) ^ [_1729247, _1729249] : [-(c_List_Oconcat(_1729247, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729247), tc_List_Olist(_1729247)), c_List_Olist_Olist__case(tc_List_Olist(_1729247), _1729247, c_List_Olist_ONil(_1729247), hAPP(hAPP(c_COMBB(tc_List_Olist(_1729247), tc_fun(tc_List_Olist(_1729247), tc_List_Olist(_1729247)), _1729247), c_COMBK(tc_List_Olist(_1729247), tc_List_Olist(_1729247))), hAPP(hAPP(c_COMBC(_1729247, tc_List_Olist(_1729247), tc_List_Olist(_1729247)), c_List_Olist_OCons(_1729247)), c_List_Olist_ONil(_1729247))))), _1729249)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729247), _1729247), c_List_Ohd(_1729247)), hAPP(c_List_Ofilter(tc_List_Olist(_1729247), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1729247)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729247), tc_List_Olist(_1729247), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1729247)))), _1729249)))], (47118 ^ _782464) ^ [_1729390, _1729392, _1729394] : [-(hAPP(c_List_Ofilter(_1729390, _1729392), c_List_Oconcat(_1729390, _1729394)) = c_List_Oconcat(_1729390, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729390), tc_List_Olist(_1729390)), c_List_Ofilter(_1729390, _1729392)), _1729394)))], (47120 ^ _782464) ^ [_1729445, _1729447, _1729449, _1729451, _1729453] : [class_Orderings_Olinorder(_1729445), -(hAPP(c_List_Ofilter(_1729447, _1729449), c_List_Olinorder__class_Osort__key(_1729447, _1729445, _1729451, _1729453)) = c_List_Olinorder__class_Osort__key(_1729447, _1729445, _1729451, hAPP(c_List_Ofilter(_1729447, _1729449), _1729453)))], (47126 ^ _782464) ^ [_1729570, _1729572, _1729574, _1729576, _1729578] : [-(hAPP(c_List_Ofilter(_1729570, _1729572), hAPP(hAPP(c_List_Omap(_1729574, _1729570), _1729576), _1729578)) = hAPP(hAPP(c_List_Omap(_1729574, _1729570), _1729576), hAPP(c_List_Ofilter(_1729574, hAPP(c_Fun_Ocomp(_1729570, tc_HOL_Obool, _1729574, _1729572), _1729576)), _1729578)))], (47128 ^ _782464) ^ [_1729639, _1729641, _1729643, _1729645, _1729647] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729639)), hAPP(c_List_Ofilter(_1729639, _1729641), hAPP(hAPP(c_List_Omap(_1729643, _1729639), _1729645), _1729647))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729643)), hAPP(c_List_Ofilter(_1729643, hAPP(c_Fun_Ocomp(_1729639, tc_HOL_Obool, _1729643, _1729641), _1729645)), _1729647)))], (47130 ^ _782464) ^ [_1729713, _1729715, _1729717, _1729719, _1729721, _1729723] : [class_Orderings_Olinorder(_1729713), -(hBOOL(hAPP(_1729715, _1729717))), -(hAPP(c_List_Ofilter(_1729719, _1729715), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1729719, _1729713, _1729721), _1729717), _1729723)) = hAPP(c_List_Ofilter(_1729719, _1729715), _1729723))], (47140 ^ _782464) ^ [_1729859, _1729861] : [-(hAPP(c_List_Ofilter(_1729859, _1729861), c_List_Olist_ONil(_1729859)) = c_List_Olist_ONil(_1729859))], (47142 ^ _782464) ^ [_1729894] : [-(c_List_Otranspose(_1729894, c_List_Olist_ONil(tc_List_Olist(_1729894))) = c_List_Olist_ONil(tc_List_Olist(_1729894)))], (47154 ^ _782464) ^ [_1730151, _1730153, _1730155] : [47156 ^ _782464 : [(47157 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730151), 47155 ^ [_1730151, _1730153, _1730155]), hAPP(c_List_Oset(_1730151), _1730155))))], (47159 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1730153, 47155 ^ [_1730151, _1730153, _1730155])))]], -(hAPP(c_List_Ofilter(_1730151, _1730153), _1730155) = c_List_Olist_ONil(_1730151))], (47144 ^ _782464) ^ [_1729946, _1729948, _1729950] : [hAPP(c_List_Ofilter(_1729946, _1729948), _1729950) = c_List_Olist_ONil(_1729946), 47147 ^ _782464 : [(47148 ^ _782464) ^ [_1730043] : [hBOOL(hAPP(hAPP(c_member(_1729946), _1730043), hAPP(c_List_Oset(_1729946), _1729950))), hBOOL(hAPP(_1729948, _1730043))]]], (47163 ^ _782464) ^ [_1730268, _1730270, _1730272] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730268)), hAPP(c_List_Ofilter(_1730268, _1730270), _1730272))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730268)), _1730272))))], (47165 ^ _782464) ^ [_1730320, _1730322, _1730324] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730320)), hAPP(c_List_Ofilter(_1730320, _1730322), _1730324))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730320)), hAPP(c_List_Ofilter(_1730320, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730320), c_fNot), _1730322)), _1730324))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730320)), _1730324))], (47167 ^ _782464) ^ [_1730396, _1730398, _1730400] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730396, tc_HOL_Obool)), hAPP(c_List_Oset(_1730396), hAPP(c_List_Ofilter(_1730396, _1730398), _1730400))), hAPP(c_List_Oset(_1730396), _1730400))))], (47179 ^ _782464) ^ [_1730667, _1730669, _1730671] : [47181 ^ _782464 : [(47182 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730667), 47180 ^ [_1730667, _1730669, _1730671]), hAPP(c_List_Oset(_1730667), _1730671))))], (47184 ^ _782464) ^ [] : [hBOOL(hAPP(_1730669, 47180 ^ [_1730667, _1730669, _1730671]))]], -(hAPP(c_List_Ofilter(_1730667, _1730669), _1730671) = _1730671)], (47169 ^ _782464) ^ [_1730467, _1730469, _1730471] : [hAPP(c_List_Ofilter(_1730467, _1730469), _1730471) = _1730471, 47172 ^ _782464 : [(47173 ^ _782464) ^ [_1730558] : [hBOOL(hAPP(hAPP(c_member(_1730467), _1730558), hAPP(c_List_Oset(_1730467), _1730471))), -(hBOOL(hAPP(_1730469, _1730558)))]]], (47188 ^ _782464) ^ [_1730859, _1730861, _1730863, _1730865] : [-(hAPP(c_List_Ofilter(_1730859, _1730861), hAPP(c_List_Ofilter(_1730859, _1730863), _1730865)) = hAPP(c_List_Ofilter(_1730859, hAPP(hAPP(c_COMBS(_1730859, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1730859), c_fconj), _1730863)), _1730861)), _1730865))], (47190 ^ _782464) ^ [_1730922, _1730924, _1730926, _1730928] : [-(hBOOL(hAPP(_1730922, _1730924))), -(c_List_Oremove1(_1730926, _1730924, hAPP(c_List_Ofilter(_1730926, _1730922), _1730928)) = hAPP(c_List_Ofilter(_1730926, _1730922), _1730928))], (47196 ^ _782464) ^ [_1730980, _1730982, _1730984, _1730986] : [-(hAPP(c_List_Ofilter(_1730980, _1730982), c_List_Oremove1(_1730980, _1730984, _1730986)) = c_List_Oremove1(_1730980, _1730984, hAPP(c_List_Ofilter(_1730980, _1730982), _1730986)))], (47198 ^ _782464) ^ [_1731044, _1731046, _1731048, _1731050] : [hBOOL(hAPP(_1731044, _1731046)), -(hAPP(c_List_Ofilter(_1731048, _1731044), hAPP(hAPP(c_List_Olist_OCons(_1731048), _1731046), _1731050)) = hAPP(hAPP(c_List_Olist_OCons(_1731048), _1731046), hAPP(c_List_Ofilter(_1731048, _1731044), _1731050)))], (47204 ^ _782464) ^ [_1731179, _1731181, _1731183, _1731185] : [-(hBOOL(hAPP(_1731179, _1731181))), -(hAPP(c_List_Ofilter(_1731183, _1731179), hAPP(hAPP(c_List_Olist_OCons(_1731183), _1731181), _1731185)) = hAPP(c_List_Ofilter(_1731183, _1731179), _1731185))], (47210 ^ _782464) ^ [_1731243, _1731245, _1731247, _1731249] : [-(hAPP(c_List_Ofilter(_1731243, _1731245), hAPP(hAPP(c_List_Oappend(_1731243), _1731247), _1731249)) = hAPP(hAPP(c_List_Oappend(_1731243), hAPP(c_List_Ofilter(_1731243, _1731245), _1731247)), hAPP(c_List_Ofilter(_1731243, _1731245), _1731249)))], (47212 ^ _782464) ^ [_1731306, _1731308, _1731310] : [hBOOL(hAPP(c_List_Odistinct(_1731306), _1731308)), -(hBOOL(hAPP(c_List_Odistinct(_1731306), hAPP(c_List_Ofilter(_1731306, _1731310), _1731308))))], (47218 ^ _782464) ^ [_1731413, _1731415, _1731417] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1731413), tc_List_Olist(_1731413)), c_List_Opartition(_1731413, _1731415, _1731417)) = hAPP(c_List_Ofilter(_1731413, _1731415), _1731417))], (47220 ^ _782464) ^ [_1731460, _1731462, _1731464] : [-(c_List_Opartition(_1731460, _1731462, _1731464) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731460), tc_List_Olist(_1731460)), hAPP(c_List_Ofilter(_1731460, _1731462), _1731464)), hAPP(c_List_Ofilter(_1731460, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1731460, c_fNot), _1731462)), _1731464)))], (47222 ^ _782464) ^ [_1731524, _1731526, _1731528] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1731524), tc_List_Olist(_1731524)), c_List_Opartition(_1731524, _1731526, _1731528)) = hAPP(c_List_Ofilter(_1731524, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1731524, c_fNot), _1731526)), _1731528))], (47224 ^ _782464) ^ [_1731579, _1731581, _1731583] : [-(c_List_Oremdups(_1731579, hAPP(c_List_Ofilter(_1731579, _1731581), _1731583)) = hAPP(c_List_Ofilter(_1731579, _1731581), c_List_Oremdups(_1731579, _1731583)))], (47226 ^ _782464) ^ [_1731624, _1731626] : [-(c_List_Otranspose(_1731624, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1731624)), c_List_Olist_ONil(_1731624)), _1731626)) = c_List_Otranspose(_1731624, _1731626))], (47228 ^ _782464) ^ [_1731667, _1731669, _1731671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731667), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731669))), c_List_Otranspose(_1731669, _1731671)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1731669)), c_List_Otranspose(_1731669, _1731671)), _1731667) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731669), _1731669), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731669), tc_Nat_Onat, _1731669), c_List_Onth(_1731669)), _1731667)), hAPP(c_List_Ofilter(tc_List_Olist(_1731669), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1731669)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731667)), c_Nat_Osize__class_Osize(tc_List_Olist(_1731669)))), _1731671)))], (47234 ^ _782464) ^ [_1731910, _1731912, _1731914, _1731916] : [-(c_List_Otranspose(_1731910, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731912), tc_List_Olist(_1731910)), hAPP(c_List_Omap(_1731912, _1731910), _1731914)), _1731916)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731912), tc_List_Olist(_1731910)), hAPP(c_List_Omap(_1731912, _1731910), _1731914)), c_List_Otranspose(_1731912, _1731916)))], (47236 ^ _782464) ^ [_1731983, _1731985, _1731987] : [-(hAPP(c_List_Oset(_1731983), hAPP(c_List_Ofilter(_1731983, _1731985), _1731987)) = hAPP(c_Set_OCollect(_1731983), hAPP(hAPP(c_COMBS(_1731983, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1731983), c_fconj), hAPP(hAPP(c_COMBC(_1731983, tc_fun(_1731983, tc_HOL_Obool), tc_HOL_Obool), c_member(_1731983)), hAPP(c_List_Oset(_1731983), _1731987)))), _1731985)))], (47238 ^ _782464) ^ [_1732066, _1732068, _1732070, _1732072] : [hBOOL(hAPP(hAPP(c_member(_1732066), _1732068), hAPP(c_List_Oset(_1732066), _1732070))), -(hBOOL(hAPP(_1732072, _1732068))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732066)), hAPP(c_List_Ofilter(_1732066, _1732072), _1732070))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732066)), _1732070))))], (47248 ^ _782464) ^ [_1732240, _1732242, _1732244] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1732240, tc_HOL_Obool)), hAPP(c_List_Oset(_1732240), _1732242)), hAPP(hAPP(c_Set_Oinsert(_1732240), _1732244), c_Orderings_Obot__class_Obot(tc_fun(_1732240, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1732240), hAPP(c_List_Ofilter(_1732240, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732240), c_fNot), hAPP(hAPP(c_COMBC(_1732240, _1732240, tc_HOL_Obool), c_fequal), _1732244))), _1732242)))], (47250 ^ _782464) ^ [_1732327, _1732329, _1732331] : [hBOOL(hAPP(c_List_Odistinct(_1732327), _1732329)), -(hAPP(c_List_Ofilter(_1732327, hAPP(hAPP(c_COMBC(_1732327, tc_fun(_1732327, tc_HOL_Obool), tc_HOL_Obool), c_member(_1732327)), hAPP(c_List_Oset(_1732327), c_List_Osublist(_1732327, _1732329, _1732331)))), _1732329) = c_List_Osublist(_1732327, _1732329, _1732331))], (47266 ^ _782464) ^ [_1732707, _1732709] : [47268 ^ _782464 : [(47269 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732707)), 47267 ^ [_1732707, _1732709]), hAPP(c_List_Oset(tc_List_Olist(_1732707)), _1732709))))], (47271 ^ _782464) ^ [] : [47267 ^ [_1732707, _1732709] = c_List_Olist_ONil(_1732707)]], -(c_List_Otranspose(_1732707, _1732709) = c_List_Olist_ONil(tc_List_Olist(_1732707)))], (47256 ^ _782464) ^ [_1732497, _1732499] : [c_List_Otranspose(_1732497, _1732499) = c_List_Olist_ONil(tc_List_Olist(_1732497)), 47259 ^ _782464 : [(47260 ^ _782464) ^ [_1732592] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732497)), _1732592), hAPP(c_List_Oset(tc_List_Olist(_1732497)), _1732499))), -(_1732592 = c_List_Olist_ONil(_1732497))]]], (47275 ^ _782464) ^ [_1732902, _1732904, _1732906] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732902)), hAPP(c_List_Ofilter(_1732902, _1732904), _1732906)) = 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(_1732902)), _1732906)))), hAPP(hAPP(c_COMBB(_1732902, tc_HOL_Obool, tc_Nat_Onat), _1732904), hAPP(c_List_Onth(_1732902), _1732906))))))], (47277 ^ _782464) ^ [_1732982, _1732984] : [-(c_List_Oconcat(tc_List_Olist(_1732982), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732982), tc_List_Olist(tc_List_Olist(_1732982))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1732982)), _1732982, c_List_Olist_ONil(tc_List_Olist(_1732982)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1732982), tc_List_Olist(tc_List_Olist(_1732982))), _1732982), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732982), tc_List_Olist(tc_List_Olist(_1732982)), tc_List_Olist(tc_List_Olist(_1732982))), c_List_Olist_OCons(tc_List_Olist(_1732982))), c_List_Olist_ONil(tc_List_Olist(_1732982)))))), _1732984)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732982), tc_List_Olist(_1732982)), c_List_Otl(_1732982)), hAPP(c_List_Ofilter(tc_List_Olist(_1732982), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1732982)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732982), tc_List_Olist(_1732982), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1732982)))), _1732984)))], (47279 ^ _782464) ^ [_1733134, _1733136, _1733138, _1733140] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1733134)), c_List_Otranspose__rel(_1733134)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733134)), hAPP(hAPP(c_List_Olist_OCons(_1733134), _1733136), _1733138)), _1733140))), -(c_List_Otranspose(_1733134, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733134)), hAPP(hAPP(c_List_Olist_OCons(_1733134), _1733136), _1733138)), _1733140)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733134)), hAPP(hAPP(c_List_Olist_OCons(_1733134), _1733136), c_List_Oconcat(_1733134, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733134), tc_List_Olist(_1733134)), c_List_Olist_Olist__case(tc_List_Olist(_1733134), _1733134, c_List_Olist_ONil(_1733134), hAPP(hAPP(c_COMBB(tc_List_Olist(_1733134), tc_fun(tc_List_Olist(_1733134), tc_List_Olist(_1733134)), _1733134), c_COMBK(tc_List_Olist(_1733134), tc_List_Olist(_1733134))), hAPP(hAPP(c_COMBC(_1733134, tc_List_Olist(_1733134), tc_List_Olist(_1733134)), c_List_Olist_OCons(_1733134)), c_List_Olist_ONil(_1733134))))), _1733140)))), c_List_Otranspose(_1733134, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733134)), _1733138), c_List_Oconcat(tc_List_Olist(_1733134), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733134), tc_List_Olist(tc_List_Olist(_1733134))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1733134)), _1733134, c_List_Olist_ONil(tc_List_Olist(_1733134)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1733134), tc_List_Olist(tc_List_Olist(_1733134))), _1733134), hAPP(hAPP(c_COMBC(tc_List_Olist(_1733134), tc_List_Olist(tc_List_Olist(_1733134)), tc_List_Olist(tc_List_Olist(_1733134))), c_List_Olist_OCons(tc_List_Olist(_1733134))), c_List_Olist_ONil(tc_List_Olist(_1733134)))))), _1733140))))))], (47285 ^ _782464) ^ [_1733667, _1733669] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1733667)), c_List_Otranspose__rel(_1733667)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733667)), c_List_Olist_ONil(_1733667)), _1733669))), -(c_List_Otranspose(_1733667, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733667)), c_List_Olist_ONil(_1733667)), _1733669)) = c_List_Otranspose(_1733667, _1733669))], (47291 ^ _782464) ^ [_1733826, _1733828, _1733830, _1733832] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1733826, tc_Nat_Onat), _1733826), c_Product__Type_Ofst(_1733826, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1733826, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1733826, tc_Nat_Onat)), _1733828), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1733826, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1733826, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1733826, tc_Nat_Onat), _1733830), _1733832))) = hAPP(hAPP(c_List_Omap(tc_prod(_1733826, tc_Nat_Onat), _1733826), c_Product__Type_Ofst(_1733826, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1733826, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1733826, tc_Nat_Onat)), _1733828), c_Product__Type_Osnd(_1733826, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1733826, tc_Nat_Onat), _1733830), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1733832)))))], (47293 ^ _782464) ^ [_1733969, _1733971] : [-(c_Random_Oselect__weight(_1733969, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1733969), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1733969, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1733969, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1733969)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1733971)) = c_Random_Oselect__weight(_1733969, _1733971))], (47295 ^ _782464) ^ [_1734032, _1734034] : [-(c_Random_Opick(_1734032, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1734032), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1734032, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1734032, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1734032)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1734034)) = c_Random_Opick(_1734032, _1734034))], (47297 ^ _782464) ^ [_1734095] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1734095)), c_List_Otranspose__rel(_1734095)), c_List_Olist_ONil(tc_List_Olist(_1734095)))), -(c_List_Otranspose(_1734095, c_List_Olist_ONil(tc_List_Olist(_1734095))) = c_List_Olist_ONil(tc_List_Olist(_1734095)))], (47303 ^ _782464) ^ [_1734222, _1734224] : [-(c_List_Ofoldr(tc_List_Olist(_1734222), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734222)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734222))), c_List_Otranspose(_1734222, _1734224), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1734222))), hAPP(c_List_Ofilter(tc_List_Olist(_1734222), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1734222)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734222), tc_List_Olist(_1734222), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1734222)))), _1734224)))], (47305 ^ _782464) ^ [_1734319, _1734321, _1734323, _1734325] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734319)), _1734321))), c_List_Ofoldr(tc_List_Olist(_1734323), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734323)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734323))), _1734325, 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(_1734319)), _1734321)), c_List_Ofoldr(tc_List_Olist(_1734323), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734323)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734323), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734323)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734323)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1734323), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1734323)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734323), tc_List_Olist(_1734323), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1734323)))), _1734325), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (47307 ^ _782464) ^ [_1734488, _1734490, _1734492, _1734494] : [-(c_List_Ofoldr(_1734488, _1734490, _1734492, c_List_Olist_ONil(_1734488), _1734494) = _1734494)], (47309 ^ _782464) ^ [_1734525, _1734527, _1734529, _1734531, _1734533, _1734535] : [-(c_List_Ofoldr(_1734525, _1734527, _1734529, hAPP(hAPP(c_List_Olist_OCons(_1734525), _1734531), _1734533), _1734535) = hAPP(hAPP(_1734529, _1734531), c_List_Ofoldr(_1734525, _1734527, _1734529, _1734533, _1734535)))], (47311 ^ _782464) ^ [_1734584, _1734586, _1734588, _1734590, _1734592, _1734594] : [-(c_List_Ofoldr(_1734584, _1734586, _1734588, hAPP(hAPP(c_List_Oappend(_1734584), _1734590), _1734592), _1734594) = c_List_Ofoldr(_1734584, _1734586, _1734588, _1734590, c_List_Ofoldr(_1734584, _1734586, _1734588, _1734592, _1734594)))], (47313 ^ _782464) ^ [_1734643, _1734645, _1734647] : [class_Groups_Oab__semigroup__add(_1734643), -(c_List_Ofoldr(_1734643, _1734643, c_Groups_Oplus__class_Oplus(_1734643), _1734645, _1734647) = hAPP(c_List_Ofoldl(_1734643, _1734643, c_Groups_Oplus__class_Oplus(_1734643), _1734647), _1734645))], (47319 ^ _782464) ^ [_1734756, _1734758, _1734760, _1734762, _1734764, _1734766, _1734768] : [-(c_List_Ofoldr(_1734756, _1734758, _1734760, hAPP(hAPP(c_List_Omap(_1734762, _1734756), _1734764), _1734766), _1734768) = c_List_Ofoldr(_1734762, _1734758, hAPP(c_Fun_Ocomp(_1734756, tc_fun(_1734758, _1734758), _1734762, _1734760), _1734764), _1734766, _1734768))], (47321 ^ _782464) ^ [_1734823, _1734825] : [class_Groups_Omonoid__add(_1734823), -(hAPP(c_List_Ofoldl(_1734823, _1734823, c_Groups_Oplus__class_Oplus(_1734823), c_Groups_Ozero__class_Ozero(_1734823)), _1734825) = c_List_Ofoldr(_1734823, _1734823, c_Groups_Oplus__class_Oplus(_1734823), _1734825, c_Groups_Ozero__class_Ozero(_1734823)))], (47327 ^ _782464) ^ [_1734942, _1734944, _1734946] : [class_Groups_Omonoid__add(_1734942), -(hAPP(c_List_Ofoldl(_1734942, _1734942, c_Groups_Oplus__class_Oplus(_1734942), _1734944), _1734946) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1734942), _1734944), c_List_Ofoldr(_1734942, _1734942, c_Groups_Oplus__class_Oplus(_1734942), _1734946, c_Groups_Ozero__class_Ozero(_1734942))))], (47333 ^ _782464) ^ [_1735075, _1735077] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735075))), c_List_Otranspose(_1735075, _1735077)) = c_List_Ofoldr(tc_List_Olist(_1735075), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1735075)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1735075))), _1735077, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47335 ^ _782464) ^ [_1735136, _1735138, _1735140] : [-(c_List_Osublist(_1735136, _1735138, _1735140) = hAPP(hAPP(c_List_Omap(tc_prod(_1735136, tc_Nat_Onat), _1735136), c_Product__Type_Ofst(_1735136, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735136, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735136, 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(_1735136, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1735136, tc_Nat_Onat))), _1735140)), hAPP(hAPP(c_List_Ozip(_1735136, tc_Nat_Onat), _1735138), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735136)), _1735138))))))], (47337 ^ _782464) ^ [_1735239, _1735241, _1735243, _1735245] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1735239, tc_Nat_Onat), _1735239), c_Product__Type_Ofst(_1735239, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735239, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735239, 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(_1735239, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1735239, tc_Nat_Onat))), _1735241)), hAPP(hAPP(c_List_Ozip(_1735239, tc_Nat_Onat), _1735243), c_List_Oupt(_1735245, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735245), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735239)), _1735243)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1735239, tc_Nat_Onat), _1735239), c_Product__Type_Ofst(_1735239, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735239, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735239, 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(_1735239, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1735239, 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(_1735239, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1735239, tc_Nat_Onat))), _1735245))), _1735241)), hAPP(hAPP(c_List_Ozip(_1735239, tc_Nat_Onat), _1735243), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735239)), _1735243))))))], (47339 ^ _782464) ^ [_1735444, _1735446] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1735444), _1735446) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1735444, _1735446)))], (47341 ^ _782464) ^ [_1735481, _1735483] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1735481, _1735483)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1735481), _1735483))], (47343 ^ _782464) ^ [_1735518, _1735520] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1735518, _1735520))))], (47345 ^ _782464) ^ [_1735548, _1735550, _1735552] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735548), _1735550)), -(c_List_Oupt(_1735548, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735550), _1735552)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735548, _1735550)), c_List_Oupt(_1735550, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735550), _1735552))))], (47351 ^ _782464) ^ [_1735700, _1735702] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735700), _1735702)), -(c_List_Oupt(_1735700, hAPP(c_Nat_OSuc, _1735702)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735700, _1735702)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1735702), c_List_Olist_ONil(tc_Nat_Onat))))], (47357 ^ _782464) ^ [_1735823, _1735825] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735823), _1735825))), -(c_List_Oupt(_1735823, hAPP(c_Nat_OSuc, _1735825)) = c_List_Olist_ONil(tc_Nat_Onat))], (47363 ^ _782464) ^ [_1735872, _1735874] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735872), _1735874)), -(c_List_Oupt(_1735872, hAPP(c_Nat_OSuc, _1735874)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735872, _1735874)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1735874), c_List_Olist_ONil(tc_Nat_Onat))))], (47369 ^ _782464) ^ [_1736001, _1736003, _1736005] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1736001), c_List_Oupt(_1736003, _1736005)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736003), _1736001), _1736005))], (47371 ^ _782464) ^ [_1736046, _1736048] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736046), _1736048)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1736046, _1736048)) = _1736046)], (47377 ^ _782464) ^ [_1736154, _1736156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736154), _1736156)), -(c_List_Oupt(_1736154, _1736156) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1736154), c_List_Oupt(hAPP(c_Nat_OSuc, _1736154), _1736156)))], (47383 ^ _782464) ^ [_1736265, _1736267] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736265), _1736267))), -(c_List_Oupt(_1736265, _1736267) = c_List_Olist_ONil(tc_Nat_Onat))], (47389 ^ _782464) ^ [_1736311, _1736313] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736311), _1736313)), -(c_List_Oupt(_1736311, _1736313) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1736311), c_List_Oupt(hAPP(c_Nat_OSuc, _1736311), _1736313)))], (47395 ^ _782464) ^ [_1736428, _1736430, _1736432] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736428), _1736430)), _1736432)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1736430), c_List_Oupt(_1736428, _1736432)) = c_List_Oupt(_1736428, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736428), _1736430)))], (47401 ^ _782464) ^ [_1736565, _1736567] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1736565), _1736567)) = c_List_Oupt(_1736565, _1736567))], (47413 ^ _782464) ^ [_1736719, _1736721] : [47414 ^ _782464 : [(47415 ^ _782464) ^ [] : [_1736721 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47417 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736721), _1736719))]], -(c_List_Oupt(_1736719, _1736721) = c_List_Olist_ONil(tc_Nat_Onat))], (47403 ^ _782464) ^ [_1736617, _1736619] : [c_List_Oupt(_1736617, _1736619) = c_List_Olist_ONil(tc_Nat_Onat), -(_1736619 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736619), _1736617)))], (47421 ^ _782464) ^ [_1736852, _1736854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736852), _1736854)), -(c_List_Oupt(_1736854, _1736852) = c_List_Olist_ONil(tc_Nat_Onat))], (47427 ^ _782464) ^ [_1736945] : [-(c_List_Oupt(_1736945, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (47429 ^ _782464) ^ [_1736971, _1736973] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1736971, _1736973)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1736973), _1736971))], (47431 ^ _782464) ^ [_1737017, _1737019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737017)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737019))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737017), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737019)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737017)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737017)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737019))))], (47437 ^ _782464) ^ [_1737170, _1737172] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737170)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737172)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737170), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737172)) = c_List_Olist_ONil(tc_Nat_Onat))], (47443 ^ _782464) ^ [_1737249, _1737251, _1737253, _1737255] : [c_List_Oupt(_1737249, _1737251) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1737253), _1737255), 47446 ^ _782464 : [(47447 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737249), _1737251)))], (47449 ^ _782464) ^ [] : [-(_1737249 = _1737253)], (47451 ^ _782464) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737249), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1737251) = _1737255)]]], (47453 ^ _782464) ^ [_1737422, _1737424, _1737426, _1737428] : [-(c_List_Oupt(_1737422, _1737424) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1737426), _1737428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737422), _1737424)), _1737422 = _1737426, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737422), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1737424) = _1737428], (47467 ^ _782464) ^ [_1737663, _1737665] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737663), _1737665)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1737663, _1737665)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1737665), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47473 ^ _782464) ^ [_1737774, _1737776] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1737774, _1737776)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1737774), hAPP(c_Nat_OSuc, _1737776)))], (47475 ^ _782464) ^ [_1737814, _1737816] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1737814, _1737816) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1737814, hAPP(c_Nat_OSuc, _1737816))))], (47477 ^ _782464) ^ [_1737852] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1737852) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1737852)))], (47479 ^ _782464) ^ [_1737884, _1737886, _1737888] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737884), _1737886)), _1737888)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1737884, _1737888)), _1737886) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737884), _1737886))], (47485 ^ _782464) ^ [_1738015, _1738017] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1738015, _1738017) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1738015), hAPP(c_Nat_OSuc, _1738017))))], (47487 ^ _782464) ^ [_1738056, _1738058] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1738056, _1738058) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1738056), _1738058)))], (47489 ^ _782464) ^ [_1738094] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1738094) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1738094))))], (47491 ^ _782464) ^ [_1738129, _1738131] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738129), hAPP(c_List_Onth(_1738129), _1738131)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738129)), _1738131))) = _1738131)], (47493 ^ _782464) ^ [_1738178, _1738180, _1738182, _1738184] : [class_Groups_Ocomm__monoid__add(_1738178), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1738178), _1738180), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1738182, _1738184))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1738178), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738178), _1738180), c_List_Oupt(_1738182, _1738184))))], (47499 ^ _782464) ^ [_1738321, _1738323, _1738325, _1738327] : [class_Groups_Ocomm__monoid__add(_1738321), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1738321), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738321), _1738323), c_List_Oupt(_1738325, _1738327))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1738321), _1738323), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1738325, _1738327))))], (47505 ^ _782464) ^ [_1738464, _1738466, _1738468, _1738470, _1738472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738464), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1738466), _1738468))), -(hAPP(hAPP(c_List_Onth(_1738470), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738470), _1738472), c_List_Oupt(_1738468, _1738466))), _1738464) = hAPP(_1738472, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1738468), _1738464)))], (47511 ^ _782464) ^ [_1738627, _1738629, _1738631] : [47512 ^ _782464 : [(47513 ^ _782464) ^ [] : [-(_1738627 = c_List_Olist_ONil(tc_List_Olist(_1738629)))], (47515 ^ _782464) ^ [] : [_1738631 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 47519 ^ _782464 : [(47520 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47518 ^ [_1738627, _1738629, _1738631]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738629))), _1738627))))], (47522 ^ _782464) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738629)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1738629)), _1738627), 47518 ^ [_1738627, _1738629, _1738631])) = _1738631]], -(c_List_Otranspose(_1738629, _1738627) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1738629)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1738629)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1738629), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1738629)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1738629)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1738629), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738629), tc_fun(tc_Nat_Onat, _1738629), tc_Nat_Onat), c_List_Onth(_1738629)), hAPP(c_List_Onth(tc_List_Olist(_1738629)), _1738627))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738629))), _1738627)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1738631)))], (47526 ^ _782464) ^ [_1739137, _1739139, _1739141, _1739143, _1739145] : [class_Orderings_Olinorder(_1739137), hBOOL(hAPP(hAPP(c_member(_1739139), _1739141), hAPP(c_List_Oset(_1739139), _1739143))), c_List_Olinorder__class_Osorted(_1739137, hAPP(hAPP(c_List_Omap(_1739139, _1739137), _1739145), _1739143)), hAPP(c_List_Ohd(_1739139), hAPP(c_List_Ofilter(_1739139, hAPP(hAPP(c_COMBB(_1739137, tc_HOL_Obool, _1739139), hAPP(c_fequal, hAPP(_1739145, _1739141))), _1739145)), _1739143)) = _1739141, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739139, _1739137, _1739145), _1739141), c_List_Oremove1(_1739139, _1739141, _1739143)) = _1739143)], (47544 ^ _782464) ^ [_1739516] : [class_Orderings_Olinorder(_1739516), -(c_List_Olinorder__class_Osorted(_1739516, c_List_Olist_ONil(_1739516)))], (47550 ^ _782464) ^ [_1739593, _1739595] : [class_Orderings_Olinorder(_1739593), -(c_List_Olinorder__class_Osorted(_1739593, hAPP(hAPP(c_List_Olist_OCons(_1739593), _1739595), c_List_Olist_ONil(_1739593))))], (47556 ^ _782464) ^ [_1739688, _1739690] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1739688, _1739690)))], (47558 ^ _782464) ^ [_1739716, _1739718] : [class_Orderings_Olinorder(_1739716), -(c_List_Olinorder__class_Osorted(_1739716, c_List_Olinorder__class_Osort__key(_1739716, _1739716, c_COMBI(_1739716), _1739718)))], (47564 ^ _782464) ^ [_1739805, _1739807, _1739809] : [class_Orderings_Olinorder(_1739805), 47567 ^ _782464 : [(47568 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1739805, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739805, _1739805, c_COMBI(_1739805)), _1739807), _1739809)), -(c_List_Olinorder__class_Osorted(_1739805, _1739809))], (47574 