%------------------------------------------------------------------------------
% File     : nanoCoP---2.0
% Problem  : SWW315+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : nanocop.sh %s %d

% Computer : n011.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 1.69s 2.48s
% Output   : Proof 1.77s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SWW315+1 : TPTP v8.1.2. Released v5.2.0.
% 0.03/0.12  % Command  : nanocop.sh %s %d
% 0.12/0.33  % Computer : n011.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 22:19:33 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 1.69/2.48  
% 1.69/2.48  /export/starexec/sandbox2/benchmark/theBenchmark.p is a Theorem
% 1.69/2.48  Start of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.69/2.48  %-----------------------------------------------------
% 1.69/2.48  ncf(matrix, plain, [(52785 ^ _782435) ^ [] : [c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)], (2 ^ _782435) ^ [_782465] : [-(_782465 = _782465)], (4 ^ _782435) ^ [_782488, _782490] : [_782490 = _782488, -(_782488 = _782490)], (10 ^ _782435) ^ [_782561, _782563, _782565] : [-(_782565 = _782561), _782565 = _782563, _782563 = _782561], (20 ^ _782435) ^ [_782698, _782700, _782702, _782704, _782706, _782708, _782710, _782712, _782714, _782716, _782718, _782720] : [-(c_Predicate_Oinv__imagep(_782718, _782714, _782710, _782706, _782702, _782698)), c_Predicate_Oinv__imagep(_782720, _782716, _782712, _782708, _782704, _782700), _782720 = _782718, _782716 = _782714, _782712 = _782710, _782708 = _782706, _782704 = _782702, _782700 = _782698], (50 ^ _782435) ^ [_783243, _783245, _783247, _783249, _783251, _783253] : [-(c_Orderings_Oorder__class_Ostrict__mono(_783251, _783247, _783243)), c_Orderings_Oorder__class_Ostrict__mono(_783253, _783249, _783245), _783253 = _783251, _783249 = _783247, _783245 = _783243], (68 ^ _782435) ^ [_783512, _783514, _783516, _783518, _783520, _783522, _783524, _783526, _783528, _783530, _783532, _783534] : [-(c_Nitpick_Ofold__graph_H(_783532, _783528, _783524, _783520, _783516, _783512)), c_Nitpick_Ofold__graph_H(_783534, _783530, _783526, _783522, _783518, _783514), _783534 = _783532, _783530 = _783528, _783526 = _783524, _783522 = _783520, _783518 = _783516, _783514 = _783512], (98 ^ _782435) ^ [_784057, _784059, _784061, _784063, _784065, _784067, _784069, _784071] : [-(c_Partial__Function_Omk__less(_784069, _784065, _784061, _784057)), c_Partial__Function_Omk__less(_784071, _784067, _784063, _784059), _784071 = _784069, _784067 = _784065, _784063 = _784061, _784059 = _784057], (120 ^ _782435) ^ [_784410, _784412, _784414, _784416, _784418, _784420, _784422, _784424] : [-(c_Finite__Set_Ofolding__idem(_784422, _784418, _784414, _784410)), c_Finite__Set_Ofolding__idem(_784424, _784420, _784416, _784412), _784424 = _784422, _784420 = _784418, _784416 = _784414, _784412 = _784410], (142 ^ _782435) ^ [_784763, _784765, _784767, _784769, _784771, _784773, _784775, _784777, _784779, _784781, _784783, _784785] : [-(c_Finite__Set_Ofolding__image__simple(_784783, _784779, _784775, _784771, _784767, _784763)), c_Finite__Set_Ofolding__image__simple(_784785, _784781, _784777, _784773, _784769, _784765), _784785 = _784783, _784781 = _784779, _784777 = _784775, _784773 = _784771, _784769 = _784767, _784765 = _784763], (172 ^ _782435) ^ [_785308, _785310, _785312, _785314, _785316, _785318] : [-(c_Big__Operators_Osemilattice__big(_785316, _785312, _785308)), c_Big__Operators_Osemilattice__big(_785318, _785314, _785310), _785318 = _785316, _785314 = _785312, _785310 = _785308], (190 ^ _782435) ^ [_785577, _785579, _785581, _785583, _785585, _785587, _785589, _785591, _785593, _785595] : [-(c_Big__Operators_Ocomm__monoid__big(_785593, _785589, _785585, _785581, _785577)), c_Big__Operators_Ocomm__monoid__big(_785595, _785591, _785587, _785583, _785579), _785595 = _785593, _785591 = _785589, _785587 = _785585, _785583 = _785581, _785579 = _785577], (216 ^ _782435) ^ [_786022, _786024] : [-(class_Rings_Odivision__ring__inverse__zero(_786022)), _786024 = _786022, class_Rings_Odivision__ring__inverse__zero(_786024)], (226 ^ _782435) ^ [_786147, _786149] : [-(class_Rings_Odivision__ring(_786147)), _786149 = _786147, class_Rings_Odivision__ring(_786149)], (236 ^ _782435) ^ [_786272, _786274] : [-(class_Fields_Ofield(_786272)), _786274 = _786272, class_Fields_Ofield(_786274)], (246 ^ _782435) ^ [_786397, _786399] : [-(c_Nat__Transfer_Ois__nat(_786397)), _786399 = _786397, c_Nat__Transfer_Ois__nat(_786399)], (256 ^ _782435) ^ [_786522, _786524] : [-(class_Fields_Olinordered__field__inverse__zero(_786522)), _786524 = _786522, class_Fields_Olinordered__field__inverse__zero(_786524)], (266 ^ _782435) ^ [_786647, _786649, _786651, _786653] : [-(c_Int_Oiszero(_786651, _786647)), c_Int_Oiszero(_786653, _786649), _786653 = _786651, _786649 = _786647], (280 ^ _782435) ^ [_786840, _786842] : [-(class_Fields_Ofield__inverse__zero(_786840)), _786842 = _786840, class_Fields_Ofield__inverse__zero(_786842)], (290 ^ _782435) ^ [_786965, _786967, _786969, _786971] : [-(c_Nitpick_Orefl_H(_786969, _786965)), c_Nitpick_Orefl_H(_786971, _786967), _786971 = _786969, _786967 = _786965], (304 ^ _782435) ^ [_787158, _787160, _787162, _787164, _787166, _787168] : [-(c_Orderings_Oorder__class_Omono(_787166, _787162, _787158)), c_Orderings_Oorder__class_Omono(_787168, _787164, _787160), _787168 = _787166, _787164 = _787162, _787160 = _787158], (322 ^ _782435) ^ [_787427, _787429, _787431, _787433] : [-(c_FunDef_Oreduction__pair(_787431, _787427)), c_FunDef_Oreduction__pair(_787433, _787429), _787433 = _787431, _787429 = _787427], (336 ^ _782435) ^ [_787620, _787622, _787624, _787626] : [-(c_Nitpick_Owf_H(_787624, _787620)), c_Nitpick_Owf_H(_787626, _787622), _787626 = _787624, _787622 = _787620], (350 ^ _782435) ^ [_787813, _787815] : [-(c_Nitpick_Ounknown(_787813)), _787815 = _787813, c_Nitpick_Ounknown(_787815)], (360 ^ _782435) ^ [_787938, _787940, _787942, _787944] : [-(c_Wellfounded_OwfP(_787942, _787938)), c_Wellfounded_OwfP(_787944, _787940), _787944 = _787942, _787940 = _787938], (374 ^ _782435) ^ [_788131, _788133, _788135, _788137] : [-(c_Relation_Oirrefl(_788135, _788131)), c_Relation_Oirrefl(_788137, _788133), _788137 = _788135, _788133 = _788131], (388 ^ _782435) ^ [_788324, _788326, _788328, _788330, _788332, _788334] : [-(c_Relation_Ototal__on(_788332, _788328, _788324)), c_Relation_Ototal__on(_788334, _788330, _788326), _788334 = _788332, _788330 = _788328, _788326 = _788324], (406 ^ _782435) ^ [_788593, _788595, _788597, _788599, _788601, _788603] : [-(c_Relation_Osingle__valued(_788601, _788597, _788593)), c_Relation_Osingle__valued(_788603, _788599, _788595), _788603 = _788601, _788599 = _788597, _788595 = _788593], (424 ^ _782435) ^ [_788862, _788864, _788866, _788868, _788870, _788872, _788874, _788876] : [-(c_Finite__Set_Ofolding(_788874, _788870, _788866, _788862)), c_Finite__Set_Ofolding(_788876, _788872, _788868, _788864), _788876 = _788874, _788872 = _788870, _788868 = _788866, _788864 = _788862], (446 ^ _782435) ^ [_789215, _789217, _789219, _789221, _789223, _789225] : [-(c_Finite__Set_Ofolding__one__idem(_789223, _789219, _789215)), c_Finite__Set_Ofolding__one__idem(_789225, _789221, _789217), _789225 = _789223, _789221 = _789219, _789217 = _789215], (464 ^ _782435) ^ [_789484, _789486, _789488, _789490, _789492, _789494] : [-(c_Finite__Set_Ofolding__one(_789492, _789488, _789484)), c_Finite__Set_Ofolding__one(_789494, _789490, _789486), _789494 = _789492, _789490 = _789488, _789486 = _789484], (482 ^ _782435) ^ [_789753, _789755, _789757, _789759, _789761, _789763, _789765, _789767, _789769, _789771, _789773, _789775] : [-(c_Finite__Set_Ofolding__image__simple__idem(_789773, _789769, _789765, _789761, _789757, _789753)), c_Finite__Set_Ofolding__image__simple__idem(_789775, _789771, _789767, _789763, _789759, _789755), _789775 = _789773, _789771 = _789769, _789767 = _789765, _789763 = _789761, _789759 = _789757, _789755 = _789753], (512 ^ _782435) ^ [_790298, _790300] : [-(class_Rings_Oinverse(_790298)), _790300 = _790298, class_Rings_Oinverse(_790300)], (522 ^ _782435) ^ [_790423, _790425, _790427, _790429, _790431, _790433] : [-(c_Nitpick_Oless__frac(_790431, _790427, _790423)), c_Nitpick_Oless__frac(_790433, _790429, _790425), _790433 = _790431, _790429 = _790427, _790425 = _790423], (540 ^ _782435) ^ [_790692, _790694, _790696, _790698, _790700, _790702] : [-(c_Nitpick_Oless__eq__frac(_790700, _790696, _790692)), c_Nitpick_Oless__eq__frac(_790702, _790698, _790694), _790702 = _790700, _790698 = _790696, _790694 = _790692], (558 ^ _782435) ^ [_790961, _790963] : [-(c_Nat__Transfer_Onat__set(_790961)), _790963 = _790961, c_Nat__Transfer_Onat__set(_790963)], (568 ^ _782435) ^ [_791086, _791088, _791090, _791092, _791094, _791096, _791098, _791100] : [-(c_List_Olistrelp(_791098, _791094, _791090, _791086)), c_List_Olistrelp(_791100, _791096, _791092, _791088), _791100 = _791098, _791096 = _791094, _791092 = _791090, _791088 = _791086], (590 ^ _782435) ^ [_791439, _791441] : [-(class_Lattices_Oab__semigroup__idem__mult(_791439)), _791441 = _791439, class_Lattices_Oab__semigroup__idem__mult(_791441)], (600 ^ _782435) ^ [_791564, _791566, _791568, _791570, _791572, _791574] : [-(c_Finite__Set_Ofun__left__comm__idem(_791572, _791568, _791564)), c_Finite__Set_Ofun__left__comm__idem(_791574, _791570, _791566), _791574 = _791572, _791570 = _791568, _791566 = _791564], (618 ^ _782435) ^ [_791833, _791835, _791837, _791839, _791841, _791843, _791845, _791847, _791849, _791851] : [-(c_Typedef_Otype__definition(_791849, _791845, _791841, _791837, _791833)), c_Typedef_Otype__definition(_791851, _791847, _791843, _791839, _791835), _791851 = _791849, _791847 = _791845, _791843 = _791841, _791839 = _791837, _791835 = _791833], (644 ^ _782435) ^ [_792278, _792280, _792282, _792284, _792286, _792288] : [-(c_Finite__Set_Ofun__left__comm(_792286, _792282, _792278)), c_Finite__Set_Ofun__left__comm(_792288, _792284, _792280), _792288 = _792286, _792284 = _792282, _792280 = _792278], (662 ^ _782435) ^ [_792547, _792549] : [-(c_List_Onat__list(_792547)), _792549 = _792547, c_List_Onat__list(_792549)], (672 ^ _782435) ^ [_792672, _792674, _792676, _792678, _792680, _792682, _792684, _792686, _792688, _792690] : [-(c_List_Olist__all2(_792688, _792684, _792680, _792676, _792672)), c_List_Olist__all2(_792690, _792686, _792682, _792678, _792674), _792690 = _792688, _792686 = _792684, _792682 = _792680, _792678 = _792676, _792674 = _792672], (698 ^ _782435) ^ [_793117, _793119, _793121, _793123] : [-(c_List_Olinorder__class_Osorted(_793121, _793117)), c_List_Olinorder__class_Osorted(_793123, _793119), _793123 = _793121, _793119 = _793117], (712 ^ _782435) ^ [_793310, _793312, _793314, _793316] : [-(c_FunDef_Ois__measure(_793314, _793310)), c_FunDef_Ois__measure(_793316, _793312), _793316 = _793314, _793312 = _793310], (726 ^ _782435) ^ [_793503, _793505, _793507, _793509, _793511, _793513, _793515, _793517] : [-(c_Nat__Transfer_Otransfer__morphism(_793515, _793511, _793507, _793503)), c_Nat__Transfer_Otransfer__morphism(_793517, _793513, _793509, _793505), _793517 = _793515, _793513 = _793511, _793509 = _793507, _793505 = _793503], (748 ^ _782435) ^ [_793856, _793858, _793860, _793862, _793864, _793866, _793868, _793870, _793872, _793874] : [-(c_Fun_Obij__betw(_793872, _793868, _793864, _793860, _793856)), c_Fun_Obij__betw(_793874, _793870, _793866, _793862, _793858), _793874 = _793872, _793870 = _793868, _793866 = _793864, _793862 = _793860, _793858 = _793856], (774 ^ _782435) ^ [_794301, _794303, _794305, _794307, _794309, _794311, _794313, _794315] : [-(c_Fun_Oinj__on(_794313, _794309, _794305, _794301)), c_Fun_Oinj__on(_794315, _794311, _794307, _794303), _794315 = _794313, _794311 = _794309, _794307 = _794305, _794303 = _794301], (796 ^ _782435) ^ [_794654, _794656] : [-(class_Fields_Olinordered__field(_794654)), _794656 = _794654, class_Fields_Olinordered__field(_794656)], (806 ^ _782435) ^ [_794779, _794781, _794783, _794785, _794787, _794789] : [-(c_List_Olist__ex1(_794787, _794783, _794779)), c_List_Olist__ex1(_794789, _794785, _794781), _794789 = _794787, _794785 = _794783, _794781 = _794779], (824 ^ _782435) ^ [_795048, _795050, _795052, _795054, _795056, _795058] : [-(c_List_Oall__interval__int(_795056, _795052, _795048)), c_List_Oall__interval__int(_795058, _795054, _795050), _795058 = _795056, _795054 = _795052, _795050 = _795048], (842 ^ _782435) ^ [_795317, _795319, _795321, _795323] : [-(c_Predicate_Oreflp(_795321, _795317)), c_Predicate_Oreflp(_795323, _795319), _795323 = _795321, _795319 = _795317], (856 ^ _782435) ^ [_795510, _795512, _795514, _795516, _795518, _795520, _795522, _795524] : [-(c_Wellfounded_Omax__extp(_795522, _795518, _795514, _795510)), c_Wellfounded_Omax__extp(_795524, _795520, _795516, _795512), _795524 = _795522, _795520 = _795518, _795516 = _795514, _795512 = _795510], (878 ^ _782435) ^ [_795863, _795865, _795867, _795869] : [-(c_Wellfounded_Oacyclic(_795867, _795863)), c_Wellfounded_Oacyclic(_795869, _795865), _795869 = _795867, _795865 = _795863], (892 ^ _782435) ^ [_796056, _796058, _796060, _796062] : [-(c_Relation_Oantisym(_796060, _796056)), c_Relation_Oantisym(_796062, _796058), _796062 = _796060, _796058 = _796056], (906 ^ _782435) ^ [_796249, _796251, _796253, _796255, _796257, _796259] : [-(c_Equiv__Relations_Oequiv(_796257, _796253, _796249)), c_Equiv__Relations_Oequiv(_796259, _796255, _796251), _796259 = _796257, _796255 = _796253, _796251 = _796249], (924 ^ _782435) ^ [_796518, _796520, _796522, _796524] : [-(c_Relation_Otrans(_796522, _796518)), c_Relation_Otrans(_796524, _796520), _796524 = _796522, _796520 = _796518], (938 ^ _782435) ^ [_796711, _796713, _796715, _796717] : [-(c_Relation_Osym(_796715, _796711)), c_Relation_Osym(_796717, _796713), _796717 = _796715, _796713 = _796711], (952 ^ _782435) ^ [_796904, _796906, _796908, _796910] : [-(c_Predicate_Osymp(_796908, _796904)), c_Predicate_Osymp(_796910, _796906), _796910 = _796908, _796906 = _796904], (966 ^ _782435) ^ [_797097, _797099, _797101, _797103] : [-(c_Predicate_Otransp(_797101, _797097)), c_Predicate_Otransp(_797103, _797099), _797103 = _797101, _797099 = _797097], (980 ^ _782435) ^ [_797290, _797292, _797294, _797296] : [-(c_Equiv__Relations_Opart__equivp(_797294, _797290)), c_Equiv__Relations_Opart__equivp(_797296, _797292), _797296 = _797294, _797292 = _797290], (994 ^ _782435) ^ [_797483, _797485, _797487, _797489, _797491, _797493] : [-(c_Relation_Orefl__on(_797491, _797487, _797483)), c_Relation_Orefl__on(_797493, _797489, _797485), _797493 = _797491, _797489 = _797487, _797485 = _797483], (1012 ^ _782435) ^ [_797752, _797754, _797756, _797758] : [-(c_Wellfounded_Owf(_797756, _797752)), c_Wellfounded_Owf(_797758, _797754), _797758 = _797756, _797754 = _797752], (1026 ^ _782435) ^ [_797945, _797947, _797949, _797951] : [-(c_Equiv__Relations_Oequivp(_797949, _797945)), c_Equiv__Relations_Oequivp(_797951, _797947), _797951 = _797949, _797947 = _797945], (1040 ^ _782435) ^ [_798138, _798140, _798142, _798144, _798146, _798148, _798150, _798152, _798154, _798156, _798158, _798160] : [-(c_Equiv__Relations_Ocongruent2(_798158, _798154, _798150, _798146, _798142, _798138)), c_Equiv__Relations_Ocongruent2(_798160, _798156, _798152, _798148, _798144, _798140), _798160 = _798158, _798156 = _798154, _798152 = _798150, _798148 = _798146, _798144 = _798142, _798140 = _798138], (1070 ^ _782435) ^ [_798683, _798685, _798687, _798689, _798691, _798693, _798695, _798697] : [-(c_Equiv__Relations_Ocongruent(_798695, _798691, _798687, _798683)), c_Equiv__Relations_Ocongruent(_798697, _798693, _798689, _798685), _798697 = _798695, _798693 = _798691, _798689 = _798687, _798685 = _798683], (1092 ^ _782435) ^ [_799036, _799038, _799040, _799042, _799044, _799046] : [-(c_List_Olist__all(_799044, _799040, _799036)), c_List_Olist__all(_799046, _799042, _799038), _799046 = _799044, _799042 = _799040, _799038 = _799036], (1110 ^ _782435) ^ [_799305, _799307, _799309, _799311, _799313, _799315] : [-(c_List_Olist__ex(_799313, _799309, _799305)), c_List_Olist__ex(_799315, _799311, _799307), _799315 = _799313, _799311 = _799309, _799307 = _799305], (1128 ^ _782435) ^ [_799574, _799576, _799578, _799580, _799582, _799584] : [-(c_List_Oall__interval__nat(_799582, _799578, _799574)), c_List_Oall__interval__nat(_799584, _799580, _799576), _799584 = _799582, _799580 = _799578, _799576 = _799574], (1146 ^ _782435) ^ [_799843, _799845, _799847, _799849, _799851, _799853, _799855, _799857, _799859, _799861] : [-(c_Finite__Set_Ofolding__image(_799859, _799855, _799851, _799847, _799843)), c_Finite__Set_Ofolding__image(_799861, _799857, _799853, _799849, _799845), _799861 = _799859, _799857 = _799855, _799853 = _799851, _799849 = _799847, _799845 = _799843], (1172 ^ _782435) ^ [_800288, _800290] : [-(class_Lattices_Obounded__lattice(_800288)), _800290 = _800288, class_Lattices_Obounded__lattice(_800290)], (1182 ^ _782435) ^ [_800413, _800415] : [-(class_Rings_Olinordered__semiring__1__strict(_800413)), _800415 = _800413, class_Rings_Olinordered__semiring__1__strict(_800415)], (1192 ^ _782435) ^ [_800538, _800540] : [-(class_Groups_Oordered__ab__group__add__abs(_800538)), _800540 = _800538, class_Groups_Oordered__ab__group__add__abs(_800540)], (1202 ^ _782435) ^ [_800663, _800665] : [-(class_Groups_Olinordered__ab__group__add(_800663)), _800665 = _800663, class_Groups_Olinordered__ab__group__add(_800665)], (1212 ^ _782435) ^ [_800788, _800790] : [-(class_Rings_Oring__1__no__zero__divisors(_800788)), _800790 = _800788, class_Rings_Oring__1__no__zero__divisors(_800790)], (1222 ^ _782435) ^ [_800913, _800915] : [-(class_Rings_Olinordered__ring__strict(_800913)), _800915 = _800913, class_Rings_Olinordered__ring__strict(_800915)], (1232 ^ _782435) ^ [_801038, _801040] : [-(class_Rings_Oring__no__zero__divisors(_801038)), _801040 = _801038, class_Rings_Oring__no__zero__divisors(_801040)], (1242 ^ _782435) ^ [_801163, _801165] : [-(class_Rings_Olinordered__semiring__1(_801163)), _801165 = _801163, class_Rings_Olinordered__semiring__1(_801165)], (1252 ^ _782435) ^ [_801288, _801290] : [-(class_Groups_Oordered__ab__group__add(_801288)), _801290 = _801288, class_Groups_Oordered__ab__group__add(_801290)], (1262 ^ _782435) ^ [_801413, _801415] : [-(class_Rings_Oordered__ring__abs(_801413)), _801415 = _801413, class_Rings_Oordered__ring__abs(_801415)], (1272 ^ _782435) ^ [_801538, _801540] : [-(class_Rings_Olinordered__ring(_801538)), _801540 = _801538, class_Rings_Olinordered__ring(_801540)], (1282 ^ _782435) ^ [_801663, _801665] : [-(class_Rings_Olinordered__idom(_801663)), _801665 = _801663, class_Rings_Olinordered__idom(_801665)], (1292 ^ _782435) ^ [_801788, _801790] : [-(class_Groups_Oab__group__add(_801788)), _801790 = _801788, class_Groups_Oab__group__add(_801790)], (1302 ^ _782435) ^ [_801913, _801915] : [-(class_Rings_Oordered__ring(_801913)), _801915 = _801913, class_Rings_Oordered__ring(_801915)], (1312 ^ _782435) ^ [_802038, _802040] : [-(class_Rings_Ocomm__ring__1(_802038)), _802040 = _802038, class_Rings_Ocomm__ring__1(_802040)], (1322 ^ _782435) ^ [_802163, _802165] : [-(class_Groups_Ogroup__add(_802163)), _802165 = _802163, class_Groups_Ogroup__add(_802165)], (1332 ^ _782435) ^ [_802288, _802290] : [-(class_Divides_Oring__div(_802288)), _802290 = _802288, class_Divides_Oring__div(_802290)], (1342 ^ _782435) ^ [_802413, _802415] : [-(class_Rings_Ocomm__ring(_802413)), _802415 = _802413, class_Rings_Ocomm__ring(_802415)], (1352 ^ _782435) ^ [_802538, _802540] : [-(class_Int_Oring__char__0(_802538)), _802540 = _802538, class_Int_Oring__char__0(_802540)], (1362 ^ _782435) ^ [_802663, _802665] : [-(class_Int_Onumber__ring(_802663)), _802665 = _802663, class_Int_Onumber__ring(_802665)], (1372 ^ _782435) ^ [_802788, _802790] : [-(class_Groups_Osgn__if(_802788)), _802790 = _802788, class_Groups_Osgn__if(_802790)], (1382 ^ _782435) ^ [_802913, _802915] : [-(class_Groups_Oabs__if(_802913)), _802915 = _802913, class_Groups_Oabs__if(_802915)], (1392 ^ _782435) ^ [_803038, _803040] : [-(class_Rings_Oring__1(_803038)), _803040 = _803038, class_Rings_Oring__1(_803040)], (1402 ^ _782435) ^ [_803163, _803165] : [-(class_Rings_Oring(_803163)), _803165 = _803163, class_Rings_Oring(_803165)], (1412 ^ _782435) ^ [_803288, _803290] : [-(class_Rings_Oidom(_803288)), _803290 = _803288, class_Rings_Oidom(_803290)], (1422 ^ _782435) ^ [_803413, _803415] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803413)), _803415 = _803413, class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_803415)], (1432 ^ _782435) ^ [_803538, _803540] : [-(class_Orderings_Owellorder(_803538)), _803540 = _803538, class_Orderings_Owellorder(_803540)], (1442 ^ _782435) ^ [_803663, _803665] : [-(class_Complete__Lattice_Ocomplete__lattice(_803663)), _803665 = _803663, class_Complete__Lattice_Ocomplete__lattice(_803665)], (1452 ^ _782435) ^ [_803788, _803790] : [-(class_Lattices_Obounded__lattice__top(_803788)), _803790 = _803788, class_Lattices_Obounded__lattice__top(_803790)], (1462 ^ _782435) ^ [_803913, _803915] : [-(class_Lattices_Obounded__lattice__bot(_803913)), _803915 = _803913, class_Lattices_Obounded__lattice__bot(_803915)], (1472 ^ _782435) ^ [_804038, _804040] : [-(class_Lattices_Osemilattice__sup(_804038)), _804040 = _804038, class_Lattices_Osemilattice__sup(_804040)], (1482 ^ _782435) ^ [_804163, _804165] : [-(class_Lattices_Osemilattice__inf(_804163)), _804165 = _804163, class_Lattices_Osemilattice__inf(_804165)], (1492 ^ _782435) ^ [_804288, _804290] : [-(class_Lattices_Odistrib__lattice(_804288)), _804290 = _804288, class_Lattices_Odistrib__lattice(_804290)], (1502 ^ _782435) ^ [_804413, _804415] : [-(class_Lattices_Oboolean__algebra(_804413)), _804415 = _804413, class_Lattices_Oboolean__algebra(_804415)], (1512 ^ _782435) ^ [_804538, _804540] : [-(class_Lattices_Olattice(_804538)), _804540 = _804538, class_Lattices_Olattice(_804540)], (1522 ^ _782435) ^ [_804663, _804665] : [-(class_Orderings_Otop(_804663)), _804665 = _804663, class_Orderings_Otop(_804665)], (1532 ^ _782435) ^ [_804788, _804790] : [-(class_Orderings_Obot(_804788)), _804790 = _804788, class_Orderings_Obot(_804790)], (1542 ^ _782435) ^ [_804913, _804915] : [-(class_Groups_Ouminus(_804913)), _804915 = _804913, class_Groups_Ouminus(_804915)], (1552 ^ _782435) ^ [_805038, _805040] : [-(class_Lazy__Sequence_Osmall__lazy(_805038)), _805040 = _805038, class_Lazy__Sequence_Osmall__lazy(_805040)], (1562 ^ _782435) ^ [_805163, _805165] : [-(class_Finite__Set_Ofinite(_805163)), _805165 = _805163, class_Finite__Set_Ofinite(_805165)], (1572 ^ _782435) ^ [_805288, _805290] : [-(class_Enum_Oenum(_805288)), _805290 = _805288, class_Enum_Oenum(_805290)], (1582 ^ _782435) ^ [_805413, _805415] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(_805413)), _805415 = _805413, class_Groups_Oordered__cancel__ab__semigroup__add(_805415)], (1592 ^ _782435) ^ [_805538, _805540] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(_805538)), _805540 = _805538, class_Groups_Oordered__ab__semigroup__add__imp__le(_805540)], (1602 ^ _782435) ^ [_805663, _805665] : [-(class_Rings_Olinordered__comm__semiring__strict(_805663)), _805665 = _805663, class_Rings_Olinordered__comm__semiring__strict(_805665)], (1612 ^ _782435) ^ [_805788, _805790] : [-(class_Groups_Olinordered__ab__semigroup__add(_805788)), _805790 = _805788, class_Groups_Olinordered__ab__semigroup__add(_805790)], (1622 ^ _782435) ^ [_805913, _805915] : [-(class_Rings_Olinordered__semiring__strict(_805913)), _805915 = _805913, class_Rings_Olinordered__semiring__strict(_805915)], (1632 ^ _782435) ^ [_806038, _806040] : [-(class_Groups_Oordered__ab__semigroup__add(_806038)), _806040 = _806038, class_Groups_Oordered__ab__semigroup__add(_806040)], (1642 ^ _782435) ^ [_806163, _806165] : [-(class_Groups_Oordered__comm__monoid__add(_806163)), _806165 = _806163, class_Groups_Oordered__comm__monoid__add(_806165)], (1652 ^ _782435) ^ [_806288, _806290] : [-(class_Groups_Ocancel__ab__semigroup__add(_806288)), _806290 = _806288, class_Groups_Ocancel__ab__semigroup__add(_806290)], (1662 ^ _782435) ^ [_806413, _806415] : [-(class_Rings_Oordered__cancel__semiring(_806413)), _806415 = _806413, class_Rings_Oordered__cancel__semiring(_806415)], (1672 ^ _782435) ^ [_806538, _806540] : [-(class_Rings_Oordered__comm__semiring(_806538)), _806540 = _806538, class_Rings_Oordered__comm__semiring(_806540)], (1682 ^ _782435) ^ [_806663, _806665] : [-(class_Groups_Ocancel__semigroup__add(_806663)), _806665 = _806663, class_Groups_Ocancel__semigroup__add(_806665)], (1692 ^ _782435) ^ [_806788, _806790] : [-(class_Rings_Olinordered__semiring(_806788)), _806790 = _806788, class_Rings_Olinordered__semiring(_806790)], (1702 ^ _782435) ^ [_806913, _806915] : [-(class_Rings_Olinordered__semidom(_806913)), _806915 = _806913, class_Rings_Olinordered__semidom(_806915)], (1712 ^ _782435) ^ [_807038, _807040] : [-(class_Groups_Oab__semigroup__mult(_807038)), _807040 = _807038, class_Groups_Oab__semigroup__mult(_807040)], (1722 ^ _782435) ^ [_807163, _807165] : [-(class_Groups_Ocomm__monoid__mult(_807163)), _807165 = _807163, class_Groups_Ocomm__monoid__mult(_807165)], (1732 ^ _782435) ^ [_807288, _807290] : [-(class_Groups_Oab__semigroup__add(_807288)), _807290 = _807288, class_Groups_Oab__semigroup__add(_807290)], (1742 ^ _782435) ^ [_807413, _807415] : [-(class_Rings_Oordered__semiring(_807413)), _807415 = _807413, class_Rings_Oordered__semiring(_807415)], (1752 ^ _782435) ^ [_807538, _807540] : [-(class_Rings_Ono__zero__divisors(_807538)), _807540 = _807538, class_Rings_Ono__zero__divisors(_807540)], (1762 ^ _782435) ^ [_807663, _807665] : [-(class_Groups_Ocomm__monoid__add(_807663)), _807665 = _807663, class_Groups_Ocomm__monoid__add(_807665)], (1772 ^ _782435) ^ [_807788, _807790] : [-(class_Rings_Ocomm__semiring__1(_807788)), _807790 = _807788, class_Rings_Ocomm__semiring__1(_807790)], (1782 ^ _782435) ^ [_807913, _807915] : [-(class_Groups_Osemigroup__add(_807913)), _807915 = _807913, class_Groups_Osemigroup__add(_807915)], (1792 ^ _782435) ^ [_808038, _808040] : [-(class_Divides_Osemiring__div(_808038)), _808040 = _808038, class_Divides_Osemiring__div(_808040)], (1802 ^ _782435) ^ [_808163, _808165] : [-(class_Rings_Ocomm__semiring(_808163)), _808165 = _808163, class_Rings_Ocomm__semiring(_808165)], (1812 ^ _782435) ^ [_808288, _808290] : [-(class_Nat_Osemiring__char__0(_808288)), _808290 = _808288, class_Nat_Osemiring__char__0(_808290)], (1822 ^ _782435) ^ [_808413, _808415] : [-(class_Rings_Ozero__neq__one(_808413)), _808415 = _808413, class_Rings_Ozero__neq__one(_808415)], (1832 ^ _782435) ^ [_808538, _808540] : [-(class_Orderings_Opreorder(_808538)), _808540 = _808538, class_Orderings_Opreorder(_808540)], (1842 ^ _782435) ^ [_808663, _808665] : [-(class_Orderings_Olinorder(_808663)), _808665 = _808663, class_Orderings_Olinorder(_808665)], (1852 ^ _782435) ^ [_808788, _808790] : [-(class_Groups_Omonoid__mult(_808788)), _808790 = _808788, class_Groups_Omonoid__mult(_808790)], (1862 ^ _782435) ^ [_808913, _808915] : [-(class_Groups_Omonoid__add(_808913)), _808915 = _808913, class_Groups_Omonoid__add(_808915)], (1872 ^ _782435) ^ [_809038, _809040] : [-(class_Rings_Osemiring__1(_809038)), _809040 = _809038, class_Rings_Osemiring__1(_809040)], (1882 ^ _782435) ^ [_809163, _809165] : [-(class_Rings_Osemiring__0(_809163)), _809165 = _809163, class_Rings_Osemiring__0(_809165)], (1892 ^ _782435) ^ [_809288, _809290] : [-(class_Rings_Omult__zero(_809288)), _809290 = _809288, class_Rings_Omult__zero(_809290)], (1902 ^ _782435) ^ [_809413, _809415] : [-(class_Orderings_Oorder(_809413)), _809415 = _809413, class_Orderings_Oorder(_809415)], (1912 ^ _782435) ^ [_809538, _809540] : [-(class_Rings_Osemiring(_809538)), _809540 = _809538, class_Rings_Osemiring(_809540)], (1922 ^ _782435) ^ [_809663, _809665] : [-(class_Orderings_Oord(_809663)), _809665 = _809663, class_Orderings_Oord(_809665)], (1932 ^ _782435) ^ [_809788, _809790] : [-(class_Groups_Ominus(_809788)), _809790 = _809788, class_Groups_Ominus(_809790)], (1942 ^ _782435) ^ [_809913, _809915] : [-(class_Power_Opower(_809913)), _809915 = _809913, class_Power_Opower(_809915)], (1952 ^ _782435) ^ [_810038, _810040] : [-(class_Groups_Ozero(_810038)), _810040 = _810038, class_Groups_Ozero(_810040)], (1962 ^ _782435) ^ [_810163, _810165] : [-(class_Int_Onumber(_810163)), _810165 = _810163, class_Int_Onumber(_810165)], (1972 ^ _782435) ^ [_810288, _810290] : [-(class_Groups_Oone(_810288)), _810290 = _810288, class_Groups_Oone(_810290)], (1982 ^ _782435) ^ [_810413, _810415] : [-(class_Rings_Odvd(_810413)), _810415 = _810413, class_Rings_Odvd(_810415)], (1992 ^ _782435) ^ [_810538, _810540] : [-(class_Nat_Osize(_810538)), _810540 = _810538, class_Nat_Osize(_810540)], (2002 ^ _782435) ^ [_810663, _810665] : [-(hBOOL(_810663)), _810665 = _810663, hBOOL(_810665)], (2012 ^ _782435) ^ [_810784, _810786, _810788, _810790, _810792, _810794] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_810792, _810788, _810784)), c_Hoare__Mirabelle_Ohoare__derivs(_810794, _810790, _810786), _810794 = _810792, _810790 = _810788, _810786 = _810784], (2030 ^ _782435) ^ [_811867, _811869, _811871, _811873, _811875, _811877] : [-(c_SetInterval_Oord_OgreaterThan(_811877, _811873, _811869) = c_SetInterval_Oord_OgreaterThan(_811875, _811871, _811867)), _811877 = _811875, _811873 = _811871, _811869 = _811867], (2044 ^ _782435) ^ [_812088, _812090, _812092, _812094, _812096, _812098] : [-(c_SetInterval_Oord_OlessThan(_812098, _812094, _812090) = c_SetInterval_Oord_OlessThan(_812096, _812092, _812088)), _812098 = _812096, _812094 = _812092, _812090 = _812088], (2058 ^ _782435) ^ [_812309, _812311, _812313, _812315, _812317, _812319] : [-(c_SetInterval_Oord_OatLeast(_812319, _812315, _812311) = c_SetInterval_Oord_OatLeast(_812317, _812313, _812309)), _812319 = _812317, _812315 = _812313, _812311 = _812309], (2072 ^ _782435) ^ [_812530, _812532, _812534, _812536, _812538, _812540] : [-(c_SetInterval_Oord_OatMost(_812540, _812536, _812532) = c_SetInterval_Oord_OatMost(_812538, _812534, _812530)), _812540 = _812538, _812536 = _812534, _812532 = _812530], (2086 ^ _782435) ^ [_812751, _812753, _812755, _812757] : [-(c_Enum_Oenum__the(_812757, _812753) = c_Enum_Oenum__the(_812755, _812751)), _812757 = _812755, _812753 = _812751], (2096 ^ _782435) ^ [_812900, _812902, _812904, _812906, _812908, _812910] : [-(c_Partial__Function_Oflat__lub(_812910, _812906, _812902) = c_Partial__Function_Oflat__lub(_812908, _812904, _812900)), _812910 = _812908, _812906 = _812904, _812902 = _812900], (2110 ^ _782435) ^ [_813121, _813123, _813125, _813127, _813129, _813131, _813133, _813135] : [-(c_Fun_Othe__inv__into(_813135, _813131, _813127, _813123) = c_Fun_Othe__inv__into(_813133, _813129, _813125, _813121)), _813135 = _813133, _813131 = _813129, _813127 = _813125, _813123 = _813121], (2128 ^ _782435) ^ [_813422, _813424, _813426, _813428, _813430, _813432, _813434, _813436, _813438, _813440] : [-(c_Fun_Ooverride__on(_813440, _813436, _813432, _813428, _813424) = c_Fun_Ooverride__on(_813438, _813434, _813430, _813426, _813422)), _813440 = _813438, _813436 = _813434, _813432 = _813430, _813428 = _813426, _813424 = _813422], (2150 ^ _782435) ^ [_813811, _813813, _813815, _813817, _813819, _813821, _813823, _813825] : [-(c_Nat_Osemiring__1__class_Oof__nat__aux(_813825, _813821, _813817, _813813) = c_Nat_Osemiring__1__class_Oof__nat__aux(_813823, _813819, _813815, _813811)), _813825 = _813823, _813821 = _813819, _813817 = _813815, _813813 = _813811], (2168 ^ _782435) ^ [_814112, _814114] : [_814114 = _814112, -(c_SetInterval_Oord__class_OgreaterThan(_814114) = c_SetInterval_Oord__class_OgreaterThan(_814112))], (2174 ^ _782435) ^ [_814197, _814199, _814201, _814203] : [-(c_Int_Onat__aux(_814203, _814199) = c_Int_Onat__aux(_814201, _814197)), _814203 = _814201, _814199 = _814197], (2184 ^ _782435) ^ [_814346, _814348, _814350, _814352, _814354, _814356, _814358, _814360] : [-(c_Sum__Type_OPlus(_814360, _814356, _814352, _814348) = c_Sum__Type_OPlus(_814358, _814354, _814350, _814346)), _814360 = _814358, _814356 = _814354, _814352 = _814350, _814348 = _814346], (2202 ^ _782435) ^ [_814647, _814649, _814651, _814653] : [-(c_Nat__Transfer_Otsub(_814653, _814649) = c_Nat__Transfer_Otsub(_814651, _814647)), _814653 = _814651, _814649 = _814647], (2212 ^ _782435) ^ [_814796, _814798, _814800, _814802] : [-(c_Inductive_Ocomplete__lattice__class_Ogfp(_814802, _814798) = c_Inductive_Ocomplete__lattice__class_Ogfp(_814800, _814796)), _814802 = _814800, _814798 = _814796], (2222 ^ _782435) ^ [_814945, _814947] : [_814947 = _814945, -(c_SetInterval_Oord__class_OatLeast(_814947) = c_SetInterval_Oord__class_OatLeast(_814945))], (2228 ^ _782435) ^ [_815030, _815032, _815034, _815036] : [-(c_Orderings_Oord_Omax(_815036, _815032) = c_Orderings_Oord_Omax(_815034, _815030)), _815036 = _815034, _815032 = _815030], (2238 ^ _782435) ^ [_815179, _815181, _815183, _815185] : [-(c_Orderings_Oord_Omin(_815185, _815181) = c_Orderings_Oord_Omin(_815183, _815179)), _815185 = _815183, _815181 = _815179], (2248 ^ _782435) ^ [_815328, _815330, _815332, _815334, _815336, _815338] : [-(c_Power_Opower_Opower(_815338, _815334, _815330) = c_Power_Opower_Opower(_815336, _815332, _815328)), _815338 = _815336, _815334 = _815332, _815330 = _815328], (2262 ^ _782435) ^ [_815549, _815551, _815553, _815555] : [-(c_SMT_Oz3div(_815555, _815551) = c_SMT_Oz3div(_815553, _815549)), _815555 = _815553, _815551 = _815549], (2272 ^ _782435) ^ [_815698, _815700, _815702, _815704] : [-(c_Nitpick_Onat__lcm(_815704, _815700) = c_Nitpick_Onat__lcm(_815702, _815698)), _815704 = _815702, _815700 = _815698], (2282 ^ _782435) ^ [_815847, _815849, _815851, _815853] : [-(c_SMT_Oz3mod(_815853, _815849) = c_SMT_Oz3mod(_815851, _815847)), _815853 = _815851, _815849 = _815847], (2292 ^ _782435) ^ [_815996, _815998] : [_815998 = _815996, -(c_Int_Oring__1__class_OInts(_815998) = c_Int_Oring__1__class_OInts(_815996))], (2298 ^ _782435) ^ [_816081, _816083, _816085, _816087, _816089, _816091] : [-(c_Nat_Onat_Onat__rec(_816091, _816087, _816083) = c_Nat_Onat_Onat__rec(_816089, _816085, _816081)), _816091 = _816089, _816087 = _816085, _816083 = _816081], (2312 ^ _782435) ^ [_816302, _816304] : [_816304 = _816302, -(c_Int_Opred(_816304) = c_Int_Opred(_816302))], (2318 ^ _782435) ^ [_816387, _816389] : [_816389 = _816387, -(c_Int_Osucc(_816389) = c_Int_Osucc(_816387))], (2324 ^ _782435) ^ [_816472, _816474, _816476, _816478, _816480, _816482, _816484, _816486] : [-(c_Nitpick_Oprod(_816486, _816482, _816478, _816474) = c_Nitpick_Oprod(_816484, _816480, _816476, _816472)), _816486 = _816484, _816482 = _816480, _816478 = _816476, _816474 = _816472], (2342 ^ _782435) ^ [_816773, _816775] : [_816775 = _816773, -(c_Enum_Oenum__class_Oenum__ex(_816775) = c_Enum_Oenum__class_Oenum__ex(_816773))], (2348 ^ _782435) ^ [_816858, _816860] : [_816860 = _816858, -(c_Enum_Oenum__class_Oenum__all(_816860) = c_Enum_Oenum__class_Oenum__all(_816858))], (2354 ^ _782435) ^ [_816943, _816945] : [_816945 = _816943, -(c_Nat_Osemiring__1__class_ONats(_816945) = c_Nat_Osemiring__1__class_ONats(_816943))], (2360 ^ _782435) ^ [_817028, _817030, _817032, _817034] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_817034, _817030) = c_Code__Numeral_Odiv__mod__code__numeral(_817032, _817028)), _817034 = _817032, _817030 = _817028], (2370 ^ _782435) ^ [_817177, _817179, _817181, _817183] : [-(c_Divides_Odivmod__int__rel(_817183, _817179) = c_Divides_Odivmod__int__rel(_817181, _817177)), _817183 = _817181, _817179 = _817177], (2380 ^ _782435) ^ [_817326, _817328, _817330, _817332] : [-(c_Groups_Osgn__class_Osgn(_817332, _817328) = c_Groups_Osgn__class_Osgn(_817330, _817326)), _817332 = _817330, _817328 = _817326], (2390 ^ _782435) ^ [_817475, _817477, _817479, _817481] : [-(c_Divides_Opdivmod(_817481, _817477) = c_Divides_Opdivmod(_817479, _817475)), _817481 = _817479, _817477 = _817475], (2400 ^ _782435) ^ [_817624, _817626] : [_817626 = _817624, -(c_Divides_Oadjust(_817626) = c_Divides_Oadjust(_817624))], (2406 ^ _782435) ^ [_817709, _817711] : [_817711 = _817709, -(c_Int_OBit0(_817711) = c_Int_OBit0(_817709))], (2412 ^ _782435) ^ [_817794, _817796, _817798, _817800] : [-(c_Nitpick_Onat__gcd(_817800, _817796) = c_Nitpick_Onat__gcd(_817798, _817794)), _817800 = _817798, _817796 = _817794], (2422 ^ _782435) ^ [_817943, _817945] : [_817945 = _817943, -(c_Nat_Onat_Onat__size(_817945) = c_Nat_Onat_Onat__size(_817943))], (2428 ^ _782435) ^ [_818028, _818030, _818032, _818034] : [-(c_Divides_Odivmod__int(_818034, _818030) = c_Divides_Odivmod__int(_818032, _818028)), _818034 = _818032, _818030 = _818028], (2438 ^ _782435) ^ [_818177, _818179, _818181, _818183] : [-(c_Divides_OnegDivAlg(_818183, _818179) = c_Divides_OnegDivAlg(_818181, _818177)), _818183 = _818181, _818179 = _818177], (2448 ^ _782435) ^ [_818326, _818328, _818330, _818332] : [-(c_Divides_OposDivAlg(_818332, _818328) = c_Divides_OposDivAlg(_818330, _818326)), _818332 = _818330, _818328 = _818326], (2458 ^ _782435) ^ [_818475, _818477, _818479, _818481, _818483, _818485, _818487, _818489, _818491, _818493] : [-(c_Product__Type_Oprod_Oprod__size(_818493, _818489, _818485, _818481, _818477) = c_Product__Type_Oprod_Oprod__size(_818491, _818487, _818483, _818479, _818475)), _818493 = _818491, _818489 = _818487, _818485 = _818483, _818481 = _818479, _818477 = _818475], (2480 ^ _782435) ^ [_818864, _818866, _818868, _818870] : [-(c_Divides_Odivmod__nat(_818870, _818866) = c_Divides_Odivmod__nat(_818868, _818864)), _818870 = _818868, _818866 = _818864], (2490 ^ _782435) ^ [_819013, _819015, _819017, _819019] : [-(c_Divides_Odivmod__nat__rel(_819019, _819015) = c_Divides_Odivmod__nat__rel(_819017, _819013)), _819019 = _819017, _819015 = _819013], (2500 ^ _782435) ^ [_819162, _819164, _819166, _819168] : [-(c_Set_Othe__elem(_819168, _819164) = c_Set_Othe__elem(_819166, _819162)), _819168 = _819166, _819164 = _819162], (2510 ^ _782435) ^ [_819311, _819313] : [_819313 = _819311, -(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819313) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_819311))], (2516 ^ _782435) ^ [_819396, _819398, _819400, _819402, _819404, _819406, _819408, _819410, _819412, _819414] : [-(c_Product__Type_Oprod_Oprod__rec(_819414, _819410, _819406, _819402, _819398) = c_Product__Type_Oprod_Oprod__rec(_819412, _819408, _819404, _819400, _819396)), _819414 = _819412, _819410 = _819408, _819406 = _819404, _819402 = _819400, _819398 = _819396], (2538 ^ _782435) ^ [_819785, _819787, _819789, _819791] : [-(c_Inductive_Ocomplete__lattice__class_Olfp(_819791, _819787) = c_Inductive_Ocomplete__lattice__class_Olfp(_819789, _819785)), _819791 = _819789, _819787 = _819785], (2548 ^ _782435) ^ [_819934, _819936, _819938, _819940] : [-(c_FunDef_Orp__inv__image(_819940, _819936) = c_FunDef_Orp__inv__image(_819938, _819934)), _819940 = _819938, _819936 = _819934], (2558 ^ _782435) ^ [_820083, _820085, _820087, _820089, _820091, _820093, _820095, _820097] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820097, _820093, _820089, _820085) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_820095, _820091, _820087, _820083)), _820097 = _820095, _820093 = _820091, _820089 = _820087, _820085 = _820083], (2576 ^ _782435) ^ [_820384, _820386] : [_820386 = _820384, -(c_Wellfounded_Omeasure(_820386) = c_Wellfounded_Omeasure(_820384))], (2582 ^ _782435) ^ [_820469, _820471, _820473, _820475] : [-(c_Wellfounded_Omin__ext(_820475, _820471) = c_Wellfounded_Omin__ext(_820473, _820469)), _820475 = _820473, _820471 = _820469], (2592 ^ _782435) ^ [_820618, _820620, _820622, _820624, _820626, _820628] : [-(c_Wellfounded_Omlex__prod(_820628, _820624, _820620) = c_Wellfounded_Omlex__prod(_820626, _820622, _820618)), _820628 = _820626, _820624 = _820622, _820620 = _820618], (2606 ^ _782435) ^ [_820839, _820841] : [_820841 = _820839, -(c_Int_Oint__ge__less__than(_820841) = c_Int_Oint__ge__less__than(_820839))], (2612 ^ _782435) ^ [_820924, _820926] : [_820926 = _820924, -(c_Int_Oint__ge__less__than2(_820926) = c_Int_Oint__ge__less__than2(_820924))], (2618 ^ _782435) ^ [_821009, _821011, _821013, _821015, _821017, _821019, _821021, _821023] : [-(c_Recdef_Osame__fst(_821023, _821019, _821015, _821011) = c_Recdef_Osame__fst(_821021, _821017, _821013, _821009)), _821023 = _821021, _821019 = _821017, _821015 = _821013, _821011 = _821009], (2636 ^ _782435) ^ [_821310, _821312] : [_821312 = _821310, -(c_Nitpick_Ozero__frac(_821312) = c_Nitpick_Ozero__frac(_821310))], (2642 ^ _782435) ^ [_821395, _821397] : [_821397 = _821395, -(c_Nitpick_Oone__frac(_821397) = c_Nitpick_Oone__frac(_821395))], (2648 ^ _782435) ^ [_821480, _821482, _821484, _821486] : [-(c_Nitpick_Onumber__of__frac(_821486, _821482) = c_Nitpick_Onumber__of__frac(_821484, _821480)), _821486 = _821484, _821482 = _821480], (2658 ^ _782435) ^ [_821629, _821631, _821633, _821635] : [-(c_Nitpick_Onorm__frac(_821635, _821631) = c_Nitpick_Onorm__frac(_821633, _821629)), _821635 = _821633, _821631 = _821629], (2668 ^ _782435) ^ [_821778, _821780] : [_821780 = _821778, -(c_Equiv__Relations_Oquotient(_821780) = c_Equiv__Relations_Oquotient(_821778))], (2674 ^ _782435) ^ [_821863, _821865, _821867, _821869, _821871, _821873, _821875, _821877] : [-(c_Product__Type_Oapsnd(_821877, _821873, _821869, _821865) = c_Product__Type_Oapsnd(_821875, _821871, _821867, _821863)), _821877 = _821875, _821873 = _821871, _821869 = _821867, _821865 = _821863], (2692 ^ _782435) ^ [_822164, _822166, _822168, _822170, _822172, _822174, _822176, _822178] : [-(c_Product__Type_Oapfst(_822178, _822174, _822170, _822166) = c_Product__Type_Oapfst(_822176, _822172, _822168, _822164)), _822178 = _822176, _822174 = _822172, _822170 = _822168, _822166 = _822164], (2710 ^ _782435) ^ [_822465, _822467, _822469, _822471, _822473, _822475] : [-(c_FunDef_Oin__rel(_822475, _822471, _822467) = c_FunDef_Oin__rel(_822473, _822469, _822465)), _822475 = _822473, _822471 = _822469, _822467 = _822465], (2724 ^ _782435) ^ [_822686, _822688, _822690, _822692] : [-(c_Predicate_OPowp(_822692, _822688) = c_Predicate_OPowp(_822690, _822686)), _822692 = _822690, _822688 = _822686], (2734 ^ _782435) ^ [_822835, _822837] : [_822837 = _822835, -(c_Set_OBall(_822837) = c_Set_OBall(_822835))], (2740 ^ _782435) ^ [_822920, _822922, _822924, _822926, _822928, _822930] : [-(c_Predicate_ODomainP(_822930, _822926, _822922) = c_Predicate_ODomainP(_822928, _822924, _822920)), _822930 = _822928, _822926 = _822924, _822922 = _822920], (2754 ^ _782435) ^ [_823141, _823143, _823145, _823147, _823149, _823151] : [-(c_Predicate_ORangeP(_823151, _823147, _823143) = c_Predicate_ORangeP(_823149, _823145, _823141)), _823151 = _823149, _823147 = _823145, _823143 = _823141], (2768 ^ _782435) ^ [_823362, _823364] : [_823364 = _823362, -(c_HOL_OAll(_823364) = c_HOL_OAll(_823362))], (2774 ^ _782435) ^ [_823447, _823449, _823451, _823453] : [-(c_Wellfounded_Omax__ext(_823453, _823449) = c_Wellfounded_Omax__ext(_823451, _823447)), _823453 = _823451, _823449 = _823447], (2784 ^ _782435) ^ [_823596, _823598, _823600, _823602, _823604, _823606, _823608, _823610] : [-(c_Random_Oiterate(_823610, _823606, _823602, _823598) = c_Random_Oiterate(_823608, _823604, _823600, _823596)), _823610 = _823608, _823606 = _823604, _823602 = _823600, _823598 = _823596], (2802 ^ _782435) ^ [_823897, _823899, _823901, _823903] : [-(c_Random_Olog(_823903, _823899) = c_Random_Olog(_823901, _823897)), _823903 = _823901, _823899 = _823897], (2812 ^ _782435) ^ [_824046, _824048, _824050, _824052, _824054, _824056] : [-(c_Random_Ominus__shift(_824056, _824052, _824048) = c_Random_Ominus__shift(_824054, _824050, _824046)), _824056 = _824054, _824052 = _824050, _824048 = _824046], (2826 ^ _782435) ^ [_824267, _824269, _824271, _824273] : [-(c_Random_Oinc__shift(_824273, _824269) = c_Random_Oinc__shift(_824271, _824267)), _824273 = _824271, _824269 = _824267], (2836 ^ _782435) ^ [_824416, _824418] : [_824418 = _824416, -(c_Relation_OField(_824418) = c_Relation_OField(_824416))], (2842 ^ _782435) ^ [_824501, _824503, _824505, _824507] : [-(c_Relation_ORange(_824507, _824503) = c_Relation_ORange(_824505, _824501)), _824507 = _824505, _824503 = _824501], (2852 ^ _782435) ^ [_824650, _824652, _824654, _824656] : [-(c_Relation_ODomain(_824656, _824652) = c_Relation_ODomain(_824654, _824650)), _824656 = _824654, _824652 = _824650], (2862 ^ _782435) ^ [_824799, _824801] : [_824801 = _824799, -(c_Nat_Ofunpow(_824801) = c_Nat_Ofunpow(_824799))], (2868 ^ _782435) ^ [_824884, _824886, _824888, _824890, _824892, _824894, _824896, _824898, _824900, _824902] : [-(c_Finite__Set_Ofold__graph(_824902, _824898, _824894, _824890, _824886) = c_Finite__Set_Ofold__graph(_824900, _824896, _824892, _824888, _824884)), _824902 = _824900, _824898 = _824896, _824894 = _824892, _824890 = _824888, _824886 = _824884], (2890 ^ _782435) ^ [_825273, _825275, _825277, _825279] : [-(c_Nitpick_Oint__lcm(_825279, _825275) = c_Nitpick_Oint__lcm(_825277, _825273)), _825279 = _825277, _825275 = _825273], (2900 ^ _782435) ^ [_825422, _825424, _825426, _825428, _825430, _825432] : [-(c_Nitpick_Otimes__frac(_825432, _825428, _825424) = c_Nitpick_Otimes__frac(_825430, _825426, _825422)), _825432 = _825430, _825428 = _825426, _825424 = _825422], (2914 ^ _782435) ^ [_825643, _825645, _825647, _825649, _825651, _825653] : [-(c_Nitpick_Oof__frac(_825653, _825649, _825645) = c_Nitpick_Oof__frac(_825651, _825647, _825643)), _825653 = _825651, _825649 = _825647, _825645 = _825643], (2928 ^ _782435) ^ [_825864, _825866] : [_825866 = _825864, -(c_Rings_Oinverse__class_Odivide(_825866) = c_Rings_Oinverse__class_Odivide(_825864))], (2934 ^ _782435) ^ [_825949, _825951] : [_825951 = _825949, -(c_Int_Oring__1__class_Oof__int(_825951) = c_Int_Oring__1__class_Oof__int(_825949))], (2940 ^ _782435) ^ [_826034, _826036, _826038, _826040] : [-(c_Nitpick_Oinverse__frac(_826040, _826036) = c_Nitpick_Oinverse__frac(_826038, _826034)), _826040 = _826038, _826036 = _826034], (2950 ^ _782435) ^ [_826183, _826185] : [_826185 = _826183, -(c_Nitpick_Ofrac(_826185) = c_Nitpick_Ofrac(_826183))], (2956 ^ _782435) ^ [_826268, _826270, _826272, _826274] : [-(c_Nitpick_OAbs__Frac(_826274, _826270) = c_Nitpick_OAbs__Frac(_826272, _826268)), _826274 = _826272, _826270 = _826268], (2966 ^ _782435) ^ [_826417, _826419, _826421, _826423, _826425, _826427] : [-(c_Nitpick_Oplus__frac(_826427, _826423, _826419) = c_Nitpick_Oplus__frac(_826425, _826421, _826417)), _826427 = _826425, _826423 = _826421, _826419 = _826417], (2980 ^ _782435) ^ [_826638, _826640, _826642, _826644] : [-(c_Nitpick_Ouminus__frac(_826644, _826640) = c_Nitpick_Ouminus__frac(_826642, _826638)), _826644 = _826642, _826640 = _826638], (2990 ^ _782435) ^ [_826787, _826789] : [_826789 = _826787, -(c_Nitpick_Onum(_826789) = c_Nitpick_Onum(_826787))], (2996 ^ _782435) ^ [_826872, _826874] : [_826874 = _826872, -(c_Nitpick_Odenom(_826874) = c_Nitpick_Odenom(_826872))], (3002 ^ _782435) ^ [_826957, _826959] : [_826959 = _826957, -(c_Nitpick_ORep__Frac(_826959) = c_Nitpick_ORep__Frac(_826957))], (3008 ^ _782435) ^ [_827042, _827044, _827046, _827048, _827050, _827052] : [-(c_Product__Type_Ointernal__split(_827052, _827048, _827044) = c_Product__Type_Ointernal__split(_827050, _827046, _827042)), _827052 = _827050, _827048 = _827046, _827044 = _827042], (3022 ^ _782435) ^ [_827263, _827265, _827267, _827269] : [-(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_827269, _827265) = c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_827267, _827263)), _827269 = _827267, _827265 = _827263], (3032 ^ _782435) ^ [_827412, _827414] : [_827414 = _827412, -(c_HOL_Obool_Obool__size(_827414) = c_HOL_Obool_Obool__size(_827412))], (3038 ^ _782435) ^ [_827497, _827499, _827501, _827503] : [-(c_List_Olenlex(_827503, _827499) = c_List_Olenlex(_827501, _827497)), _827503 = _827501, _827499 = _827497], (3048 ^ _782435) ^ [_827646, _827648, _827650, _827652, _827654, _827656, _827658, _827660, _827662, _827664, _827666, _827668] : [-(c_Product__Type_Omap__pair(_827668, _827664, _827660, _827656, _827652, _827648) = c_Product__Type_Omap__pair(_827666, _827662, _827658, _827654, _827650, _827646)), _827668 = _827666, _827664 = _827662, _827660 = _827658, _827656 = _827654, _827652 = _827650, _827648 = _827646], (3074 ^ _782435) ^ [_828131, _828133, _828135, _828137] : [-(c_List_Olexn(_828137, _828133) = c_List_Olexn(_828135, _828131)), _828137 = _828135, _828133 = _828131], (3084 ^ _782435) ^ [_828280, _828282, _828284, _828286] : [-(c_Wellfounded_Oacc(_828286, _828282) = c_Wellfounded_Oacc(_828284, _828280)), _828286 = _828284, _828282 = _828280], (3094 ^ _782435) ^ [_828429, _828431] : [_828431 = _828429, -(c_Set_OPow(_828431) = c_Set_OPow(_828429))], (3100 ^ _782435) ^ [_828514, _828516, _828518, _828520] : [-(c_Product__Type_OSigma(_828520, _828516) = c_Product__Type_OSigma(_828518, _828514)), _828520 = _828518, _828516 = _828514], (3110 ^ _782435) ^ [_828663, _828665, _828667, _828669] : [-(c_Nitpick_Ocard_H(_828669, _828665) = c_Nitpick_Ocard_H(_828667, _828663)), _828669 = _828667, _828665 = _828663], (3120 ^ _782435) ^ [_828812, _828814, _828816, _828818, _828820, _828822] : [-(c_List_Oset__Cons(_828822, _828818, _828814) = c_List_Oset__Cons(_828820, _828816, _828812)), _828822 = _828820, _828818 = _828816, _828814 = _828812], (3134 ^ _782435) ^ [_829033, _829035, _829037, _829039] : [-(c_List_Olistset(_829039, _829035) = c_List_Olistset(_829037, _829033)), _829039 = _829037, _829035 = _829033], (3144 ^ _782435) ^ [_829182, _829184, _829186, _829188] : [-(c_List_Olistrel1(_829188, _829184) = c_List_Olistrel1(_829186, _829182)), _829188 = _829186, _829184 = _829182], (3154 ^ _782435) ^ [_829331, _829333, _829335, _829337, _829339, _829341, _829343, _829345] : [-(c_Nat_Onat_Onat__case(_829345, _829341, _829337, _829333) = c_Nat_Onat_Onat__case(_829343, _829339, _829335, _829331)), _829345 = _829343, _829341 = _829339, _829337 = _829335, _829333 = _829331], (3172 ^ _782435) ^ [_829632, _829634, _829636, _829638] : [-(c_Nat_Ocompow(_829638, _829634) = c_Nat_Ocompow(_829636, _829632)), _829638 = _829636, _829634 = _829632], (3182 ^ _782435) ^ [_829781, _829783] : [_829783 = _829781, -(c_List_Orotate1(_829783) = c_List_Orotate1(_829781))], (3188 ^ _782435) ^ [_829866, _829868, _829870, _829872] : [-(c_Finite__Set_Ofold1(_829872, _829868) = c_Finite__Set_Ofold1(_829870, _829866)), _829872 = _829870, _829868 = _829866], (3198 ^ _782435) ^ [_830015, _830017, _830019, _830021] : [-(c_Big__Operators_Olattice__class_OSup__fin(_830021, _830017) = c_Big__Operators_Olattice__class_OSup__fin(_830019, _830015)), _830021 = _830019, _830017 = _830015], (3208 ^ _782435) ^ [_830164, _830166, _830168, _830170] : [-(c_Big__Operators_Olattice__class_OInf__fin(_830170, _830166) = c_Big__Operators_Olattice__class_OInf__fin(_830168, _830164)), _830170 = _830168, _830166 = _830164], (3218 ^ _782435) ^ [_830313, _830315, _830317, _830319] : [-(c_Big__Operators_Olinorder__class_OMin(_830319, _830315) = c_Big__Operators_Olinorder__class_OMin(_830317, _830313)), _830319 = _830317, _830315 = _830313], (3228 ^ _782435) ^ [_830462, _830464, _830466, _830468] : [-(c_Big__Operators_Olinorder__class_OMax(_830468, _830464) = c_Big__Operators_Olinorder__class_OMax(_830466, _830462)), _830468 = _830466, _830464 = _830462], (3238 ^ _782435) ^ [_830611, _830613, _830615, _830617, _830619, _830621] : [-(c_Big__Operators_Olattice_OInf__fin(_830621, _830617, _830613) = c_Big__Operators_Olattice_OInf__fin(_830619, _830615, _830611)), _830621 = _830619, _830617 = _830615, _830613 = _830611], (3252 ^ _782435) ^ [_830832, _830834, _830836, _830838, _830840, _830842] : [-(c_Big__Operators_Olattice_OSup__fin(_830842, _830838, _830834) = c_Big__Operators_Olattice_OSup__fin(_830840, _830836, _830832)), _830842 = _830840, _830838 = _830836, _830834 = _830832], (3266 ^ _782435) ^ [_831053, _831055, _831057, _831059, _831061, _831063, _831065, _831067, _831069, _831071] : [-(c_Fun_Ofun__upd(_831071, _831067, _831063, _831059, _831055) = c_Fun_Ofun__upd(_831069, _831065, _831061, _831057, _831053)), _831071 = _831069, _831067 = _831065, _831063 = _831061, _831059 = _831057, _831055 = _831053], (3288 ^ _782435) ^ [_831442, _831444, _831446, _831448, _831450, _831452, _831454, _831456] : [-(c_Enum_Oproduct(_831456, _831452, _831448, _831444) = c_Enum_Oproduct(_831454, _831450, _831446, _831442)), _831456 = _831454, _831452 = _831450, _831448 = _831446, _831444 = _831442], (3306 ^ _782435) ^ [_831743, _831745, _831747, _831749, _831751, _831753, _831755, _831757] : [-(c_Nitpick_Osetsum_H(_831757, _831753, _831749, _831745) = c_Nitpick_Osetsum_H(_831755, _831751, _831747, _831743)), _831757 = _831755, _831753 = _831751, _831749 = _831747, _831745 = _831743], (3324 ^ _782435) ^ [_832044, _832046, _832048, _832050] : [-(c_HOL_OLet(_832050, _832046) = c_HOL_OLet(_832048, _832044)), _832050 = _832048, _832046 = _832044], (3334 ^ _782435) ^ [_832193, _832195, _832197, _832199] : [-(c_Enum_Osublists(_832199, _832195) = c_Enum_Osublists(_832197, _832193)), _832199 = _832197, _832195 = _832193], (3344 ^ _782435) ^ [_832342, _832344, _832346, _832348, _832350, _832352] : [-(c_List_Olist_Olist__size(_832352, _832348, _832344) = c_List_Olist_Olist__size(_832350, _832346, _832342)), _832352 = _832350, _832348 = _832346, _832344 = _832342], (3358 ^ _782435) ^ [_832563, _832565, _832567, _832569] : [-(c_Random_Oselect(_832569, _832565) = c_Random_Oselect(_832567, _832563)), _832569 = _832567, _832565 = _832563], (3368 ^ _782435) ^ [_832712, _832714] : [_832714 = _832712, -(c_Random_Orange(_832714) = c_Random_Orange(_832712))], (3374 ^ _782435) ^ [_832797, _832799, _832801, _832803] : [-(c_Code__Numeral_Onat__of__aux(_832803, _832799) = c_Code__Numeral_Onat__of__aux(_832801, _832797)), _832803 = _832801, _832799 = _832797], (3384 ^ _782435) ^ [_832946, _832948] : [_832948 = _832946, -(c_Lazy__Sequence_Ohb__not__seq(_832948) = c_Lazy__Sequence_Ohb__not__seq(_832946))], (3390 ^ _782435) ^ [_833031, _833033] : [_833033 = _833031, -(c_Int_OBit1(_833033) = c_Int_OBit1(_833031))], (3396 ^ _782435) ^ [_833116, _833118, _833120, _833122] : [-(c_List_Olistsp(_833122, _833118) = c_List_Olistsp(_833120, _833116)), _833122 = _833120, _833118 = _833116], (3406 ^ _782435) ^ [_833265, _833267, _833269, _833271] : [-(c_List_Olists(_833271, _833267) = c_List_Olists(_833269, _833265)), _833271 = _833269, _833267 = _833265], (3416 ^ _782435) ^ [_833414, _833416, _833418, _833420, _833422, _833424] : [-(c_Finite__Set_Ofold(_833424, _833420, _833416) = c_Finite__Set_Ofold(_833422, _833418, _833414)), _833424 = _833422, _833420 = _833418, _833416 = _833414], (3430 ^ _782435) ^ [_833635, _833637, _833639, _833641, _833643, _833645] : [-(c_Enum_On__lists(_833645, _833641, _833637) = c_Enum_On__lists(_833643, _833639, _833635)), _833645 = _833643, _833641 = _833639, _833637 = _833635], (3444 ^ _782435) ^ [_833856, _833858, _833860, _833862, _833864, _833866] : [-(c_List_Opartition(_833866, _833862, _833858) = c_List_Opartition(_833864, _833860, _833856)), _833866 = _833864, _833862 = _833860, _833858 = _833856], (3458 ^ _782435) ^ [_834077, _834079] : [_834079 = _834077, -(c_Finite__Set_Ocard(_834079) = c_Finite__Set_Ocard(_834077))], (3464 ^ _782435) ^ [_834162, _834164, _834166, _834168, _834170, _834172, _834174, _834176] : [-(c_List_Olist_Olist__case(_834176, _834172, _834168, _834164) = c_List_Olist_Olist__case(_834174, _834170, _834166, _834162)), _834176 = _834174, _834172 = _834170, _834168 = _834166, _834164 = _834162], (3482 ^ _782435) ^ [_834463, _834465, _834467, _834469] : [-(c_Random_Oselect__weight(_834469, _834465) = c_Random_Oselect__weight(_834467, _834463)), _834469 = _834467, _834465 = _834463], (3492 ^ _782435) ^ [_834612, _834614, _834616, _834618] : [-(c_Random_Opick(_834618, _834614) = c_Random_Opick(_834616, _834612)), _834618 = _834616, _834614 = _834612], (3502 ^ _782435) ^ [_834761, _834763] : [_834763 = _834761, -(c_List_Otranspose__rel(_834763) = c_List_Otranspose__rel(_834761))], (3508 ^ _782435) ^ [_834846, _834848, _834850, _834852, _834854, _834856] : [-(c_List_Osublist(_834856, _834852, _834848) = c_List_Osublist(_834854, _834850, _834846)), _834856 = _834854, _834852 = _834850, _834848 = _834846], (3522 ^ _782435) ^ [_835067, _835069] : [_835069 = _835067, -(c_Int_Onumber__class_Onumber__of(_835069) = c_Int_Onumber__class_Onumber__of(_835067))], (3528 ^ _782435) ^ [_835152, _835154] : [_835154 = _835152, -(c_SetInterval_Oord__class_OlessThan(_835154) = c_SetInterval_Oord__class_OlessThan(_835152))], (3534 ^ _782435) ^ [_835237, _835239, _835241, _835243, _835245, _835247] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(_835247, _835243, _835239) = c_SetInterval_Oord__class_OgreaterThanAtMost(_835245, _835241, _835237)), _835247 = _835245, _835243 = _835241, _835239 = _835237], (3548 ^ _782435) ^ [_835458, _835460, _835462, _835464, _835466, _835468] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(_835468, _835464, _835460) = c_SetInterval_Oord__class_OgreaterThanLessThan(_835466, _835462, _835458)), _835468 = _835466, _835464 = _835462, _835460 = _835458], (3562 ^ _782435) ^ [_835679, _835681] : [_835681 = _835679, -(c_SetInterval_Oord__class_OatMost(_835681) = c_SetInterval_Oord__class_OatMost(_835679))], (3568 ^ _782435) ^ [_835764, _835766, _835768, _835770, _835772, _835774, _835776, _835778] : [-(c_List_Olinorder__class_Osort__key(_835778, _835774, _835770, _835766) = c_List_Olinorder__class_Osort__key(_835776, _835772, _835768, _835764)), _835778 = _835776, _835774 = _835772, _835770 = _835768, _835766 = _835764], (3586 ^ _782435) ^ [_836065, _836067, _836069, _836071, _836073, _836075, _836077, _836079, _836081, _836083] : [-(c_List_Olinorder__class_Oinsort__insert__key(_836083, _836079, _836075, _836071, _836067) = c_List_Olinorder__class_Oinsort__insert__key(_836081, _836077, _836073, _836069, _836065)), _836083 = _836081, _836079 = _836077, _836075 = _836073, _836071 = _836069, _836067 = _836065], (3608 ^ _782435) ^ [_836454, _836456, _836458, _836460] : [-(c_List_Olinorder__class_Osorted__list__of__set(_836460, _836456) = c_List_Olinorder__class_Osorted__list__of__set(_836458, _836454)), _836460 = _836458, _836456 = _836454], (3618 ^ _782435) ^ [_836603, _836605, _836607, _836609] : [-(c_List_Orotate(_836609, _836605) = c_List_Orotate(_836607, _836603)), _836609 = _836607, _836605 = _836603], (3628 ^ _782435) ^ [_836752, _836754, _836756, _836758, _836760, _836762] : [-(c_Divides_Odiv__class_Omod(_836762, _836758, _836754) = c_Divides_Odiv__class_Omod(_836760, _836756, _836752)), _836762 = _836760, _836758 = _836756, _836754 = _836752], (3642 ^ _782435) ^ [_836973, _836975, _836977, _836979] : [-(c_List_Olist__update(_836979, _836975) = c_List_Olist__update(_836977, _836973)), _836979 = _836977, _836975 = _836973], (3652 ^ _782435) ^ [_837122, _837124, _837126, _837128, _837130, _837132, _837134, _837136, _837138, _837140] : [-(c_List_Ofoldr(_837140, _837136, _837132, _837128, _837124) = c_List_Ofoldr(_837138, _837134, _837130, _837126, _837122)), _837140 = _837138, _837136 = _837134, _837132 = _837130, _837128 = _837126, _837124 = _837122], (3674 ^ _782435) ^ [_837511, _837513] : [_837513 = _837511, -(c_Orderings_Oord__class_Omax(_837513) = c_Orderings_Oord__class_Omax(_837511))], (3680 ^ _782435) ^ [_837596, _837598, _837600, _837602] : [-(c_List_Otranspose(_837602, _837598) = c_List_Otranspose(_837600, _837596)), _837602 = _837600, _837598 = _837596], (3690 ^ _782435) ^ [_837745, _837747, _837749, _837751] : [-(c_List_Obutlast(_837751, _837747) = c_List_Obutlast(_837749, _837745)), _837751 = _837749, _837747 = _837745], (3700 ^ _782435) ^ [_837894, _837896] : [_837896 = _837894, -(c_List_Oreturn__list(_837896) = c_List_Oreturn__list(_837894))], (3706 ^ _782435) ^ [_837979, _837981] : [_837981 = _837979, -(c_List_Oembed__list(_837981) = c_List_Oembed__list(_837979))], (3712 ^ _782435) ^ [_838064, _838066] : [_838066 = _838064, -(c_List_Omonoid__add__class_Olistsum(_838066) = c_List_Omonoid__add__class_Olistsum(_838064))], (3718 ^ _782435) ^ [_838149, _838151, _838153, _838155] : [-(c_List_Oremdups(_838155, _838151) = c_List_Oremdups(_838153, _838149)), _838155 = _838153, _838151 = _838149], (3728 ^ _782435) ^ [_838298, _838300, _838302, _838304, _838306, _838308] : [-(c_List_Oremove1(_838308, _838304, _838300) = c_List_Oremove1(_838306, _838302, _838298)), _838308 = _838306, _838304 = _838302, _838300 = _838298], (3742 ^ _782435) ^ [_838519, _838521, _838523, _838525] : [-(c_List_OremoveAll(_838525, _838521) = c_List_OremoveAll(_838523, _838519)), _838525 = _838523, _838521 = _838519], (3752 ^ _782435) ^ [_838668, _838670, _838672, _838674, _838676, _838678] : [-(c_List_Oinsert(_838678, _838674, _838670) = c_List_Oinsert(_838676, _838672, _838668)), _838678 = _838676, _838674 = _838672, _838670 = _838668], (3766 ^ _782435) ^ [_838889, _838891, _838893, _838895, _838897, _838899, _838901, _838903] : [-(c_List_Omaps(_838903, _838899, _838895, _838891) = c_List_Omaps(_838901, _838897, _838893, _838889)), _838903 = _838901, _838899 = _838897, _838895 = _838893, _838891 = _838889], (3784 ^ _782435) ^ [_839190, _839192, _839194, _839196] : [-(c_List_Olex(_839196, _839192) = c_List_Olex(_839194, _839190)), _839196 = _839194, _839192 = _839190], (3794 ^ _782435) ^ [_839339, _839341, _839343, _839345] : [-(c_List_Omeasures(_839345, _839341) = c_List_Omeasures(_839343, _839339)), _839345 = _839343, _839341 = _839339], (3804 ^ _782435) ^ [_839488, _839490, _839492, _839494, _839496, _839498, _839500, _839502] : [-(c_List_Ofoldl(_839502, _839498, _839494, _839490) = c_List_Ofoldl(_839500, _839496, _839492, _839488)), _839502 = _839500, _839498 = _839496, _839494 = _839492, _839490 = _839488], (3822 ^ _782435) ^ [_839789, _839791, _839793, _839795, _839797, _839799, _839801, _839803] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_839803, _839799, _839795, _839791) = c_New__Random__Sequence_Opos__not__random__dseq(_839801, _839797, _839793, _839789)), _839803 = _839801, _839799 = _839797, _839795 = _839793, _839791 = _839789], (3840 ^ _782435) ^ [_840090, _840092] : [_840092 = _840090, -(c_New__DSequence_Opos__not__seq(_840092) = c_New__DSequence_Opos__not__seq(_840090))], (3846 ^ _782435) ^ [_840175, _840177, _840179, _840181, _840183, _840185] : [-(c_List_OdropWhile(_840185, _840181, _840177) = c_List_OdropWhile(_840183, _840179, _840175)), _840185 = _840183, _840181 = _840179, _840177 = _840175], (3860 ^ _782435) ^ [_840396, _840398] : [_840398 = _840396, -(c_List_Odistinct(_840398) = c_List_Odistinct(_840396))], (3866 ^ _782435) ^ [_840481, _840483, _840485, _840487, _840489, _840491] : [-(c_List_OtakeWhile(_840491, _840487, _840483) = c_List_OtakeWhile(_840489, _840485, _840481)), _840491 = _840489, _840487 = _840485, _840483 = _840481], (3880 ^ _782435) ^ [_840702, _840704, _840706, _840708, _840710, _840712] : [-(c_List_Olinorder__class_Oinsort__key(_840712, _840708, _840704) = c_List_Olinorder__class_Oinsort__key(_840710, _840706, _840702)), _840712 = _840710, _840708 = _840706, _840704 = _840702], (3894 ^ _782435) ^ [_840923, _840925] : [_840925 = _840923, -(c_Groups_Oabs__class_Oabs(_840925) = c_Groups_Oabs__class_Oabs(_840923))], (3900 ^ _782435) ^ [_841008, _841010] : [_841010 = _841008, -(c_Nat_Osemiring__1__class_Oof__nat(_841010) = c_Nat_Osemiring__1__class_Oof__nat(_841008))], (3906 ^ _782435) ^ [_841093, _841095] : [_841095 = _841093, -(c_Lazy__Sequence_Ohit__bound(_841095) = c_Lazy__Sequence_Ohit__bound(_841093))], (3912 ^ _782435) ^ [_841178, _841180, _841182, _841184, _841186, _841188, _841190, _841192, _841194, _841196, _841198, _841200, _841202, _841204] : [-(c_New__Random__Sequence_Oneg__decr__bind(_841204, _841200, _841196, _841192, _841188, _841184, _841180) = c_New__Random__Sequence_Oneg__decr__bind(_841202, _841198, _841194, _841190, _841186, _841182, _841178)), _841204 = _841202, _841200 = _841198, _841196 = _841194, _841192 = _841190, _841188 = _841186, _841184 = _841182, _841180 = _841178], (3942 ^ _782435) ^ [_841767, _841769, _841771, _841773, _841775, _841777, _841779, _841781] : [-(c_New__DSequence_Oneg__decr__bind(_841781, _841777, _841773, _841769) = c_New__DSequence_Oneg__decr__bind(_841779, _841775, _841771, _841767)), _841781 = _841779, _841777 = _841775, _841773 = _841771, _841769 = _841767], (3960 ^ _782435) ^ [_842068, _842070, _842072, _842074, _842076, _842078, _842080, _842082] : [-(c_Lazy__Sequence_Ohb__bind(_842082, _842078, _842074, _842070) = c_Lazy__Sequence_Ohb__bind(_842080, _842076, _842072, _842068)), _842082 = _842080, _842078 = _842076, _842074 = _842072, _842070 = _842068], (3978 ^ _782435) ^ [_842369, _842371, _842373, _842375, _842377, _842379, _842381, _842383] : [-(c_New__DSequence_Oneg__bind(_842383, _842379, _842375, _842371) = c_New__DSequence_Oneg__bind(_842381, _842377, _842373, _842369)), _842383 = _842381, _842379 = _842377, _842375 = _842373, _842371 = _842369], (3996 ^ _782435) ^ [_842670, _842672, _842674, _842676, _842678, _842680, _842682, _842684, _842686, _842688, _842690, _842692, _842694, _842696] : [-(c_New__Random__Sequence_Opos__decr__bind(_842696, _842692, _842688, _842684, _842680, _842676, _842672) = c_New__Random__Sequence_Opos__decr__bind(_842694, _842690, _842686, _842682, _842678, _842674, _842670)), _842696 = _842694, _842692 = _842690, _842688 = _842686, _842684 = _842682, _842680 = _842678, _842676 = _842674, _842672 = _842670], (4026 ^ _782435) ^ [_843259, _843261, _843263, _843265, _843267, _843269, _843271, _843273] : [-(c_New__DSequence_Opos__decr__bind(_843273, _843269, _843265, _843261) = c_New__DSequence_Opos__decr__bind(_843271, _843267, _843263, _843259)), _843273 = _843271, _843269 = _843267, _843265 = _843263, _843261 = _843259], (4044 ^ _782435) ^ [_843560, _843562, _843564, _843566, _843568, _843570, _843572, _843574] : [-(c_New__Random__Sequence_Opos__empty(_843574, _843570, _843566, _843562) = c_New__Random__Sequence_Opos__empty(_843572, _843568, _843564, _843560)), _843574 = _843572, _843570 = _843568, _843566 = _843564, _843562 = _843560], (4062 ^ _782435) ^ [_843861, _843863] : [_843863 = _843861, -(c_New__DSequence_Opos__empty(_843863) = c_New__DSequence_Opos__empty(_843861))], (4068 ^ _782435) ^ [_843946, _843948, _843950, _843952, _843954, _843956, _843958, _843960] : [-(c_New__DSequence_Opos__bind(_843960, _843956, _843952, _843948) = c_New__DSequence_Opos__bind(_843958, _843954, _843950, _843946)), _843960 = _843958, _843956 = _843954, _843952 = _843950, _843948 = _843946], (4086 ^ _782435) ^ [_844247, _844249, _844251, _844253, _844255, _844257, _844259, _844261] : [-(c_New__Random__Sequence_Oneg__map(_844261, _844257, _844253, _844249) = c_New__Random__Sequence_Oneg__map(_844259, _844255, _844251, _844247)), _844261 = _844259, _844257 = _844255, _844253 = _844251, _844249 = _844247], (4104 ^ _782435) ^ [_844548, _844550, _844552, _844554, _844556, _844558, _844560, _844562] : [-(c_New__Random__Sequence_Oneg__bind(_844562, _844558, _844554, _844550) = c_New__Random__Sequence_Oneg__bind(_844560, _844556, _844552, _844548)), _844562 = _844560, _844558 = _844556, _844554 = _844552, _844550 = _844548], (4122 ^ _782435) ^ [_844849, _844851] : [_844851 = _844849, -(c_New__Random__Sequence_Oneg__single(_844851) = c_New__Random__Sequence_Oneg__single(_844849))], (4128 ^ _782435) ^ [_844934, _844936, _844938, _844940, _844942, _844944, _844946, _844948] : [-(c_New__Random__Sequence_Opos__map(_844948, _844944, _844940, _844936) = c_New__Random__Sequence_Opos__map(_844946, _844942, _844