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1739805, _1739809), -(c_List_Olinorder__class_Osorted(_1739805, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739805, _1739805, c_COMBI(_1739805)), _1739807), _1739809)))]]], (47580 ^ _782464) ^ [_1740052, _1740054] : [class_Orderings_Olinorder(_1740052), c_List_Olinorder__class_Osorted(_1740052, _1740054), -(c_List_Olinorder__class_Osorted(_1740052, hAPP(c_List_Otl(_1740052), _1740054)))], (47590 ^ _782464) ^ [_1740189] : [class_Orderings_Olinorder(_1740189), -(c_List_Olinorder__class_Osorted(_1740189, c_List_Olist_ONil(_1740189)))], (47596 ^ _782464) ^ [_1740266, _1740268] : [class_Orderings_Olinorder(_1740266), -(_1740268 = c_List_Olist_ONil(_1740266)), c_List_Olinorder__class_Osorted(_1740266, _1740268), -(c_List_Olinorder__class_Osorted(_1740266, c_List_Obutlast(_1740266, _1740268)))], (47610 ^ _782464) ^ [_1740458, _1740460, _1740462] : [class_Orderings_Olinorder(_1740458), c_List_Olinorder__class_Osorted(_1740458, _1740460), -(c_List_Olinorder__class_Osorted(_1740458, hAPP(hAPP(c_List_Otake(_1740458), _1740462), _1740460)))], (47620 ^ _782464) ^ [_1740605, _1740607] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1740605, _1740607)))], (47622 ^ _782464) ^ [_1740633, _1740635, _1740637] : [class_Orderings_Olinorder(_1740633), c_List_Olinorder__class_Osorted(_1740633, _1740635), -(c_List_Olinorder__class_Osorted(_1740633, c_List_Oremove1(_1740633, _1740637, _1740635)))], (47632 ^ _782464) ^ [_1740772, _1740774, _1740776, _1740778] : [class_Orderings_Olinorder(_1740772), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1740772), _1740774), _1740776)), c_List_Olinorder__class_Osorted(_1740772, hAPP(hAPP(c_List_Olist_OCons(_1740772), _1740776), _1740778)), -(c_List_Olinorder__class_Osorted(_1740772, hAPP(hAPP(c_List_Olist_OCons(_1740772), _1740774), hAPP(hAPP(c_List_Olist_OCons(_1740772), _1740776), _1740778))))], (47646 ^ _782464) ^ [_1741025, _1741027, _1741029, _1741031] : [class_Orderings_Olinorder(_1741025), 47649 ^ _782464 : [(47650 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1741025, hAPP(hAPP(c_List_Olist_OCons(_1741025), _1741027), hAPP(hAPP(c_List_Olist_OCons(_1741025), _1741029), _1741031))), 47653 ^ _782464 : [(47654 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1741025), _1741027), _1741029)))], (47656 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1741025, hAPP(hAPP(c_List_Olist_OCons(_1741025), _1741029), _1741031)))]]], (47658 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1741025, hAPP(hAPP(c_List_Olist_OCons(_1741025), _1741027), hAPP(hAPP(c_List_Olist_OCons(_1741025), _1741029), _1741031)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1741025), _1741027), _1741029)), c_List_Olinorder__class_Osorted(_1741025, hAPP(hAPP(c_List_Olist_OCons(_1741025), _1741029), _1741031))]]], (47668 ^ _782464) ^ [_1741411, _1741413, _1741415] : [class_Orderings_Olinorder(_1741411), c_List_Olinorder__class_Osorted(_1741411, _1741413), -(c_List_Olinorder__class_Osorted(_1741411, hAPP(hAPP(c_List_Odrop(_1741411), _1741415), _1741413)))], (47678 ^ _782464) ^ [_1741558, _1741560, _1741562] : [class_Orderings_Olinorder(_1741558), c_List_Olinorder__class_Osorted(_1741558, _1741560), -(c_List_Olinorder__class_Osorted(_1741558, c_List_Olinorder__class_Oinsort__insert__key(_1741558, _1741558, c_COMBI(_1741558), _1741562, _1741560)))], (47688 ^ _782464) ^ [_1741705, _1741707] : [class_Orderings_Olinorder(_1741705), c_List_Olinorder__class_Osorted(_1741705, _1741707), -(c_List_Olinorder__class_Osorted(_1741705, c_List_Oremdups(_1741705, _1741707)))], (47698 ^ _782464) ^ [_1741838, _1741840, _1741842] : [class_Orderings_Olinorder(_1741838), c_List_Olinorder__class_Osorted(_1741838, _1741840), hBOOL(hAPP(c_List_Odistinct(_1741838), _1741840)), c_List_Olinorder__class_Osorted(_1741838, _1741842), hBOOL(hAPP(c_List_Odistinct(_1741838), _1741842)), hAPP(c_List_Oset(_1741838), _1741840) = hAPP(c_List_Oset(_1741838), _1741842), -(_1741840 = _1741842)], (47724 ^ _782464) ^ [_1742221, _1742223, _1742225, _1742227] : [class_Orderings_Olinorder(_1742221), -(c_List_Olinorder__class_Osorted(_1742221, hAPP(hAPP(c_List_Omap(_1742223, _1742221), _1742225), c_List_Olinorder__class_Osort__key(_1742223, _1742221, _1742225, _1742227))))], (47730 ^ _782464) ^ [_1742328, _1742330, _1742332, _1742334, _1742336] : [class_Orderings_Olinorder(_1742328), c_List_Olinorder__class_Osorted(_1742328, hAPP(hAPP(c_List_Omap(_1742330, _1742328), _1742332), _1742334)), -(c_List_Olinorder__class_Osorted(_1742328, hAPP(hAPP(c_List_Omap(_1742330, _1742328), _1742332), c_List_Olinorder__class_Oinsort__insert__key(_1742330, _1742328, _1742332, _1742336, _1742334))))], (47740 ^ _782464) ^ [_1742515, _1742517, _1742519, _1742521, _1742523] : [class_Orderings_Olinorder(_1742515), c_List_Olinorder__class_Osorted(_1742515, hAPP(hAPP(c_List_Omap(_1742517, _1742515), _1742519), _1742521)), -(c_List_Olinorder__class_Osorted(_1742515, hAPP(hAPP(c_List_Omap(_1742517, _1742515), _1742519), c_List_Oremove1(_1742517, _1742523, _1742521))))], (47750 ^ _782464) ^ [_1742698, _1742700, _1742702, _1742704, _1742706] : [class_Orderings_Olinorder(_1742698), 47753 ^ _782464 : [(47754 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1742698, hAPP(hAPP(c_List_Omap(_1742700, _1742698), _1742702), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742700, _1742698, _1742702), _1742704), _1742706))), -(c_List_Olinorder__class_Osorted(_1742698, hAPP(hAPP(c_List_Omap(_1742700, _1742698), _1742702), _1742706)))], (47760 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1742698, hAPP(hAPP(c_List_Omap(_1742700, _1742698), _1742702), _1742706)), -(c_List_Olinorder__class_Osorted(_1742698, hAPP(hAPP(c_List_Omap(_1742700, _1742698), _1742702), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742700, _1742698, _1742702), _1742704), _1742706))))]]], (47766 ^ _782464) ^ [_1743005, _1743007, _1743009, _1743011, _1743013] : [class_Orderings_Olinorder(_1743005), c_List_Olinorder__class_Osorted(_1743005, hAPP(hAPP(c_List_Omap(_1743007, _1743005), _1743009), _1743011)), -(c_List_Olinorder__class_Osorted(_1743005, hAPP(hAPP(c_List_Omap(_1743007, _1743005), _1743009), hAPP(c_List_Ofilter(_1743007, _1743013), _1743011))))], (47776 ^ _782464) ^ [_1743192, _1743194, _1743196, _1743198, _1743200] : [class_Orderings_Olinorder(_1743192), -(c_List_Olinorder__class_Osorted(_1743192, hAPP(hAPP(c_List_Omap(_1743194, _1743192), _1743196), hAPP(c_List_Ofilter(_1743194, hAPP(hAPP(c_COMBC(_1743194, _1743192, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1743192, tc_fun(_1743192, tc_HOL_Obool), _1743194), c_fequal), _1743196)), hAPP(_1743198, _1743200))), _1743200))))], (47782 ^ _782464) ^ [_1743355, _1743357, _1743359] : [class_Orderings_Olinorder(_1743355), -(c_List_Olinorder__class_Osorted(_1743355, hAPP(c_List_Ofilter(_1743355, hAPP(hAPP(c_COMBC(_1743355, _1743355, tc_HOL_Obool), c_fequal), hAPP(_1743357, _1743359))), _1743359)))], (47788 ^ _782464) ^ [_1743470, _1743472, _1743474] : [class_Orderings_Olinorder(_1743470), 47791 ^ _782464 : [(47792 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1743470, hAPP(hAPP(c_List_Olist_OCons(_1743470), _1743472), _1743474)), 47795 ^ _782464 : [(47796 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743470, _1743474))], (47798 ^ _782464) ^ [_1743656] : [hBOOL(hAPP(hAPP(c_member(_1743470), _1743656), hAPP(c_List_Oset(_1743470), _1743474))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743470), _1743472), _1743656)))]]], (47804 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743470, hAPP(hAPP(c_List_Olist_OCons(_1743470), _1743472), _1743474))), c_List_Olinorder__class_Osorted(_1743470, _1743474), 47810 ^ _782464 : [(47811 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743470), 47809 ^ [_1743470, _1743472, _1743474]), hAPP(c_List_Oset(_1743470), _1743474))))], (47813 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743470), _1743472), 47809 ^ [_1743470, _1743472, _1743474]))]]]]], (47817 ^ _782464) ^ [_1743995, _1743997, _1743999] : [class_Orderings_Olinorder(_1743995), 47820 ^ _782464 : [(47821 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1743995, hAPP(hAPP(c_List_Oappend(_1743995), _1743997), _1743999)), 47824 ^ _782464 : [(47825 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743995, _1743997))], (47827 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743995, _1743999))], (47829 ^ _782464) ^ [_1744231] : [hBOOL(hAPP(hAPP(c_member(_1743995), _1744231), hAPP(c_List_Oset(_1743995), _1743997))), 47832 ^ _782464 : [(47833 ^ _782464) ^ [_1744341] : [hBOOL(hAPP(hAPP(c_member(_1743995), _1744341), hAPP(c_List_Oset(_1743995), _1743999))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743995), _1744231), _1744341)))]]]]], (47839 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743995, hAPP(hAPP(c_List_Oappend(_1743995), _1743997), _1743999))), c_List_Olinorder__class_Osorted(_1743995, _1743997), c_List_Olinorder__class_Osorted(_1743995, _1743999), 47849 ^ _782464 : [(47850 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743995), 47848 ^ [_1743995, _1743997, _1743999]), hAPP(c_List_Oset(_1743995), _1743997))))], (47853 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743995), 47851 ^ [_1743995, _1743997, _1743999]), hAPP(c_List_Oset(_1743995), _1743999))))], (47855 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743995), 47848 ^ [_1743995, _1743997, _1743999]), 47851 ^ [_1743995, _1743997, _1743999]))]]]]], (47859 ^ _782464) ^ [_1744843, _1744845, _1744847, _1744849, _1744851, _1744853] : [class_Orderings_Olinorder(_1744843), c_List_Olinorder__class_Osorted(_1744843, hAPP(hAPP(c_List_Omap(_1744845, _1744843), _1744847), _1744849)), hBOOL(hAPP(_1744851, _1744853)), -(hAPP(c_List_Ofilter(_1744845, _1744851), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744845, _1744843, _1744847), _1744853), _1744849)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744845, _1744843, _1744847), _1744853), hAPP(c_List_Ofilter(_1744845, _1744851), _1744849)))], (47873 ^ _782464) ^ [_1745132, _1745134, _1745136] : [class_Orderings_Olinorder(_1745132), 47876 ^ _782464 : [(47877 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1745132, hAPP(hAPP(c_List_Olist_OCons(_1745132), _1745134), _1745136)), 47880 ^ _782464 : [(47887 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745132, _1745136))], (47881 ^ _782464) ^ [_1745300] : [hBOOL(hAPP(hAPP(c_member(_1745132), _1745300), hAPP(c_List_Oset(_1745132), _1745136))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745132), _1745134), _1745300)))]]], (47889 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745132, hAPP(hAPP(c_List_Olist_OCons(_1745132), _1745134), _1745136))), 47893 ^ _782464 : [(47894 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745132), 47892 ^ [_1745132, _1745134, _1745136]), hAPP(c_List_Oset(_1745132), _1745136))))], (47896 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745132), _1745134), 47892 ^ [_1745132, _1745134, _1745136]))]], c_List_Olinorder__class_Osorted(_1745132, _1745136)]]], (47902 ^ _782464) ^ [_1745658, _1745660] : [class_Orderings_Olinorder(_1745658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745658), _1745660)), 47909 ^ _782464 : [(47910 ^ _782464) ^ [] : [-(hAPP(c_List_Oset(_1745658), c_List_Olinorder__class_Osorted__list__of__set(_1745658, _1745660)) = _1745660)], (47912 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745658, c_List_Olinorder__class_Osorted__list__of__set(_1745658, _1745660)))], (47914 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1745658), c_List_Olinorder__class_Osorted__list__of__set(_1745658, _1745660))))]]], (47916 ^ _782464) ^ [_1745879, _1745881, _1745883] : [class_Orderings_Olinorder(_1745879), hBOOL(hAPP(hAPP(c_member(_1745879), _1745881), hAPP(c_List_Oset(_1745879), _1745883))), c_List_Olinorder__class_Osorted(_1745879, _1745883), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1745879, _1745879, c_COMBI(_1745879)), _1745881), c_List_Oremove1(_1745879, _1745881, _1745883)) = _1745883)], (47930 ^ _782464) ^ [_1746120, _1746122, _1746124, _1746126] : [class_Orderings_Olinorder(_1746120), c_List_Olinorder__class_Osorted(_1746120, _1746122), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746124), _1746126)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746126), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746120)), _1746122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746120), hAPP(hAPP(c_List_Onth(_1746120), _1746122), _1746124)), hAPP(hAPP(c_List_Onth(_1746120), _1746122), _1746126))))], (47948 ^ _782464) ^ [_1746447, _1746449] : [class_Orderings_Olinorder(_1746447), 47951 ^ _782464 : [(47966 ^ _782464) ^ [] : [47968 ^ _782464 : [(47969 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47967 ^ [_1746447, _1746449]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746447)), _1746449))))], (47972 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47970 ^ [_1746447, _1746449]), 47967 ^ [_1746447, _1746449])))], (47974 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746447), hAPP(hAPP(c_List_Onth(_1746447), _1746449), 47970 ^ [_1746447, _1746449])), hAPP(hAPP(c_List_Onth(_1746447), _1746449), 47967 ^ [_1746447, _1746449])))]], -(c_List_Olinorder__class_Osorted(_1746447, _1746449))], (47952 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1746447, _1746449), 47955 ^ _782464 : [(47956 ^ _782464) ^ [_1746618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746618), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746447)), _1746449))), 47959 ^ _782464 : [(47960 ^ _782464) ^ [_1746735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746735), _1746618)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746447), hAPP(hAPP(c_List_Onth(_1746447), _1746449), _1746735)), hAPP(hAPP(c_List_Onth(_1746447), _1746449), _1746618))))]]]]]]], (47978 ^ _782464) ^ [_1747171, _1747173, _1747175, _1747177, _1747179] : [class_Orderings_Olinorder(_1747171), c_Fun_Oinj__on(_1747173, _1747171, _1747175, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747173, tc_HOL_Obool)), hAPP(c_List_Oset(_1747173), _1747177)), hAPP(c_List_Oset(_1747173), _1747179))), c_List_Olinorder__class_Osorted(_1747171, hAPP(hAPP(c_List_Omap(_1747173, _1747171), _1747175), _1747177)), hBOOL(hAPP(c_List_Odistinct(_1747171), hAPP(hAPP(c_List_Omap(_1747173, _1747171), _1747175), _1747177))), c_List_Olinorder__class_Osorted(_1747171, hAPP(hAPP(c_List_Omap(_1747173, _1747171), _1747175), _1747179)), hBOOL(hAPP(c_List_Odistinct(_1747171), hAPP(hAPP(c_List_Omap(_1747173, _1747171), _1747175), _1747179))), hAPP(c_List_Oset(_1747173), _1747177) = hAPP(c_List_Oset(_1747173), _1747179), -(_1747177 = _1747179)], (48008 ^ _782464) ^ [_1747754, _1747756, _1747758] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747754), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1747754))), _1747756))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747758), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1747754))), _1747756))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747754), _1747754), hAPP(hAPP(c_COMBC(tc_List_Olist(_1747754), tc_Nat_Onat, _1747754), c_List_Onth(_1747754)), _1747758)), hAPP(c_List_Ofilter(tc_List_Olist(_1747754), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1747754)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747758)), c_Nat_Osize__class_Osize(tc_List_Olist(_1747754)))), c_List_Otranspose(_1747754, _1747756))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1747754)), _1747756), _1747758))], (48018 ^ _782464) ^ [_1748081, _1748083, _1748085, _1748087] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1748081), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1748081))), _1748083))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748085), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748081))), c_List_Otranspose(_1748081, _1748083)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748087), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748081))), hAPP(c_List_Ofilter(tc_List_Olist(_1748081), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1748081)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748085)), c_Nat_Osize__class_Osize(tc_List_Olist(_1748081)))), _1748083)))), -(hAPP(hAPP(c_List_Onth(_1748081), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1748081)), c_List_Otranspose(_1748081, _1748083)), _1748085)), _1748087) = hAPP(hAPP(c_List_Onth(_1748081), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1748081)), _1748083), _1748087)), _1748085))], (48032 ^ _782464) ^ [_1748504, _1748506] : [-(c_Fun_Oinj__on(tc_List_Olist(_1748504), tc_List_Olist(_1748504), c_List_Orev(_1748504), _1748506))], (48034 ^ _782464) ^ [_1748552, _1748554] : [hAPP(c_List_Orev(_1748552), _1748554) = c_List_Olist_ONil(_1748552), -(_1748554 = c_List_Olist_ONil(_1748552))], (48040 ^ _782464) ^ [_1748643, _1748645] : [_1748645 = c_List_Olist_ONil(_1748643), -(hAPP(c_List_Orev(_1748643), _1748645) = c_List_Olist_ONil(_1748643))], (48046 ^ _782464) ^ [_1748755, _1748757] : [c_List_Olist_ONil(_1748755) = hAPP(c_List_Orev(_1748755), _1748757), -(_1748757 = c_List_Olist_ONil(_1748755))], (48052 ^ _782464) ^ [_1748846, _1748848] : [_1748848 = c_List_Olist_ONil(_1748846), -(c_List_Olist_ONil(_1748846) = hAPP(c_List_Orev(_1748846), _1748848))], (48058 ^ _782464) ^ [_1748943] : [-(hAPP(c_List_Orev(_1748943), c_List_Olist_ONil(_1748943)) = c_List_Olist_ONil(_1748943))], (48060 ^ _782464) ^ [_1748993, _1748995, _1748997] : [hAPP(hAPP(c_List_Olist_OCons(_1748993), _1748995), c_List_Olist_ONil(_1748993)) = hAPP(c_List_Orev(_1748993), _1748997), -(_1748997 = hAPP(hAPP(c_List_Olist_OCons(_1748993), _1748995), c_List_Olist_ONil(_1748993)))], (48066 ^ _782464) ^ [_1749118, _1749120, _1749122] : [_1749122 = hAPP(hAPP(c_List_Olist_OCons(_1749118), _1749120), c_List_Olist_ONil(_1749118)), -(hAPP(hAPP(c_List_Olist_OCons(_1749118), _1749120), c_List_Olist_ONil(_1749118)) = hAPP(c_List_Orev(_1749118), _1749122))], (48072 ^ _782464) ^ [_1749267, _1749269, _1749271] : [hAPP(c_List_Orev(_1749267), _1749269) = hAPP(hAPP(c_List_Olist_OCons(_1749267), _1749271), c_List_Olist_ONil(_1749267)), -(_1749269 = hAPP(hAPP(c_List_Olist_OCons(_1749267), _1749271), c_List_Olist_ONil(_1749267)))], (48078 ^ _782464) ^ [_1749392, _1749394, _1749396] : [_1749394 = hAPP(hAPP(c_List_Olist_OCons(_1749392), _1749396), c_List_Olist_ONil(_1749392)), -(hAPP(c_List_Orev(_1749392), _1749394) = hAPP(hAPP(c_List_Olist_OCons(_1749392), _1749396), c_List_Olist_ONil(_1749392)))], (48084 ^ _782464) ^ [_1749523, _1749525, _1749527] : [-(hAPP(c_List_Orev(_1749523), hAPP(hAPP(c_List_Oappend(_1749523), _1749525), _1749527)) = hAPP(hAPP(c_List_Oappend(_1749523), hAPP(c_List_Orev(_1749523), _1749527)), hAPP(c_List_Orev(_1749523), _1749525)))], (48086 ^ _782464) ^ [_1749596, _1749598] : [hBOOL(hAPP(c_List_Odistinct(_1749596), hAPP(c_List_Orev(_1749596), _1749598))), -(hBOOL(hAPP(c_List_Odistinct(_1749596), _1749598)))], (48092 ^ _782464) ^ [_1749695, _1749697] : [hBOOL(hAPP(c_List_Odistinct(_1749695), _1749697)), -(hBOOL(hAPP(c_List_Odistinct(_1749695), hAPP(c_List_Orev(_1749695), _1749697))))], (48098 ^ _782464) ^ [_1749800, _1749802] : [-(hAPP(c_List_Orev(_1749800), c_List_Oconcat(_1749800, _1749802)) = c_List_Oconcat(_1749800, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1749800), tc_List_Olist(_1749800)), c_List_Orev(_1749800)), hAPP(c_List_Orev(tc_List_Olist(_1749800)), _1749802))))], (48100 ^ _782464) ^ [_1749858, _1749860, _1749862, _1749864] : [-(hAPP(c_List_Orev(_1749858), hAPP(hAPP(c_List_Omap(_1749860, _1749858), _1749862), _1749864)) = hAPP(hAPP(c_List_Omap(_1749860, _1749858), _1749862), hAPP(c_List_Orev(_1749860), _1749864)))], (48102 ^ _782464) ^ [_1749915, _1749917, _1749919] : [-(hAPP(c_List_Orev(_1749915), hAPP(c_List_Ofilter(_1749915, _1749917), _1749919)) = hAPP(c_List_Ofilter(_1749915, _1749917), hAPP(c_List_Orev(_1749915), _1749919)))], (48104 ^ _782464) ^ [_1749964, _1749966, _1749968, _1749970] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749964)), _1749966) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749968)), _1749970), -(hAPP(hAPP(c_List_Ozip(_1749964, _1749968), hAPP(c_List_Orev(_1749964), _1749966)), hAPP(c_List_Orev(_1749968), _1749970)) = hAPP(c_List_Orev(tc_prod(_1749964, _1749968)), hAPP(hAPP(c_List_Ozip(_1749964, _1749968), _1749966), _1749970)))], (48110 ^ _782464) ^ [_1750145, _1750147] : [-(hAPP(c_List_Oset(_1750145), hAPP(c_List_Orev(_1750145), _1750147)) = hAPP(c_List_Oset(_1750145), _1750147))], (48112 ^ _782464) ^ [_1750185, _1750187] : [class_Groups_Ocomm__monoid__add(_1750185), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1750185), hAPP(c_List_Orev(_1750185), _1750187)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1750185), _1750187))], (48118 ^ _782464) ^ [_1750308, _1750310, _1750312] : [hAPP(c_List_Orev(_1750308), _1750310) = hAPP(c_List_Orev(_1750308), _1750312), -(_1750310 = _1750312)], (48124 ^ _782464) ^ [_1750403, _1750405, _1750407] : [_1750405 = _1750407, -(hAPP(c_List_Orev(_1750403), _1750405) = hAPP(c_List_Orev(_1750403), _1750407))], (48130 ^ _782464) ^ [_1750522, _1750524, _1750526] : [hAPP(c_List_Orev(_1750522), _1750524) = _1750526, -(_1750524 = hAPP(c_List_Orev(_1750522), _1750526))], (48136 ^ _782464) ^ [_1750617, _1750619, _1750621] : [_1750619 = hAPP(c_List_Orev(_1750617), _1750621), -(hAPP(c_List_Orev(_1750617), _1750619) = _1750621)], (48142 ^ _782464) ^ [_1750718, _1750720] : [-(hAPP(c_List_Orev(_1750718), hAPP(c_List_Orev(_1750718), _1750720)) = _1750720)], (48144 ^ _782464) ^ [_1750753, _1750755] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750753)), hAPP(c_List_Orev(_1750753), _1750755)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750753)), _1750755))], (48146 ^ _782464) ^ [_1750821, _1750823, _1750825, _1750827, _1750829] : [c_List_Olist__all2(_1750821, _1750823, _1750825, hAPP(c_List_Orev(_1750821), _1750827), _1750829), -(c_List_Olist__all2(_1750821, _1750823, _1750825, _1750827, hAPP(c_List_Orev(_1750823), _1750829)))], (48152 ^ _782464) ^ [_1750932, _1750934, _1750936, _1750938, _1750940] : [c_List_Olist__all2(_1750932, _1750934, _1750936, _1750938, hAPP(c_List_Orev(_1750934), _1750940)), -(c_List_Olist__all2(_1750932, _1750934, _1750936, hAPP(c_List_Orev(_1750932), _1750938), _1750940))], (48158 ^ _782464) ^ [_1751073, _1751075, _1751077, _1751079, _1751081] : [c_List_Olist__all2(_1751073, _1751075, _1751077, hAPP(c_List_Orev(_1751073), _1751079), hAPP(c_List_Orev(_1751075), _1751081)), -(c_List_Olist__all2(_1751073, _1751075, _1751077, _1751079, _1751081))], (48164 ^ _782464) ^ [_1751184, _1751186, _1751188, _1751190, _1751192] : [c_List_Olist__all2(_1751184, _1751186, _1751188, _1751190, _1751192), -(c_List_Olist__all2(_1751184, _1751186, _1751188, hAPP(c_List_Orev(_1751184), _1751190), hAPP(c_List_Orev(_1751186), _1751192)))], (48170 ^ _782464) ^ [_1751301, _1751303, _1751305, _1751307, _1751309] : [-(hAPP(c_List_Ofoldl(_1751301, _1751303, _1751305, _1751307), _1751309) = c_List_Ofoldr(_1751303, _1751301, hAPP(c_COMBC(_1751301, _1751303, _1751301), _1751305), hAPP(c_List_Orev(_1751303), _1751309), _1751307))], (48172 ^ _782464) ^ [_1751358, _1751360, _1751362, _1751364, _1751366] : [-(c_List_Ofoldr(_1751358, _1751360, _1751362, _1751364, _1751366) = hAPP(c_List_Ofoldl(_1751360, _1751358, hAPP(c_COMBC(_1751358, _1751360, _1751360), _1751362), _1751366), hAPP(c_List_Orev(_1751358), _1751364)))], (48174 ^ _782464) ^ [_1751415, _1751417, _1751419] : [-(hAPP(c_List_Orev(_1751415), hAPP(hAPP(c_List_Olist_OCons(_1751415), _1751417), _1751419)) = hAPP(hAPP(c_List_Oappend(_1751415), hAPP(c_List_Orev(_1751415), _1751419)), hAPP(hAPP(c_List_Olist_OCons(_1751415), _1751417), c_List_Olist_ONil(_1751415))))], (48176 ^ _782464) ^ [_1751499, _1751501, _1751503, _1751505] : [hAPP(c_List_Orev(_1751499), _1751501) = hAPP(hAPP(c_List_Olist_OCons(_1751499), _1751503), _1751505), -(_1751501 = hAPP(hAPP(c_List_Oappend(_1751499), hAPP(c_List_Orev(_1751499), _1751505)), hAPP(hAPP(c_List_Olist_OCons(_1751499), _1751503), c_List_Olist_ONil(_1751499))))], (48182 ^ _782464) ^ [_1751648, _1751650, _1751652, _1751654] : [_1751650 = hAPP(hAPP(c_List_Oappend(_1751648), hAPP(c_List_Orev(_1751648), _1751654)), hAPP(hAPP(c_List_Olist_OCons(_1751648), _1751652), c_List_Olist_ONil(_1751648))), -(hAPP(c_List_Orev(_1751648), _1751650) = hAPP(hAPP(c_List_Olist_OCons(_1751648), _1751652), _1751654))], (48188 ^ _782464) ^ [_1751799, _1751801] : [-(_1751799 = c_List_Olist_ONil(_1751801)), -(c_List_Olast(_1751801, hAPP(c_List_Orev(_1751801), _1751799)) = hAPP(c_List_Ohd(_1751801), _1751799))], (48194 ^ _782464) ^ [_1751846, _1751848] : [-(_1751846 = c_List_Olist_ONil(_1751848)), -(hAPP(c_List_Ohd(_1751848), hAPP(c_List_Orev(_1751848), _1751846)) = c_List_Olast(_1751848, _1751846))], (48200 ^ _782464) ^ [_1751897, _1751899] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1751897), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1751897))), c_List_Otranspose(_1751897, _1751899)))))], (48202 ^ _782464) ^ [_1751943, _1751945] : [-(hAPP(c_List_Orev(_1751943), _1751945) = hAPP(c_List_Ofoldl(tc_List_Olist(_1751943), _1751943, hAPP(c_COMBC(_1751943, tc_List_Olist(_1751943), tc_List_Olist(_1751943)), c_List_Olist_OCons(_1751943)), c_List_Olist_ONil(_1751943)), _1751945))], (48204 ^ _782464) ^ [_1751998, _1752000, _1752002] : [-(hAPP(c_List_Orev(_1751998), hAPP(hAPP(c_List_Odrop(_1751998), _1752000), _1752002)) = hAPP(hAPP(c_List_Otake(_1751998), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751998)), _1752002)), _1752000)), hAPP(c_List_Orev(_1751998), _1752002)))], (48206 ^ _782464) ^ [_1752064, _1752066, _1752068] : [-(hAPP(c_List_Orev(_1752064), hAPP(hAPP(c_List_Otake(_1752064), _1752066), _1752068)) = hAPP(hAPP(c_List_Odrop(_1752064), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752064)), _1752068)), _1752066)), hAPP(c_List_Orev(_1752064), _1752068)))], (48208 ^ _782464) ^ [_1752130, _1752132, _1752134] : [-(hAPP(c_List_Orotate(_1752130, _1752132), hAPP(c_List_Orev(_1752130), _1752134)) = hAPP(c_List_Orev(_1752130), hAPP(c_List_Orotate(_1752130, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752130)), _1752134)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1752132, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752130)), _1752134)))), _1752134)))], (48210 ^ _782464) ^ [_1752203, _1752205, _1752207] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752203), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752205)), _1752207))), -(hAPP(hAPP(c_List_Onth(_1752205), hAPP(c_List_Orev(_1752205), _1752207)), _1752203) = hAPP(hAPP(c_List_Onth(_1752205), _1752207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752205)), _1752207)), hAPP(c_Nat_OSuc, _1752203))))], (48216 ^ _782464) ^ [_1752380, _1752382, _1752384, _1752386] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752380), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752382)), _1752384))), -(hAPP(c_List_Orev(_1752382), hAPP(hAPP(c_List_Olist__update(_1752382, _1752384), _1752380), _1752386)) = hAPP(hAPP(c_List_Olist__update(_1752382, hAPP(c_List_Orev(_1752382), _1752384)), 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(_1752382)), _1752384)), _1752380)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1752386))], (48222 ^ _782464) ^ [_1752579, _1752581, _1752583, _1752585] : [class_Orderings_Olinorder(_1752579), c_List_Olinorder__class_Osorted(_1752579, hAPP(c_List_Orev(_1752579), _1752581)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1752583), _1752585)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752585), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752579)), _1752581))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1752579), hAPP(hAPP(c_List_Onth(_1752579), _1752581), _1752585)), hAPP(hAPP(c_List_Onth(_1752579), _1752581), _1752583))))], (48240 ^ _782464) ^ [_1752916, _1752918, _1752920] : [class_Orderings_Olinorder(_1752916), c_List_Olinorder__class_Osorted(_1752916, hAPP(c_List_Orev(_1752916), _1752918)), 48247 ^ _782464 : [(48248 ^ _782464) ^ [] : [_1752918 = c_List_Olist_ONil(_1752916), -(c_List_Ofoldr(_1752916, _1752916, c_Orderings_Oord__class_Omax(_1752916), _1752918, _1752920) = _1752920)], (48254 ^ _782464) ^ [] : [-(_1752918 = c_List_Olist_ONil(_1752916)), -(c_List_Ofoldr(_1752916, _1752916, c_Orderings_Oord__class_Omax(_1752916), _1752918, _1752920) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1752916), hAPP(hAPP(c_List_Onth(_1752916), _1752918), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1752920))]]], (48260 ^ _782464) ^ [_1753230, _1753232] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753230), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753230))), _1753232))), 48263 ^ _782464 : [(48264 ^ _782464) ^ [] : [_1753232 = c_List_Olist_ONil(tc_List_Olist(_1753230)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753230))), c_List_Otranspose(_1753230, _1753232)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48270 ^ _782464) ^ [] : [-(_1753232 = c_List_Olist_ONil(tc_List_Olist(_1753230))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753230))), c_List_Otranspose(_1753230, _1753232)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753230)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753230)), _1753232), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (48276 ^ _782464) ^ [_1753540, _1753542, _1753544] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753540), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753540))), _1753542))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753544), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753540))), _1753542))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753540))), hAPP(c_List_Ofilter(tc_List_Olist(_1753540), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1753540)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753544)), c_Nat_Osize__class_Osize(tc_List_Olist(_1753540)))), c_List_Otranspose(_1753540, _1753542))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753540)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753540)), _1753542), _1753544)))], (48286 ^ _782464) ^ [_1753849, _1753851] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753849), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753849))), _1753851))), -(c_List_Otranspose(_1753849, c_List_Otranspose(_1753849, _1753851)) = c_List_OtakeWhile(tc_List_Olist(_1753849), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1753849)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1753849), tc_List_Olist(_1753849), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1753849))), _1753851))], (48292 ^ _782464) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (48294 ^ _782464) ^ [_1754060, _1754062, _1754064] : [class_Orderings_Olinorder(_1754060), c_List_Olinorder__class_Osorted(_1754060, _1754062), -(c_List_Olinorder__class_Osorted(_1754060, c_List_OtakeWhile(_1754060, _1754064, _1754062)))], (48304 ^ _782464) ^ [_1754199, _1754201, _1754203] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754199)), c_List_OtakeWhile(_1754199, _1754201, _1754203))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754199)), _1754203))))], (48306 ^ _782464) ^ [_1754249, _1754251, _1754253, _1754255] : [hBOOL(hAPP(hAPP(c_member(_1754249), _1754251), hAPP(c_List_Oset(_1754249), c_List_OtakeWhile(_1754249, _1754253, _1754255)))), 48309 ^ _782464 : [(48310 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754249), _1754251), hAPP(c_List_Oset(_1754249), _1754255))))], (48312 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1754253, _1754251)))]]], (48324 ^ _782464) ^ [_1754630, _1754632, _1754634] : [48326 ^ _782464 : [(48327 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754630), 48325 ^ [_1754630, _1754632, _1754634]), hAPP(c_List_Oset(_1754630), _1754634))))], (48329 ^ _782464) ^ [] : [hBOOL(hAPP(_1754632, 48325 ^ [_1754630, _1754632, _1754634]))]], -(c_List_OtakeWhile(_1754630, _1754632, _1754634) = _1754634)], (48314 ^ _782464) ^ [_1754434, _1754436, _1754438] : [c_List_OtakeWhile(_1754434, _1754436, _1754438) = _1754438, 48317 ^ _782464 : [(48318 ^ _782464) ^ [_1754521] : [hBOOL(hAPP(hAPP(c_member(_1754434), _1754521), hAPP(c_List_Oset(_1754434), _1754438))), -(hBOOL(hAPP(_1754436, _1754521)))]]], (48333 ^ _782464) ^ [_1754818, _1754820, _1754822, _1754824, _1754826] : [-(hAPP(hAPP(c_List_Ozip(_1754818, _1754820), c_List_OtakeWhile(_1754818, _1754822, _1754824)), _1754826) = c_List_OtakeWhile(tc_prod(_1754818, _1754820), hAPP(c_Fun_Ocomp(_1754818, tc_HOL_Obool, tc_prod(_1754818, _1754820), _1754822), c_Product__Type_Ofst(_1754818, _1754820)), hAPP(hAPP(c_List_Ozip(_1754818, _1754820), _1754824), _1754826)))], (48335 ^ _782464) ^ [_1754892, _1754894, _1754896, _1754898, _1754900] : [-(hAPP(hAPP(c_List_Ozip(_1754892, _1754894), _1754896), c_List_OtakeWhile(_1754894, _1754898, _1754900)) = c_List_OtakeWhile(tc_prod(_1754892, _1754894), hAPP(c_Fun_Ocomp(_1754894, tc_HOL_Obool, tc_prod(_1754892, _1754894), _1754898), c_Product__Type_Osnd(_1754892, _1754894)), hAPP(hAPP(c_List_Ozip(_1754892, _1754894), _1754896), _1754900)))], (48337 ^ _782464) ^ [_1754966, _1754968, _1754970, _1754972, _1754974] : [-(c_List_OtakeWhile(_1754966, _1754968, hAPP(hAPP(c_List_Omap(_1754970, _1754966), _1754972), _1754974)) = hAPP(hAPP(c_List_Omap(_1754970, _1754966), _1754972), c_List_OtakeWhile(_1754970, hAPP(c_Fun_Ocomp(_1754966, tc_HOL_Obool, _1754970, _1754968), _1754972), _1754974)))], (48339 ^ _782464) ^ [_1755031, _1755033, _1755035] : [hBOOL(hAPP(c_List_Odistinct(_1755031), _1755033)), -(hBOOL(hAPP(c_List_Odistinct(_1755031), c_List_OtakeWhile(_1755031, _1755035, _1755033))))], (48345 ^ _782464) ^ [_1755130, _1755132, _1755134, _1755136, _1755138] : [-(hBOOL(hAPP(_1755130, _1755132))), -(c_List_OtakeWhile(_1755134, _1755130, hAPP(hAPP(c_List_Oappend(_1755134), _1755136), hAPP(hAPP(c_List_Olist_OCons(_1755134), _1755132), _1755138))) = c_List_OtakeWhile(_1755134, _1755130, _1755136))], (48351 ^ _782464) ^ [_1755213, _1755215, _1755217, _1755219] : [hBOOL(hAPP(_1755213, _1755215)), -(c_List_OtakeWhile(_1755217, _1755213, hAPP(hAPP(c_List_Olist_OCons(_1755217), _1755215), _1755219)) = hAPP(hAPP(c_List_Olist_OCons(_1755217), _1755215), c_List_OtakeWhile(_1755217, _1755213, _1755219)))], (48357 ^ _782464) ^ [_1755340, _1755342, _1755344, _1755346] : [-(hBOOL(hAPP(_1755340, _1755342))), -(c_List_OtakeWhile(_1755344, _1755340, hAPP(hAPP(c_List_Olist_OCons(_1755344), _1755342), _1755346)) = c_List_Olist_ONil(_1755344))], (48363 ^ _782464) ^ [_1755398, _1755400, _1755402] : [-(c_List_OtakeWhile(_1755398, _1755400, _1755402) = hAPP(hAPP(c_List_Otake(_1755398), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755398)), c_List_OtakeWhile(_1755398, _1755400, _1755402))), _1755402))], (48365 ^ _782464) ^ [_1755448, _1755450] : [-(c_List_OtakeWhile(_1755448, _1755450, c_List_Olist_ONil(_1755448)) = c_List_Olist_ONil(_1755448))], (48367 ^ _782464) ^ [_1755481] : [-(c_List_Oreturn__list(_1755481) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1755481))], (48369 ^ _782464) ^ [_1755509, _1755511, _1755513, _1755515, _1755517] : [hBOOL(hAPP(hAPP(c_member(_1755509), _1755511), hAPP(c_List_Oset(_1755509), _1755513))), -(hBOOL(hAPP(_1755515, _1755511))), -(c_List_OtakeWhile(_1755509, _1755515, hAPP(hAPP(c_List_Oappend(_1755509), _1755513), _1755517)) = c_List_OtakeWhile(_1755509, _1755515, _1755513))], (48379 ^ _782464) ^ [_1755667, _1755669, _1755671, _1755673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755667), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755669)), c_List_OtakeWhile(_1755669, _1755671, _1755673)))), -(hAPP(hAPP(c_List_Onth(_1755669), c_List_OtakeWhile(_1755669, _1755671, _1755673)), _1755667) = hAPP(hAPP(c_List_Onth(_1755669), _1755673), _1755667))], (48385 ^ _782464) ^ [_1755820, _1755822, _1755824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755820)), c_List_OtakeWhile(_1755820, _1755822, _1755824))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755820)), _1755824))), hBOOL(hAPP(_1755822, hAPP(hAPP(c_List_Onth(_1755820), _1755824), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755820)), c_List_OtakeWhile(_1755820, _1755822, _1755824)))))], (48391 ^ _782464) ^ [_1755987, _1755989] : [-(_1755987 = c_List_Olist_ONil(_1755989)), hBOOL(hAPP(c_List_Odistinct(_1755989), _1755987)), -(c_List_OtakeWhile(_1755989, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1755989), c_fNot), hAPP(hAPP(c_COMBC(_1755989, _1755989, tc_HOL_Obool), c_fequal), c_List_Olast(_1755989, _1755987))), _1755987) = c_List_Obutlast(_1755989, _1755987))], (48401 ^ _782464) ^ [_1756184, _1756186, _1756188, _1756190, _1756192] : [class_Orderings_Olinorder(_1756184), c_List_Olinorder__class_Osorted(_1756184, hAPP(c_List_Orev(_1756184), hAPP(hAPP(c_List_Omap(_1756186, _1756184), _1756188), _1756190))), -(hAPP(c_List_Ofilter(_1756186, hAPP(hAPP(c_COMBB(_1756184, tc_HOL_Obool, _1756186), hAPP(c_Orderings_Oord__class_Oless(_1756184), _1756192)), _1756188)), _1756190) = c_List_OtakeWhile(_1756186, hAPP(hAPP(c_COMBB(_1756184, tc_HOL_Obool, _1756186), hAPP(c_Orderings_Oord__class_Oless(_1756184), _1756192)), _1756188), _1756190))], (48411 ^ _782464) ^ [_1756431] : [c_List_Onat__list(_1756431), -(c_List_Oembed__list(c_List_Oreturn__list(_1756431)) = _1756431)], (48417 ^ _782464) ^ [_1756512, _1756514] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1756512), _1756514) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1756512)), c_List_Oembed__list(_1756514))))], (48419 ^ _782464) ^ [_1756555] : [-(c_List_Oembed__list(_1756555) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1756555))], (48421 ^ _782464) ^ [_1756583, _1756585, _1756587] : [hBOOL(hAPP(c_List_Odistinct(_1756583), _1756585)), hBOOL(hAPP(hAPP(c_member(_1756583), _1756587), hAPP(c_List_Oset(_1756583), _1756585))), -(c_List_OtakeWhile(_1756583, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756583), c_fNot), hAPP(hAPP(c_COMBC(_1756583, _1756583, tc_HOL_Obool), c_fequal), _1756587)), hAPP(c_List_Orev(_1756583), _1756585)) = hAPP(c_List_Orev(_1756583), hAPP(c_List_Otl(_1756583), c_List_OdropWhile(_1756583, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756583), c_fNot), hAPP(hAPP(c_COMBC(_1756583, _1756583, tc_HOL_Obool), c_fequal), _1756587)), _1756585))))], (48431 ^ _782464) ^ [_1756874, _1756876, _1756878] : [hBOOL(hAPP(c_List_Odistinct(_1756874), _1756876)), hBOOL(hAPP(hAPP(c_member(_1756874), _1756878), hAPP(c_List_Oset(_1756874), _1756876))), -(c_List_OdropWhile(_1756874, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756874), c_fNot), hAPP(hAPP(c_COMBC(_1756874, _1756874, tc_HOL_Obool), c_fequal), _1756878)), hAPP(c_List_Orev(_1756874), _1756876)) = hAPP(hAPP(c_List_Olist_OCons(_1756874), _1756878), hAPP(c_List_Orev(_1756874), c_List_OtakeWhile(_1756874, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756874), c_fNot), hAPP(hAPP(c_COMBC(_1756874, _1756874, tc_HOL_Obool), c_fequal), _1756878)), _1756876))))], (48441 ^ _782464) ^ [_1757171, _1757173, _1757175] : [-(hAPP(hAPP(c_List_Oappend(_1757171), c_List_OtakeWhile(_1757171, _1757173, _1757175)), c_List_OdropWhile(_1757171, _1757173, _1757175)) = _1757175)], (48443 ^ _782464) ^ [_1757214, _1757216, _1757218] : [class_Orderings_Olinorder(_1757214), c_List_Olinorder__class_Osorted(_1757214, _1757216), -(c_List_Olinorder__class_Osorted(_1757214, c_List_OdropWhile(_1757214, _1757218, _1757216)))], (48453 ^ _782464) ^ [_1757352, _1757354, _1757356] : [-(c_List_OdropWhile(_1757352, _1757354, _1757356) = c_List_Olist_ONil(_1757352)), hBOOL(hAPP(_1757354, hAPP(c_List_Ohd(_1757352), c_List_OdropWhile(_1757352, _1757354, _1757356))))], (48459 ^ _782464) ^ [_1757458, _1757460, _1757462] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757458)), c_List_OdropWhile(_1757458, _1757460, _1757462))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757458)), _1757462))))], (48471 ^ _782464) ^ [_1757726, _1757728, _1757730] : [48473 ^ _782464 : [(48474 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757726), 48472 ^ [_1757726, _1757728, _1757730]), hAPP(c_List_Oset(_1757726), _1757730))))], (48476 ^ _782464) ^ [] : [hBOOL(hAPP(_1757728, 48472 ^ [_1757726, _1757728, _1757730]))]], -(c_List_OdropWhile(_1757726, _1757728, _1757730) = c_List_Olist_ONil(_1757726))], (48461 ^ _782464) ^ [_1757526, _1757528, _1757530] : [c_List_OdropWhile(_1757526, _1757528, _1757530) = c_List_Olist_ONil(_1757526), 48464 ^ _782464 : [(48465 ^ _782464) ^ [_1757617] : [hBOOL(hAPP(hAPP(c_member(_1757526), _1757617), hAPP(c_List_Oset(_1757526), _1757530))), -(hBOOL(hAPP(_1757528, _1757617)))]]], (48480 ^ _782464) ^ [_1757918, _1757920, _1757922] : [hBOOL(hAPP(c_List_Odistinct(_1757918), _1757920)), -(hBOOL(hAPP(c_List_Odistinct(_1757918), c_List_OdropWhile(_1757918, _1757922, _1757920))))], (48486 ^ _782464) ^ [_1758036, _1758038, _1758040, _1758042] : [hBOOL(hAPP(_1758036, _1758038)), -(c_List_OdropWhile(_1758040, _1758036, hAPP(hAPP(c_List_Olist_OCons(_1758040), _1758038), _1758042)) = c_List_OdropWhile(_1758040, _1758036, _1758042))], (48492 ^ _782464) ^ [_1758147, _1758149, _1758151, _1758153] : [-(hBOOL(hAPP(_1758147, _1758149))), -(c_List_OdropWhile(_1758151, _1758147, hAPP(hAPP(c_List_Olist_OCons(_1758151), _1758149), _1758153)) = hAPP(hAPP(c_List_Olist_OCons(_1758151), _1758149), _1758153))], (48498 ^ _782464) ^ [_1758211, _1758213] : [-(c_List_OdropWhile(_1758211, _1758213, c_List_Olist_ONil(_1758211)) = c_List_Olist_ONil(_1758211))], (48500 ^ _782464) ^ [_1758244, _1758246, _1758248, _1758250, _1758252] : [-(c_List_OdropWhile(_1758244, _1758246, hAPP(hAPP(c_List_Omap(_1758248, _1758244), _1758250), _1758252)) = hAPP(hAPP(c_List_Omap(_1758248, _1758244), _1758250), c_List_OdropWhile(_1758248, hAPP(c_Fun_Ocomp(_1758244, tc_HOL_Obool, _1758248, _1758246), _1758250), _1758252)))], (48502 ^ _782464) ^ [_1758309, _1758311, _1758313, _1758315, _1758317] : [hBOOL(hAPP(hAPP(c_member(_1758309), _1758311), hAPP(c_List_Oset(_1758309), _1758313))), -(hBOOL(hAPP(_1758315, _1758311))), -(c_List_OdropWhile(_1758309, _1758315, hAPP(hAPP(c_List_Oappend(_1758309), _1758313), _1758317)) = hAPP(hAPP(c_List_Oappend(_1758309), c_List_OdropWhile(_1758309, _1758315, _1758313)), _1758317))], (48512 ^ _782464) ^ [_1758507, _1758509, _1758511, _1758513, _1758515] : [c_List_OdropWhile(_1758507, _1758509, _1758511) = hAPP(hAPP(c_List_Olist_OCons(_1758507), _1758513), _1758515), 48515 ^ _782464 : [(48516 ^ _782464) ^ [] : [-(_1758511 = hAPP(hAPP(c_List_Oappend(_1758507), c_List_OtakeWhile(_1758507, _1758509, _1758511)), hAPP(hAPP(c_List_Olist_OCons(_1758507), _1758513), _1758515)))], (48518 ^ _782464) ^ [] : [hBOOL(hAPP(_1758509, _1758513))]]], (48520 ^ _782464) ^ [_1758688, _1758690, _1758692, _1758694, _1758696] : [-(c_List_OdropWhile(_1758688, _1758690, _1758692) = hAPP(hAPP(c_List_Olist_OCons(_1758688), _1758694), _1758696)), _1758692 = hAPP(hAPP(c_List_Oappend(_1758688), c_List_OtakeWhile(_1758688, _1758690, _1758692)), hAPP(hAPP(c_List_Olist_OCons(_1758688), _1758694), _1758696)), -(hBOOL(hAPP(_1758690, _1758694)))], (48530 ^ _782464) ^ [_1758902, _1758904, _1758906] : [-(c_List_OdropWhile(_1758902, _1758904, _1758906) = hAPP(hAPP(c_List_Odrop(_1758902), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758902)), c_List_OtakeWhile(_1758902, _1758904, _1758906))), _1758906))], (48532 ^ _782464) ^ [_1758952, _1758954, _1758956, _1758958] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758952), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758954)), c_List_OdropWhile(_1758954, _1758956, _1758958)))), -(hAPP(hAPP(c_List_Onth(_1758954), c_List_OdropWhile(_1758954, _1758956, _1758958)), _1758952) = hAPP(hAPP(c_List_Onth(_1758954), _1758958), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758952), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758954)), c_List_OtakeWhile(_1758954, _1758956, _1758958)))))], (48538 ^ _782464) ^ [_1759139, _1759141, _1759143, _1759145, _1759147] : [class_Groups_Omonoid__add(_1759139), 48544 ^ _782464 : [(48545 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759141), 48543 ^ [_1759139, _1759141, _1759143, _1759145, _1759147]), hAPP(c_List_Oset(_1759141), _1759143))))], (48547 ^ _782464) ^ [] : [hBOOL(hAPP(_1759145, 48543 ^ [_1759139, _1759141, _1759143, _1759145, _1759147]))], (48549 ^ _782464) ^ [] : [hAPP(_1759147, 48543 ^ [_1759139, _1759141, _1759143, _1759145, _1759147]) = c_Groups_Ozero__class_Ozero(_1759139)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1759139), hAPP(hAPP(c_List_Omap(_1759141, _1759139), _1759147), hAPP(c_List_Ofilter(_1759141, _1759145), _1759143))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1759139), hAPP(hAPP(c_List_Omap(_1759141, _1759139), _1759147), _1759143)))], (48553 ^ _782464) ^ [_1759530, _1759532] : [class_Orderings_Olinorder(_1759530), 48560 ^ _782464 : [(48561 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48558 ^ [_1759530, _1759532]), 48559 ^ [_1759530, _1759532])))], (48563 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48559 ^ [_1759530, _1759532]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759530)), _1759532))))], (48565 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759530), hAPP(hAPP(c_List_Onth(_1759530), _1759532), 48558 ^ [_1759530, _1759532])), hAPP(hAPP(c_List_Onth(_1759530), _1759532), 48559 ^ [_1759530, _1759532])))]], -(c_List_Olinorder__class_Osorted(_1759530, _1759532))], (48569 ^ _782464) ^ [_1759901, _1759903, _1759905] : [48571 ^ _782464 : [(48572 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759901), 48570 ^ [_1759901, _1759903, _1759905]), hAPP(c_List_Oset(_1759901), c_List_OdropWhile(_1759901, _1759903, _1759905)))))], (48574 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1759903, 48570 ^ [_1759901, _1759903, _1759905])))]], -(c_List_OtakeWhile(_1759901, _1759903, _1759905) = hAPP(c_List_Ofilter(_1759901, _1759903), _1759905))], (48578 ^ _782464) ^ [_1760022, _1760024, _1760026, _1760028] : [48580 ^ _782464 : [(48581 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48579 ^ [_1760022, _1760024, _1760026, _1760028]), _1760022)))], (48583 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48579 ^ [_1760022, _1760024, _1760026, _1760028]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760024)), _1760026))))], (48585 ^ _782464) ^ [] : [hBOOL(hAPP(_1760028, hAPP(hAPP(c_List_Onth(_1760024), _1760026), 48579 ^ [_1760022, _1760024, _1760026, _1760028])))]], 48588 ^ _782464 : [(48589 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1760022), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760024)), _1760026))))], (48591 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1760028, hAPP(hAPP(c_List_Onth(_1760024), _1760026), _1760022))))]], -(c_List_OtakeWhile(_1760024, _1760028, _1760026) = hAPP(hAPP(c_List_Otake(_1760024), _1760022), _1760026))], (48595 ^ _782464) ^ [_1760426, _1760428, _1760430, _1760432] : [48597 ^ _782464 : [(48598 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48596 ^ [_1760426, _1760428, _1760430, _1760432]), _1760426)))], (48600 ^ _782464) ^ [] : [hBOOL(hAPP(_1760428, hAPP(hAPP(c_List_Onth(_1760430), _1760432), 48596 ^ [_1760426, _1760428, _1760430, _1760432])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760430)), _1760432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760426), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760430)), c_List_OtakeWhile(_1760430, _1760428, _1760432)))))], (48608 ^ _782464) ^ [_1760734, _1760736] : [class_Orderings_Olinorder(_1760734), 48611 ^ _782464 : [(48612 ^ _782464) ^ [] : [c_List_Olinorder__class_Osorted(_1760734, _1760736), -(_1760736 = c_List_Olist_ONil(_1760734)), 48621 ^ _782464 : [(48622 ^ _782464) ^ [] : [-(_1760736 = hAPP(hAPP(c_List_Olist_OCons(_1760734), 48620 ^ [_1760734, _1760736]), 48619 ^ [_1760734, _1760736]))], (48630 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760734, 48619 ^ [_1760734, _1760736]))], (48624 ^ _782464) ^ [_1761068] : [hBOOL(hAPP(hAPP(c_member(_1760734), _1761068), hAPP(c_List_Oset(_1760734), 48619 ^ [_1760734, _1760736]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760734), 48620 ^ [_1760734, _1760736]), _1761068)))]]], (48632 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760734, _1760736)), 48633 ^ _782464 : [(48634 ^ _782464) ^ [] : [_1760736 = c_List_Olist_ONil(_1760734)], (48636 ^ _782464) ^ [_1761294, _1761296] : [_1760736 = hAPP(hAPP(c_List_Olist_OCons(_1760734), _1761294), _1761296), 48642 ^ _782464 : [(48643 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760734), 48641 ^ [_1760734, _1760736, _1761294, _1761296]), hAPP(c_List_Oset(_1760734), _1761296))))], (48645 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760734), _1761294), 48641 ^ [_1760734, _1760736, _1761294, _1761296]))]], c_List_Olinorder__class_Osorted(_1760734, _1761296)]]]]], (48651 ^ _782464) ^ [_1761603, _1761605, _1761607, _1761609, _1761611] : [c_Fun_Oinj__on(_1761603, _1761605, _1761607, hAPP(hAPP(c_Set_Oinsert(_1761603), _1761609), hAPP(c_List_Oset(_1761603), _1761611))), -(hAPP(hAPP(c_List_Omap(_1761603, _1761605), _1761607), hAPP(c_List_OremoveAll(_1761603, _1761609), _1761611)) = hAPP(c_List_OremoveAll(_1761605, hAPP(_1761607, _1761609)), hAPP(hAPP(c_List_Omap(_1761603, _1761605), _1761607), _1761611)))], (48657 ^ _782464) ^ [_1761778, _1761780, _1761782] : [-(hBOOL(hAPP(hAPP(c_member(_1761778), _1761780), hAPP(c_List_Oset(_1761778), _1761782)))), -(c_List_Oinsert(_1761778, _1761780, _1761782) = hAPP(hAPP(c_List_Olist_OCons(_1761778), _1761780), _1761782))], (48663 ^ _782464) ^ [_1761840, _1761842, _1761844, _1761846] : [-(hAPP(c_List_OremoveAll(_1761840, _1761842), hAPP(hAPP(c_List_Oappend(_1761840), _1761844), _1761846)) = hAPP(hAPP(c_List_Oappend(_1761840), hAPP(c_List_OremoveAll(_1761840, _1761842), _1761844)), hAPP(c_List_OremoveAll(_1761840, _1761842), _1761846)))], (48665 ^ _782464) ^ [_1761903, _1761905, _1761907] : [-(c_List_Oinsert(_1761903, _1761905, c_List_Oremdups(_1761903, _1761907)) = c_List_Oremdups(_1761903, c_List_Oinsert(_1761903, _1761905, _1761907)))], (48667 ^ _782464) ^ [_1761944, _1761946] : [-(c_List_OremoveAll(_1761944, _1761946) = c_List_Ofilter(_1761944, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1761944), c_fNot), hAPP(c_fequal, _1761946))))], (48669 ^ _782464) ^ [_1761984, _1761986, _1761988, _1761990] : [-(hBOOL(hAPP(_1761984, _1761986))), -(hAPP(c_List_OremoveAll(_1761988, _1761986), hAPP(c_List_Ofilter(_1761988, _1761984), _1761990)) = hAPP(c_List_Ofilter(_1761988, _1761984), _1761990))], (48675 ^ _782464) ^ [_1762044, _1762046, _1762048] : [hBOOL(hAPP(c_List_Odistinct(_1762044), _1762046)), -(hBOOL(hAPP(c_List_Odistinct(_1762044), c_List_Oinsert(_1762044, _1762048, _1762046))))], (48681 ^ _782464) ^ [_1762147, _1762149, _1762151] : [hBOOL(hAPP(c_List_Odistinct(_1762147), _1762149)), -(hBOOL(hAPP(c_List_Odistinct(_1762147), hAPP(c_List_OremoveAll(_1762147, _1762151), _1762149))))], (48687 ^ _782464) ^ [_1762269, _1762271, _1762273, _1762275] : [_1762269 = _1762271, -(hAPP(c_List_OremoveAll(_1762273, _1762269), hAPP(hAPP(c_List_Olist_OCons(_1762273), _1762271), _1762275)) = hAPP(c_List_OremoveAll(_1762273, _1762269), _1762275))], (48693 ^ _782464) ^ [_1762384, _1762386, _1762388, _1762390] : [-(_1762384 = _1762386), -(hAPP(c_List_OremoveAll(_1762388, _1762384), hAPP(hAPP(c_List_Olist_OCons(_1762388), _1762386), _1762390)) = hAPP(hAPP(c_List_Olist_OCons(_1762388), _1762386), hAPP(c_List_OremoveAll(_1762388, _1762384), _1762390)))], (48699 ^ _782464) ^ [_1762454, _1762456] : [-(hAPP(c_List_OremoveAll(_1762454, _1762456), c_List_Olist_ONil(_1762454)) = c_List_Olist_ONil(_1762454))], (48701 ^ _782464) ^ [_1762485, _1762487, _1762489] : [-(hBOOL(hAPP(hAPP(c_member(_1762485), _1762487), hAPP(c_List_Oset(_1762485), _1762489)))), -(hAPP(c_List_OremoveAll(_1762485, _1762487), _1762489) = _1762489)], (48707 ^ _782464) ^ [_1762541, _1762543, _1762545] : [hBOOL(hAPP(c_List_Odistinct(_1762541), _1762543)), -(c_List_Oremove1(_1762541, _1762545, _1762543) = hAPP(c_List_OremoveAll(_1762541, _1762545), _1762543))], (48713 ^ _782464) ^ [_1762648, _1762650, _1762652] : [hBOOL(hAPP(hAPP(c_member(_1762648), _1762650), hAPP(c_List_Oset(_1762648), _1762652))), -(c_List_Oinsert(_1762648, _1762650, _1762652) = _1762652)], (48719 ^ _782464) ^ [_1762759, _1762761, _1762763] : [-(hAPP(c_List_Oset(_1762759), c_List_Oinsert(_1762759, _1762761, _1762763)) = hAPP(hAPP(c_Set_Oinsert(_1762759), _1762761), hAPP(c_List_Oset(_1762759), _1762763)))], (48721 ^ _782464) ^ [_1762808, _1762810] : [-(c_List_Oinsert(_1762808, _1762810, c_List_Olist_ONil(_1762808)) = hAPP(hAPP(c_List_Olist_OCons(_1762808), _1762810), c_List_Olist_ONil(_1762808)))], (48723 ^ _782464) ^ [_1762849, _1762851, _1762853, _1762855, _1762857] : [c_Fun_Oinj__on(_1762849, _1762851, _1762853, c_Orderings_Otop__class_Otop(tc_fun(_1762849, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1762849, _1762851), _1762853), hAPP(c_List_OremoveAll(_1762849, _1762855), _1762857)) = hAPP(c_List_OremoveAll(_1762851, hAPP(_1762853, _1762855)), hAPP(hAPP(c_List_Omap(_1762849, _1762851), _1762853), _1762857)))], (48729 ^ _782464) ^ [_1763012, _1763014, _1763016] : [-(hAPP(c_List_Oset(_1763012), hAPP(c_List_OremoveAll(_1763012, _1763014), _1763016)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1763012, tc_HOL_Obool)), hAPP(c_List_Oset(_1763012), _1763016)), hAPP(hAPP(c_Set_Oinsert(_1763012), _1763014), c_Orderings_Obot__class_Obot(tc_fun(_1763012, tc_HOL_Obool)))))], (48731 ^ _782464) ^ [_1763091, _1763093, _1763095] : [hBOOL(hAPP(hAPP(c_member(_1763091), _1763093), hAPP(c_List_Oset(_1763091), _1763095))), -(c_List_Oinsert(_1763091, _1763093, _1763095) = _1763095)], (48737 ^ _782464) ^ [_1763196, _1763198, _1763200] : [-(hBOOL(hAPP(hAPP(c_member(_1763196), _1763198), hAPP(c_List_Oset(_1763196), _1763200)))), -(c_List_Oinsert(_1763196, _1763198, _1763200) = hAPP(hAPP(c_List_Olist_OCons(_1763196), _1763198), _1763200))], (48743 ^ _782464) ^ [_1763260, _1763262, _1763264, _1763266] : [-(c_List_Omaps(_1763260, _1763262, _1763264, _1763266) = c_List_Oconcat(_1763262, hAPP(hAPP(c_List_Omap(_1763260, tc_List_Olist(_1763262)), _1763264), _1763266)))], (48745 ^ _782464) ^ [_1763308, _1763310, _1763312, _1763314] : [-(c_List_Oconcat(_1763308, hAPP(hAPP(c_List_Omap(_1763310, tc_List_Olist(_1763308)), _1763312), _1763314)) = c_List_Omaps(_1763310, _1763308, _1763312, _1763314))], (48747 ^ _782464) ^ [_1763356, _1763358, _1763360] : [-(c_List_Omaps(_1763356, _1763358, _1763360, c_List_Olist_ONil(_1763356)) = c_List_Olist_ONil(_1763358))], (48749 ^ _782464) ^ [_1763392, _1763394, _1763396, _1763398, _1763400] : [-(c_List_Omaps(_1763392, _1763394, _1763396, hAPP(hAPP(c_List_Olist_OCons(_1763392), _1763398), _1763400)) = hAPP(hAPP(c_List_Oappend(_1763394), hAPP(_1763396, _1763398)), c_List_Omaps(_1763392, _1763394, _1763396, _1763400)))], (48751 ^ _782464) ^ [_1763452, _1763454] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1763452)), _1763454)), 48757 ^ _782464 : [(48758 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763452)), 48756 ^ [_1763452, _1763454]), hAPP(c_List_Oset(tc_List_Olist(_1763452)), _1763454))))], (48760 ^ _782464) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1763452), 48756 ^ [_1763452, _1763454]))]], 48764 ^ _782464 : [(48765 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763452)), 48763 ^ [_1763452, _1763454]), hAPP(c_List_Oset(tc_List_Olist(_1763452)), _1763454))))], (48768 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763452)), 48766 ^ [_1763452, _1763454]), hAPP(c_List_Oset(tc_List_Olist(_1763452)), _1763454))))], (48770 ^ _782464) ^ [] : [48763 ^ [_1763452, _1763454] = 48766 ^ [_1763452, _1763454]], (48772 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1763452, tc_HOL_Obool)), hAPP(c_List_Oset(_1763452), 48763 ^ [_1763452, _1763454])), hAPP(c_List_Oset(_1763452), 48766 ^ [_1763452, _1763454])) = c_Orderings_Obot__class_Obot(tc_fun(_1763452, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1763452), c_List_Oconcat(_1763452, _1763454))))], (48776 ^ _782464) ^ [_1764169, _1764171, _1764173, _1764175, _1764177] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1764169, _1764171)), hAPP(_1764169, _1764173))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764175, _1764175)), hAPP(hAPP(c_Product__Type_OPair(_1764175, _1764175), _1764171), _1764173)), c_List_Omeasures(_1764175, _1764177))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764175, _1764175)), hAPP(hAPP(c_Product__Type_OPair(_1764175, _1764175), _1764171), _1764173)), c_List_Omeasures(_1764175, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764175, tc_Nat_Onat)), _1764169), _1764177)))))], (48786 ^ _782464) ^ [_1764442, _1764444] : [-(c_Wellfounded_Owf(_1764442, c_List_Omeasures(_1764442, _1764444)))], (48788 ^ _782464) ^ [_1764485, _1764487, _1764489] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764485, _1764485)), hAPP(hAPP(c_Product__Type_OPair(_1764485, _1764485), _1764487), _1764489)), c_List_Omeasures(_1764485, c_List_Olist_ONil(tc_fun(_1764485, tc_Nat_Onat)))))], (48790 ^ _782464) ^ [_1764539, _1764541] : [-(c_List_Omeasures(_1764539, _1764541) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1764539), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1764539, tc_List_Olist(tc_fun(_1764539, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764539, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1764539, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1764539), c_List_Omap(tc_fun(_1764539, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1764539, tc_Nat_Onat), _1764539, tc_Nat_Onat), c_COMBI(tc_fun(_1764539, tc_Nat_Onat))))), _1764541)))], (48792 ^ _782464) ^ [_1764660, _1764662, _1764664, _1764666, _1764668] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764660, _1764660)), hAPP(hAPP(c_Product__Type_OPair(_1764660, _1764660), _1764662), _1764664)), c_List_Omeasures(_1764660, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764660, tc_Nat_Onat)), _1764666), _1764668)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764666, _1764662)), hAPP(_1764666, _1764664)))), 48799 ^ _782464 : [(48800 ^ _782464) ^ [] : [-(hAPP(_1764666, _1764662) = hAPP(_1764666, _1764664))], (48802 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764660, _1764660)), hAPP(hAPP(c_Product__Type_OPair(_1764660, _1764660), _1764662), _1764664)), c_List_Omeasures(_1764660, _1764668))))]]], (48804 ^ _782464) ^ [_1764939, _1764941, _1764943, _1764945, _1764947] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764939, _1764939)), hAPP(hAPP(c_Product__Type_OPair(_1764939, _1764939), _1764941), _1764943)), c_List_Omeasures(_1764939, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764939, tc_Nat_Onat)), _1764945), _1764947))))), 48805 ^ _782464 : [(48806 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764945, _1764941)), hAPP(_1764945, _1764943)))], (48808 ^ _782464) ^ [] : [hAPP(_1764945, _1764941) = hAPP(_1764945, _1764943), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764939, _1764939)), hAPP(hAPP(c_Product__Type_OPair(_1764939, _1764939), _1764941), _1764943)), c_List_Omeasures(_1764939, _1764947)))]]], (48816 ^ _782464) ^ [_1765262, _1765264, _1765266, _1765268, _1765270] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1765262, _1765264)), hAPP(_1765262, _1765266))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765268, _1765268)), hAPP(hAPP(c_Product__Type_OPair(_1765268, _1765268), _1765264), _1765266)), c_List_Omeasures(_1765268, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1765268, tc_Nat_Onat)), _1765262), _1765270)))))], (48822 ^ _782464) ^ [_1765433, _1765435, _1765437, _1765439, _1765441, _1765443, _1765445, _1765447] : [48824 ^ _782464 : [(48825 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765433), 48823 ^ [_1765433, _1765435, _1765437, _1765439, _1765441, _1765443, _1765445, _1765447]), hAPP(c_List_Oset(_1765433), _1765435))))], (48827 ^ _782464) ^ [] : [hAPP(c_Fun_Ocomp(_1765437, _1765437, _1765439, hAPP(_1765441, 48823 ^ [_1765433, _1765435, _1765437, _1765439, _1765441, _1765443, _1765445, _1765447])), _1765443) = hAPP(c_Fun_Ocomp(_1765439, _1765437, _1765439, _1765443), hAPP(_1765445, 48823 ^ [_1765433, _1765435, _1765437, _1765439, _1765441, _1765443, _1765445, _1765447]))]], -(hAPP(c_List_Ofoldl(_1765437, _1765433, hAPP(c_COMBC(_1765433, _1765437, _1765437), _1765441), hAPP(_1765443, _1765447)), _1765435) = hAPP(_1765443, hAPP(c_List_Ofoldl(_1765439, _1765433, hAPP(c_COMBC(_1765433, _1765439, _1765439), _1765445), _1765447), _1765435)))], (48831 ^ _782464) ^ [_1765802, _1765804, _1765806, _1765808, _1765810] : [48832 ^ _782464 : [(48833 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765802)), hAPP(hAPP(c_List_Otake(_1765802), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765802)), _1765804)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765806)), _1765808))), _1765804)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765806)), hAPP(hAPP(c_List_Otake(_1765806), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765802)), _1765804)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765806)), _1765808))), _1765808)))], (48835 ^ _782464) ^ [] : [hBOOL(hAPP(_1765810, hAPP(hAPP(c_List_Ozip(_1765802, _1765806), hAPP(hAPP(c_List_Otake(_1765802), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765802)), _1765804)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765806)), _1765808))), _1765804)), hAPP(hAPP(c_List_Otake(_1765806), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765802)), _1765804)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765806)), _1765808))), _1765808))))]], -(hBOOL(hAPP(_1765810, hAPP(hAPP(c_List_Ozip(_1765802, _1765806), _1765804), _1765808))))], (48839 ^ _782464) ^ [_1766214, _1766216, _1766218, _1766220] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1766214, _1766216, _1766218, _1766220) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1766214, _1766216), _1766218), _1766220)))], (48841 ^ _782464) ^ [_1766259, _1766261, _1766263, _1766265] : [48843 ^ _782464 : [(48844 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766259), 48842 ^ [_1766259, _1766261, _1766263, _1766265]), hAPP(c_List_Oset(_1766259), _1766261))))], (48846 ^ _782464) ^ [] : [hBOOL(hAPP(_1766263, 48842 ^ [_1766259, _1766261, _1766263, _1766265]))]], -(c_List_OdropWhile(_1766259, _1766263, hAPP(hAPP(c_List_Oappend(_1766259), _1766261), _1766265)) = c_List_OdropWhile(_1766259, _1766263, _1766265))], (48850 ^ _782464) ^ [_1766477, _1766479, _1766481, _1766483, _1766485] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766477)), _1766479) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766481)), _1766483), 48856 ^ _782464 : [(48857 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48855 ^ [_1766477, _1766479, _1766481, _1766483, _1766485]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766477)), _1766479))))], (48859 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1766485, hAPP(hAPP(c_List_Onth(_1766477), _1766479), 48855 ^ [_1766477, _1766479, _1766481, _1766483, _1766485])), hAPP(hAPP(c_List_Onth(_1766481), _1766483), 48855 ^ [_1766477, _1766479, _1766481, _1766483, _1766485])))]], -(c_List_Olist__all2(_1766477, _1766481, _1766485, _1766479, _1766483))], (48863 ^ _782464) ^ [_1766835, _1766837] : [class_Orderings_Olinorder(_1766835), hBOOL(hAPP(c_Finite__Set_Ofinite(_1766835), _1766837)), 48871 ^ _782464 : [(48872 ^ _782464) ^ [] : [-(hAPP(c_List_Oset(_1766835), 48870 ^ [_1766835, _1766837]) = _1766837)], (48874 ^ _782464) ^ [] : [-(c_List_Olinorder__class_Osorted(_1766835, 48870 ^ [_1766835, _1766837]))], (48876 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1766835), 48870 ^ [_1766835, _1766837])))], (48878 ^ _782464) ^ [_1767161] : [-(_1767161 = 48870 ^ [_1766835, _1766837]), hAPP(c_List_Oset(_1766835), _1767161) = _1766837, c_List_Olinorder__class_Osorted(_1766835, _1767161), hBOOL(hAPP(c_List_Odistinct(_1766835), _1767161))]]], (48892 ^ _782464) ^ [_1767392, _1767394, _1767396, _1767398] : [48894 ^ _782464 : [(48895 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767392), 48893 ^ [_1767392, _1767394, _1767396, _1767398]), hAPP(c_List_Oset(_1767392), _1767394))))], (48897 ^ _782464) ^ [] : [hBOOL(hAPP(_1767396, 48893 ^ [_1767392, _1767394, _1767396, _1767398]))]], -(c_List_OtakeWhile(_1767392, _1767396, hAPP(hAPP(c_List_Oappend(_1767392), _1767394), _1767398)) = hAPP(hAPP(c_List_Oappend(_1767392), _1767394), c_List_OtakeWhile(_1767392, _1767396, _1767398)))], (48901 ^ _782464) ^ [_1767626, _1767628, _1767630, _1767632, _1767634] : [class_Orderings_Olinorder(_1767626), 48907 ^ _782464 : [(48908 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767628), 48906 ^ [_1767626, _1767628, _1767630, _1767632, _1767634]), hAPP(c_List_Oset(_1767628), _1767630))))], (48910 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767626), hAPP(_1767632, _1767634)), hAPP(_1767632, 48906 ^ [_1767626, _1767628, _1767630, _1767632, _1767634])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1767628, _1767626, _1767632), _1767634), _1767630) = hAPP(hAPP(c_List_Olist_OCons(_1767628), _1767634), _1767630))], (48914 ^ _782464) ^ [_1767969, _1767971, _1767973, _1767975, _1767977] : [hAPP(hAPP(c_List_Olist_OCons(_1767969), _1767971), _1767973) = hAPP(c_List_Ofilter(_1767969, _1767975), _1767977), 48919 ^ _782464 : [(48920 ^ _782464) ^ [] : [-(_1767977 = hAPP(hAPP(c_List_Oappend(_1767969), 48917 ^ [_1767969, _1767971, _1767973, _1767975, _1767977]), hAPP(hAPP(c_List_Olist_OCons(_1767969), _1767971), 48918 ^ [_1767969, _1767971, _1767973, _1767975, _1767977])))], (48928 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1767975, _1767971)))], (48930 ^ _782464) ^ [] : [-(_1767973 = hAPP(c_List_Ofilter(_1767969, _1767975), 48918 ^ [_1767969, _1767971, _1767973, _1767975, _1767977]))], (48922 ^ _782464) ^ [_1768283] : [hBOOL(hAPP(hAPP(c_member(_1767969), _1768283), hAPP(c_List_Oset(_1767969), 48917 ^ [_1767969, _1767971, _1767973, _1767975, _1767977]))), hBOOL(hAPP(_1767975, _1768283))]]], (48932 ^ _782464) ^ [_1768487, _1768489, _1768491, _1768493, _1768495] : [-(hAPP(hAPP(c_List_Olist_OCons(_1768487), _1768489), _1768491) = hAPP(c_List_Ofilter(_1768487, _1768493), _1768495)), 48933 ^ _782464 : [(48934 ^ _782464) ^ [_1768615, _1768617] : [_1768495 = hAPP(hAPP(c_List_Oappend(_1768487), _1768617), hAPP(hAPP(c_List_Olist_OCons(_1768487), _1768489), _1768615)), 48940 ^ _782464 : [(48941 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768487), 48939 ^ [_1768487, _1768489, _1768491, _1768493, _1768495, _1768615, _1768617]), hAPP(c_List_Oset(_1768487), _1768617))))], (48943 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1768493, 48939 ^ [_1768487, _1768489, _1768491, _1768493, _1768495, _1768615, _1768617])))]], hBOOL(hAPP(_1768493, _1768489)), _1768491 = hAPP(c_List_Ofilter(_1768487, _1768493), _1768615)]]], (48953 ^ _782464) ^ [_1769037, _1769039, _1769041, _1769043, _1769045] : [hAPP(c_List_Ofilter(_1769037, _1769039), _1769041) = hAPP(hAPP(c_List_Olist_OCons(_1769037), _1769043), _1769045), 48958 ^ _782464 : [(48959 ^ _782464) ^ [] : [-(_1769041 = hAPP(hAPP(c_List_Oappend(_1769037), 48956 ^ [_1769037, _1769039, _1769041, _1769043, _1769045]), hAPP(hAPP(c_List_Olist_OCons(_1769037), _1769043), 48957 ^ [_1769037, _1769039, _1769041, _1769043, _1769045])))], (48967 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1769039, _1769043)))], (48969 ^ _782464) ^ [] : [-(_1769045 = hAPP(c_List_Ofilter(_1769037, _1769039), 48957 ^ [_1769037, _1769039, _1769041, _1769043, _1769045]))], (48961 ^ _782464) ^ [_1769351] : [hBOOL(hAPP(hAPP(c_member(_1769037), _1769351), hAPP(c_List_Oset(_1769037), 48956 ^ [_1769037, _1769039, _1769041, _1769043, _1769045]))), hBOOL(hAPP(_1769039, _1769351))]]], (48971 ^ _782464) ^ [_1769555, _1769557, _1769559, _1769561, _1769563] : [-(hAPP(c_List_Ofilter(_1769555, _1769557), _1769559) = hAPP(hAPP(c_List_Olist_OCons(_1769555), _1769561), _1769563)), 48972 ^ _782464 : [(48973 ^ _782464) ^ [_1769683, _1769685] : [_1769559 = hAPP(hAPP(c_List_Oappend(_1769555), _1769685), hAPP(hAPP(c_List_Olist_OCons(_1769555), _1769561), _1769683)), 48979 ^ _782464 : [(48980 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769555), 48978 ^ [_1769555, _1769557, _1769559, _1769561, _1769563, _1769683, _1769685]), hAPP(c_List_Oset(_1769555), _1769685))))], (48982 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1769557, 48978 ^ [_1769555, _1769557, _1769559, _1769561, _1769563, _1769683, _1769685])))]], hBOOL(hAPP(_1769557, _1769561)), _1769563 = hAPP(c_List_Ofilter(_1769555, _1769557), _1769683)]]], (48992 ^ _782464) ^ [_1770081, _1770083, _1770085, _1770087] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770081), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770083)), _1770085))), 48998 ^ _782464 : [(48999 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770083), 48997 ^ [_1770081, _1770083, _1770085, _1770087]), hAPP(c_List_Oset(_1770083), _1770085))))], (49001 ^ _782464) ^ [] : [hBOOL(hAPP(_1770087, 48997 ^ [_1770081, _1770083, _1770085, _1770087]))]], -(hBOOL(hAPP(_1770087, hAPP(hAPP(c_List_Onth(_1770083), _1770085), _1770081))))], (49005 ^ _782464) ^ [_1770367, _1770369, _1770371] : [class_Orderings_Olinorder(_1770367), 49011 ^ _782464 : [(49012 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770367), 49010 ^ [_1770367, _1770369, _1770371]), hAPP(c_List_Oset(_1770367), _1770369))))], (49014 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770367), _1770371), 49010 ^ [_1770367, _1770369, _1770371]))]], c_List_Olinorder__class_Osorted(_1770367, _1770369), -(c_List_Olinorder__class_Osorted(_1770367, hAPP(hAPP(c_List_Olist_OCons(_1770367), _1770371), _1770369)))], (49022 ^ _782464) ^ [_1770701, _1770703, _1770705] : [c_List_Olist__ex(_1770701, _1770703, _1770705), 49026 ^ _782464 : [(49027 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49025 ^ [_1770701, _1770703, _1770705]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770701)), _1770705))))], (49029 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1770703, hAPP(hAPP(c_List_Onth(_1770701), _1770705), 49025 ^ [_1770701, _1770703, _1770705]))))]]], (49031 ^ _782464) ^ [_1770871, _1770873, _1770875] : [-(c_List_Olist__ex(_1770871, _1770873, _1770875)), 49032 ^ _782464 : [(49033 ^ _782464) ^ [_1770936] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770936), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770871)), _1770875))), hBOOL(hAPP(_1770873, hAPP(hAPP(c_List_Onth(_1770871), _1770875), _1770936)))]]], (49041 ^ _782464) ^ [_1771109, _1771111, _1771113] : [hBOOL(hAPP(hAPP(c_member(_1771109), _1771111), hAPP(c_List_Oset(_1771109), _1771113))), -(_1771113 = hAPP(hAPP(c_List_Oappend(_1771109), 49044 ^ [_1771109, _1771111, _1771113]), hAPP(hAPP(c_List_Olist_OCons(_1771109), _1771111), 49045 ^ [_1771109, _1771111, _1771113])))], (49049 ^ _782464) ^ [_1771268, _1771270, _1771272] : [49050 ^ _782464 : [(49051 ^ _782464) ^ [_1771345, _1771347] : [_1771272 = hAPP(hAPP(c_List_Oappend(_1771268), _1771347), hAPP(hAPP(c_List_Olist_OCons(_1771268), _1771270), _1771345))]], -(hBOOL(hAPP(hAPP(c_member(_1771268), _1771270), hAPP(c_List_Oset(_1771268), _1771272))))], (49065 ^ _782464) ^ [_1771563, _1771565, _1771567, _1771569] : [49066 ^ _782464 : [(49067 ^ _782464) ^ [] : [hBOOL(hAPP(_1771565, _1771567))], (49069 ^ _782464) ^ [] : [c_List_Olist__ex(_1771563, _1771565, _1771569)]], -(c_List_Olist__ex(_1771563, _1771565, hAPP(hAPP(c_List_Olist_OCons(_1771563), _1771567), _1771569)))], (49055 ^ _782464) ^ [_1771449, _1771451, _1771453, _1771455] : [c_List_Olist__ex(_1771449, _1771451, hAPP(hAPP(c_List_Olist_OCons(_1771449), _1771453), _1771455)), -(hBOOL(hAPP(_1771451, _1771453))), -(c_List_Olist__ex(_1771449, _1771451, _1771455))], (49073 ^ _782464) ^ [_1771726, _1771728, _1771730] : [c_List_Olist__ex(_1771726, _1771728, hAPP(c_List_Orev(_1771726), _1771730)), -(c_List_Olist__ex(_1771726, _1771728, _1771730))], (49079 ^ _782464) ^ [_1771815, _1771817, _1771819] : [c_List_Olist__ex(_1771815, _1771817, _1771819), -(c_List_Olist__ex(_1771815, _1771817, hAPP(c_List_Orev(_1771815), _1771819)))], (49085 ^ _782464) ^ [_1771928, _1771930, _1771932] : [c_List_Olist__ex(_1771928, _1771930, _1771932), 49089 ^ _782464 : [(49090 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771928), 49088 ^ [_1771928, _1771930, _1771932]), hAPP(c_List_Oset(_1771928), _1771932))))], (49092 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1771930, 49088 ^ [_1771928, _1771930, _1771932])))]]], (49094 ^ _782464) ^ [_1772082, _1772084, _1772086] : [-(c_List_Olist__ex(_1772082, _1772084, _1772086)), 49095 ^ _782464 : [(49096 ^ _782464) ^ [_1772139] : [hBOOL(hAPP(hAPP(c_member(_1772082), _1772139), hAPP(c_List_Oset(_1772082), _1772086))), hBOOL(hAPP(_1772084, _1772139))]]], (49114 ^ _782464) ^ [_1772411, _1772413, _1772415, _1772417] : [49115 ^ _782464 : [(49116 ^ _782464) ^ [] : [c_List_Olist__ex(_1772411, _1772413, _1772415)], (49118 ^ _782464) ^ [] : [c_List_Olist__ex(_1772411, _1772413, _1772417)]], -(c_List_Olist__ex(_1772411, _1772413, hAPP(hAPP(c_List_Oappend(_1772411), _1772415), _1772417)))], (49104 ^ _782464) ^ [_1772299, _1772301, _1772303, _1772305] : [c_List_Olist__ex(_1772299, _1772301, hAPP(hAPP(c_List_Oappend(_1772299), _1772303), _1772305)), -(c_List_Olist__ex(_1772299, _1772301, _1772303)), -(c_List_Olist__ex(_1772299, _1772301, _1772305))], (49122 ^ _782464) ^ [_1772566, _1772568] : [c_List_Olist__ex(_1772566, _1772568, c_List_Olist_ONil(_1772566))], (49124 ^ _782464) ^ [_1772612, _1772614, _1772616] : [hBOOL(hAPP(hAPP(c_member(_1772612), _1772614), hAPP(c_List_Oset(_1772612), _1772616))), 49129 ^ _782464 : [(49130 ^ _782464) ^ [] : [-(_1772616 = hAPP(hAPP(c_List_Oappend(_1772612), 49127 ^ [_1772612, _1772614, _1772616]), hAPP(hAPP(c_List_Olist_OCons(_1772612), _1772614), 49128 ^ [_1772612, _1772614, _1772616])))], (49132 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1772612), _1772614), hAPP(c_List_Oset(_1772612), 49127 ^ [_1772612, _1772614, _1772616])))]]], (49134 ^ _782464) ^ [_1772867, _1772869, _1772871] : [-(hBOOL(hAPP(hAPP(c_member(_1772867), _1772869), hAPP(c_List_Oset(_1772867), _1772871)))), 49135 ^ _782464 : [(49136 ^ _782464) ^ [_1772956] : [49137 ^ _782464 : [(49138 ^ _782464) ^ [_1773029] : [_1772871 = hAPP(hAPP(c_List_Oappend(_1772867), _1772956), hAPP(hAPP(c_List_Olist_OCons(_1772867), _1772869), _1773029))]], -(hBOOL(hAPP(hAPP(c_member(_1772867), _1772869), hAPP(c_List_Oset(_1772867), _1772956))))]]], (49144 ^ _782464) ^ [_1773168, _1773170, _1773172] : [hBOOL(hAPP(hAPP(c_member(_1773168), _1773170), hAPP(c_List_Oset(_1773168), _1773172))), 49149 ^ _782464 : [(49150 ^ _782464) ^ [] : [-(_1773172 = hAPP(hAPP(c_List_Oappend(_1773168), 49147 ^ [_1773168, _1773170, _1773172]), hAPP(hAPP(c_List_Olist_OCons(_1773168), _1773170), 49148 ^ [_1773168, _1773170, _1773172])))], (49152 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1773168), _1773170), hAPP(c_List_Oset(_1773168), 49148 ^ [_1773168, _1773170, _1773172])))]]], (49154 ^ _782464) ^ [_1773423, _1773425, _1773427] : [-(hBOOL(hAPP(hAPP(c_member(_1773423), _1773425), hAPP(c_List_Oset(_1773423), _1773427)))), 49155 ^ _782464 : [(49156 ^ _782464) ^ [_1773512, _1773514] : [_1773427 = hAPP(hAPP(c_List_Oappend(_1773423), _1773514), hAPP(hAPP(c_List_Olist_OCons(_1773423), _1773425), _1773512)), -(hBOOL(hAPP(hAPP(c_member(_1773423), _1773425), hAPP(c_List_Oset(_1773423), _1773512))))]]], (49174 ^ _782464) ^ [_1773927, _1773929, _1773931] : [49176 ^ _782464 : [(49177 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49175 ^ [_1773927, _1773929, _1773931]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773927)), _1773931))))], (49179 ^ _782464) ^ [] : [hBOOL(hAPP(_1773929, hAPP(hAPP(c_List_Onth(_1773927), _1773931), 49175 ^ [_1773927, _1773929, _1773931])))]], -(c_List_Olist__all(_1773927, _1773929, _1773931))], (49164 ^ _782464) ^ [_1773713, _1773715, _1773717] : [c_List_Olist__all(_1773713, _1773715, _1773717), 49167 ^ _782464 : [(49168 ^ _782464) ^ [_1773802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773802), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773713)), _1773717))), -(hBOOL(hAPP(_1773715, hAPP(hAPP(c_List_Onth(_1773713), _1773717), _1773802))))]]], (49183 ^ _782464) ^ [_1774135, _1774137, _1774139] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1774135), _1774137)), hBOOL(hAPP(_1774139, c_Orderings_Obot__class_Obot(tc_fun(_1774135, tc_HOL_Obool)))), 49194 ^ _782464 : [(49195 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1774135), 49193 ^ [_1774135, _1774137, _1774139])))], (49197 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1774135), 49192 ^ [_1774135, _1774137, _1774139]), 49193 ^ [_1774135, _1774137, _1774139]))], (49199 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1774139, 49193 ^ [_1774135, _1774137, _1774139])))], (49201 ^ _782464) ^ [] : [hBOOL(hAPP(_1774139, hAPP(hAPP(c_Set_Oinsert(_1774135), 49192 ^ [_1774135, _1774137, _1774139]), 49193 ^ [_1774135, _1774137, _1774139])))]], -(hBOOL(hAPP(_1774139, _1774137)))], (49205 ^ _782464) ^ [_1774643, _1774645, _1774647, _1774649] : [c_List_Olist__all(_1774643, _1774645, hAPP(hAPP(c_List_Olist_OCons(_1774643), _1774647), _1774649)), 49208 ^ _782464 : [(49209 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1774645, _1774647)))], (49211 ^ _782464) ^ [] : [-(c_List_Olist__all(_1774643, _1774645, _1774649))]]], (49213 ^ _782464) ^ [_1774770, _1774772, _1774774, _1774776] : [-(c_List_Olist__all(_1774770, _1774772, hAPP(hAPP(c_List_Olist_OCons(_1774770), _1774774), _1774776))), hBOOL(hAPP(_1774772, _1774774)), c_List_Olist__all(_1774770, _1774772, _1774776)], (49223 ^ _782464) ^ [_1774951, _1774953, _1774955] : [c_List_Olist__all(_1774951, _1774953, hAPP(c_List_Orev(_1774951), _1774955)), -(c_List_Olist__all(_1774951, _1774953, _1774955))], (49229 ^ _782464) ^ [_1775040, _1775042, _1775044] : [c_List_Olist__all(_1775040, _1775042, _1775044), -(c_List_Olist__all(_1775040, _1775042, hAPP(c_List_Orev(_1775040), _1775044)))], (49245 ^ _782464) ^ [_1775343, _1775345, _1775347] : [49247 ^ _782464 : [(49248 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775343), 49246 ^ [_1775343, _1775345, _1775347]), hAPP(c_List_Oset(_1775343), _1775347))))], (49250 ^ _782464) ^ [] : [hBOOL(hAPP(_1775345, 49246 ^ [_1775343, _1775345, _1775347]))]], -(c_List_Olist__all(_1775343, _1775345, _1775347))], (49235 ^ _782464) ^ [_1775153, _1775155, _1775157] : [c_List_Olist__all(_1775153, _1775155, _1775157), 49238 ^ _782464 : [(49239 ^ _782464) ^ [_1775234] : [hBOOL(hAPP(hAPP(c_member(_1775153), _1775234), hAPP(c_List_Oset(_1775153), _1775157))), -(hBOOL(hAPP(_1775155, _1775234)))]]], (49254 ^ _782464) ^ [_1775546, _1775548, _1775550, _1775552] : [c_List_Olist__all(_1775546, _1775548, hAPP(hAPP(c_List_Oappend(_1775546), _1775550), _1775552)), 49257 ^ _782464 : [(49258 ^ _782464) ^ [] : [-(c_List_Olist__all(_1775546, _1775548, _1775550))], (49260 ^ _782464) ^ [] : [-(c_List_Olist__all(_1775546, _1775548, _1775552))]]], (49262 ^ _782464) ^ [_1775671, _1775673, _1775675, _1775677] : [-(c_List_Olist__all(_1775671, _1775673, hAPP(hAPP(c_List_Oappend(_1775671), _1775675), _1775677))), c_List_Olist__all(_1775671, _1775673, _1775675), c_List_Olist__all(_1775671, _1775673, _1775677)], (49272 ^ _782464) ^ [_1775832, _1775834] : [-(c_List_Olist__all(_1775832, _1775834, c_List_Olist_ONil(_1775832)))], (49274 ^ _782464) ^ [_1775878, _1775880, _1775882] : [49276 ^ _782464 : [(49277 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775878), 49275 ^ [_1775878, _1775880, _1775882]), hAPP(c_List_Oset(_1775878), _1775880))))], (49279 ^ _782464) ^ [] : [hBOOL(hAPP(_1775882, 49275 ^ [_1775878, _1775880, _1775882]))]], -(c_List_Olist__all(_1775878, _1775882, _1775880))], (49283 ^ _782464) ^ [_1776054, _1776056, _1776058] : [c_List_Olist__all(_1776054, _1776058, _1776056), 49286 ^ _782464 : [(49287 ^ _782464) ^ [_1776135] : [hBOOL(hAPP(hAPP(c_member(_1776054), _1776135), hAPP(c_List_Oset(_1776054), _1776056))), -(hBOOL(hAPP(_1776058, _1776135)))]]], (49303 ^ _782464) ^ [_1776458, _1776460, _1776462] : [49305 ^ _782464 : [(49306 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776458), 49304 ^ [_1776458, _1776460, _1776462]), hAPP(c_List_Oset(_1776458), _1776462))))], (49308 ^ _782464) ^ [] : [hBOOL(hAPP(_1776460, 49304 ^ [_1776458, _1776460, _1776462]))]], -(c_List_Olist__all(_1776458, _1776460, _1776462))], (49293 ^ _782464) ^ [_1776268, _1776270, _1776272] : [c_List_Olist__all(_1776268, _1776270, _1776272), 49296 ^ _782464 : [(49297 ^ _782464) ^ [_1776349] : [hBOOL(hAPP(hAPP(c_member(_1776268), _1776349), hAPP(c_List_Oset(_1776268), _1776272))), -(hBOOL(hAPP(_1776270, _1776349)))]]], (49328 ^ _782464) ^ [_1776937, _1776939, _1776941, _1776943] : [-(c_List_Olist__ex1(_1776937, _1776939, hAPP(hAPP(c_List_Olist_OCons(_1776937), _1776941), _1776943))), 49331 ^ _782464 : [(49332 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1776939, _1776941)))], (49334 ^ _782464) ^ [] : [c_List_Olist__all(_1776937, hAPP(hAPP(c_COMBS(_1776937, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1776937), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1776937), c_fNot), _1776939))), hAPP(c_fequal, _1776941)), _1776943)]], 49335 ^ _782464 : [(49336 ^ _782464) ^ [] : [hBOOL(hAPP(_1776939, _1776941))], (49338 ^ _782464) ^ [] : [c_List_Olist__ex1(_1776937, _1776939, _1776943)]]], (49312 ^ _782464) ^ [_1776661, _1776663, _1776665, _1776667] : [c_List_Olist__ex1(_1776661, _1776663, hAPP(hAPP(c_List_Olist_OCons(_1776661), _1776665), _1776667)), 49315 ^ _782464 : [(49316 ^ _782464) ^ [] : [hBOOL(hAPP(_1776663, _1776665)), -(c_List_Olist__all(_1776661, hAPP(hAPP(c_COMBS(_1776661, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1776661), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1776661), c_fNot), _1776663))), hAPP(c_fequal, _1776665)), _1776667))], (49322 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1776663, _1776665))), -(c_List_Olist__ex1(_1776661, _1776663, _1776667))]]], (49342 ^ _782464) ^ [] : [-(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))))], (49344 ^ _782464) ^ [_1777275, _1777277] : [c_List_Olist__ex1(_1777275, _1777277, c_List_Olist_ONil(_1777275))], (49346 ^ _782464) ^ [_1777303, _1777305] : [-(c_FunDef_Ois__measure(_1777303, _1777305))], (49348 ^ _782464) ^ [_1777328, _1777330] : [-(c_FunDef_Ois__measure(_1777328, _1777330))], (49350 ^ _782464) ^ [_1777353, _1777355] : [-(c_FunDef_Ois__measure(_1777353, _1777355))], (49352 ^ _782464) ^ [_1777378] : [class_Nat_Osize(_1777378), -(c_FunDef_Ois__measure(_1777378, c_Nat_Osize__class_Osize(_1777378)))], (49358 ^ _782464) ^ [_1777455, _1777457, _1777459] : [c_FunDef_Ois__measure(_1777455, _1777457), -(c_FunDef_Ois__measure(tc_prod(_1777459, _1777455), hAPP(hAPP(c_COMBB(_1777455, tc_Nat_Onat, tc_prod(_1777459, _1777455)), _1777457), c_Product__Type_Osnd(_1777459, _1777455))))], (49364 ^ _782464) ^ [_1777572, _1777574, _1777576] : [c_FunDef_Ois__measure(_1777572, _1777574), -(c_FunDef_Ois__measure(tc_prod(_1777572, _1777576), hAPP(hAPP(c_COMBB(_1777572, tc_Nat_Onat, tc_prod(_1777572, _1777576)), _1777574), c_Product__Type_Ofst(_1777572, _1777576))))], (49370 ^ _782464) ^ [_1777707, _1777709, _1777711] : [c_List_Olist__ex1(_1777707, _1777709, _1777711), 49374 ^ _782464 : [(49375 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777707), 49373 ^ [_1777707, _1777709, _1777711]), hAPP(c_List_Oset(_1777707), _1777711))))], (49377 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1777709, 49373 ^ [_1777707, _1777709, _1777711])))], (49379 ^ _782464) ^ [_1777953] : [-(_1777953 = 49373 ^ [_1777707, _1777709, _1777711]), hBOOL(hAPP(hAPP(c_member(_1777707), _1777953), hAPP(c_List_Oset(_1777707), _1777711))), hBOOL(hAPP(_1777709, _1777953))]]], (49389 ^ _782464) ^ [_1778140, _1778142, _1778144] : [-(c_List_Olist__ex1(_1778140, _1778142, _1778144)), 49390 ^ _782464 : [(49391 ^ _782464) ^ [_1778234] : [hBOOL(hAPP(hAPP(c_member(_1778140), _1778234), hAPP(c_List_Oset(_1778140), _1778144))), hBOOL(hAPP(_1778142, _1778234)), 49399 ^ _782464 : [(49400 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778140), 49398 ^ [_1778140, _1778142, _1778144, _1778234]), hAPP(c_List_Oset(_1778140), _1778144))))], (49402 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1778142, 49398 ^ [_1778140, _1778142, _1778144, _1778234])))], (49404 ^ _782464) ^ [] : [49398 ^ [_1778140, _1778142, _1778144, _1778234] = _1778234]]]]], (49408 ^ _782464) ^ [] : [-(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)))], (49410 ^ _782464) ^ [_1778605, _1778607, _1778609, _1778611, _1778613] : [_1778605 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1778607, _1778609, _1778611, _1778613), _1778605) = c_Lazy__Sequence_Ohit__bound(_1778609))], (49416 ^ _782464) ^ [_1778702, _1778704, _1778706, _1778708, _1778710] : [-(_1778702 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1778704, _1778706, _1778708, _1778710), _1778702) = c_Lazy__Sequence_Ohb__bind(_1778704, _1778706, hAPP(_1778708, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1778702), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1778704, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1778706))), _1778710), _1778702)))], (49422 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49424 ^ _782464) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49426 ^ _782464) ^ [_1778818, _1778820, _1778822, _1778824, _1778826, _1778828, _1778830] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1778818, _1778820, _1778822, _1778824, _1778826, _1778828, _1778830) = c_New__DSequence_Oneg__decr__bind(_1778818, _1778820, hAPP(hAPP(hAPP(_1778822, _1778826), _1778828), _1778830), hAPP(hAPP(c_COMBC(_1778818, 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(_1778820)))), hAPP(hAPP(c_COMBC(_1778818, 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(_1778820))))), hAPP(hAPP(c_COMBC(_1778818, 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(_1778820)))))), _1778824), _1778826)), _1778828)), _1778830)))], (49428 ^ _782464) ^ [_1778935, _1778937, _1778939, _1778941, _1778943] : [-(hAPP(c_New__DSequence_Oneg__bind(_1778935, _1778937, _1778939, _1778941), _1778943) = c_Lazy__Sequence_Ohb__bind(_1778935, _1778937, hAPP(_1778939, _1778943), hAPP(hAPP(c_COMBC(_1778935, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1778937))), _1778941), _1778943)))], (49430 ^ _782464) ^ [_1778996, _1778998, _1779000, _1779002, _1779004, _1779006, _1779008] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1778996, _1778998, _1779000, _1779002), _1779004), _1779006), _1779008) = c_New__DSequence_Oneg__bind(_1778996, _1778998, hAPP(hAPP(hAPP(_1779000, _1779004), _1779006), _1779008), hAPP(hAPP(c_COMBC(_1778996, 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(_1778998)))), hAPP(hAPP(c_COMBC(_1778996, 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(_1778998))))), hAPP(hAPP(c_COMBC(_1778996, 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(_1778998)))))), _1779002), _1779004)), _1779006)), _1779008)))], (49432 ^ _782464) ^ [_1779137, _1779139, _1779141, _1779143, _1779145] : [_1779137 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1779139, _1779141, _1779143, _1779145), _1779137) = c_Lazy__Sequence_Oempty(_1779141))], (49438 ^ _782464) ^ [_1779234, _1779236, _1779238, _1779240, _1779242] : [-(_1779234 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1779236, _1779238, _1779240, _1779242), _1779234) = hAPP(c_Lazy__Sequence_Obind(_1779236, _1779238, hAPP(_1779240, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1779234), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1779236, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779238)), _1779242), _1779234)))], (49444 ^ _782464) ^ [_1779314, _1779316, _1779318, _1779320, _1779322, _1779324, _1779326] : [-(c_New__Random__Sequence_Opos__decr__bind(_1779314, _1779316, _1779318, _1779320, _1779322, _1779324, _1779326) = c_New__DSequence_Opos__decr__bind(_1779314, _1779316, hAPP(hAPP(hAPP(_1779318, _1779322), _1779324), _1779326), hAPP(hAPP(c_COMBC(_1779314, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779316))), hAPP(hAPP(c_COMBC(_1779314, 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(_1779316)))), hAPP(hAPP(c_COMBC(_1779314, 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(_1779316))))), _1779320), _1779322)), _1779324)), _1779326)))], (49446 ^ _782464) ^ [_1779425, _1779427] : [-(hAPP(c_New__DSequence_Opos__empty(_1779425), _1779427) = c_Lazy__Sequence_Oempty(_1779425))], (49448 ^ _782464) ^ [_1779457, _1779459, _1779461, _1779463] : [-(c_New__Random__Sequence_Opos__empty(_1779457, _1779459, _1779461, _1779463) = c_New__DSequence_Opos__empty(_1779457))], (49450 ^ _782464) ^ [_1779493, _1779495, _1779497, _1779499, _1779501] : [-(hAPP(c_New__DSequence_Opos__bind(_1779493, _1779495, _1779497, _1779499), _1779501) = hAPP(c_Lazy__Sequence_Obind(_1779493, _1779495, hAPP(_1779497, _1779501)), hAPP(hAPP(c_COMBC(_1779493, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779495)), _1779499), _1779501)))], (49452 ^ _782464) ^ [_1779554, _1779556, _1779558, _1779560, _1779562, _1779564, _1779566] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1779554, _1779556, _1779558, _1779560), _1779562), _1779564), _1779566) = c_New__DSequence_Opos__bind(_1779554, _1779556, hAPP(hAPP(hAPP(_1779558, _1779562), _1779564), _1779566), hAPP(hAPP(c_COMBC(_1779554, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779556))), hAPP(hAPP(c_COMBC(_1779554, 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(_1779556)))), hAPP(hAPP(c_COMBC(_1779554, 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(_1779556))))), _1779560), _1779562)), _1779564)), _1779566)))], (49454 ^ _782464) ^ [_1779671, _1779673, _1779675, _1779677] : [-(c_New__Random__Sequence_Oneg__map(_1779671, _1779673, _1779675, _1779677) = c_New__Random__Sequence_Oneg__bind(_1779671, _1779673, _1779677, hAPP(c_Fun_Ocomp(_1779673, 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(_1779673)))))), _1779671, c_New__Random__Sequence_Oneg__single(_1779673)), _1779675)))], (49456 ^ _782464) ^ [_1779736, _1779738, _1779740, _1779742, _1779744] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1779736), _1779738), _1779740), _1779742), _1779744) = c_New__DSequence_Oneg__single(_1779736, _1779738))], (49458 ^ _782464) ^ [_1779784, _1779786, _1779788, _1779790] : [-(c_New__Random__Sequence_Opos__map(_1779784, _1779786, _1779788, _1779790) = c_New__Random__Sequence_Opos__bind(_1779784, _1779786, _1779790, hAPP(c_Fun_Ocomp(_1779786, 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(_1779786))))), _1779784, c_New__Random__Sequence_Opos__single(_1779786)), _1779788)))], (49460 ^ _782464) ^ [_1779847, _1779849, _1779851] : [-(hAPP(c_New__DSequence_Oneg__single(_1779847, _1779849), _1779851) = c_Lazy__Sequence_Ohb__single(_1779847, _1779849))], (49462 ^ _782464) ^ [_1779883, _1779885, _1779887, _1779889, _1779891] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1779883), _1779885), _1779887), _1779889), _1779891) = c_New__DSequence_Opos__single(_1779883, _1779885))], (49464 ^ _782464) ^ [_1779931, _1779933, _1779935] : [-(hAPP(c_New__DSequence_Opos__single(_1779931, _1779933), _1779935) = hAPP(c_Lazy__Sequence_Osingle(_1779931), _1779933))], (49466 ^ _782464) ^ [_1779969, _1779971, _1779973] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779969)), c_List_Osplice(_1779969, _1779971, _1779973)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779969)), _1779971)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779969)), _1779973)))], (49468 ^ _782464) ^ [_1780027, _1780029, _1780031, _1780033, _1780035] : [-(c_List_Osplice(_1780027, hAPP(hAPP(c_List_Olist_OCons(_1780027), _1780029), _1780031), hAPP(hAPP(c_List_Olist_OCons(_1780027), _1780033), _1780035)) = hAPP(hAPP(c_List_Olist_OCons(_1780027), _1780029), hAPP(hAPP(c_List_Olist_OCons(_1780027), _1780033), c_List_Osplice(_1780027, _1780031, _1780035))))], (49470 ^ _782464) ^ [_1780098, _1780100] : [-(c_List_Osplice(_1780098, c_List_Olist_ONil(_1780098), _1780100) = _1780100)], (49472 ^ _782464) ^ [_1780129, _1780131] : [-(c_List_Osplice(_1780129, _1780131, c_List_Olist_ONil(_1780129)) = _1780131)], (49474 ^ _782464) ^ [_1780160, _1780162, _1780164] : [-(c_List_Osplice(_1780160, hAPP(hAPP(c_List_Olist_OCons(_1780160), _1780162), _1780164), c_List_Olist_ONil(_1780160)) = hAPP(hAPP(c_List_Olist_OCons(_1780160), _1780162), _1780164))], (49476 ^ _782464) ^ [_1780209, _1780211, _1780213, _1780215] : [-(c_Lazy__Sequence_Oproduct(_1780209, _1780211, _1780213, _1780215) = hAPP(c_Lazy__Sequence_Obind(_1780209, tc_prod(_1780209, _1780211), _1780213), hAPP(hAPP(c_COMBB(tc_fun(_1780211, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780209, _1780211))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780209, _1780211)), _1780209), c_Lazy__Sequence_Obind(_1780211, tc_prod(_1780209, _1780211), _1780215)), hAPP(hAPP(c_COMBB(tc_fun(_1780211, tc_prod(_1780209, _1780211)), tc_fun(_1780211, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780209, _1780211))), _1780209), hAPP(c_COMBB(tc_prod(_1780209, _1780211), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780209, _1780211)), _1780211), c_Lazy__Sequence_Osingle(tc_prod(_1780209, _1780211)))), c_Product__Type_OPair(_1780209, _1780211)))))], (49478 ^ _782464) ^ [_1780330, _1780332, _1780334, _1780336] : [c_Fun_Obij__betw(_1780330, _1780332, _1780334, c_Orderings_Otop__class_Otop(tc_fun(_1780330, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1780332, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1780330, _1780332, _1780334), hAPP(c_Set_OCollect(_1780330), _1780336)) = hAPP(c_Set_OCollect(_1780332), hAPP(hAPP(c_COMBB(_1780330, tc_HOL_Obool, _1780332), _1780336), c_Hilbert__Choice_Oinv__into(_1780330, _1780332, c_Orderings_Otop__class_Otop(tc_fun(_1780330, tc_HOL_Obool)), _1780334))))], (49484 ^ _782464) ^ [_1780511, _1780513, _1780515, _1780517, _1780519, _1780521] : [c_Fun_Oinj__on(_1780511, _1780513, _1780515, _1780517), hBOOL(hAPP(hAPP(c_member(_1780511), _1780519), _1780517)), hAPP(_1780515, _1780519) = _1780521, -(hAPP(c_Hilbert__Choice_Oinv__into(_1780511, _1780513, _1780517, _1780515), _1780521) = _1780519)], (49498 ^ _782464) ^ [_1780756, _1780758, _1780760, _1780762, _1780764] : [c_Fun_Oinj__on(_1780756, _1780758, _1780760, _1780762), hBOOL(hAPP(hAPP(c_member(_1780756), _1780764), _1780762)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1780756, _1780758, _1780762, _1780760), hAPP(_1780760, _1780764)) = _1780764)], (49508 ^ _782464) ^ [_1780937, _1780939, _1780941, _1780943] : [c_Fun_Oinj__on(_1780937, _1780939, _1780941, c_Orderings_Otop__class_Otop(tc_fun(_1780937, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1780937, _1780939, c_Orderings_Otop__class_Otop(tc_fun(_1780937, tc_HOL_Obool)), _1780941), hAPP(_1780941, _1780943)) = _1780943)], (49514 ^ _782464) ^ [_1781064, _1781066, _1781068, _1781070, _1781072] : [c_Fun_Oinj__on(_1781064, _1781066, _1781068, c_Orderings_Otop__class_Otop(tc_fun(_1781064, tc_HOL_Obool))), hAPP(_1781068, _1781070) = _1781072, -(hAPP(c_Hilbert__Choice_Oinv__into(_1781064, _1781066, c_Orderings_Otop__class_Otop(tc_fun(_1781064, tc_HOL_Obool)), _1781068), _1781072) = _1781070)], (49524 ^ _782464) ^ [_1781251, _1781253, _1781255, _1781257, _1781259] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1781251, _1781253, _1781255, _1781257), _1781259) = c_Hilbert__Choice_OEps(_1781251, hAPP(hAPP(c_COMBS(_1781251, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1781251), c_fconj), hAPP(hAPP(c_COMBC(_1781251, tc_fun(_1781251, tc_HOL_Obool), tc_HOL_Obool), c_member(_1781251)), _1781255))), hAPP(hAPP(c_COMBC(_1781251, _1781253, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1781253, tc_fun(_1781253, tc_HOL_Obool), _1781251), c_fequal), _1781257)), _1781259))))], (49526 ^ _782464) ^ [_1781351, _1781353, _1781355] : [c_Fun_Obij__betw(_1781351, _1781353, _1781355, c_Orderings_Otop__class_Otop(tc_fun(_1781351, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781353, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1781353, _1781351, c_Orderings_Otop__class_Otop(tc_fun(_1781353, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1781351, _1781353, c_Orderings_Otop__class_Otop(tc_fun(_1781351, tc_HOL_Obool)), _1781355)) = _1781355)], (49532 ^ _782464) ^ [_1781496, _1781498, _1781500] : [c_Fun_Obij__betw(_1781496, _1781498, _1781500, c_Orderings_Otop__class_Otop(tc_fun(_1781496, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781498, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1781498, _1781496, c_Hilbert__Choice_Oinv__into(_1781496, _1781498, c_Orderings_Otop__class_Otop(tc_fun(_1781496, tc_HOL_Obool)), _1781500), c_Orderings_Otop__class_Otop(tc_fun(_1781498, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781496, tc_HOL_Obool))))], (49538 ^ _782464) ^ [_1781647, _1781649, _1781651, _1781653, _1781655] : [c_Fun_Obij__betw(_1781647, _1781649, _1781651, _1781653, _1781655), -(c_Fun_Obij__betw(_1781649, _1781647, c_Hilbert__Choice_Oinv__into(_1781647, _1781649, _1781653, _1781651), _1781655, _1781653))], (49544 ^ _782464) ^ [_1781752, _1781754, _1781756, _1781758, _1781760, _1781762] : [c_Fun_Obij__betw(_1781752, _1781754, _1781756, _1781758, _1781760), hBOOL(hAPP(hAPP(c_member(_1781752), _1781762), _1781758)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1781754, _1781752, _1781760, c_Hilbert__Choice_Oinv__into(_1781752, _1781754, _1781758, _1781756)), _1781762) = hAPP(_1781756, _1781762))], (49554 ^ _782464) ^ [_1781949, _1781951, _1781953, _1781955, _1781957, _1781959] : [hAPP(c_Set_Oimage(_1781949, _1781951, _1781953), _1781955) = _1781957, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781951, tc_HOL_Obool)), _1781959), _1781957)), -(hAPP(c_Set_Oimage(_1781949, _1781951, _1781953), hAPP(c_Set_Oimage(_1781951, _1781949, c_Hilbert__Choice_Oinv__into(_1781949, _1781951, _1781955, _1781953)), _1781959)) = _1781959)], (49564 ^ _782464) ^ [_1782184, _1782186, _1782188] : [hAPP(c_Set_Oimage(_1782184, _1782186, _1782188), c_Orderings_Otop__class_Otop(tc_fun(_1782184, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782186, tc_HOL_Obool)), 49567 ^ _782464 : [(49568 ^ _782464) ^ [_1782295] : [-(hAPP(_1782188, hAPP(c_Hilbert__Choice_Oinv__into(_1782184, _1782186, c_Orderings_Otop__class_Otop(tc_fun(_1782184, tc_HOL_Obool)), _1782188), _1782295)) = _1782295)]]], (49570 ^ _782464) ^ [_1782334, _1782336, _1782338] : [hAPP(_1782338, hAPP(c_Hilbert__Choice_Oinv__into(_1782334, _1782336, c_Orderings_Otop__class_Otop(tc_fun(_1782334, tc_HOL_Obool)), _1782338), 49571 ^ [_1782334, _1782336, _1782338])) = 49571 ^ [_1782334, _1782336, _1782338], -(hAPP(c_Set_Oimage(_1782334, _1782336, _1782338), c_Orderings_Otop__class_Otop(tc_fun(_1782334, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782336, tc_HOL_Obool)))], (49577 ^ _782464) ^ [_1782534, _1782536, _1782538, _1782540] : [hAPP(c_Set_Oimage(_1782534, _1782536, _1782538), c_Orderings_Otop__class_Otop(tc_fun(_1782534, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782536, tc_HOL_Obool)), -(hAPP(_1782538, hAPP(c_Hilbert__Choice_Oinv__into(_1782534, _1782536, c_Orderings_Otop__class_Otop(tc_fun(_1782534, tc_HOL_Obool)), _1782538), _1782540)) = _1782540)], (49583 ^ _782464) ^ [_1782681, _1782683, _1782685, _1782687] : [hAPP(c_Set_Oimage(_1782681, _1782683, _1782685), c_Orderings_Otop__class_Otop(tc_fun(_1782681, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782683, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782681, _1782683, _1782685), hAPP(c_Set_Oimage(_1782683, _1782681, c_Hilbert__Choice_Oinv__into(_1782681, _1782683, c_Orderings_Otop__class_Otop(tc_fun(_1782681, tc_HOL_Obool)), _1782685)), _1782687)) = _1782687)], (49589 ^ _782464) ^ [_1782844, _1782846, _1782848, _1782850, _1782852, _1782854] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782844, _1782846, _1782848, _1782850), _1782852) = hAPP(c_Hilbert__Choice_Oinv__into(_1782844, _1782846, _1782848, _1782850), _1782854), hBOOL(hAPP(hAPP(c_member(_1782846), _1782852), hAPP(c_Set_Oimage(_1782844, _1782846, _1782850), _1782848))), hBOOL(hAPP(hAPP(c_member(_1782846), _1782854), hAPP(c_Set_Oimage(_1782844, _1782846, _1782850), _1782848))), -(_1782852 = _1782854)], (49603 ^ _782464) ^ [_1783137, _1783139, _1783141, _1783143, _1783145] : [hBOOL(hAPP(hAPP(c_member(_1783137), _1783139), hAPP(c_Set_Oimage(_1783141, _1783137, _1783143), _1783145))), -(hBOOL(hAPP(hAPP(c_member(_1783141), hAPP(c_Hilbert__Choice_Oinv__into(_1783141, _1783137, _1783145, _1783143), _1783139)), _1783145)))], (49609 ^ _782464) ^ [_1783278, _1783280, _1783282, _1783284, _1783286] : [hBOOL(hAPP(hAPP(c_member(_1783278), _1783280), hAPP(c_Set_Oimage(_1783282, _1783278, _1783284), _1783286))), -(hAPP(_1783284, hAPP(c_Hilbert__Choice_Oinv__into(_1783282, _1783278, _1783286, _1783284), _1783280)) = _1783280)], (49615 ^ _782464) ^ [_1783411] : [-(c_Hilbert__Choice_Oinv__into(_1783411, _1783411, c_Orderings_Otop__class_Otop(tc_fun(_1783411, tc_HOL_Obool)), c_Fun_Oid(_1783411)) = c_Fun_Oid(_1783411))], (49617 ^ _782464) ^ [_1783448, _1783450, _1783452, _1783454] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783448, _1783450, c_Orderings_Otop__class_Otop(tc_fun(_1783448, tc_HOL_Obool)), _1783452), _1783454) = c_Hilbert__Choice_OEps(_1783448, hAPP(hAPP(c_COMBC(_1783448, _1783450, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783450, tc_fun(_1783450, tc_HOL_Obool), _1783448), c_fequal), _1783452)), _1783454)))], (49619 ^ _782464) ^ [_1783516, _1783518, _1783520, _1783522, _1783524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783516, tc_HOL_Obool)), _1783518), hAPP(c_Set_Oimage(_1783520, _1783516, _1783522), _1783524))), -(c_Fun_Oinj__on(_1783516, _1783520, c_Hilbert__Choice_Oinv__into(_1783520, _1783516, _1783524, _1783522), _1783518))], (49625 ^ _782464) ^ [_1783647, _1783649, _1783651, _1783653, _1783655] : [c_Fun_Oinj__on(_1783647, _1783649, _1783651, _1783653), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783647, tc_HOL_Obool)), _1783655), _1783653)), -(hAPP(c_Set_Oimage(_1783649, _1783647, c_Hilbert__Choice_Oinv__into(_1783647, _1783649, _1783653, _1783651)), hAPP(c_Set_Oimage(_1783647, _1783649, _1783651), _1783655)) = _1783655)], (49635 ^ _782464) ^ [_1783850, _1783852, _1783854] : [c_Fun_Oinj__on(_1783850, _1783852, _1783854, c_Orderings_Otop__class_Otop(tc_fun(_1783850, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1783852, _1783850, c_Hilbert__Choice_Oinv__into(_1783850, _1783852, c_Orderings_Otop__class_Otop(tc_fun(_1783850, tc_HOL_Obool)), _1783854)), c_Orderings_Otop__class_Otop(tc_fun(_1783852, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783850, tc_HOL_Obool)))], (49641 ^ _782464) ^ [_1783997, _1783999, _1784001, _1784003] : [c_Fun_Oinj__on(_1783997, _1783999, _1784001, c_Orderings_Otop__class_Otop(tc_fun(_1783997, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1783999, _1783997, c_Hilbert__Choice_Oinv__into(_1783997, _1783999, c_Orderings_Otop__class_Otop(tc_fun(_1783997, tc_HOL_Obool)), _1784001)), hAPP(c_Set_Oimage(_1783997, _1783999, _1784001), _1784003)) = _1784003)], (49647 ^ _782464) ^ [_1784140, _1784142, _1784144, _1784146] : [c_Fun_Oinj__on(_1784140, _1784142, _1784144, c_Orderings_Otop__class_Otop(tc_fun(_1784140, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1784142, _1784140, c_Hilbert__Choice_Oinv__into(_1784140, _1784142, c_Orderings_Otop__class_Otop(tc_fun(_1784140, tc_HOL_Obool)), _1784144)), hAPP(c_Set_Oimage(_1784140, _1784142, _1784144), _1784146)) = _1784146)], (49653 ^ _782464) ^ [_1784283, _1784285, _1784287] : [hAPP(c_Set_Oimage(_1784283, _1784285, _1784287), c_Orderings_Otop__class_Otop(tc_fun(_1784283, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784285, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1784285, _1784283, c_Hilbert__Choice_Oinv__into(_1784283, _1784285, c_Orderings_Otop__class_Otop(tc_fun(_1784283, tc_HOL_Obool)), _1784287), c_Orderings_Otop__class_Otop(tc_fun(_1784285, tc_HOL_Obool))))], (49659 ^ _782464) ^ [_1784430, _1784432, _1784434, _1784436, _1784438] : [c_Fun_Oinj__on(_1784430, _1784432, _1784434, c_Orderings_Otop__class_Otop(tc_fun(_1784430, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784432, _1784436, _1784430, hAPP(c_Fun_Ocomp(_1784430, _1784436, _1784432, _1784438), c_Hilbert__Choice_Oinv__into(_1784430, _1784432, c_Orderings_Otop__class_Otop(tc_fun(_1784430, tc_HOL_Obool)), _1784434))), _1784434) = _1784438)], (49665 ^ _782464) ^ [_1784579, _1784581, _1784583, _1784585, _1784587] : [c_Fun_Obij__betw(_1784579, _1784581, _1784583, c_Orderings_Otop__class_Otop(tc_fun(_1784579, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1784581, tc_HOL_Obool))), c_Fun_Obij__betw(_1784585, _1784579, _1784587, c_Orderings_Otop__class_Otop(tc_fun(_1784585, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1784579, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1784585, _1784581, c_Orderings_Otop__class_Otop(tc_fun(_1784585, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1784579, _1784581, _1784585, _1784583), _1784587)) = hAPP(c_Fun_Ocomp(_1784579, _1784585, _1784581, c_Hilbert__Choice_Oinv__into(_1784585, _1784579, c_Orderings_Otop__class_Otop(tc_fun(_1784585, tc_HOL_Obool)), _1784587)), c_Hilbert__Choice_Oinv__into(_1784579, _1784581, c_Orderings_Otop__class_Otop(tc_fun(_1784579, tc_HOL_Obool)), _1784583)))], (49675 ^ _782464) ^ [_1784864, _1784866, _1784868, _1784870, _1784872, _1784874, _1784876] : [c_Fun_Oinj__on(_1784864, _1784866, _1784868, hAPP(c_Set_Oimage(_1784870, _1784864, _1784872), _1784874)), c_Fun_Oinj__on(_1784870, _1784864, _1784872, _1784874), hBOOL(hAPP(hAPP(c_member(_1784866), _1784876), hAPP(c_Set_Oimage(_1784864, _1784866, _1784868), hAPP(c_Set_Oimage(_1784870, _1784864, _1784872), _1784874)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784870, _1784866, _1784874, hAPP(c_Fun_Ocomp(_1784864, _1784866, _1784870, _1784868), _1784872)), _1784876) = hAPP(hAPP(c_Fun_Ocomp(_1784864, _1784870, _1784866, c_Hilbert__Choice_Oinv__into(_1784870, _1784864, _1784874, _1784872)), c_Hilbert__Choice_Oinv__into(_1784864, _1784866, hAPP(c_Set_Oimage(_1784870, _1784864, _1784872), _1784874), _1784868)), _1784876))], (49689 ^ _782464) ^ [_1785245, _1785247, _1785249] : [hAPP(c_Set_Oimage(_1785245, _1785247, _1785249), c_Orderings_Otop__class_Otop(tc_fun(_1785245, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785247, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1785245, _1785247, _1785247, _1785249), c_Hilbert__Choice_Oinv__into(_1785245, _1785247, c_Orderings_Otop__class_Otop(tc_fun(_1785245, tc_HOL_Obool)), _1785249)) = c_Fun_Oid(_1785247))], (49695 ^ _782464) ^ [_1785394, _1785396, _1785398] : [hAPP(c_Fun_Ocomp(_1785394, _1785396, _1785396, _1785398), c_Hilbert__Choice_Oinv__into(_1785394, _1785396, c_Orderings_Otop__class_Otop(tc_fun(_1785394, tc_HOL_Obool)), _1785398)) = c_Fun_Oid(_1785396), -(hAPP(c_Set_Oimage(_1785394, _1785396, _1785398), c_Orderings_Otop__class_Otop(tc_fun(_1785394, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785396, tc_HOL_Obool)))], (49701 ^ _782464) ^ [_1785549, _1785551, _1785553] : [c_Fun_Oinj__on(_1785549, _1785551, _1785553, c_Orderings_Otop__class_Otop(tc_fun(_1785549, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785551, _1785549, _1785549, c_Hilbert__Choice_Oinv__into(_1785549, _1785551, c_Orderings_Otop__class_Otop(tc_fun(_1785549, tc_HOL_Obool)), _1785553)), _1785553) = c_Fun_Oid(_1785549))], (49707 ^ _782464) ^ [_1785700, _1785702, _1785704] : [c_Fun_Oinj__on(_1785700, _1785702, _1785704, c_Orderings_Otop__class_Otop(tc_fun(_1785700, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785702, _1785700, _1785700, c_Hilbert__Choice_Oinv__into(_1785700, _1785702, c_Orderings_Otop__class_Otop(tc_fun(_1785700, tc_HOL_Obool)), _1785704)), _1785704) = c_Fun_Oid(_1785700))], (49713 ^ _782464) ^ [_1785829, _1785831, _1785833] : [hAPP(c_Fun_Ocomp(_1785831, _1785829, _1785829, c_Hilbert__Choice_Oinv__into(_1785829, _1785831, c_Orderings_Otop__class_Otop(tc_fun(_1785829, tc_HOL_Obool)), _1785833)), _1785833) = c_Fun_Oid(_1785829), -(c_Fun_Oinj__on(_1785829, _1785831, _1785833, c_Orderings_Otop__class_Otop(tc_fun(_1785829, tc_HOL_Obool))))], (49719 ^ _782464) ^ [_1785964, _1785966, _1785968, _1785970] : [c_Fun_Obij__betw(_1785964, _1785966, _1785968, c_Orderings_Otop__class_Otop(tc_fun(_1785964, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1785966, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1785964, _1785966, _1785968), _1785970) = hAPP(c_Set_Oimage(_1785966, _1785964, c_Hilbert__Choice_Oinv__into(_1785964, _1785966, c_Orderings_Otop__class_Otop(tc_fun(_1785964, tc_HOL_Obool)), _1785968)), _1785970))], (49725 ^ _782464) ^ [_1786119, _1786121, _1786123, _1786125, _1786127] : [c_Fun_Oinj__on(_1786119, _1786121, _1786123, c_Orderings_Otop__class_Otop(tc_fun(_1786119, tc_HOL_Obool))), 49731 ^ _782464 : [(49732 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786121), 49730 ^ [_1786119, _1786121, _1786123, _1786125, _1786127]), hAPP(c_Set_Oimage(_1786119, _1786121, _1786123), c_Orderings_Otop__class_Otop(tc_fun(_1786119, tc_HOL_Obool))))))], (49734 ^ _782464) ^ [] : [hBOOL(hAPP(_1786125, hAPP(c_Hilbert__Choice_Oinv__into(_1786119, _1786121, c_Orderings_Otop__class_Otop(tc_fun(_1786119, tc_HOL_Obool)), _1786123), 49730 ^ [_1786119, _1786121, _1786123, _1786125, _1786127])))]], -(hBOOL(hAPP(_1786125, _1786127)))], (49738 ^ _782464) ^ [_1786445, _1786447] : [class_Lazy__Sequence_Osmall__lazy(_1786445), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786445), _1786447) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1786445), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1786445)), c_List_Olist_ONil(_1786445)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786445))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1786447)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1786445, tc_List_Olist(_1786445)), tc_List_Olist(_1786445), c_Lazy__Sequence_Oproduct(_1786445, tc_List_Olist(_1786445), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786445, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786447), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786447), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1786445, tc_List_Olist(_1786445), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786445))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1786445), tc_List_Olist(_1786445)), tc_fun(tc_List_Olist(_1786445), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786445))), _1786445), hAPP(c_COMBB(tc_List_Olist(_1786445), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786445)), tc_List_Olist(_1786445)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1786445)))), c_List_Olist_OCons(_1786445))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1786445)))))], (49744 ^ _782464) ^ [_1786806, _1786808, _1786810] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1786806, _1786808), _1786810) = c_Lazy__Sequence_Oproduct(_1786806, _1786808, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786806, _1786810), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786808, _1786810))), class_Lazy__Sequence_Osmall__lazy(_1786806), class_Lazy__Sequence_Osmall__lazy(_1786808)], (49754 ^ _782464) ^ [_1786969, _1786971, _1786973, _1786975] : [-(hAPP(c_New__DSequence_Opos__union(_1786969, _1786971, _1786973), _1786975) = c_Lazy__Sequence_Oappend(_1786969, hAPP(_1786971, _1786975), hAPP(_1786973, _1786975)))], (49756 ^ _782464) ^ [_1787030, _1787032] : [c_Wellfounded_Oacyclic(_1787030, hAPP(c_Set_OCollect(tc_prod(_1787030, _1787030)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787030, _1787030, tc_HOL_Obool), c_Predicate_Oconversep(_1787030, _1787030, _1787032)))), -(c_Wellfounded_Oacyclic(_1787030, hAPP(c_Set_OCollect(tc_prod(_1787030, _1787030)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787030, _1787030, tc_HOL_Obool), _1787032))))], (49762 ^ _782464) ^ [_1787171, _1787173] : [c_Wellfounded_Oacyclic(_1787171, hAPP(c_Set_OCollect(tc_prod(_1787171, _1787171)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787171, _1787171, tc_HOL_Obool), _1787173))), -(c_Wellfounded_Oacyclic(_1787171, hAPP(c_Set_OCollect(tc_prod(_1787171, _1787171)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787171, _1787171, tc_HOL_Obool), c_Predicate_Oconversep(_1787171, _1787171, _1787173)))))], (49768 ^ _782464) ^ [_1787318, _1787320, _1787322, _1787324] : [-(c_Predicate_Oconversep(_1787318, _1787320, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1787318, tc_fun(_1787320, tc_HOL_Obool))), _1787322), _1787324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1787320, tc_fun(_1787318, tc_HOL_Obool))), c_Predicate_Oconversep(_1787318, _1787320, _1787322)), c_Predicate_Oconversep(_1787318, _1787320, _1787324)))], (49770 ^ _782464) ^ [_1787387] : [-(c_Predicate_Oconversep(_1787387, _1787387, c_fequal) = c_fequal)], (49772 ^ _782464) ^ [_1787414, _1787416, _1787418] : [-(c_Predicate_Oconversep(_1787414, _1787416, c_Predicate_Oconversep(_1787416, _1787414, _1787418)) = _1787418)], (49774 ^ _782464) ^ [_1787473, _1787475, _1787477, _1787479, _1787481] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787473, _1787475, _1787477), _1787479), _1787481)), -(hBOOL(hAPP(hAPP(_1787477, _1787481), _1787479)))], (49780 ^ _782464) ^ [_1787580, _1787582, _1787584, _1787586, _1787588] : [hBOOL(hAPP(hAPP(_1787584, _1787588), _1787586)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787580, _1787582, _1787584), _1787586), _1787588)))], (49786 ^ _782464) ^ [_1787717, _1787719, _1787721, _1787723, _1787725] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787717, _1787719, _1787721), _1787723), _1787725)), -(hBOOL(hAPP(hAPP(_1787721, _1787725), _1787723)))], (49792 ^ _782464) ^ [_1787824, _1787826, _1787828, _1787830, _1787832] : [hBOOL(hAPP(hAPP(_1787828, _1787832), _1787830)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787824, _1787826, _1787828), _1787830), _1787832)))], (49798 ^ _782464) ^ [_1787937, _1787939, _1787941, _1787943, _1787945] : [hBOOL(hAPP(hAPP(_1787937, _1787939), _1787941)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787943, _1787945, _1787937), _1787941), _1787939)))], (49804 ^ _782464) ^ [_1788048, _1788050, _1788052, _1788054, _1788056] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788048, _1788050, _1788052), _1788054), _1788056)), -(hBOOL(hAPP(hAPP(_1788052, _1788056), _1788054)))], (49810 ^ _782464) ^ [_1788177, _1788179, _1788181] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788177, _1788177, hAPP(hAPP(c_COMBB(tc_fun(_1788177, tc_HOL_Obool), tc_fun(_1788177, tc_HOL_Obool), _1788177), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788177), c_fNot)), c_fequal)), _1788179), _1788181)), _1788179 = _1788181], (49816 ^ _782464) ^ [_1788315, _1788317, _1788319] : [-(_1788317 = _1788319), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788315, _1788315, hAPP(hAPP(c_COMBB(tc_fun(_1788315, tc_HOL_Obool), tc_fun(_1788315, tc_HOL_Obool), _1788315), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788315), c_fNot)), c_fequal)), _1788317), _1788319)))], (49822 ^ _782464) ^ [_1788387, _1788389, _1788391, _1788393, _1788395] : [-(c_Predicate_Oconversep(_1788387, _1788389, c_Predicate_Opred__comp(_1788387, _1788391, _1788389, _1788393, _1788395)) = c_Predicate_Opred__comp(_1788389, _1788391, _1788387, c_Predicate_Oconversep(_1788391, _1788389, _1788395), c_Predicate_Oconversep(_1788387, _1788391, _1788393)))], (49824 ^ _782464) ^ [_1788442, _1788444, _1788446, _1788448] : [-(c_Predicate_Oconversep(_1788442, _1788444, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788442, tc_fun(_1788444, tc_HOL_Obool))), _1788446), _1788448)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788444, tc_fun(_1788442, tc_HOL_Obool))), c_Predicate_Oconversep(_1788442, _1788444, _1788446)), c_Predicate_Oconversep(_1788442, _1788444, _1788448)))], (49826 ^ _782464) ^ [_1788535, _1788537, _1788539, _1788541, _1788543] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788535, _1788537, hAPP(hAPP(c_COMBC(_1788535, tc_fun(tc_prod(_1788535, _1788537), tc_HOL_Obool), tc_fun(_1788537, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788537, tc_fun(tc_fun(tc_prod(_1788535, _1788537), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1788535, _1788537), tc_HOL_Obool), tc_fun(_1788537, tc_HOL_Obool)), _1788535), c_COMBC(_1788537, tc_fun(tc_prod(_1788535, _1788537), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788537, tc_prod(_1788535, _1788537)), tc_fun(_1788537, tc_fun(tc_fun(tc_prod(_1788535, _1788537), tc_HOL_Obool), tc_HOL_Obool)), _1788535), hAPP(c_COMBB(tc_prod(_1788535, _1788537), tc_fun(tc_fun(tc_prod(_1788535, _1788537), tc_HOL_Obool), tc_HOL_Obool), _1788537), c_member(tc_prod(_1788535, _1788537)))), c_Product__Type_OPair(_1788535, _1788537)))), _1788539)), _1788541), _1788543)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788537, _1788535)), hAPP(hAPP(c_Product__Type_OPair(_1788537, _1788535), _1788541), _1788543)), hAPP(c_Relation_Oconverse(_1788535, _1788537), _1788539))))], (49832 ^ _782464) ^ [_1788918, _1788920, _1788922, _1788924, _1788926] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788920, _1788918)), hAPP(hAPP(c_Product__Type_OPair(_1788920, _1788918), _1788924), _1788926)), hAPP(c_Relation_Oconverse(_1788918, _1788920), _1788922))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788918, _1788920, hAPP(hAPP(c_COMBC(_1788918, tc_fun(tc_prod(_1788918, _1788920), tc_HOL_Obool), tc_fun(_1788920, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788920, tc_fun(tc_fun(tc_prod(_1788918, _1788920), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1788918, _1788920), tc_HOL_Obool), tc_fun(_1788920, tc_HOL_Obool)), _1788918), c_COMBC(_1788920, tc_fun(tc_prod(_1788918, _1788920), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788920, tc_prod(_1788918, _1788920)), tc_fun(_1788920, tc_fun(tc_fun(tc_prod(_1788918, _1788920), tc_HOL_Obool), tc_HOL_Obool)), _1788918), hAPP(c_COMBB(tc_prod(_1788918, _1788920), tc_fun(tc_fun(tc_prod(_1788918, _1788920), tc_HOL_Obool), tc_HOL_Obool), _1788920), c_member(tc_prod(_1788918, _1788920)))), c_Product__Type_OPair(_1788918, _1788920)))), _1788922)), _1788924), _1788926)))], (49838 ^ _782464) ^ [_1789307, _1789309, _1789311, _1789313, _1789315, _1789317] : [-(c_New__Random__Sequence_Opos__union(_1789307, _1789309, _1789311, _1789313, _1789315, _1789317) = c_New__DSequence_Opos__union(_1789307, hAPP(hAPP(hAPP(_1789309, _1789313), _1789315), _1789317), hAPP(hAPP(hAPP(_1789311, _1789313), _1789315), _1789317)))], (49840 ^ _782464) ^ [_1789378, _1789380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789378), _1789380)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789378, _1789380) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (49846 ^ _782464) ^ [_1789465, _1789467] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789465), _1789467))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789465, _1789467) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789467), c_Lazy__Sequence_Osmall__lazy_H(_1789465, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789467), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49852 ^ _782464) ^ [_1789527] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1789527) = c_Lazy__Sequence_Osmall__lazy_H(_1789527, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1789527)))], (49854 ^ _782464) ^ [_1789559, _1789561] : [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), _1789559), _1789561))), 49857 ^ _782464 : [(49858 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789559), _1789561)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789559, _1789561) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (49864 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789559), _1789561))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789559, _1789561) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789561), c_Lazy__Sequence_Osmall__lazy_H(_1789559, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789561), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (49870 ^ _782464) ^ [_1789811, _1789813, _1789815] : [-(_1789811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1789813), c_List_Oreplicate(_1789813, _1789811, _1789815)) = c_List_Oreplicate(_1789813, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1789811), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1789815))], (49876 ^ _782464) ^ [_1789868, _1789870, _1789872, _1789874, _1789876] : [-(hAPP(hAPP(c_List_Omap(_1789868, _1789870), _1789872), c_List_Oreplicate(_1789868, _1789874, _1789876)) = c_List_Oreplicate(_1789870, _1789874, hAPP(_1789872, _1789876)))], (49878 ^ _782464) ^ [_1789919, _1789921] : [-(c_List_Oreplicate(_1789919, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1789921) = c_List_Olist_ONil(_1789919))], (49880 ^ _782464) ^ [_1789968, _1789970, _1789972] : [c_List_Olist_ONil(_1789968) = c_List_Oreplicate(_1789968, _1789970, _1789972), -(_1789970 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49886 ^ _782464) ^ [_1790055, _1790057, _1790059] : [_1790057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1790055) = c_List_Oreplicate(_1790055, _1790057, _1790059))], (49892 ^ _782464) ^ [_1790166, _1790168, _1790170] : [c_List_Oreplicate(_1790166, _1790168, _1790170) = c_List_Olist_ONil(_1790166), -(_1790168 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49898 ^ _782464) ^ [_1790253, _1790255, _1790257] : [_1790255 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1790253, _1790255, _1790257) = c_List_Olist_ONil(_1790253))], (49904 ^ _782464) ^ [_1790346, _1790348] : [-(c_List_Oconcat(_1790346, c_List_Oreplicate(tc_List_Olist(_1790346), _1790348, c_List_Olist_ONil(_1790346))) = c_List_Olist_ONil(_1790346))], (49906 ^ _782464) ^ [_1790399, _1790401, _1790403, _1790405] : [hBOOL(hAPP(_1790399, _1790401)), -(hAPP(c_List_Ofilter(_1790403, _1790399), c_List_Oreplicate(_1790403, _1790405, _1790401)) = c_List_Oreplicate(_1790403, _1790405, _1790401))], (49912 ^ _782464) ^ [_1790506, _1790508, _1790510, _1790512] : [-(hBOOL(hAPP(_1790506, _1790508))), -(hAPP(c_List_Ofilter(_1790510, _1790506), c_List_Oreplicate(_1790510, _1790512, _1790508)) = c_List_Olist_ONil(_1790510))], (49918 ^ _782464) ^ [_1790562, _1790564, _1790566, _1790568] : [-(hAPP(hAPP(c_List_Oappend(_1790562), c_List_Oreplicate(_1790562, _1790564, _1790566)), c_List_Oreplicate(_1790562, _1790568, _1790566)) = hAPP(hAPP(c_List_Oappend(_1790562), c_List_Oreplicate(_1790562, _1790568, _1790566)), c_List_Oreplicate(_1790562, _1790564, _1790566)))], (49920 ^ _782464) ^ [_1790623, _1790625, _1790627, _1790629] : [-(c_List_Oreplicate(_1790623, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790625), _1790627), _1790629) = hAPP(hAPP(c_List_Oappend(_1790623), c_List_Oreplicate(_1790623, _1790625, _1790629)), c_List_Oreplicate(_1790623, _1790627, _1790629)))], (49922 ^ _782464) ^ [_1790678, _1790680, _1790682, _1790684] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790678), _1790680)), -(hAPP(hAPP(c_List_Onth(_1790682), c_List_Oreplicate(_1790682, _1790680, _1790684)), _1790678) = _1790684)], (49928 ^ _782464) ^ [_1790817, _1790819, _1790821, _1790823, _1790825] : [c_List_Oreplicate(_1790817, _1790819, _1790821) = c_List_Oreplicate(_1790817, _1790823, _1790825), 49931 ^ _782464 : [(49932 ^ _782464) ^ [] : [-(_1790819 = _1790823)], (49934 ^ _782464) ^ [] : [-(_1790819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1790821 = _1790825)]]], (49940 ^ _782464) ^ [_1790953, _1790955, _1790957, _1790959, _1790961] : [-(c_List_Oreplicate(_1790953, _1790955, _1790957) = c_List_Oreplicate(_1790953, _1790959, _1790961)), _1790955 = _1790959, 49945 ^ _782464 : [(49946 ^ _782464) ^ [] : [_1790955 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49948 ^ _782464) ^ [] : [_1790957 = _1790961]]], (49952 ^ _782464) ^ [_1791173, _1791175, _1791177, _1791179] : [49959 ^ _782464 : [(49960 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1791179, _1791177)))], (49962 ^ _782464) ^ [] : [_1791175 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 49953 ^ _782464 : [(49954 ^ _782464) ^ [_1791245] : [hBOOL(hAPP(hAPP(c_member(_1791173), _1791245), hAPP(c_List_Oset(_1791173), c_List_Oreplicate(_1791173, _1791175, _1791177)))), hBOOL(hAPP(_1791179, _1791245))]]], (49964 ^ _782464) ^ [_1791415, _1791417, _1791419, _1791421] : [49972 ^ _782464 : [(49973 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791415), 49971 ^ [_1791415, _1791417, _1791419, _1791421]), hAPP(c_List_Oset(_1791415), c_List_Oreplicate(_1791415, _1791417, _1791419)))))], (49975 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1791421, 49971 ^ [_1791415, _1791417, _1791419, _1791421])))]], hBOOL(hAPP(_1791421, _1791419)), -(_1791417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49977 ^ _782464) ^ [_1791671, _1791673, _1791675, _1791677] : [49979 ^ _782464 : [(49980 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791671), 49978 ^ [_1791671, _1791673, _1791675, _1791677]), hAPP(c_List_Oset(_1791671), c_List_Oreplicate(_1791671, _1791673, _1791675)))))], (49982 ^ _782464) ^ [] : [hBOOL(hAPP(_1791677, 49978 ^ [_1791671, _1791673, _1791675, _1791677]))]], -(hBOOL(hAPP(_1791677, _1791675))), -(_1791673 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49990 ^ _782464) ^ [_1791878, _1791880, _1791882, _1791884] : [49991 ^ _782464 : [(49992 ^ _782464) ^ [] : [hBOOL(hAPP(_1791884, _1791882))], (49994 ^ _782464) ^ [] : [_1791880 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 49995 ^ _782464 : [(49996 ^ _782464) ^ [_1792003] : [hBOOL(hAPP(hAPP(c_member(_1791878), _1792003), hAPP(c_List_Oset(_1791878), c_List_Oreplicate(_1791878, _1791880, _1791882)))), -(hBOOL(hAPP(_1791884, _1792003)))]]], (50002 ^ _782464) ^ [_1792130, _1792132, _1792134, _1792136, _1792138, _1792140] : [-(hAPP(hAPP(c_List_Ozip(_1792130, _1792132), c_List_Oreplicate(_1792130, _1792134, _1792136)), c_List_Oreplicate(_1792132, _1792138, _1792140)) = c_List_Oreplicate(tc_prod(_1792130, _1792132), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792134), _1792138), hAPP(hAPP(c_Product__Type_OPair(_1792130, _1792132), _1792136), _1792140)))], (50004 ^ _782464) ^ [_1792202, _1792204, _1792206, _1792208] : [-(hAPP(hAPP(c_List_Odrop(_1792202), _1792204), c_List_Oreplicate(_1792202, _1792206, _1792208)) = c_List_Oreplicate(_1792202, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1792206), _1792204), _1792208))], (50006 ^ _782464) ^ [_1792249, _1792251, _1792253] : [-(_1792249 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1792251), c_List_Oreplicate(_1792251, _1792249, _1792253)) = _1792253)], (50012 ^ _782464) ^ [_1792296, _1792298, _1792300, _1792302] : [-(hAPP(hAPP(c_List_Otake(_1792296), _1792298), c_List_Oreplicate(_1792296, _1792300, _1792302)) = c_List_Oreplicate(_1792296, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792298), _1792300), _1792302))], (50014 ^ _782464) ^ [_1792343, _1792345, _1792347] : [-(_1792343 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1792345, c_List_Oreplicate(_1792345, _1792343, _1792347)) = _1792347)], (50020 ^ _782464) ^ [_1792388, _1792390, _1792392] : [-(hAPP(c_List_Orev(_1792388), c_List_Oreplicate(_1792388, _1792390, _1792392)) = c_List_Oreplicate(_1792388, _1792390, _1792392))], (50022 ^ _782464) ^ [_1792428, _1792430, _1792432] : [-(c_List_Oreplicate(_1792428, hAPP(c_Nat_OSuc, _1792430), _1792432) = hAPP(hAPP(c_List_Olist_OCons(_1792428), _1792432), c_List_Oreplicate(_1792428, _1792430, _1792432)))], (50024 ^ _782464) ^ [_1792474, _1792476, _1792478, _1792480] : [-(hAPP(hAPP(c_List_Oappend(_1792474), c_List_Oreplicate(_1792474, _1792476, _1792478)), hAPP(hAPP(c_List_Olist_OCons(_1792474), _1792478), _1792480)) = hAPP(hAPP(c_List_Olist_OCons(_1792474), _1792478), hAPP(hAPP(c_List_Oappend(_1792474), c_List_Oreplicate(_1792474, _1792476, _1792478)), _1792480)))], (50026 ^ _782464) ^ [_1792543, _1792545, _1792547, _1792549] : [-(hAPP(hAPP(c_List_Omap(_1792543, _1792545), hAPP(c_COMBK(_1792545, _1792543), _1792547)), _1792549) = c_List_Oreplicate(_1792545, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792543)), _1792549), _1792547))], (50028 ^ _782464) ^ [_1792598, _1792600, _1792602] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792598)), c_List_Oreplicate(_1792598, _1792600, _1792602)) = _1792600)], (50030 ^ _782464) ^ [_1792636, _1792638, _1792640] : [-(c_List_Oreplicate(_1792636, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792636)), hAPP(c_List_Ofilter(_1792636, hAPP(c_fequal, _1792638)), _1792640)), _1792638) = hAPP(c_List_Ofilter(_1792636, hAPP(c_fequal, _1792638)), _1792640))], (50032 ^ _782464) ^ [_1792713, _1792715, _1792717, _1792719] : [hBOOL(hAPP(hAPP(c_member(_1792713), _1792715), hAPP(c_List_Oset(_1792713), c_List_Oreplicate(_1792713, _1792717, _1792719)))), 50035 ^ _782464 : [(50036 ^ _782464) ^ [] : [-(_1792715 = _1792719)], (50038 ^ _782464) ^ [] : [_1792717 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50040 ^ _782464) ^ [_1792856, _1792858, _1792860, _1792862] : [-(hBOOL(hAPP(hAPP(c_member(_1792856), _1792858), hAPP(c_List_Oset(_1792856), c_List_Oreplicate(_1792856, _1792860, _1792862))))), _1792858 = _1792862, -(_1792860 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50050 ^ _782464) ^ [_1793030, _1793032, _1793034] : [-(hAPP(hAPP(c_List_Oappend(_1793030), c_List_Oreplicate(_1793030, _1793032, _1793034)), hAPP(hAPP(c_List_Olist_OCons(_1793030), _1793034), c_List_Olist_ONil(_1793030))) = hAPP(hAPP(c_List_Olist_OCons(_1793030), _1793034), c_List_Oreplicate(_1793030, _1793032, _1793034)))], (50052 ^ _782464) ^ [_1793091, _1793093, _1793095] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1793091), hAPP(c_COMBK(_1793091, tc_Nat_Onat), _1793093)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1793095)) = c_List_Oreplicate(_1793091, _1793095, _1793093))], (50054 ^ _782464) ^ [_1793136, _1793138, _1793140] : [-(_1793136 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1793138), c_List_Oreplicate(_1793138, _1793136, _1793140)) = hAPP(hAPP(c_Set_Oinsert(_1793138), _1793140), c_Orderings_Obot__class_Obot(tc_fun(_1793138, tc_HOL_Obool))))], (50060 ^ _782464) ^ [_1793208, _1793210, _1793212] : [_1793208 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1793210), c_List_Oreplicate(_1793210, _1793208, _1793212)) = c_Orderings_Obot__class_Obot(tc_fun(_1793210, tc_HOL_Obool)))], (50066 ^ _782464) ^ [_1793309, _1793311, _1793313] : [-(_1793309 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1793311), c_List_Oreplicate(_1793311, _1793309, _1793313)) = hAPP(hAPP(c_Set_Oinsert(_1793311), _1793313), c_Orderings_Obot__class_Obot(tc_fun(_1793311, tc_HOL_Obool))))], (50072 ^ _782464) ^ [_1793371, _1793373, _1793375] : [-(hAPP(c_List_Oset(_1793371), c_List_Oreplicate(_1793371, hAPP(c_Nat_OSuc, _1793373), _1793375)) = hAPP(hAPP(c_Set_Oinsert(_1793371), _1793375), c_Orderings_Obot__class_Obot(tc_fun(_1793371, tc_HOL_Obool))))], (50074 ^ _782464) ^ [_1793423, _1793425, _1793427] : [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), _1793423), _1793425))), -(hBOOL(hAPP(hAPP(_1793427, _1793423), _1793425))), 50081 ^ _782464 : [(50082 ^ _782464) ^ [] : [-(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), 50079 ^ [_1793423, _1793425, _1793427]), 50080 ^ [_1793423, _1793425, _1793427]))))], (50090 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1793427, 50079 ^ [_1793423, _1793425, _1793427]), 50080 ^ [_1793423, _1793425, _1793427]))], (50084 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50079 ^ [_1793423, _1793425, _1793427]), 50080 ^ [_1793423, _1793425, _1793427]))), -(hBOOL(hAPP(hAPP(_1793427, 50079 ^ [_1793423, _1793425, _1793427]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50080 ^ [_1793423, _1793425, _1793427]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (50094 ^ _782464) ^ [_1793875, _1793877] : [-(c_Predicate_Opred__comp(_1793875, _1793875, _1793875, c_fequal, c_Predicate_Opred__comp(_1793875, _1793875, _1793875, _1793877, c_fequal)) = _1793877)], (50096 ^ _782464) ^ [_1793912, _1793914, _1793916] : [class_Fields_Olinordered__field(_1793912), 50102 ^ _782464 : [(50103 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1793912), c_Groups_Ozero__class_Ozero(_1793912)), 50101 ^ [_1793912, _1793914, _1793916])))], (50105 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793912), _1793914), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1793912), _1793916), 50101 ^ [_1793912, _1793914, _1793916])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793912), _1793914), _1793916)))], (50109 ^ _782464) ^ [_1794190, _1794192, _1794194] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794190)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1794190, _1794192, _1794194)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794190)), _1794194)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50111 ^ _782464) ^ [_1794241, _1794243, _1794245, _1794247] : [-(c_Lazy__Sequence_Oappend(_1794241, c_Lazy__Sequence_Olazy__sequence_OInsert(_1794241, _1794243, _1794245), _1794247) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794241, _1794243, c_Lazy__Sequence_Oappend(_1794241, _1794245, _1794247)))], (50113 ^ _782464) ^ [_1794310, _1794312, _1794314, _1794316, _1794318] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1794310, _1794312, _1794314) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794310, _1794316, _1794318), 50116 ^ _782464 : [(50117 ^ _782464) ^ [] : [-(_1794312 = _1794316)], (50119 ^ _782464) ^ [] : [-(_1794314 = _1794318)]]], (50121 ^ _782464) ^ [_1794431, _1794433, _1794435, _1794437, _1794439] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1794431, _1794433, _1794435) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794431, _1794437, _1794439)), _1794433 = _1794437, _1794435 = _1794439], (50131 ^ _782464) ^ [_1794590, _1794592, _1794594, _1794596] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794590, _1794592), c_Lazy__Sequence_Olazy__sequence_OInsert(_1794590, _1794594, _1794596)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1794592, _1794594)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794590, _1794592), _1794596))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50133 ^ _782464) ^ [_1794650, _1794652] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794650)), _1794652) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1794650, tc_Lazy__Sequence_Olazy__sequence(_1794650)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1794650, tc_Lazy__Sequence_Olazy__sequence(_1794650), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794650), tc_Nat_Onat), _1794650), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1794650), 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(_1794650)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794650)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1794650), _1794652)))], (50135 ^ _782464) ^ [_1794746, _1794748, _1794750] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794746, _1794748), _1794750) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1794746, tc_Lazy__Sequence_Olazy__sequence(_1794746)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1794746, tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1794746, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat)), _1794746), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1794746), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1794746)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1794746, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794746), tc_Nat_Onat)), _1794746), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1794746))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1794746), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1794748))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794746, _1794748))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1794746), _1794750)))], (50137 ^ _782464) ^ [_1794939, _1794941, _1794943, _1794945, _1794947] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1794939, _1794941, _1794943, _1794945, _1794947) = c_Option_Ooption_Ooption__case(_1794939, tc_prod(_1794941, tc_Lazy__Sequence_Olazy__sequence(_1794941)), _1794943, hAPP(c_Product__Type_Oprod_Oprod__case(_1794941, tc_Lazy__Sequence_Olazy__sequence(_1794941), _1794939), _1794945), hAPP(c_Lazy__Sequence_Oyield(_1794941), _1794947)))], (50139 ^ _782464) ^ [_1795001] : [-(c_Lazy__Sequence_Oyieldn(_1795001) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1795001), _1795001, c_Lazy__Sequence_Oyield(_1795001)))], (50141 ^ _782464) ^ [_1795034, _1795036, _1795038, _1795040, _1795042, _1795044] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1795034, _1795036, _1795038, _1795040, c_Lazy__Sequence_Olazy__sequence_OInsert(_1795036, _1795042, _1795044)) = hAPP(hAPP(_1795040, _1795042), _1795044))], (50143 ^ _782464) ^ [_1795083, _1795085, _1795087, _1795089, _1795091] : [50145 ^ _782464 : [(50146 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795083), 50144 ^ [_1795083, _1795085, _1795087, _1795089, _1795091]), _1795085)))], (50148 ^ _782464) ^ [] : [c_Relation_Orefl__on(_1795087, hAPP(_1795089, 50144 ^ [_1795083, _1795085, _1795087, _1795089, _1795091]), hAPP(_1795091, 50144 ^ [_1795083, _1795085, _1795087, _1795089, _1795091]))]], -(c_Relation_Orefl__on(_1795087, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1795083, tc_fun(_1795087, tc_HOL_Obool)), _1795085), _1795089), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1795083, tc_fun(tc_prod(_1795087, _1795087), tc_HOL_Obool)), _1795085), _1795091)))], (50152 ^ _782464) ^ [_1795369, _1795371, _1795373] : [hBOOL(hAPP(hAPP(c_member(_1795369), _1795371), hAPP(c_List_Oset(_1795369), _1795373))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1795369), _1795373), _1795371)))], (50158 ^ _782464) ^ [_1795482, _1795484, _1795486] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795482), _1795486), _1795484)), -(hBOOL(hAPP(hAPP(c_member(_1795482), _1795484), hAPP(c_List_Oset(_1795482), _1795486))))], (50174 ^ _782464) ^ [_1795756, _1795758, _1795760, _1795762] : [50175 ^ _782464 : [(50176 ^ _782464) ^ [] : [_1795758 = _1795762], (50178 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795756), _1795760), _1795762))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1795756), hAPP(hAPP(c_List_Olist_OCons(_1795756), _1795758), _1795760)), _1795762)))], (50164 ^ _782464) ^ [_1795622, _1795624, _1795626, _1795628] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795622), hAPP(hAPP(c_List_Olist_OCons(_1795622), _1795624), _1795626)), _1795628)), -(_1795624 = _1795628), -(hBOOL(hAPP(hAPP(c_List_Omember(_1795622), _1795626), _1795628)))], (50182 ^ _782464) ^ [_1795921] : [-(c_List_Omember(_1795921) = c_List_Oset(_1795921))], (50184 ^ _782464) ^ [_1795960, _1795962] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795960), c_List_Olist_ONil(_1795960)), _1795962))], (50186 ^ _782464) ^ [_1796012, _1796014, _1796016] : [hBOOL(hAPP(hAPP(c_List_Omember(_1796012), _1796014), _1796016)), -(hBOOL(hAPP(hAPP(c_member(_1796012), _1796016), hAPP(c_List_Oset(_1796012), _1796014))))], (50192 ^ _782464) ^ [_1796125, _1796127, _1796129] : [hBOOL(hAPP(hAPP(c_member(_1796125), _1796129), hAPP(c_List_Oset(_1796125), _1796127))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1796125), _1796127), _1796129)))], (50198 ^ _782464) ^ [_1796244, _1796246, _1796248, _1796250, _1796252, _1796254] : [-(c_Nitpick_Opair__box_Opair__box__size(_1796244, _1796246, _1796248, _1796250, c_Nitpick_Opair__box_OPairBox(_1796244, _1796246, _1796252, _1796254)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1796248, _1796252)), hAPP(_1796250, _1796254))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50200 ^ _782464) ^ [_1796324, _1796326, _1796328] : [c_List_Olist__ex1(_1796324, _1796326, _1796328), 50204 ^ _782464 : [(50205 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796324), 50203 ^ [_1796324, _1796326, _1796328]), hAPP(c_List_Oset(_1796324), _1796328))))], (50207 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1796326, 50203 ^ [_1796324, _1796326, _1796328])))], (50209 ^ _782464) ^ [_1796570] : [-(_1796570 = 50203 ^ [_1796324, _1796326, _1796328]), hBOOL(hAPP(hAPP(c_member(_1796324), _1796570), hAPP(c_List_Oset(_1796324), _1796328))), hBOOL(hAPP(_1796326, _1796570))]]], (50219 ^ _782464) ^ [_1796757, _1796759, _1796761] : [-(c_List_Olist__ex1(_1796757, _1796759, _1796761)), 50220 ^ _782464 : [(50221 ^ _782464) ^ [_1796851] : [hBOOL(hAPP(hAPP(c_member(_1796757), _1796851), hAPP(c_List_Oset(_1796757), _1796761))), hBOOL(hAPP(_1796759, _1796851)), 50229 ^ _782464 : [(50230 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796757), 50228 ^ [_1796757, _1796759, _1796761, _1796851]), hAPP(c_List_Oset(_1796757), _1796761))))], (50232 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1796759, 50228 ^ [_1796757, _1796759, _1796761, _1796851])))], (50234 ^ _782464) ^ [] : [50228 ^ [_1796757, _1796759, _1796761, _1796851] = _1796851]]]]], (50238 ^ _782464) ^ [_1797213, _1797215, _1797217, _1797219, _1797221, _1797223] : [c_Nitpick_Opair__box_OPairBox(_1797213, _1797215, _1797217, _1797219) = c_Nitpick_Opair__box_OPairBox(_1797213, _1797215, _1797221, _1797223), 50241 ^ _782464 : [(50242 ^ _782464) ^ [] : [-(_1797217 = _1797221)], (50244 ^ _782464) ^ [] : [-(_1797219 = _1797223)]]], (50246 ^ _782464) ^ [_1797340, _1797342, _1797344, _1797346, _1797348, _1797350] : [-(c_Nitpick_Opair__box_OPairBox(_1797340, _1797342, _1797344, _1797346) = c_Nitpick_Opair__box_OPairBox(_1797340, _1797342, _1797348, _1797350)), _1797344 = _1797348, _1797346 = _1797350], (50256 ^ _782464) ^ [_1797507, _1797509, _1797511, _1797513] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1797507, _1797509)), c_Nitpick_Opair__box_OPairBox(_1797507, _1797509, _1797511, _1797513)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50258 ^ _782464) ^ [_1797549, _1797551, _1797553, _1797555, _1797557, _1797559] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1797549, _1797551, _1797553, _1797555, c_Nitpick_Opair__box_OPairBox(_1797549, _1797551, _1797557, _1797559)) = hAPP(hAPP(_1797555, _1797557), _1797559))], (50260 ^ _782464) ^ [_1797599, _1797601, _1797603, _1797605, _1797607, _1797609] : [-(c_Nitpick_Opair__box_Opair__box__case(_1797599, _1797601, _1797603, _1797605, c_Nitpick_Opair__box_OPairBox(_1797599, _1797601, _1797607, _1797609)) = hAPP(hAPP(_1797605, _1797607), _1797609))], (50262 ^ _782464) ^ [_1797661, _1797663, _1797665] : [-(c_FunDef_OTHE__default(_1797663, _1797665, _1797661) = c_HOL_OThe(_1797663, _1797661)), 50263 ^ _782464 : [(50264 ^ _782464) ^ [_1797725] : [hBOOL(hAPP(_1797661, _1797725)), 50268 ^ _782464 : [(50269 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1797661, 50267 ^ [_1797661, _1797663, _1797665, _1797725])))], (50271 ^ _782464) ^ [] : [50267 ^ [_1797661, _1797663, _1797665, _1797725] = _1797725]]]]], (50275 ^ _782464) ^ [_1797919, _1797921, _1797923] : [-(c_FunDef_OTHE__default(_1797921, _1797923, _1797919) = _1797923), 50277 ^ _782464 : [(50278 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1797919, 50276 ^ [_1797919, _1797921, _1797923])))], (50280 ^ _782464) ^ [_1798041] : [hBOOL(hAPP(_1797919, _1798041)), -(_1798041 = 50276 ^ [_1797919, _1797921, _1797923])]]], (50288 ^ _782464) ^ [_1798180, _1798182, _1798184, _1798186] : [class_Groups_Ocomm__monoid__add(_1798180), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1798182, tc_HOL_Obool)), _1798184)), 50298 ^ _782464 : [(50299 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798182, tc_HOL_Obool)), 50297 ^ [_1798180, _1798182, _1798184, _1798186]), _1798184)))], (50301 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1798182), 50297 ^ [_1798180, _1798182, _1798184, _1798186]))]], 50305 ^ _782464 : [(50306 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798182, tc_HOL_Obool)), 50304 ^ [_1798180, _1798182, _1798184, _1798186]), _1798184)))], (50309 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798182, tc_HOL_Obool)), 50307 ^ [_1798180, _1798182, _1798184, _1798186]), _1798184)))], (50311 ^ _782464) ^ [] : [50304 ^ [_1798180, _1798182, _1798184, _1798186] = 50307 ^ [_1798180, _1798182, _1798184, _1798186]], (50314 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798182), 50312 ^ [_1798180, _1798182, _1798184, _1798186]), 50304 ^ [_1798180, _1798182, _1798184, _1798186])))], (50316 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798182), 50312 ^ [_1798180, _1798182, _1798184, _1798186]), 50307 ^ [_1798180, _1798182, _1798184, _1798186])))], (50318 ^ _782464) ^ [] : [hAPP(_1798186, 50312 ^ [_1798180, _1798182, _1798184, _1798186]) = c_Groups_Ozero__class_Ozero(_1798180)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1798182, _1798180), _1798186), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1798182, tc_HOL_Obool), _1798184)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1798182, tc_HOL_Obool), _1798180), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1798182, _1798180), _1798186)), _1798184))], (50322 ^ _782464) ^ [_1799177, _1799179] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1799177)), _1799179)), 50326 ^ _782464 : [(50327 ^ _782464) ^ [_1799278] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1799177)), _1799278), _1799179)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799177)), _1799278)), 50325 ^ [_1799177, _1799179])))]]], (50333 ^ _782464) ^ [_1799417] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1799417)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799417)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50335 ^ _782464) ^ [_1799464, _1799466, _1799468] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799464) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1799464, _1799466, _1799468)], (50337 ^ _782464) ^ [_1799512, _1799514, _1799516] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1799512, _1799514, _1799516) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799512)], (50339 ^ _782464) ^ [_1799545, _1799547] : [-(c_Lazy__Sequence_Oappend(_1799545, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799545), _1799547) = _1799547)], (50341 ^ _782464) ^ [_1799576, _1799578, _1799580, _1799582] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1799576, _1799578, _1799580, _1799582, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799578)) = _1799580)], (50343 ^ _782464) ^ [_1799613, _1799615] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1799613, _1799615), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799613)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50345 ^ _782464) ^ [_1799664, _1799666, _1799668] : [c_List_Olist__all(tc_Int_Oint, _1799664, c_List_Oupto(_1799666, _1799668)), -(c_List_Oall__interval__int(_1799664, _1799666, _1799668))], (50351 ^ _782464) ^ [_1799749, _1799751, _1799753] : [c_List_Oall__interval__int(_1799749, _1799751, _1799753), -(c_List_Olist__all(tc_Int_Oint, _1799749, c_List_Oupto(_1799751, _1799753)))], (50357 ^ _782464) ^ [_1799858, _1799860, _1799862] : [c_List_Olist__ex(tc_Int_Oint, _1799858, c_List_Oupto(_1799860, _1799862)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1799858), _1799860, _1799862)], (50363 ^ _782464) ^ [_1799948, _1799950, _1799952] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1799948), _1799950, _1799952)), -(c_List_Olist__ex(tc_Int_Oint, _1799948, c_List_Oupto(_1799950, _1799952)))], (50379 ^ _782464) ^ [_1800195, _1800197, _1800199] : [50381 ^ _782464 : [(50382 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 50380 ^ [_1800195, _1800197, _1800199]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1800197, _1800199))))], (50384 ^ _782464) ^ [] : [hBOOL(hAPP(_1800195, 50380 ^ [_1800195, _1800197, _1800199]))]], -(c_List_Oall__interval__int(_1800195, _1800197, _1800199))], (50369 ^ _782464) ^ [_1800014, _1800016, _1800018] : [c_List_Oall__interval__int(_1800014, _1800016, _1800018), 50372 ^ _782464 : [(50373 ^ _782464) ^ [_1800092] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1800092), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1800016, _1800018))), -(hBOOL(hAPP(_1800014, _1800092)))]]], (50388 ^ _782464) ^ [_1800371, _1800373, _1800375, _1800377] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800371, _1800373, _1800375, c_Code__Numeral_OSuc__code__numeral(_1800377)) = hAPP(hAPP(_1800375, _1800377), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800371, _1800373, _1800375, _1800377)))], (50390 ^ _782464) ^ [_1800433, _1800435, _1800437, _1800439] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1800433), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1800435, _1800437, _1800433, _1800439) = 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(_1800435)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1800435)))], (50396 ^ _782464) ^ [_1800564, _1800566, _1800568, _1800570] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1800564), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1800566, _1800568, _1800564, _1800570) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1800566, 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(_1800566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1800568, _1800570)), 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(_1800566)))), 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(_1800566)))), 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(_1800566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1800566, 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(_1800566)))), 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(_1800566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1800566, _1800568, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1800564), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1800570))), 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(_1800566)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800566))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800566)))), 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(_1800566)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1800566, 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(_1800566)))), 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(_1800566)))), 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(_1800566))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800566)))), 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(_1800566)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800566)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800566))))), tc_prod(_1800566, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1800566)), hAPP(hAPP(c_COMBB(_1800566, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800566)))), tc_prod(_1800566, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1800566)), c_Product__Type_Ofst(_1800566, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (50402 ^ _782464) ^ [_1800943, _1800945, _1800947] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800943, _1800945, _1800947, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1800945)], (50404 ^ _782464) ^ [_1800975, _1800977, _1800979] : [-(c_Random__Sequence_Oempty(_1800975, _1800977, _1800979) = 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(_1800975)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1800975)))], (50406 ^ _782464) ^ [_1801024, _1801026, _1801028, _1801030] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1801024), _1801026), _1801028), _1801030) = 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(_1801024)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1801024), _1801026)))], (50408 ^ _782464) ^ [_1801085, _1801087, _1801089, _1801091] : [-(c_Random__Sequence_Omap(_1801085, _1801087, _1801089, _1801091) = c_Random__Sequence_Obind(_1801085, _1801087, _1801091, hAPP(c_Fun_Ocomp(_1801087, 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(_1801087)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1801085, c_Random__Sequence_Osingle(_1801087)), _1801089)))], (50410 ^ _782464) ^ [_1801156, _1801158, _1801160, _1801162, _1801164, _1801166, _1801168] : [hBOOL(hAPP(hAPP(_1801156, hAPP(c_Product__Type_Osnd(_1801158, _1801160), _1801162)), hAPP(c_Product__Type_Ofst(_1801158, _1801160), _1801162))), 50417 ^ _782464 : [(50418 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1801156, 50416 ^ [_1801156, _1801158, _1801160, _1801162, _1801164, _1801166, _1801168]), 50415 ^ [_1801156, _1801158, _1801160, _1801162, _1801164, _1801166, _1801168])))], (50420 ^ _782464) ^ [] : [hBOOL(hAPP(_1801164, hAPP(hAPP(_1801166, 50415 ^ [_1801156, _1801158, _1801160, _1801162, _1801164, _1801166, _1801168]), 50416 ^ [_1801156, _1801158, _1801160, _1801162, _1801164, _1801166, _1801168])))]], -(hBOOL(hAPP(_1801164, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1801158, _1801160, _1801168), _1801166), _1801162))))], (50424 ^ _782464) ^ [_1801553, _1801555, _1801557, _1801559] : [-(hAPP(c_Relation_OImage(_1801553, _1801555, hAPP(c_Set_OCollect(tc_prod(_1801553, _1801555)), hAPP(c_Product__Type_Oprod_Oprod__case(_1801553, _1801555, tc_HOL_Obool), _1801557))), _1801559) = hAPP(c_Set_OCollect(_1801555), hAPP(hAPP(c_COMBB(tc_fun(_1801553, tc_HOL_Obool), tc_HOL_Obool, _1801555), c_HOL_OEx(_1801553)), hAPP(hAPP(c_COMBB(tc_fun(_1801553, tc_HOL_Obool), tc_fun(_1801553, tc_HOL_Obool), _1801555), hAPP(c_COMBS(_1801553, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1801553), c_fconj), hAPP(hAPP(c_COMBC(_1801553, tc_fun(_1801553, tc_HOL_Obool), tc_HOL_Obool), c_member(_1801553)), _1801559)))), hAPP(c_COMBC(_1801553, _1801555, tc_HOL_Obool), _1801557)))))], (50426 ^ _782464) ^ [_1801679, _1801681, _1801683, _1801685, _1801687] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801679), tc_List_Olist(_1801679))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801679), tc_List_Olist(_1801679)), _1801681), _1801683)), c_List_Olexord(_1801679, _1801685))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801679), tc_List_Olist(_1801679))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801679), tc_List_Olist(_1801679)), _1801683), _1801687)), c_List_Olexord(_1801679, _1801685))), c_Relation_Otrans(_1801679, _1801685), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801679), tc_List_Olist(_1801679))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801679), tc_List_Olist(_1801679)), _1801681), _1801687)), c_List_Olexord(_1801679, _1801685))))], (50440 ^ _782464) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (50442 ^ _782464) ^ [_1802076, _1802078, _1802080, _1802082] : [c_Relation_Otrans(_1802076, _1802078), c_Relation_Otrans(_1802080, _1802082), -(c_Relation_Otrans(tc_prod(_1802076, _1802080), c_Wellfounded_Olex__prod(_1802076, _1802080, _1802078, _1802082)))], (50452 ^ _782464) ^ [_1802229, _1802231, _1802233, _1802235, _1802237] : [c_Relation_Otrans(_1802229, _1802231), hBOOL(hAPP(hAPP(c_member(tc_prod(_1802229, _1802229)), hAPP(hAPP(c_Product__Type_OPair(_1802229, _1802229), _1802233), _1802235)), _1802231)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1802229, _1802229)), hAPP(hAPP(c_Product__Type_OPair(_1802229, _1802229), _1802235), _1802237)), _1802231)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802229, _1802229)), hAPP(hAPP(c_Product__Type_OPair(_1802229, _1802229), _1802233), _1802237)), _1802231)))], (50480 ^ _782464) ^ [_1802999, _1803001] : [50483 ^ _782464 : [(50484 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802999, _1802999)), hAPP(hAPP(c_Product__Type_OPair(_1802999, _1802999), 50481 ^ [_1802999, _1803001]), 50482 ^ [_1802999, _1803001])), _1803001)))], (50487 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802999, _1802999)), hAPP(hAPP(c_Product__Type_OPair(_1802999, _1802999), 50482 ^ [_1802999, _1803001]), 50485 ^ [_1802999, _1803001])), _1803001)))], (50489 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802999, _1802999)), hAPP(hAPP(c_Product__Type_OPair(_1802999, _1802999), 50481 ^ [_1802999, _1803001]), 50485 ^ [_1802999, _1803001])), _1803001))]], -(c_Relation_Otrans(_1802999, _1803001))], (50466 ^ _782464) ^ [_1802557, _1802559] : [c_Relation_Otrans(_1802557, _1802559), 50469 ^ _782464 : [(50470 ^ _782464) ^ [_1802693, _1802695] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802557, _1802557)), hAPP(hAPP(c_Product__Type_OPair(_1802557, _1802557), _1802695), _1802693)), _1802559)), 50473 ^ _782464 : [(50474 ^ _782464) ^ [_1802836] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802557, _1802557)), hAPP(hAPP(c_Product__Type_OPair(_1802557, _1802557), _1802693), _1802836)), _1802559)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802557, _1802557)), hAPP(hAPP(c_Product__Type_OPair(_1802557, _1802557), _1802695), _1802836)), _1802559)))]]]]], (50493 ^ _782464) ^ [_1803419, _1803421, _1803423, _1803425] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803419, tc_fun(_1803421, tc_HOL_Obool)), _1803423), _1803425) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803421, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1803421, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1803419, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1803421, tc_HOL_Obool)), c_HOL_OEx(_1803419)), hAPP(hAPP(c_COMBB(tc_fun(_1803419, tc_HOL_Obool), tc_fun(_1803419, tc_HOL_Obool), tc_fun(_1803421, tc_HOL_Obool)), hAPP(c_COMBS(_1803419, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803419), c_fconj), hAPP(hAPP(c_COMBC(_1803419, tc_fun(_1803419, tc_HOL_Obool), tc_HOL_Obool), c_member(_1803419)), _1803423)))), hAPP(hAPP(c_COMBC(tc_fun(_1803421, tc_HOL_Obool), tc_fun(_1803419, tc_fun(_1803421, tc_HOL_Obool)), tc_fun(_1803419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803421, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803419, tc_fun(_1803421, tc_HOL_Obool)), tc_fun(_1803419, tc_HOL_Obool)), tc_fun(_1803421, tc_HOL_Obool)), c_COMBB(tc_fun(_1803421, tc_HOL_Obool), tc_HOL_Obool, _1803419)), c_fequal)), _1803425))))))], (50495 ^ _782464) ^ [_1803603, _1803605] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803603, tc_HOL_Obool), _1803605) = hAPP(c_Set_OCollect(_1803603), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803603, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1803603), c_HOL_OEx(tc_fun(_1803603, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803603, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803603, tc_HOL_Obool), tc_HOL_Obool), _1803603), hAPP(c_COMBS(tc_fun(_1803603, 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(_1803603, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1803603, tc_HOL_Obool), tc_fun(tc_fun(_1803603, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1803603, tc_HOL_Obool))), _1803605)))), c_member(_1803603)))))], (50497 ^ _782464) ^ [_1803731, _1803733, _1803735, _1803737] : [c_Relation_Otrans(_1803731, _1803733), -(c_Relation_Otrans(_1803735, hAPP(hAPP(c_Relation_Oinv__image(_1803731, _1803735), _1803733), _1803737)))], (50503 ^ _782464) ^ [_1803830, _1803832] : [c_Relation_Otrans(_1803830, _1803832), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1803830, _1803830), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1803830, _1803830, _1803830), _1803832), _1803832)), _1803832)))], (50509 ^ _782464) ^ [_1803953] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803953, tc_HOL_Obool) = c_Set_OBex(_1803953))], (50511 ^ _782464) ^ [_1803981, _1803983, _1803985] : [c_Relation_Otrans(_1803981, _1803983), c_Relation_Otrans(_1803981, _1803985), -(c_Relation_Otrans(_1803981, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1803981, _1803981), tc_HOL_Obool)), _1803983), _1803985)))], (50532 ^ _782464) ^ [_1804357, _1804359] : [50533 ^ _782464 : [(50534 ^ _782464) ^ [_1804423] : [hBOOL(hAPP(_1804359, _1804423))]], 50536 ^ _782464 : [(50537 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804357), 50535 ^ [_1804357, _1804359]), c_Orderings_Otop__class_Otop(tc_fun(_1804357, tc_HOL_Obool)))))], (50539 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1804359, 50535 ^ [_1804357, _1804359])))]]], (50521 ^ _782464) ^ [_1804157, _1804159] : [-(hBOOL(hAPP(_1804159, 50528 ^ [_1804157, _1804159]))), 50522 ^ _782464 : [(50523 ^ _782464) ^ [_1804218] : [hBOOL(hAPP(hAPP(c_member(_1804157), _1804218), c_Orderings_Otop__class_Otop(tc_fun(_1804157, tc_HOL_Obool)))), hBOOL(hAPP(_1804159, _1804218))]]], (50541 ^ _782464) ^ [_1804526, _1804528] : [-(c_Relation_Otrans(_1804526, c_Transitive__Closure_Ortrancl(_1804526, _1804528)))], (50543 ^ _782464) ^ [_1804554, _1804556] : [c_Relation_Otrans(_1804554, _1804556), -(c_Relation_Otrans(tc_List_Olist(_1804554), c_List_Olexord(_1804554, _1804556)))], (50549 ^ _782464) ^ [_1804641] : [-(c_Relation_Otrans(tc_fun(_1804641, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1804641)))], (50551 ^ _782464) ^ [_1804669, _1804671] : [-(c_Relation_Otrans(_1804669, c_Relation_OId__on(_1804669, _1804671)))], (50553 ^ _782464) ^ [_1804697, _1804699] : [c_Relation_Otrans(_1804697, _1804699), -(c_Transitive__Closure_Otrancl(_1804697, _1804699) = _1804699)], (50559 ^ _782464) ^ [_1804780, _1804782] : [-(c_Relation_Otrans(_1804780, c_Transitive__Closure_Otrancl(_1804780, _1804782)))], (50561 ^ _782464) ^ [_1804808] : [-(c_Relation_Otrans(_1804808, c_Relation_OId(_1804808)))], (50563 ^ _782464) ^ [_1804848, _1804850] : [c_Relation_Otrans(_1804848, hAPP(c_Relation_Oconverse(_1804848, _1804848), _1804850)), -(c_Relation_Otrans(_1804848, _1804850))], (50569 ^ _782464) ^ [_1804933, _1804935] : [c_Relation_Otrans(_1804933, _1804935), -(c_Relation_Otrans(_1804933, hAPP(c_Relation_Oconverse(_1804933, _1804933), _1804935)))], (50575 ^ _782464) ^ [_1805024, _1805026] : [c_Relation_Otrans(_1805024, _1805026), -(c_Relation_Otrans(tc_List_Olist(_1805024), c_List_Olistrel(_1805024, _1805026)))], (50581 ^ _782464) ^ [_1805111, _1805113, _1805115] : [hBOOL(hAPP(hAPP(c_member(_1805113), _1805111), c_Orderings_Obot__class_Obot(tc_fun(_1805113, tc_HOL_Obool)))), hBOOL(hAPP(_1805115, _1805111))], (50587 ^ _782464) ^ [_1805231, _1805233, _1805235, _1805237] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805231), _1805233)), 50590 ^ _782464 : [(50601 ^ _782464) ^ [] : [50603 ^ _782464 : [(50604 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805231), 50602 ^ [_1805231, _1805233, _1805235, _1805237]), _1805233)))], (50606 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805235), hAPP(c_Set_OCollect(_1805235), hAPP(hAPP(c_COMBC(_1805235, _1805231, tc_HOL_Obool), _1805237), 50602 ^ [_1805231, _1805233, _1805235, _1805237]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805235), hAPP(c_Set_OCollect(_1805235), hAPP(hAPP(c_COMBB(tc_fun(_1805231, tc_HOL_Obool), tc_HOL_Obool, _1805235), c_HOL_OEx(_1805231)), hAPP(hAPP(c_COMBB(tc_fun(_1805231, tc_HOL_Obool), tc_fun(_1805231, tc_HOL_Obool), _1805235), hAPP(c_COMBS(_1805231, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805231), c_fconj), hAPP(hAPP(c_COMBC(_1805231, tc_fun(_1805231, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805231)), _1805233)))), _1805237))))))], (50591 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805235), hAPP(c_Set_OCollect(_1805235), hAPP(hAPP(c_COMBB(tc_fun(_1805231, tc_HOL_Obool), tc_HOL_Obool, _1805235), c_HOL_OEx(_1805231)), hAPP(hAPP(c_COMBB(tc_fun(_1805231, tc_HOL_Obool), tc_fun(_1805231, tc_HOL_Obool), _1805235), hAPP(c_COMBS(_1805231, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805231), c_fconj), hAPP(hAPP(c_COMBC(_1805231, tc_fun(_1805231, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805231)), _1805233)))), _1805237))))), 50594 ^ _782464 : [(50595 ^ _782464) ^ [_1805670] : [hBOOL(hAPP(hAPP(c_member(_1805231), _1805670), _1805233)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805235), hAPP(c_Set_OCollect(_1805235), hAPP(hAPP(c_COMBC(_1805235, _1805231, tc_HOL_Obool), _1805237), _1805670)))))]]]]], (50610 ^ _782464) ^ [_1806389, _1806391] : [c_Relation_Otrans(_1806389, _1806391), -(c_Relation_Otrans(_1806389, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1806389, _1806389), tc_HOL_Obool)), _1806391), c_Relation_OId(_1806389))))], (50616 ^ _782464) ^ [_1806674, _1806676, _1806678] : [c_List_Olist__ex(_1806674, _1806676, _1806678), 50620 ^ _782464 : [(50621 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806674), 50619 ^ [_1806674, _1806676, _1806678]), hAPP(c_List_Oset(_1806674), _1806678))))], (50623 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1806676, 50619 ^ [_1806674, _1806676, _1806678])))]]], (50625 ^ _782464) ^ [_1807041, _1807043, _1807045] : [-(c_List_Olist__ex(_1807041, _1807043, _1807045)), 50626 ^ _782464 : [(50627 ^ _782464) ^ [_1807150] : [hBOOL(hAPP(hAPP(c_member(_1807041), _1807150), hAPP(c_List_Oset(_1807041), _1807045))), hBOOL(hAPP(_1807043, _1807150))]]], (50645 ^ _782464) ^ [_1807874, _1807876, _1807878] : [c_List_Olist__ex(_1807874, _1807878, _1807876), 50649 ^ _782464 : [(50650 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1807874), 50648 ^ [_1807874, _1807876, _1807878]), hAPP(c_List_Oset(_1807874), _1807876))))], (50652 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1807878, 50648 ^ [_1807874, _1807876, _1807878])))]]], (50635 ^ _782464) ^ [_1807504, _1807506, _1807508] : [-(c_List_Olist__ex(_1807504, _1807508, _1807506)), 50636 ^ _782464 : [(50637 ^ _782464) ^ [_1807613] : [hBOOL(hAPP(hAPP(c_member(_1807504), _1807613), hAPP(c_List_Oset(_1807504), _1807506))), hBOOL(hAPP(_1807508, _1807613))]]], (50654 ^ _782464) ^ [_1808304, _1808306, _1808308, _1808310] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1808304, tc_fun(_1808306, tc_HOL_Obool)), _1808308), _1808310) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1808306, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1808306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808304, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1808306, tc_HOL_Obool)), c_HOL_OEx(_1808304)), hAPP(hAPP(c_COMBB(tc_fun(_1808304, tc_HOL_Obool), tc_fun(_1808304, tc_HOL_Obool), tc_fun(_1808306, tc_HOL_Obool)), hAPP(c_COMBS(_1808304, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1808304), c_fconj), hAPP(hAPP(c_COMBC(_1808304, tc_fun(_1808304, tc_HOL_Obool), tc_HOL_Obool), c_member(_1808304)), _1808308)))), hAPP(hAPP(c_COMBC(tc_fun(_1808306, tc_HOL_Obool), tc_fun(_1808304, tc_fun(_1808306, tc_HOL_Obool)), tc_fun(_1808304, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808306, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1808304, tc_fun(_1808306, tc_HOL_Obool)), tc_fun(_1808304, tc_HOL_Obool)), tc_fun(_1808306, tc_HOL_Obool)), c_COMBB(tc_fun(_1808306, tc_HOL_Obool), tc_HOL_Obool, _1808304)), c_fequal)), _1808310))))))], (50656 ^ _782464) ^ [_1808600, _1808602, _1808604, _1808606] : [class_Complete__Lattice_Ocomplete__lattice(_1808600), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1808602, _1808600), _1808604), _1808606) = c_Complete__Lattice_OSup__class_OSup(_1808600, hAPP(c_Set_OCollect(_1808600), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808602, _1808600), tc_HOL_Obool), tc_HOL_Obool, _1808600), c_HOL_OEx(tc_fun(_1808602, _1808600))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808602, _1808600), tc_HOL_Obool), tc_fun(tc_fun(_1808602, _1808600), tc_HOL_Obool), _1808600), hAPP(c_COMBS(tc_fun(_1808602, _1808600), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1808602, _1808600)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1808602, _1808600), tc_fun(tc_fun(_1808602, _1808600), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1808602, _1808600))), _1808604)))), hAPP(hAPP(c_COMBC(_1808600, tc_fun(tc_fun(_1808602, _1808600), _1808600), tc_fun(tc_fun(_1808602, _1808600), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808600, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1808602, _1808600), _1808600), tc_fun(tc_fun(_1808602, _1808600), tc_HOL_Obool)), _1808600), c_COMBB(_1808600, tc_HOL_Obool, tc_fun(_1808602, _1808600))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1808602, _1808600), _1808602, _1808600), c_COMBI(tc_fun(_1808602, _1808600))), _1808606)))))))], (50662 ^ _782464) ^ [_1809212, _1809214, _1809216, _1809218] : [class_Complete__Lattice_Ocomplete__lattice(_1809212), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1809214, _1809212), _1809216), _1809218) = c_Complete__Lattice_OSup__class_OSup(_1809212, hAPP(c_Set_OCollect(_1809212), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809214, _1809212), tc_HOL_Obool), tc_HOL_Obool, _1809212), c_HOL_OEx(tc_fun(_1809214, _1809212))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809214, _1809212), tc_HOL_Obool), tc_fun(tc_fun(_1809214, _1809212), tc_HOL_Obool), _1809212), hAPP(c_COMBS(tc_fun(_1809214, _1809212), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1809214, _1809212)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1809214, _1809212), tc_fun(tc_fun(_1809214, _1809212), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1809214, _1809212))), _1809216)))), hAPP(hAPP(c_COMBC(_1809212, tc_fun(tc_fun(_1809214, _1809212), _1809212), tc_fun(tc_fun(_1809214, _1809212), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1809212, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1809214, _1809212), _1809212), tc_fun(tc_fun(_1809214, _1809212), tc_HOL_Obool)), _1809212), c_COMBB(_1809212, tc_HOL_Obool, tc_fun(_1809214, _1809212))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1809214, _1809212), _1809214, _1809212), c_COMBI(tc_fun(_1809214, _1809212))), _1809218)))))))], (50668 ^ _782464) ^ [_1809824, _1809826, _1809828, _1809830] : [class_Complete__Lattice_Ocomplete__lattice(_1809824), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1809826, _1809824), _1809828), _1809830) = c_Complete__Lattice_OInf__class_OInf(_1809824, hAPP(c_Set_OCollect(_1809824), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809826, _1809824), tc_HOL_Obool), tc_HOL_Obool, _1809824), c_HOL_OEx(tc_fun(_1809826, _1809824))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1809826, _1809824), tc_HOL_Obool), tc_fun(tc_fun(_1809826, _1809824), tc_HOL_Obool), _1809824), hAPP(c_COMBS(tc_fun(_1809826, _1809824), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1809826, _1809824)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1809826, _1809824), tc_fun(tc_fun(_1809826, _1809824), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1809826, _1809824))), _1809828)))), hAPP(hAPP(c_COMBC(_1809824, tc_fun(tc_fun(_1809826, _1809824), _1809824), tc_fun(tc_fun(_1809826, _1809824), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1809824, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1809826, _1809824), _1809824), tc_fun(tc_fun(_1809826, _1809824), tc_HOL_Obool)), _1809824), c_COMBB(_1809824, tc_HOL_Obool, tc_fun(_1809826, _1809824))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1809826, _1809824), _1809826, _1809824), c_COMBI(tc_fun(_1809826, _1809824))), _1809830)))))))], (50674 ^ _782464) ^ [_1810436, _1810438, _1810440, _1810442] : [class_Complete__Lattice_Ocomplete__lattice(_1810436), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1810438, _1810436), _1810440), _1810442) = c_Complete__Lattice_OInf__class_OInf(_1810436, hAPP(c_Set_OCollect(_1810436), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1810438, _1810436), tc_HOL_Obool), tc_HOL_Obool, _1810436), c_HOL_OEx(tc_fun(_1810438, _1810436))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1810438, _1810436), tc_HOL_Obool), tc_fun(tc_fun(_1810438, _1810436), tc_HOL_Obool), _1810436), hAPP(c_COMBS(tc_fun(_1810438, _1810436), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1810438, _1810436)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1810438, _1810436), tc_fun(tc_fun(_1810438, _1810436), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1810438, _1810436))), _1810440)))), hAPP(hAPP(c_COMBC(_1810436, tc_fun(tc_fun(_1810438, _1810436), _1810436), tc_fun(tc_fun(_1810438, _1810436), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1810436, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1810438, _1810436), _1810436), tc_fun(tc_fun(_1810438, _1810436), tc_HOL_Obool)), _1810436), c_COMBB(_1810436, tc_HOL_Obool, tc_fun(_1810438, _1810436))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1810438, _1810436), _1810438, _1810436), c_COMBI(tc_fun(_1810438, _1810436))), _1810442)))))))], (50680 ^ _782464) ^ [_1811048, _1811050, _1811052, _1811054] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1811048), _1811050)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1811048), _1811052)), -(_1811052 = c_Orderings_Obot__class_Obot(tc_fun(_1811048, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1811048, _1811054, _1811050, _1811052)), 50694 ^ _782464 : [(50695 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1811048), 50693 ^ [_1811048, _1811050, _1811052, _1811054]), _1811050)))], (50697 ^ _782464) ^ [_1811661] : [hBOOL(hAPP(hAPP(c_member(_1811048), _1811661), _1811052)), hBOOL(hAPP(hAPP(_1811054, 50693 ^ [_1811048, _1811050, _1811052, _1811054]), _1811661))]]], (50705 ^ _782464) ^ [_1812042, _1812044] : [c_Predicate_Otransp(_1812042, _1812044), -(c_Relation_Otrans(_1812042, hAPP(c_Set_OCollect(tc_prod(_1812042, _1812042)), hAPP(c_Product__Type_Oprod_Oprod__case(_1812042, _1812042, tc_HOL_Obool), _1812044))))], (50711 ^ _782464) ^ [_1812234, _1812236] : [c_Relation_Otrans(_1812234, hAPP(c_Set_OCollect(tc_prod(_1812234, _1812234)), hAPP(c_Product__Type_Oprod_Oprod__case(_1812234, _1812234, tc_HOL_Obool), _1812236))), -(c_Predicate_Otransp(_1812234, _1812236))], (50717 ^ _782464) ^ [_1812518, _1812520, _1812522, _1812524, _1812526] : [c_Predicate_Otransp(_1812518, _1812520), hBOOL(hAPP(hAPP(_1812520, _1812522), _1812524)), hBOOL(hAPP(hAPP(_1812520, _1812524), _1812526)), -(hBOOL(hAPP(hAPP(_1812520, _1812522), _1812526)))], (50731 ^ _782464) ^ [_1812978, _1812980] : [c_Equiv__Relations_Oequivp(_1812978, _1812980), 50734 ^ _782464 : [(50735 ^ _782464) ^ [] : [-(c_Predicate_Oreflp(_1812978, _1812980))], (50737 ^ _782464) ^ [] : [-(c_Predicate_Osymp(_1812978, _1812980))], (50739 ^ _782464) ^ [] : [-(c_Predicate_Otransp(_1812978, _1812980))]]], (50741 ^ _782464) ^ [_1813341, _1813343] : [c_Predicate_Oreflp(_1813341, _1813343), c_Predicate_Osymp(_1813341, _1813343), c_Predicate_Otransp(_1813341, _1813343), -(c_Equiv__Relations_Oequivp(_1813341, _1813343))], (50755 ^ _782464) ^ [_1813757, _1813759, _1813761, _1813763] : [c_Predicate_Osymp(_1813757, _1813759), hBOOL(hAPP(hAPP(_1813759, _1813761), _1813763)), -(hBOOL(hAPP(hAPP(_1813759, _1813763), _1813761)))], (50765 ^ _782464) ^ [_1814125, _1814127] : [c_Equiv__Relations_Oequivp(_1814125, _1814127), 50768 ^ _782464 : [(50769 ^ _782464) ^ [] : [-(c_Predicate_Oreflp(_1814125, _1814127))], (50771 ^ _782464) ^ [] : [-(c_Predicate_Osymp(_1814125, _1814127))], (50773 ^ _782464) ^ [] : [-(c_Predicate_Otransp(_1814125, _1814127))]]], (50775 ^ _782464) ^ [_1814436, _1814438] : [-(c_Equiv__Relations_Oequivp(_1814436, _1814438)), c_Predicate_Oreflp(_1814436, _1814438), c_Predicate_Osymp(_1814436, _1814438), c_Predicate_Otransp(_1814436, _1814438)], (50789 ^ _782464) ^ [_1814883, _1814885, _1814887, _1814889] : [c_Wellfounded_Omax__extp(_1814883, _1814885, _1814887, _1814889), 50792 ^ _782464 : [(50793 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1814883), _1814887)))], (50795 ^ _782464) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1814883), _1814889)))], (50797 ^ _782464) ^ [] : [_1814889 = c_Orderings_Obot__class_Obot(tc_fun(_1814883, tc_HOL_Obool))], (50799 ^ _782464) ^ [_1815317] : [hBOOL(hAPP(hAPP(c_member(_1814883), _1815317), _1814887)), 50803 ^ _782464 : [(50804 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1814883), 50802 ^ [_1814883, _1814885, _1814887, _1814889, _1815317]), _1814889)))], (50806 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1814885, _1815317), 50802 ^ [_1814883, _1814885, _1814887, _1814889, _1815317])))]]]]], (50808 ^ _782464) ^ [_1815741, _1815743, _1815745, _1815747] : [-(c_Wellfounded_Omax__extp(_1815741, _1815743, _1815745, _1815747)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1815741), _1815745)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1815741), _1815747)), -(_1815747 = c_Orderings_Obot__class_Obot(tc_fun(_1815741, tc_HOL_Obool))), 50822 ^ _782464 : [(50823 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1815741), 50821 ^ [_1815741, _1815743, _1815745, _1815747]), _1815745)))], (50825 ^ _782464) ^ [_1816354] : [hBOOL(hAPP(hAPP(c_member(_1815741), _1816354), _1815747)), hBOOL(hAPP(hAPP(_1815743, 50821 ^ [_1815741, _1815743, _1815745, _1815747]), _1816354))]]], (50833 ^ _782464) ^ [_1816708, _1816710] : [c_Relation_Otrans(_1816708, _1816710), c_Relation_Oantisym(_1816708, _1816710), -(c_Relation_Otrans(_1816708, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1816708, _1816708), tc_HOL_Obool)), _1816710), c_Relation_OId(_1816708))))], (50843 ^ _782464) ^ [_1817010] : [-(c_Relation_Oantisym(_1817010, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1817010, _1817010), tc_HOL_Obool))))], (50845 ^ _782464) ^ [_1817154, _1817156] : [c_Relation_Oantisym(_1817154, hAPP(c_Relation_Oconverse(_1817154, _1817154), _1817156)), -(c_Relation_Oantisym(_1817154, _1817156))], (50851 ^ _782464) ^ [_1817328, _1817330] : [c_Relation_Oantisym(_1817328, _1817330), -(c_Relation_Oantisym(_1817328, hAPP(c_Relation_Oconverse(_1817328, _1817328), _1817330)))], (50857 ^ _782464) ^ [_1817523] : [-(c_Relation_Oantisym(_1817523, c_Relation_OId(_1817523)))], (50859 ^ _782464) ^ [_1817617, _1817619] : [-(c_Relation_Oantisym(_1817617, c_Relation_OId__on(_1817617, _1817619)))], (50861 ^ _782464) ^ [_1817743, _1817745, _1817747] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1817743, _1817743), tc_HOL_Obool)), _1817745), _1817747)), c_Relation_Oantisym(_1817743, _1817747), -(c_Relation_Oantisym(_1817743, _1817745))], (50885 ^ _782464) ^ [_1818663, _1818665] : [50888 ^ _782464 : [(50889 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1818663, _1818663)), hAPP(hAPP(c_Product__Type_OPair(_1818663, _1818663), 50886 ^ [_1818663, _1818665]), 50887 ^ [_1818663, _1818665])), _1818665)))], (50891 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1818663, _1818663)), hAPP(hAPP(c_Product__Type_OPair(_1818663, _1818663), 50887 ^ [_1818663, _1818665]), 50886 ^ [_1818663, _1818665])), _1818665)))], (50893 ^ _782464) ^ [] : [50886 ^ [_1818663, _1818665] = 50887 ^ [_1818663, _1818665]]], -(c_Relation_Oantisym(_1818663, _1818665))], (50871 ^ _782464) ^ [_1818107, _1818109] : [c_Relation_Oantisym(_1818107, _1818109), 50874 ^ _782464 : [(50875 ^ _782464) ^ [_1818307, _1818309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1818107, _1818107)), hAPP(hAPP(c_Product__Type_OPair(_1818107, _1818107), _1818309), _1818307)), _1818109)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1818107, _1818107)), hAPP(hAPP(c_Product__Type_OPair(_1818107, _1818107), _1818307), _1818309)), _1818109)), -(_1818309 = _1818307)]]], (50897 ^ _782464) ^ [_1819396, _1819398, _1819400, _1819402] : [c_Relation_Oantisym(_1819396, _1819398), hBOOL(hAPP(hAPP(c_member(tc_prod(_1819396, _1819396)), hAPP(hAPP(c_Product__Type_OPair(_1819396, _1819396), _1819400), _1819402)), _1819398)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1819396, _1819396)), hAPP(hAPP(c_Product__Type_OPair(_1819396, _1819396), _1819402), _1819400)), _1819398)), -(_1819400 = _1819402)], (50911 ^ _782464) ^ [_1819917, _1819919] : [c_Relation_Oantisym(_1819917, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1819917, _1819917), tc_HOL_Obool)), _1819919), c_Relation_OId(_1819917))), -(c_Relation_Oantisym(_1819917, _1819919))], (50917 ^ _782464) ^ [_1820111, _1820113] : [c_Relation_Oantisym(_1820111, _1820113), -(c_Relation_Oantisym(_1820111, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1820111, _1820111), tc_HOL_Obool)), _1820113), c_Relation_OId(_1820111))))], (50923 ^ _782464) ^ [_1820355, _1820357] : [c_Wellfounded_Oacyclic(_1820355, _1820357), -(c_Relation_Oantisym(_1820355, c_Transitive__Closure_Ortrancl(_1820355, _1820357)))], (50929 ^ _782464) ^ [_1820612, _1820614, _1820616, _1820618, _1820620, _1820622] : [-(c_Partial__Function_Ofun__lub(_1820612, _1820614, _1820616, _1820618, _1820620, _1820622) = hAPP(_1820618, hAPP(c_Set_OCollect(_1820612), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820616, _1820612), tc_HOL_Obool), tc_HOL_Obool, _1820612), c_HOL_OEx(tc_fun(_1820616, _1820612))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1820616, _1820612), tc_HOL_Obool), tc_fun(tc_fun(_1820616, _1820612), tc_HOL_Obool), _1820612), hAPP(c_COMBS(tc_fun(_1820616, _1820612), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1820616, _1820612)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1820616, _1820612), tc_fun(tc_fun(_1820616, _1820612), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1820616, _1820612))), _1820620)))), hAPP(hAPP(c_COMBC(_1820612, tc_fun(tc_fun(_1820616, _1820612), _1820612), tc_fun(tc_fun(_1820616, _1820612), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1820612, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1820616, _1820612), _1820612), tc_fun(tc_fun(_1820616, _1820612), tc_HOL_Obool)), _1820612), c_COMBB(_1820612, tc_HOL_Obool, tc_fun(_1820616, _1820612))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1820616, _1820612), _1820616, _1820612), c_COMBI(tc_fun(_1820616, _1820612))), _1820622)))))))], (50931 ^ _782464) ^ [_1820909, _1820911] : [c_Relation_Osym(_1820909, _1820911), c_Relation_Otrans(_1820909, _1820911), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1820909, _1820909), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1820909, _1820909, _1820909), hAPP(c_Relation_Oconverse(_1820909, _1820909), _1820911)), _1820911)), _1820911)))], (50941 ^ _782464) ^ [_1821294, _1821296, _1821298, _1821300] : [c_Relation_Osym(_1821294, _1821296), hBOOL(hAPP(hAPP(c_member(tc_prod(_1821294, _1821294)), hAPP(hAPP(c_Product__Type_OPair(_1821294, _1821294), _1821298), _1821300)), _1821296)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821294, _1821294)), hAPP(hAPP(c_Product__Type_OPair(_1821294, _1821294), _1821300), _1821298)), _1821296)))], (50961 ^ _782464) ^ [_1822171, _1822173] : [50964 ^ _782464 : [(50965 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1822171, _1822171)), hAPP(hAPP(c_Product__Type_OPair(_1822171, _1822171), 50962 ^ [_1822171, _1822173]), 50963 ^ [_1822171, _1822173])), _1822173)))], (50967 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1822171, _1822171)), hAPP(hAPP(c_Product__Type_OPair(_1822171, _1822171), 50963 ^ [_1822171, _1822173]), 50962 ^ [_1822171, _1822173])), _1822173))]], -(c_Relation_Osym(_1822171, _1822173))], (50951 ^ _782464) ^ [_1821718, _1821720] : [c_Relation_Osym(_1821718, _1821720), 50954 ^ _782464 : [(50955 ^ _782464) ^ [_1821912, _1821914] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1821718, _1821718)), hAPP(hAPP(c_Product__Type_OPair(_1821718, _1821718), _1821914), _1821912)), _1821720)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1821718, _1821718)), hAPP(hAPP(c_Product__Type_OPair(_1821718, _1821718), _1821912), _1821914)), _1821720)))]]], (50971 ^ _782464) ^ [_1822797, _1822799, _1822801, _1822803] : [c_Relation_Osym(_1822797, _1822799), -(c_Relation_Osym(_1822801, hAPP(hAPP(c_Relation_Oinv__image(_1822797, _1822801), _1822799), _1822803)))], (50977 ^ _782464) ^ [_1823022, _1823024] : [-(c_Relation_Osym(_1823022, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1823022, _1823022), tc_HOL_Obool)), _1823024), hAPP(c_Relation_Oconverse(_1823022, _1823022), _1823024))))], (50979 ^ _782464) ^ [_1823165, _1823167, _1823169] : [c_Relation_Osym(_1823165, _1823167), c_Relation_Osym(_1823165, _1823169), -(c_Relation_Osym(_1823165, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1823165, _1823165), tc_HOL_Obool)), _1823167), _1823169)))], (50989 ^ _782464) ^ [_1823502, _1823504] : [c_Relation_Osym(_1823502, _1823504), -(c_Relation_Osym(_1823502, c_Transitive__Closure_Ortrancl(_1823502, _1823504)))], (50995 ^ _782464) ^ [_1823703, _1823705] : [-(c_Relation_Osym(_1823703, c_Relation_OId__on(_1823703, _1823705)))], (50997 ^ _782464) ^ [_1823815, _1823817] : [c_Relation_Osym(_1823815, _1823817), -(c_Relation_Osym(_1823815, c_Transitive__Closure_Otrancl(_1823815, _1823817)))], (51003 ^ _782464) ^ [_1824045, _1824047, _1824049] : [c_Relation_Osym(_1824045, _1824047), c_Relation_Osym(_1824045, _1824049), -(c_Relation_Osym(_1824045, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1824045, _1824045), tc_HOL_Obool)), _1824047), _1824049)))], (51013 ^ _782464) ^ [_1824353] : [-(c_Relation_Osym(_1824353, c_Relation_OId(_1824353)))], (51015 ^ _782464) ^ [_1824491, _1824493] : [c_Relation_Osym(_1824491, _1824493), -(hAPP(c_Relation_Oconverse(_1824491, _1824491), _1824493) = _1824493)], (51021 ^ _782464) ^ [_1824665, _1824667] : [hAPP(c_Relation_Oconverse(_1824665, _1824665), _1824667) = _1824667, -(c_Relation_Osym(_1824665, _1824667))], (51027 ^ _782464) ^ [_1824918, _1824920] : [c_Relation_Osym(_1824918, hAPP(c_Relation_Oconverse(_1824918, _1824918), _1824920)), -(c_Relation_Osym(_1824918, _1824920))], (51033 ^ _782464) ^ [_1825092, _1825094] : [c_Relation_Osym(_1825092, _1825094), -(c_Relation_Osym(_1825092, hAPP(c_Relation_Oconverse(_1825092, _1825092), _1825094)))], (51039 ^ _782464) ^ [_1825316, _1825318] : [c_Relation_Osym(_1825316, _1825318), -(c_Relation_Osym(tc_List_Olist(_1825316), c_List_Olistrel(_1825316, _1825318)))], (51045 ^ _782464) ^ [_1825521, _1825523] : [-(c_Relation_Osym(_1825521, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1825521, _1825521), tc_HOL_Obool)), _1825523), hAPP(c_Relation_Oconverse(_1825521, _1825521), _1825523))))], (51047 ^ _782464) ^ [_1825693, _1825695, _1825697] : [c_Equiv__Relations_Oequiv(_1825693, _1825695, _1825697), 51050 ^ _782464 : [(51051 ^ _782464) ^ [] : [-(c_Relation_Orefl__on(_1825693, _1825695, _1825697))], (51053 ^ _782464) ^ [] : [-(c_Relation_Osym(_1825693, _1825697))], (51055 ^ _782464) ^ [] : [-(c_Relation_Otrans(_1825693, _1825697))]]], (51057 ^ _782464) ^ [_1826018, _1826020, _1826022] : [-(c_Equiv__Relations_Oequiv(_1826018, _1826020, _1826022)), c_Relation_Orefl__on(_1826018, _1826020, _1826022), c_Relation_Osym(_1826018, _1826022), c_Relation_Otrans(_1826018, _1826022)], (51071 ^ _782464) ^ [_1826440, _1826442, _1826444] : [c_Relation_Orefl__on(_1826440, _1826442, _1826444), c_Relation_Osym(_1826440, _1826444), c_Relation_Otrans(_1826440, _1826444), -(c_Equiv__Relations_Oequiv(_1826440, _1826442, _1826444))], (51085 ^ _782464) ^ [_1826860, _1826862, _1826864] : [c_Equiv__Relations_Oequiv(_1826860, _1826862, _1826864), 51088 ^ _782464 : [(51089 ^ _782464) ^ [] : [-(c_Relation_Orefl__on(_1826860, _1826862, _1826864))], (51091 ^ _782464) ^ [] : [-(c_Relation_Osym(_1826860, _1826864))], (51093 ^ _782464) ^ [] : [-(c_Relation_Otrans(_1826860, _1826864))]]], (51095 ^ _782464) ^ [_1827266, _1827268] : [c_Predicate_Osymp(_1827266, _1827268), -(c_Relation_Osym(_1827266, hAPP(c_Set_OCollect(tc_prod(_1827266, _1827266)), hAPP(c_Product__Type_Oprod_Oprod__case(_1827266, _1827266, tc_HOL_Obool), _1827268))))], (51101 ^ _782464) ^ [_1827458, _1827460] : [c_Relation_Osym(_1827458, hAPP(c_Set_OCollect(tc_prod(_1827458, _1827458)), hAPP(c_Product__Type_Oprod_Oprod__case(_1827458, _1827458, tc_HOL_Obool), _1827460))), -(c_Predicate_Osymp(_1827458, _1827460))], (51107 ^ _782464) ^ [_1827700, _1827702] : [51108 ^ _782464 : [(51109 ^ _782464) ^ [_1827787] : [hBOOL(hAPP(hAPP(_1827700, _1827787), _1827787))]], c_Predicate_Osymp(_1827702, _1827700), c_Predicate_Otransp(_1827702, _1827700), -(c_Equiv__Relations_Opart__equivp(_1827702, _1827700))], (51121 ^ _782464) ^ [_1828149, _1828151] : [c_Equiv__Relations_Opart__equivp(_1828149, _1828151), 51125 ^ _782464 : [(51126 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1828151, 51124 ^ [_1828149, _1828151]), 51124 ^ [_1828149, _1828151])))], (51128 ^ _782464) ^ [] : [-(c_Predicate_Osymp(_1828149, _1828151))], (51130 ^ _782464) ^ [] : [-(c_Predicate_Otransp(_1828149, _1828151))]]], (51132 ^ _782464) ^ [_1828539, _1828541] : [-(c_Equiv__Relations_Opart__equivp(_1828539, _1828541)), 51135 ^ _782464 : [(51136 ^ _782464) ^ [_1828660] : [hBOOL(hAPP(hAPP(_1828541, _1828660), _1828660))]], c_Predicate_Osymp(_1828539, _1828541), c_Predicate_Otransp(_1828539, _1828541)], (51146 ^ _782464) ^ [_1829003, _1829005, _1829007, _1829009, _1829011] : [c_Equiv__Relations_Opart__equivp(_1829003, _1829005), hBOOL(hAPP(hAPP(_1829005, _1829007), _1829009)), hBOOL(hAPP(hAPP(_1829005, _1829009), _1829011)), -(hBOOL(hAPP(hAPP(_1829005, _1829007), _1829011)))], (51160 ^ _782464) ^ [_1829491, _1829493, _1829495, _1829497] : [c_Equiv__Relations_Opart__equivp(_1829491, _1829493), hBOOL(hAPP(hAPP(_1829493, _1829495), _1829497)), -(hBOOL(hAPP(hAPP(_1829493, _1829497), _1829495)))], (51201 ^ _782464) ^ [_1831028, _1831030] : [-(c_Equiv__Relations_Opart__equivp(_1831028, _1831030)), 51204 ^ _782464 : [(51205 ^ _782464) ^ [_1831192] : [hBOOL(hAPP(hAPP(_1831030, _1831192), _1831192))]], 51222 ^ _782464 : [(51223 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1831030, 51206 ^ [_1831028, _1831030]), 51206 ^ [_1831028, _1831030])))], (51225 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1831030, 51207 ^ [_1831028, _1831030]), 51207 ^ [_1831028, _1831030])))], (51227 ^ _782464) ^ [] : [-(hAPP(_1831030, 51206 ^ [_1831028, _1831030]) = hAPP(_1831030, 51207 ^ [_1831028, _1831030]))], (51229 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1831030, 51206 ^ [_1831028, _1831030]), 51207 ^ [_1831028, _1831030]))]], 51210 ^ _782464 : [(51211 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1831030, 51206 ^ [_1831028, _1831030]), 51207 ^ [_1831028, _1831030])))], (51213 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1831030, 51206 ^ [_1831028, _1831030]), 51206 ^ [_1831028, _1831030])), hBOOL(hAPP(hAPP(_1831030, 51207 ^ [_1831028, _1831030]), 51207 ^ [_1831028, _1831030])), hAPP(_1831030, 51206 ^ [_1831028, _1831030]) = hAPP(_1831030, 51207 ^ [_1831028, _1831030])]]], (51170 ^ _782464) ^ [_1829859, _1829861] : [c_Equiv__Relations_Opart__equivp(_1829859, _1829861), 51174 ^ _782464 : [(51175 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1829861, 51173 ^ [_1829859, _1829861]), 51173 ^ [_1829859, _1829861])))], (51177 ^ _782464) ^ [_1830228, _1830230] : [hBOOL(hAPP(hAPP(_1829861, _1830230), _1830228)), 51180 ^ _782464 : [(51181 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1829861, _1830230), _1830230)))], (51183 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1829861, _1830228), _1830228)))], (51185 ^ _782464) ^ [] : [-(hAPP(_1829861, _1830230) = hAPP(_1829861, _1830228))]]], (51187 ^ _782464) ^ [_1830605, _1830607] : [-(hBOOL(hAPP(hAPP(_1829861, _1830607), _1830605))), hBOOL(hAPP(hAPP(_1829861, _1830607), _1830607)), hBOOL(hAPP(hAPP(_1829861, _1830605), _1830605)), hAPP(_1829861, _1830607) = hAPP(_1829861, _1830605)]]], (51233 ^ _782464) ^ [_1832301, _1832303] : [c_Equiv__Relations_Oequivp(_1832301, _1832303), -(c_Equiv__Relations_Opart__equivp(_1832301, _1832303))], (51239 ^ _782464) ^ [_1832511, _1832513] : [c_Equiv__Relations_Opart__equivp(_1832511, _1832513), 51243 ^ _782464 : [(51244 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1832513, 51242 ^ [_1832511, _1832513]), 51242 ^ [_1832511, _1832513])))], (51246 ^ _782464) ^ [] : [-(c_Predicate_Osymp(_1832511, _1832513))], (51248 ^ _782464) ^ [] : [-(c_Predicate_Otransp(_1832511, _1832513))]]], (51250 ^ _782464) ^ [_1832953, _1832955] : [c_Equiv__Relations_Opart__equivp(_1832953, _1832955), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1832953, tc_HOL_Obool)), 51253 ^ [_1832953, _1832955]), hAPP(hAPP(c_COMBB(tc_fun(_1832953, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1832953, tc_HOL_Obool)), c_HOL_OEx(_1832953)), hAPP(hAPP(c_COMBB(tc_fun(_1832953, tc_HOL_Obool), tc_fun(_1832953, tc_HOL_Obool), tc_fun(_1832953, tc_HOL_Obool)), hAPP(c_COMBS(_1832953, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1832953), c_fconj), hAPP(hAPP(c_COMBS(_1832953, _1832953, tc_HOL_Obool), _1832955), c_COMBI(_1832953))))), hAPP(hAPP(c_COMBC(tc_fun(_1832953, tc_HOL_Obool), tc_fun(_1832953, tc_fun(_1832953, tc_HOL_Obool)), tc_fun(_1832953, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1832953, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1832953, tc_fun(_1832953, tc_HOL_Obool)), tc_fun(_1832953, tc_HOL_Obool)), tc_fun(_1832953, tc_HOL_Obool)), c_COMBB(tc_fun(_1832953, tc_HOL_Obool), tc_HOL_Obool, _1832953)), c_fequal)), _1832955))))))], (51257 ^ _782464) ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694] : [class_Groups_Ocomm__monoid__mult(_1833684), hBOOL(hAPP(c_Finite__Set_Ofinite(_1833686), _1833688)), 51267 ^ _782464 : [(51268 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1833686), 51266 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694]), _1833688)))], (51270 ^ _782464) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1833690), hAPP(_1833692, 51266 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694])))]], 51274 ^ _782464 : [(51275 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1833686), 51273 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694]), _1833688)))], (51278 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1833686), 51276 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694]), _1833688)))], (51280 ^ _782464) ^ [] : [51273 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694] = 51276 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694]], (51282 ^ _782464) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1833690, tc_HOL_Obool)), hAPP(_1833692, 51273 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694])), hAPP(_1833692, 51276 ^ [_1833684, _1833686, _1833688, _1833690, _1833692, _1833694])) = c_Orderings_Obot__class_Obot(tc_fun(_1833690, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1833684, _1833690, c_Groups_Otimes__class_Otimes(_1833684)), _1833694), c_Groups_Oone__class_Oone(_1833684)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1833686, tc_fun(_1833690, tc_HOL_Obool)), _1833688), _1833692)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1833684, _1833686, c_Groups_Otimes__class_Otimes(_1833684)), hAPP(hAPP(c_COMBB(tc_fun(_1833690, tc_HOL_Obool), _1833684, _1833686), hAPP(hAPP(c_Finite__Set_Ofold__image(_1833684, _1833690, c_Groups_Otimes__class_Otimes(_1833684)), _1833694), c_Groups_Oone__class_Oone(_1833684))), _1833692)), c_Groups_Oone__class_Oone(_1833684)), _1833688))], (51286 ^ _782464) ^ [_1835274] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1835274), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1835274 = hAPP(c_Code__Numeral_Onat__of, 51289 ^ [_1835274]))], (51293 ^ _782464) ^ [_1835554, _1835556] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1835554), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1835556, hAPP(c_Code__Numeral_Onat__of, 51298 ^ [_1835554, _1835556]))), -(hBOOL(hAPP(_1835556, _1835554)))], (51305 ^ _782464) ^ [_1835985] : [-(_1835985 = hAPP(c_Code__Numeral_Oof__nat, 51303 ^ [_1835985]))], (51307 ^ _782464) ^ [_1836037] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51303 ^ [_1836037]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (51309 ^ _782464) ^ [_1836156, _1836158] : [51311 ^ _782464 : [(51312 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51310 ^ [_1836156, _1836158]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (51314 ^ _782464) ^ [] : [hBOOL(hAPP(_1836156, hAPP(c_Code__Numeral_Oof__nat, 51310 ^ [_1836156, _1836158])))]], -(hBOOL(hAPP(_1836156, _1836158)))], (51318 ^ _782464) ^ [_1836558, _1836560, _1836562, _1836564] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1836558, _1836560, _1836562, _1836564, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1836560)) = _1836562)], (51320 ^ _782464) ^ [_1836720, _1836722, _1836724, _1836726, _1836728, _1836730] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1836720, _1836722, _1836724, _1836726, c_Lazy__Sequence_Olazy__sequence_OInsert(_1836722, _1836728, _1836730)) = hAPP(hAPP(hAPP(_1836726, _1836728), _1836730), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1836720, _1836722, _1836724, _1836726, _1836730)))], (51322 ^ _782464) ^ [_1836890, _1836892, _1836894, _1836896] : [hBOOL(hAPP(_1836890, _1836892)), hBOOL(hAPP(_1836894, _1836896)), -(hBOOL(hAPP(_1836890, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1836890) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1836894))), 51338 ^ _782464 : [(51339 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1836890, hAPP(c_Nat_OSuc, 51335 ^ [_1836890, _1836892, _1836894, _1836896]))))], (51341 ^ _782464) ^ [] : [hBOOL(hAPP(_1836894, 51335 ^ [_1836890, _1836892, _1836894, _1836896]))]], 51342 ^ _782464 : [(51343 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1836894, 51335 ^ [_1836890, _1836892, _1836894, _1836896])))], (51345 ^ _782464) ^ [] : [hBOOL(hAPP(_1836890, hAPP(c_Nat_OSuc, 51335 ^ [_1836890, _1836892, _1836894, _1836896])))]]], (51349 ^ _782464) ^ [_1837844, _1837846] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1837844), _1837846)), -(c_Quickcheck_Obeyond(_1837844, _1837846) = _1837846)], (51355 ^ _782464) ^ [_1838022, _1838024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1838022), _1838024))), -(c_Quickcheck_Obeyond(_1838022, _1838024) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (51361 ^ _782464) ^ [_1838224] : [-(c_Quickcheck_Obeyond(_1838224, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (51363 ^ _782464) ^ [_1838375, _1838377, _1838379, _1838381, _1838383, _1838385] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1838375, _1838377, _1838379, _1838381), _1838383), _1838385) = hAPP(_1838381, hAPP(hAPP(c_Product__Type_OPair(_1838375, _1838377), _1838383), _1838385)))], (51365 ^ _782464) ^ [_1838557, _1838559, _1838561, _1838563, _1838565] : [51367 ^ _782464 : [(51368 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1838557), 51366 ^ [_1838557, _1838559, _1838561, _1838563, _1838565]), _1838559)))], (51370 ^ _782464) ^ [] : [c_Relation_Orefl__on(_1838561, hAPP(_1838563, 51366 ^ [_1838557, _1838559, _1838561, _1838563, _1838565]), hAPP(_1838565, 51366 ^ [_1838557, _1838559, _1838561, _1838563, _1838565]))]], -(c_Relation_Orefl__on(_1838561, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1838557, tc_fun(_1838561, tc_HOL_Obool)), _1838559), _1838563), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1838557, tc_fun(tc_prod(_1838561, _1838561), tc_HOL_Obool)), _1838559), _1838565)))], (51374 ^ _782464) ^ [_1839113, _1839115, _1839117, _1839119, _1839121] : [hBOOL(hAPP(_1839113, hAPP(hAPP(c_Product__Type_OPair(_1839115, _1839117), _1839119), _1839121))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1839115, _1839117, tc_HOL_Obool, _1839113), _1839119), _1839121)))], (51380 ^ _782464) ^ [_1839396, _1839398, _1839400, _1839402] : [-(c_Product__Type_Ocurry(_1839396, _1839398, _1839400, hAPP(c_Product__Type_Oprod_Oprod__case(_1839396, _1839398, _1839400), _1839402)) = _1839402)], (51382 ^ _782464) ^ [_1839534, _1839536, _1839538, _1839540] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1839534, _1839536, _1839538), c_Product__Type_Ocurry(_1839534, _1839536, _1839538, _1839540)) = _1839540)], (51384 ^ _782464) ^ [_1839700, _1839702, _1839704, _1839706, _1839708, _1839710] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1839700, _1839702, _1839704, _1839706), _1839708), _1839710) = hAPP(_1839706, hAPP(hAPP(c_Product__Type_OPair(_1839700, _1839702), _1839708), _1839710)))], (51386 ^ _782464) ^ [_1839882, _1839884, _1839886, _1839888, _1839890] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1839882, _1839884, tc_HOL_Obool, _1839886), _1839888), _1839890)), -(hBOOL(hAPP(_1839886, hAPP(hAPP(c_Product__Type_OPair(_1839882, _1839884), _1839888), _1839890))))], (51392 ^ _782464) ^ [_1840194, _1840196, _1840198, _1840200, _1840202] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1840194, _1840196, tc_HOL_Obool, _1840198), _1840200), _1840202)), -(hBOOL(hAPP(_1840198, hAPP(hAPP(c_Product__Type_OPair(_1840194, _1840196), _1840200), _1840202))))], (51398 ^ _782464) ^ [_1840478, _1840480, _1840482] : [c_Equiv__Relations_Oequivp(_1840478, _1840480), 51401 ^ _782464 : [(51413 ^ _782464) ^ [] : [51414 ^ _782464 : [(51415 ^ _782464) ^ [_1841061] : [hBOOL(hAPP(_1840482, _1841061))]], 51417 ^ _782464 : [(51418 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1840478), 51416 ^ [_1840478, _1840480, _1840482]), c_Quotient_ORespects(_1840478, _1840480))))], (51420 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1840482, 51416 ^ [_1840478, _1840480, _1840482])))]]], (51402 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1840482, 51409 ^ [_1840478, _1840480, _1840482]))), 51403 ^ _782464 : [(51404 ^ _782464) ^ [_1840709] : [hBOOL(hAPP(hAPP(c_member(_1840478), _1840709), c_Quotient_ORespects(_1840478, _1840480))), hBOOL(hAPP(_1840482, _1840709))]]]]], (51422 ^ _782464) ^ [_1841418, _1841420, _1841422] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1841418, _1841418)), hAPP(hAPP(c_Product__Type_OPair(_1841418, _1841418), hAPP(_1841420, hAPP(c_Nat_OSuc, 51423 ^ [_1841418, _1841420, _1841422]))), hAPP(_1841420, 51423 ^ [_1841418, _1841420, _1841422]))), c_Transitive__Closure_Ortrancl(_1841418, _1841422))), c_Wellfounded_Owf(_1841418, c_Transitive__Closure_Otrancl(_1841418, _1841422)), 51431 ^ _782464 : [(51432 ^ _782464) ^ [_1841881] : [-(hAPP(_1841420, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 51430 ^ [_1841418, _1841420, _1841422]), _1841881)) = hAPP(_1841420, 51430 ^ [_1841418, _1841420, _1841422]))]]], (51434 ^ _782464) ^ [_1842076, _1842078, _1842080] : [hBOOL(hAPP(hAPP(c_member(_1842076), _1842078), c_Quotient_ORespects(_1842076, _1842080))), -(hBOOL(hAPP(hAPP(_1842080, _1842078), _1842078)))], (51440 ^ _782464) ^ [_1842274, _1842276, _1842278] : [hBOOL(hAPP(hAPP(_1842278, _1842276), _1842276)), -(hBOOL(hAPP(hAPP(c_member(_1842274), _1842276), c_Quotient_ORespects(_1842274, _1842278))))], (51446 ^ _782464) ^ [_1842565, _1842567, _1842569] : [hBOOL(hAPP(c_Quotient_ORespects(_1842565, _1842567), _1842569)), -(hBOOL(hAPP(hAPP(_1842567, _1842569), _1842569)))], (51452 ^ _782464) ^ [_1842753, _1842755, _1842757] : [hBOOL(hAPP(hAPP(_1842755, _1842757), _1842757)), -(hBOOL(hAPP(c_Quotient_ORespects(_1842753, _1842755), _1842757)))], (51458 ^ _782464) ^ [_1843019, _1843021, _1843023, _1843025] : [c_Equiv__Relations_Oequivp(_1843019, _1843021), 51464 ^ _782464 : [(51465 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1843023, 51463 ^ [_1843019, _1843021, _1843023, _1843025])))], (51467 ^ _782464) ^ [] : [hBOOL(hAPP(_1843025, 51463 ^ [_1843019, _1843021, _1843023, _1843025]))]], 51470 ^ _782464 : [(51471 ^ _782464) ^ [_1843480] : [hBOOL(hAPP(_1843023, _1843480))]], 51473 ^ _782464 : [(51474 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1843019), 51472 ^ [_1843019, _1843021, _1843023, _1843025]), c_Quotient_ORespects(_1843019, _1843021))))], (51476 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1843025, 51472 ^ [_1843019, _1843021, _1843023, _1843025])))]]], (51478 ^ _782464) ^ [_1843867, _1843869, _1843871, _1843873] : [c_Equiv__Relations_Oequivp(_1843867, _1843869), -(c_Quotient_OBabs(_1843867, _1843871, c_Quotient_ORespects(_1843867, _1843869), _1843873) = _1843873)], (51484 ^ _782464) ^ [_1844147, _1844149, _1844151, _1844153, _1844155] : [hBOOL(hAPP(hAPP(c_member(_1844147), _1844149), _1844151)), -(hAPP(c_Quotient_OBabs(_1844147, _1844153, _1844151, _1844155), _1844149) = hAPP(_1844155, _1844149))], (51490 ^ _782464) ^ [_1844481, _1844483, _1844485, _1844487, _1844489, _1844491, _1844493] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1844481, _1844483), tc_prod(_1844481, _1844483))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1844481, _1844483), tc_prod(_1844481, _1844483)), hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), _1844485), _1844487)), hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), _1844489), _1844491))), c_Transitive__Closure_Ortrancl(tc_prod(_1844481, _1844483), _1844493))), -(hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), _1844485), _1844487) = hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), _1844489), _1844491)), 51499 ^ _782464 : [(51500 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1844481, _1844483), tc_prod(_1844481, _1844483))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1844481, _1844483), tc_prod(_1844481, _1844483)), hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), _1844485), _1844487)), hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), 51497 ^ [_1844481, _1844483, _1844485, _1844487, _1844489, _1844491, _1844493]), 51498 ^ [_1844481, _1844483, _1844485, _1844487, _1844489, _1844491, _1844493]))), _1844493)))], (51502 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1844481, _1844483), tc_prod(_1844481, _1844483))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1844481, _1844483), tc_prod(_1844481, _1844483)), hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), 51497 ^ [_1844481, _1844483, _1844485, _1844487, _1844489, _1844491, _1844493]), 51498 ^ [_1844481, _1844483, _1844485, _1844487, _1844489, _1844491, _1844493])), hAPP(hAPP(c_Product__Type_OPair(_1844481, _1844483), _1844489), _1844491))), c_Transitive__Closure_Ortrancl(tc_prod(_1844481, _1844483), _1844493))))]]], (51504 ^ _782464) ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1845831, _1845833), tc_prod(_1845831, _1845833))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1845831, _1845833), tc_prod(_1845831, _1845833)), hAPP(hAPP(c_Product__Type_OPair(_1845831, _1845833), _1845835), _1845837)), hAPP(hAPP(c_Product__Type_OPair(_1845831, _1845833), _1845839), _1845841))), c_Transitive__Closure_Ortrancl(tc_prod(_1845831, _1845833), _1845843))), hBOOL(hAPP(hAPP(_1845845, _1845839), _1845841)), 51517 ^ _782464 : [(51518 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1845831, _1845833), tc_prod(_1845831, _1845833))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1845831, _1845833), tc_prod(_1845831, _1845833)), hAPP(hAPP(c_Product__Type_OPair(_1845831, _1845833), 51513 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]), 51514 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845])), hAPP(hAPP(c_Product__Type_OPair(_1845831, _1845833), 51515 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]), 51516 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]))), _1845843)))], (51520 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1845831, _1845833), tc_prod(_1845831, _1845833))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1845831, _1845833), tc_prod(_1845831, _1845833)), hAPP(hAPP(c_Product__Type_OPair(_1845831, _1845833), 51515 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]), 51516 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845])), hAPP(hAPP(c_Product__Type_OPair(_1845831, _1845833), _1845839), _1845841))), c_Transitive__Closure_Ortrancl(tc_prod(_1845831, _1845833), _1845843))))], (51522 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1845845, 51515 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]), 51516 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845])))], (51524 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1845845, 51513 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]), 51514 ^ [_1845831, _1845833, _1845835, _1845837, _1845839, _1845841, _1845843, _1845845]))]], -(hBOOL(hAPP(hAPP(_1845845, _1845835), _1845837)))], (51528 ^ _782464) ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1848295, _1848297), tc_prod(_1848295, _1848297))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1848295, _1848297), tc_prod(_1848295, _1848297)), hAPP(hAPP(c_Product__Type_OPair(_1848295, _1848297), _1848299), _1848301)), hAPP(hAPP(c_Product__Type_OPair(_1848295, _1848297), _1848303), _1848305))), c_Transitive__Closure_Ortrancl(tc_prod(_1848295, _1848297), _1848307))), hBOOL(hAPP(hAPP(_1848309, _1848299), _1848301)), 51539 ^ _782464 : [(51540 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1848295, _1848297), tc_prod(_1848295, _1848297))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1848295, _1848297), tc_prod(_1848295, _1848297)), hAPP(hAPP(c_Product__Type_OPair(_1848295, _1848297), _1848299), _1848301)), hAPP(hAPP(c_Product__Type_OPair(_1848295, _1848297), 51537 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]), 51538 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]))), c_Transitive__Closure_Ortrancl(tc_prod(_1848295, _1848297), _1848307))))], (51544 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1848295, _1848297), tc_prod(_1848295, _1848297))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1848295, _1848297), tc_prod(_1848295, _1848297)), hAPP(hAPP(c_Product__Type_OPair(_1848295, _1848297), 51537 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]), 51538 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309])), hAPP(hAPP(c_Product__Type_OPair(_1848295, _1848297), 51541 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]), 51542 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]))), _1848307)))], (51546 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(_1848309, 51537 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]), 51538 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309])))], (51548 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(_1848309, 51541 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]), 51542 ^ [_1848295, _1848297, _1848299, _1848301, _1848303, _1848305, _1848307, _1848309]))]], -(hBOOL(hAPP(hAPP(_1848309, _1848303), _1848305)))], (51552 ^ _782464) ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619] : [51555 ^ _782464 : [(51556 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1850609, _1850609)), hAPP(hAPP(c_Product__Type_OPair(_1850609, _1850609), 51553 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619]), 51554 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619])), _1850611)))], (51560 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1850613, _1850613)), hAPP(hAPP(c_Product__Type_OPair(_1850613, _1850613), 51557 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619]), 51558 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619])), _1850615)))], (51562 ^ _782464) ^ [] : [hAPP(hAPP(_1850617, 51553 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619]), 51557 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619]) = hAPP(hAPP(_1850617, 51554 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619]), 51558 ^ [_1850609, _1850611, _1850613, _1850615, _1850617, _1850619])]], -(c_Equiv__Relations_Ocongruent2(_1850609, _1850613, _1850619, _1850611, _1850615, _1850617))], (51566 ^ _782464) ^ [_1851876, _1851878, _1851880, _1851882] : [51569 ^ _782464 : [(51570 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1851876, _1851876)), hAPP(hAPP(c_Product__Type_OPair(_1851876, _1851876), 51567 ^ [_1851876, _1851878, _1851880, _1851882]), 51568 ^ [_1851876, _1851878, _1851880, _1851882])), _1851878)))], (51572 ^ _782464) ^ [] : [hAPP(_1851880, 51567 ^ [_1851876, _1851878, _1851880, _1851882]) = hAPP(_1851880, 51568 ^ [_1851876, _1851878, _1851880, _1851882])]], -(c_Equiv__Relations_Ocongruent(_1851876, _1851882, _1851878, _1851880))], (51576 ^ _782464) ^ [_1852479, _1852481, _1852483] : [-(c_Lazy__Sequence_Oflat(_1852479, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1852479), _1852481, _1852483)) = c_Lazy__Sequence_Oappend(_1852479, _1852481, c_Lazy__Sequence_Oflat(_1852479, _1852483)))], (51578 ^ _782464) ^ [_1852577] : [-(c_Lazy__Sequence_Oflat(_1852577, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1852577))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1852577))], (51580 ^ _782464) ^ [_1852706, _1852708, _1852710, _1852712] : [-(hAPP(c_Lazy__Sequence_Obind(_1852706, _1852708, _1852710), _1852712) = c_Lazy__Sequence_Oflat(_1852708, c_Lazy__Sequence_Omap(_1852706, tc_Lazy__Sequence_Olazy__sequence(_1852708), _1852712, _1852710)))], (51592 ^ _782464) ^ [_1853246, _1853248, _1853250] : [51594 ^ _782464 : [(51595 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51593 ^ [_1853246, _1853248, _1853250]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1853248), _1853250))))], (51597 ^ _782464) ^ [] : [hBOOL(hAPP(_1853246, 51593 ^ [_1853246, _1853248, _1853250]))]], -(c_List_Oall__interval__nat(_1853246, _1853248, _1853250))], (51582 ^ _782464) ^ [_1852879, _1852881, _1852883] : [c_List_Oall__interval__nat(_1852879, _1852881, _1852883), 51585 ^ _782464 : [(51586 ^ _782464) ^ [_1853035] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1853035), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1852881), _1852883))), -(hBOOL(hAPP(_1852879, _1853035)))]]], (51601 ^ _782464) ^ [_1853687, _1853689, _1853691, _1853693, _1853695] : [-(c_Lazy__Sequence_Omap(_1853687, _1853689, _1853691, c_Lazy__Sequence_Olazy__sequence_OInsert(_1853687, _1853693, _1853695)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1853689, hAPP(_1853691, _1853693), c_Lazy__Sequence_Omap(_1853687, _1853689, _1853691, _1853695)))], (51603 ^ _782464) ^ [_1853822, _1853824, _1853826] : [-(c_Lazy__Sequence_Omap(_1853822, _1853824, _1853826, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1853822)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1853824))], (51605 ^ _782464) ^ [_1853985, _1853987, _1853989] : [c_List_Olist__all(tc_Nat_Onat, _1853985, c_List_Oupt(_1853987, _1853989)), -(c_List_Oall__interval__nat(_1853985, _1853987, _1853989))], (51611 ^ _782464) ^ [_1854163, _1854165, _1854167] : [c_List_Oall__interval__nat(_1854163, _1854165, _1854167), -(c_List_Olist__all(tc_Nat_Onat, _1854163, c_List_Oupt(_1854165, _1854167)))], (51617 ^ _782464) ^ [_1854434, _1854436, _1854438] : [c_List_Olist__ex(tc_Nat_Onat, _1854434, c_List_Oupt(_1854436, _1854438)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1854434), _1854436, _1854438)], (51623 ^ _782464) ^ [_1854619, _1854621, _1854623] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1854619), _1854621, _1854623)), -(c_List_Olist__ex(tc_Nat_Onat, _1854619, c_List_Oupt(_1854621, _1854623)))], (51629 ^ _782464) ^ [_1854883, _1854885, _1854887, _1854889, _1854891] : [-(c_New__DSequence_Opos__map(_1854883, _1854885, _1854887, _1854889, _1854891) = c_Lazy__Sequence_Omap(_1854883, _1854885, _1854887, hAPP(_1854889, _1854891)))], (51631 ^ _782464) ^ [_1855096, _1855098, _1855100, _1855102, _1855104, _1855106, _1855108, _1855110] : [c_Finite__Set_Ofolding__image(_1855096, _1855098, _1855100, _1855102, _1855104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1855098), _1855106)), 51641 ^ _782464 : [(51642 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1855098), 51640 ^ [_1855096, _1855098, _1855100, _1855102, _1855104, _1855106, _1855108, _1855110]), _1855106)))], (51644 ^ _782464) ^ [] : [hAPP(_1855108, 51640 ^ [_1855096, _1855098, _1855100, _1855102, _1855104, _1855106, _1855108, _1855110]) = hAPP(_1855110, 51640 ^ [_1855096, _1855098, _1855100, _1855102, _1855104, _1855106, _1855108, _1855110])]], -(hAPP(hAPP(_1855104, _1855108), _1855106) = hAPP(hAPP(_1855104, _1855110), _1855106))], (51648 ^ _782464) ^ [_1855883, _1855885, _1855887] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1855883), _1855885)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1855883), _1855887))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1855883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1855885), _1855887)))], (51658 ^ _782464) ^ [_1856254, _1856256, _1856258] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1856254), _1856256)), -(_1856256 = c_Orderings_Obot__class_Obot(tc_fun(_1856254, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1856254, _1856258, _1856256), 51665 ^ [_1856254, _1856256, _1856258])))], (51669 ^ _782464) ^ [_1856636] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1856636), _1856636)))], (51671 ^ _782464) ^ [_1856748, _1856750] : [class_Rings_Ocomm__semiring__1(_1856748), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1856748), _1856750), c_Groups_Ozero__class_Ozero(_1856748))))], (51677 ^ _782464) ^ [_1856945] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1856945)))], (51679 ^ _782464) ^ [_1857068, _1857070, _1857072] : [class_Rings_Odvd(_1857068), class_Rings_Osemiring__0(_1857068), 51686 ^ _782464 : [(51687 ^ _782464) ^ [] : [51688 ^ _782464 : [(51689 ^ _782464) ^ [_1857387] : [hBOOL(hAPP(_1857070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1857068), _1857072), _1857387)))]], 51691 ^ _782464 : [(51692 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1857068), _1857072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1857068), 51690 ^ [_1857068, _1857070, _1857072]), c_Groups_Ozero__class_Ozero(_1857068)))))], (51694 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1857070, 51690 ^ [_1857068, _1857070, _1857072])))]]], (51696 ^ _782464) ^ [] : [-(hBOOL(hAPP(_1857070, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1857068), _1857072), 51703 ^ [_1857068, _1857070, _1857072])))), 51697 ^ _782464 : [(51698 ^ _782464) ^ [_1857747] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1857068), _1857072), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1857068), _1857747), c_Groups_Ozero__class_Ozero(_1857068)))), hBOOL(hAPP(_1857070, _1857747))]]]]], (51707 ^ _782464) ^ [_1858166, _1858168, _1858170] : [class_Divides_Osemiring__div(_1858166), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1858166), _1858168), _1858170)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1858166), _1858168), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1858166), _1858170), _1858168)) = _1858170)], (51717 ^ _782464) ^ [_1858547, _1858549, _1858551, _1858553] : [class_Divides_Osemiring__div(_1858547), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1858547), _1858549), _1858551)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1858547), _1858553), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1858547), _1858551), _1858549)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1858547), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1858547), _1858553), _1858551)), _1858549))], (51727 ^ _782464) ^ [_1858956, _1858958, _1858960] : [class_Divides_Osemiring__div(_1858956), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1858956), _1858958), _1858960)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1858956), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1858956), _1858960), _1858958)), _1858958) = _1858960)], (51737 ^ _782464) ^ [_1859337, _1859339, _1859341, _1859343] : [class_Divides_Osemiring__div(_1859337), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1859337), _1859339), _1859341)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1859337), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1859337), _1859341), _1859339)), _1859343) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1859337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1859337), _1859341), _1859343)), _1859339))], (51747 ^ _782464) ^ [_1859774, _1859776, _1859778, _1859780, _1859782] : [class_Divides_Osemiring__div(_1859774), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1859774), _1859776), _1859778)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1859774), _1859780), _1859782)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1859774), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1859774), _1859778), _1859776)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1859774), _1859782), _1859780)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1859774), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1859774), _1859778), _1859782)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1859774), _1859776), _1859780)))], (51761 ^ _782464) ^ [_1860354, _1860356, _1860358, _1860360] : [class_Rings_Oidom(_1860354), 51764 ^ _782464 : [(51775 ^ _782464) ^ [] : [51776 ^ _782464 : [(51777 ^ _782464) ^ [] : [_1860356 = c_Groups_Ozero__class_Ozero(_1860354)], (51779 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1860354), _1860358), _1860360))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1860354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1860354), _1860356), _1860358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1860354), _1860356), _1860360))))], (51765 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1860354), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1860354), _1860356), _1860358)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1860354), _1860356), _1860360))), -(_1860356 = c_Groups_Ozero__class_Ozero(_1860354)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1860354), _1860358), _1860360)))]]], (51783 ^ _782464) ^ [_1861138, _1861140, _1861142, _1861144] : [class_Rings_Oidom(_1861138), 51786 ^ _782464 : [(51797 ^ _782464) ^ [] : [51798 ^ _782464 : [(51799 ^ _782464) ^ [] : [_1861142 = c_Groups_Ozero__class_Ozero(_1861138)], (51801 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1861138), _1861140), _1861144))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1861138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1861138), _1861140), _1861142)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1861138), _1861144), _1861142))))], (51787 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1861138), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1861138), _1861140), _1861142)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1861138), _1861144), _1861142))), -(_1861142 = c_Groups_Ozero__class_Ozero(_1861138)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1861138), _1861140), _1861144)))]]], (51805 ^ _782464) ^ [_1861922, _1861924, _1861926, _1861928] : [class_Rings_Ocomm__semiring__1(_1861922), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1861922), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1861922), _1861924), _1861926)), _1861928)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1861922), _1861926), _1861928)))], (51815 ^ _782464) ^ [_1862311, _1862313, _1862315, _1862317] : [class_Rings_Ocomm__semiring__1(_1862311), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862311), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1862311), _1862313), _1862315)), _1862317)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862311), _1862313), _1862317)))], (51825 ^ _782464) ^ [_1862700, _1862702, _1862704, _1862706] : [class_Rings_Odvd(_1862700), _1862702 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1862700), _1862704), _1862706), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1862700), _1862704), _1862702)))], (51835 ^ _782464) ^ [_1863089, _1863091, _1863093, _1863095, _1863097] : [class_Rings_Ocomm__semiring__1(_1863089), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1863089), _1863091), _1863093)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1863089), _1863095), _1863097)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1863089), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1863089), _1863091), _1863095)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1863089), _1863093), _1863097))))], (51849 ^ _782464) ^ [_1863619, _1863621, _1863623, _1863625] : [class_Rings_Ocomm__semiring__1(_1863619), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1863619), _1863621), _1863623)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1863619), _1863621), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1863619), _1863625), _1863623))))], (51859 ^ _782464) ^ [_1864008, _1864010, _1864012, _1864014] : [class_Rings_Ocomm__semiring__1(_1864008), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864008), _1864010), _1864012)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864008), _1864010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864008), _1864012), _1864014))))], (51869 ^ _782464) ^ [_1864383, _1864385, _1864387] : [class_Rings_Ocomm__semiring__1(_1864383), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864383), _1864385), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864383), _1864387), _1864385))))], (51875 ^ _782464) ^ [_1864641, _1864643, _1864645] : [class_Rings_Ocomm__semiring__1(_1864641), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1864641), _1864643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1864641), _1864643), _1864645))))], (51891 ^ _782464) ^ [_1865234, _1865236, _1865238] : [51892 ^ _782464 : [(51893 ^ _782464) ^ [] : [_1865234 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51895 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1865236), _1865238))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1865234), _1865236)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1865234), _1865238))))], (51881 ^ _782464) ^ [_1864928, _1864930, _1864932] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1864928), _1864930)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1864928), _1864932))), -(_1864928 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1864930), _1864932)))], (51899 ^ _782464) ^ [_1865600, _1865602, _1865604, _1865606] : [class_Rings_Ocomm__ring(_1865600), class_Rings_Odvd(_1865600), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865600), _1865602), _1865604)), 51910 ^ _782464 : [(51911 ^ _782464) ^ [_1866039, _1866041] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865600), _1865602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865600), _1866041), _1865606))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865600), _1865602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865600), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1865600), _1866041), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865600), _1866039), _1865604))), _1865606))))], (51917 ^ _782464) ^ [_1866325, _1866327] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865600), _1865602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865600), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1865600), _1866327), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1865600), _1866325), _1865604))), _1865606))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1865600), _1865602), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1865600), _1866327), _1865606))))]]], (51923 ^ _782464) ^ [_1866700, _1866702, _1866704, _1866706] : [class_Rings_Ocomm__ring(_1866700), class_Rings_Odvd(_1866700), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866700), _1866702), _1866704)), 51934 ^ _782464 : [(51935 ^ _782464) ^ [_1867139, _1867141] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866700), _1866702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1866700), _1867141), _1866706))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866700), _1866702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1866700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1866700), _1867141), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1866700), _1867139), _1866704))), _1866706))))], (51941 ^ _782464) ^ [_1867425, _1867427] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866700), _1866702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1866700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1866700), _1867427), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1866700), _1867425), _1866704))), _1866706))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1866700), _1866702), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1866700), _1867427), _1866706))))]]], (51947 ^ _782464) ^ [_1867814, _1867816, _1867818, _1867820, _1867822] : [class_Divides_Osemiring__div(_1867814), -(_1867816 = c_Groups_Ozero__class_Ozero(_1867814)), -(_1867818 = c_Groups_Ozero__class_Ozero(_1867814)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1867814), _1867816), _1867820)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1867814), _1867818), _1867822)), 51966 ^ _782464 : [(51967 ^ _782464) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867814), _1867820), _1867816) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867814), _1867822), _1867818), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867814), _1867820), _1867818) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867814), _1867816), _1867822))], (51973 ^ _782464) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867814), _1867820), _1867818) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1867814), _1867816), _1867822), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867814), _1867820), _1867816) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1867814), _1867822), _1867818))]]], (51979 ^ _782464) ^ [_1868890, _1868892, _1868894, _1868896] : [class_Divides_Osemiring__div(_1868890), -(_1868892 = c_Groups_Ozero__class_Ozero(_1868890)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1868890), _1868892), _1868894)), 51990 ^ _782464 : [(51991 ^ _782464) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868890), _1868894), _1868892) = _1868896, -(_1868894 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868890), _1868896), _1868892))], (51997 ^ _782464) ^ [] : [_1868894 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1868890), _1868896), _1868892), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1868890), _1868894), _1868892) = _1868896)]]], (52003 ^ _782464) ^ [_1869686, _1869688, _1869690] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1869686, _1869688) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1869690), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 52006 ^ _782464 : [(52007 ^ _782464) ^ [] : [-(_1869686 = _1869688)], (52009 ^ _782464) ^ [] : [-(_1869688 = _1869690)]]], (52011 ^ _782464) ^ [_1869953, _1869955, _1869957] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1869953, _1869955) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1869957), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1869953 = _1869955, _1869955 = _1869957], (52021 ^ _782464) ^ [_1870257] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1870257, _1870257) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1870257), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52023 ^ _782464) ^ [_1870375, _1870377] : [_1870375 = _1870377, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1870375, _1870377) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1870375), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52029 ^ _782464) ^ [_1870607, _1870609] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1870607), _1870609)), -(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)))), _1870609, _1870607) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52035 ^ _782464) ^ [_1870839, _1870841] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1870839), _1870841)), -(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)))), _1870841, _1870839) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52041 ^ _782464) ^ [_1871071, _1871073] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871071), _1871073)), -(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)))), _1871073, _1871071) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52057 ^ _782464) ^ [_1871617, _1871619] : [52058 ^ _782464 : [(52059 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871617), _1871619)))], (52061 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871619), _1871617))]], -(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)))), _1871617, _1871619) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52047 ^ _782464) ^ [_1871330, _1871332] : [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)))), _1871330, _1871332) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871330), _1871332)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871332), _1871330)))], (52075 ^ _782464) ^ [_1872256, _1872258] : [52076 ^ _782464 : [(52077 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1872256), _1872258)))], (52079 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1872258), _1872256))]], -(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)))), _1872256, _1872258) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52065 ^ _782464) ^ [_1871969, _1871971] : [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)))), _1871969, _1871971) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871969), _1871971)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1871971), _1871969)))], (52093 ^ _782464) ^ [_1872895, _1872897] : [52094 ^ _782464 : [(52095 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1872895), _1872897)))], (52097 ^ _782464) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1872897), _1872895))]], -(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)))), _1872895, _1872897))], (52083 ^ _782464) ^ [_1872608, _1872610] : [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)))), _1872608, _1872610), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1872608), _1872610)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1872610), _1872608)))], (52101 ^ _782464) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (52103 ^ _782464) ^ [_1873271, _1873273] : [class_Lattices_Obounded__lattice(_1873271), -(class_Lattices_Obounded__lattice(tc_fun(_1873273, _1873271)))], (52109 ^ _782464) ^ [_1873483, _1873485] : [class_Complete__Lattice_Ocomplete__lattice(_1873483), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1873485, _1873483)))], (52115 ^ _782464) ^ [_1873695, _1873697] : [class_Lattices_Obounded__lattice(_1873695), -(class_Lattices_Obounded__lattice__top(tc_fun(_1873697, _1873695)))], (52121 ^ _782464) ^ [_1873907, _1873909] : [class_Lattices_Obounded__lattice(_1873907), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1873909, _1873907)))], (52127 ^ _782464) ^ [_1874119, _1874121] : [class_Lattices_Olattice(_1874119), -(class_Lattices_Osemilattice__sup(tc_fun(_1874121, _1874119)))], (52133 ^ _782464) ^ [_1874331, _1874333] : [class_Lattices_Olattice(_1874331), -(class_Lattices_Osemilattice__inf(tc_fun(_1874333, _1874331)))], (52139 ^ _782464) ^ [_1874543, _1874545] : [class_Lattices_Odistrib__lattice(_1874543), -(class_Lattices_Odistrib__lattice(tc_fun(_1874545, _1874543)))], (52145 ^ _782464) ^ [_1874755, _1874757] : [class_Lattices_Oboolean__algebra(_1874755), -(class_Lattices_Oboolean__algebra(tc_fun(_1874757, _1874755)))], (52151 ^ _782464) ^ [_1874967, _1874969] : [class_Orderings_Opreorder(_1874967), -(class_Orderings_Opreorder(tc_fun(_1874969, _1874967)))], (52157 ^ _782464) ^ [_1875179, _1875181] : [-(class_Finite__Set_Ofinite(tc_fun(_1875179, _1875181))), class_Finite__Set_Ofinite(_1875179), class_Finite__Set_Ofinite(_1875181)], (52167 ^ _782464) ^ [_1875478, _1875480] : [class_Lattices_Olattice(_1875478), -(class_Lattices_Olattice(tc_fun(_1875480, _1875478)))], (52173 ^ _782464) ^ [_1875690, _1875692] : [class_Orderings_Oorder(_1875690), -(class_Orderings_Oorder(tc_fun(_1875692, _1875690)))], (52179 ^ _782464) ^ [_1875902, _1875904] : [class_Orderings_Otop(_1875902), -(class_Orderings_Otop(tc_fun(_1875904, _1875902)))], (52185 ^ _782464) ^ [_1876114, _1876116] : [class_Orderings_Oord(_1876114), -(class_Orderings_Oord(tc_fun(_1876116, _1876114)))], (52191 ^ _782464) ^ [_1876326, _1876328] : [class_Orderings_Obot(_1876326), -(class_Orderings_Obot(tc_fun(_1876328, _1876326)))], (52197 ^ _782464) ^ [_1876538, _1876540] : [class_Groups_Ouminus(_1876538), -(class_Groups_Ouminus(tc_fun(_1876540, _1876538)))], (52203 ^ _782464) ^ [_1876750, _1876752] : [class_Groups_Ominus(_1876750), -(class_Groups_Ominus(tc_fun(_1876752, _1876750)))], (52209 ^ _782464) ^ [_1876962, _1876964] : [-(class_Enum_Oenum(tc_fun(_1876962, _1876964))), class_Enum_Oenum(_1876962), class_Enum_Oenum(_1876964)], (52219 ^ _782464) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (52221 ^ _782464) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (52223 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (52225 ^ _782464) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (52227 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (52229 ^ _782464) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (52231 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (52233 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (52235 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (52237 ^ _782464) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (52239 ^ _782464) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (52241 ^ _782464) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (52243 ^ _782464) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (52245 ^ _782464) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (52247 ^ _782464) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (52249 ^ _782464) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (52251 ^ _782464) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (52253 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (52255 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (52257 ^ _782464) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (52259 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (52261 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (52263 ^ _782464) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (52265 ^ _782464) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (52267 ^ _782464) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (52269 ^ _782464) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (52271 ^ _782464) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (52273 ^ _782464) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (52275 ^ _782464) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (52277 ^ _782464) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52279 ^ _782464) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52281 ^ _782464) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (52283 ^ _782464) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (52285 ^ _782464) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (52287 ^ _782464) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (52289 ^ _782464) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52291 ^ _782464) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (52293 ^ _782464) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52295 ^ _782464) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (52297 ^ _782464) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (52299 ^ _782464) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52301 ^ _782464) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52303 ^ _782464) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (52305 ^ _782464) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (52307 ^ _782464) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (52309 ^ _782464) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52311 ^ _782464) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52313 ^ _782464) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (52315 ^ _782464) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (52317 ^ _782464) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (52319 ^ _782464) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (52321 ^ _782464) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (52323 ^ _782464) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (52325 ^ _782464) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52327 ^ _782464) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (52329 ^ _782464) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (52331 ^ _782464) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52333 ^ _782464) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52335 ^ _782464) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52337 ^ _782464) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (52339 ^ _782464) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52341 ^ _782464) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (52343 ^ _782464) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (52345 ^ _782464) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (52347 ^ _782464) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52349 ^ _782464) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52351 ^ _782464) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52353 ^ _782464) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52355 ^ _782464) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52357 ^ _782464) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52359 ^ _782464) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52361 ^ _782464) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52363 ^ _782464) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52365 ^ _782464) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52367 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52369 ^ _782464) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52371 ^ _782464) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52373 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52375 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52377 ^ _782464) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52379 ^ _782464) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52381 ^ _782464) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52383 ^ _782464) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52385 ^ _782464) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52387 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52389 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52391 ^ _782464) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52393 ^ _782464) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52395 ^ _782464) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52397 ^ _782464) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52399 ^ _782464) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52401 ^ _782464) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52403 ^ _782464) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52405 ^ _782464) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52407 ^ _782464) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52409 ^ _782464) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52411 ^ _782464) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52413 ^ _782464) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52415 ^ _782464) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52417 ^ _782464) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52419 ^ _782464) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52421 ^ _782464) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52423 ^ _782464) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52425 ^ _782464) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52427 ^ _782464) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52429 ^ _782464) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52431 ^ _782464) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52433 ^ _782464) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52435 ^ _782464) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52437 ^ _782464) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52439 ^ _782464) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52441 ^ _782464) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52443 ^ _782464) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52445 ^ _782464) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52447 ^ _782464) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52449 ^ _782464) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52451 ^ _782464) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52453 ^ _782464) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52455 ^ _782464) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52457 ^ _782464) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52459 ^ _782464) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52461 ^ _782464) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52463 ^ _782464) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52465 ^ _782464) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52467 ^ _782464) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52469 ^ _782464) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52471 ^ _782464) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52473 ^ _782464) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52475 ^ _782464) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52477 ^ _782464) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52479 ^ _782464) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52481 ^ _782464) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52483 ^ _782464) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52485 ^ _782464) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52487 ^ _782464) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52489 ^ _782464) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52491 ^ _782464) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52493 ^ _782464) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52495 ^ _782464) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52497 ^ _782464) ^ [_1884614] : [class_Lazy__Sequence_Osmall__lazy(_1884614), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1884614)))], (52503 ^ _782464) ^ [_1884789] : [-(class_Nat_Osize(tc_List_Olist(_1884789)))], (52505 ^ _782464) ^ [_1884897, _1884899] : [-(class_Finite__Set_Ofinite(tc_sum(_1884897, _1884899))), class_Finite__Set_Ofinite(_1884897), class_Finite__Set_Ofinite(_1884899)], (52515 ^ _782464) ^ [_1885196, _1885198] : [-(class_Enum_Oenum(tc_sum(_1885196, _1885198))), class_Enum_Oenum(_1885196), class_Enum_Oenum(_1885198)], (52525 ^ _782464) ^ [_1885480, _1885482] : [-(class_Nat_Osize(tc_sum(_1885480, _1885482)))], (52527 ^ _782464) ^ [_1885577] : [class_Finite__Set_Ofinite(_1885577), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1885577)))], (52533 ^ _782464) ^ [_1885767] : [class_Enum_Oenum(_1885767), -(class_Enum_Oenum(tc_Option_Ooption(_1885767)))], (52539 ^ _782464) ^ [_1885942] : [-(class_Nat_Osize(tc_Option_Ooption(_1885942)))], (52541 ^ _782464) ^ [_1886035, _1886037] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1886035, _1886037)))], (52543 ^ _782464) ^ [_1886146, _1886148] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1886146, _1886148))), class_Lazy__Sequence_Osmall__lazy(_1886146), class_Lazy__Sequence_Osmall__lazy(_1886148)], (52553 ^ _782464) ^ [_1886445, _1886447] : [-(class_Finite__Set_Ofinite(tc_prod(_1886445, _1886447))), class_Finite__Set_Ofinite(_1886445), class_Finite__Set_Ofinite(_1886447)], (52563 ^ _782464) ^ [_1886744, _1886746] : [-(class_Enum_Oenum(tc_prod(_1886744, _1886746))), class_Enum_Oenum(_1886744), class_Enum_Oenum(_1886746)], (52573 ^ _782464) ^ [_1887028, _1887030] : [-(class_Nat_Osize(tc_prod(_1887028, _1887030)))], (52575 ^ _782464) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52577 ^ _782464) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52579 ^ _782464) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52581 ^ _782464) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52583 ^ _782464) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52585 ^ _782464) ^ [_1887375] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1887375)))], (52587 ^ _782464) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52589 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52591 ^ _782464) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52593 ^ _782464) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52595 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52597 ^ _782464) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52599 ^ _782464) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52601 ^ _782464) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52603 ^ _782464) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52605 ^ _782464) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52607 ^ _782464) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52609 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52611 ^ _782464) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52613 ^ _782464) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52615 ^ _782464) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52617 ^ _782464) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52619 ^ _782464) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52621 ^ _782464) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52623 ^ _782464) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52625 ^ _782464) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52627 ^ _782464) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52629 ^ _782464) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52631 ^ _782464) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52633 ^ _782464) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52635 ^ _782464) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52637 ^ _782464) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52639 ^ _782464) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52641 ^ _782464) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52643 ^ _782464) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52645 ^ _782464) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52647 ^ _782464) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52649 ^ _782464) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52651 ^ _782464) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52653 ^ _782464) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52655 ^ _782464) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52657 ^ _782464) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52659 ^ _782464) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52661 ^ _782464) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52663 ^ _782464) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52665 ^ _782464) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52667 ^ _782464) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52669 ^ _782464) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52671 ^ _782464) ^ [_1889680] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1889680)))], (52673 ^ _782464) ^ [_1889773, _1889775] : [-(hAPP(c_COMBI(_1889773), _1889775) = _1889775)], (52675 ^ _782464) ^ [_1889900, _1889902, _1889904, _1889906] : [-(hAPP(hAPP(c_COMBK(_1889900, _1889902), _1889904), _1889906) = _1889904)], (52677 ^ _782464) ^ [_1890063, _1890065, _1890067, _1890069, _1890071, _1890073] : [-(hAPP(hAPP(hAPP(c_COMBB(_1890063, _1890065, _1890067), _1890069), _1890071), _1890073) = hAPP(_1890069, hAPP(_1890071, _1890073)))], (52679 ^ _782464) ^ [_1890240, _1890242, _1890244, _1890246, _1890248, _1890250] : [-(hAPP(hAPP(hAPP(c_COMBC(_1890240, _1890242, _1890244), _1890246), _1890248), _1890250) = hAPP(hAPP(_1890246, _1890250), _1890248))], (52681 ^ _782464) ^ [_1890417, _1890419, _1890421, _1890423, _1890425, _1890427] : [-(hAPP(hAPP(hAPP(c_COMBS(_1890417, _1890419, _1890421), _1890423), _1890425), _1890427) = hAPP(hAPP(_1890423, _1890427), hAPP(_1890425, _1890427)))], (52683 ^ _782464) ^ [_1890556, _1890558] : [hBOOL(hAPP(hAPP(c_fequal, _1890556), _1890558)), -(_1890556 = _1890558)], (52689 ^ _782464) ^ [_1890778, _1890780] : [_1890778 = _1890780, -(hBOOL(hAPP(hAPP(c_fequal, _1890778), _1890780)))], (52695 ^ _782464) ^ [] : [hBOOL(c_fFalse)], (52697 ^ _782464) ^ [] : [-(hBOOL(c_fTrue))], (52699 ^ _782464) ^ [_1891091] : [hBOOL(hAPP(c_fNot, _1891091)), hBOOL(_1891091)], (52705 ^ _782464) ^ [_1891286] : [-(hBOOL(_1891286)), -(hBOOL(hAPP(c_fNot, _1891286)))], (52711 ^ _782464) ^ [_1891497, _1891499] : [hBOOL(_1891497), hBOOL(_1891499), -(hBOOL(hAPP(hAPP(c_fconj, _1891497), _1891499)))], (52721 ^ _782464) ^ [_1891806, _1891808] : [hBOOL(hAPP(hAPP(c_fconj, _1891806), _1891808)), -(hBOOL(_1891806))], (52727 ^ _782464) ^ [_1892026, _1892028] : [hBOOL(hAPP(hAPP(c_fconj, _1892026), _1892028)), -(hBOOL(_1892028))], (52733 ^ _782464) ^ [_1892246, _1892248] : [hBOOL(_1892246), -(hBOOL(hAPP(hAPP(c_fdisj, _1892246), _1892248)))], (52739 ^ _782464) ^ [_1892466, _1892468] : [hBOOL(_1892466), -(hBOOL(hAPP(hAPP(c_fdisj, _1892468), _1892466)))], (52745 ^ _782464) ^ [_1892686, _1892688] : [hBOOL(hAPP(hAPP(c_fdisj, _1892686), _1892688)), -(hBOOL(_1892686)), -(hBOOL(_1892688))], (52755 ^ _782464) ^ [_1892994, _1892996] : [-(hBOOL(_1892994)), -(hBOOL(hAPP(hAPP(c_fimplies, _1892994), _1892996)))], (52761 ^ _782464) ^ [_1893213, _1893215] : [hBOOL(_1893213), -(hBOOL(hAPP(hAPP(c_fimplies, _1893215), _1893213)))], (52777 ^ _782464) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts))], (52785 ^ _782464) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, v_G_H))], (52787 ^ _782464) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))], (52789 ^ _782464) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_G_H))], (52779 ^ _782464) ^ [_1893781] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G_H), _1893781)), -(c_Hoare__Mirabelle_Ohoare__derivs(t_a, _1893781, v_ts))], (52767 ^ _782464) ^ [_1893433, _1893435] : [hBOOL(hAPP(hAPP(c_fimplies, _1893433), _1893435)), hBOOL(_1893433), -(hBOOL(_1893435))]], input).
% 1.71/2.44  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)],start(52791 ^ 0)).
% 1.71/2.44  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_G_H)],extension(5767 ^ 1,bind([[_873636, _873638, _873640, _873642], [t_a, v_G_H, v_ts, v_Ga]]))).
% 1.71/2.44  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G_H, v_ts))],extension(52777 ^ 2)).
% 1.71/2.44  ncf('1.1.2',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_G_H))],extension(52789 ^ 2)).
% 1.71/2.44  %-----------------------------------------------------
% 1.71/2.44  End of proof for /export/starexec/sandbox/benchmark/theBenchmark.p
%------------------------------------------------------------------------------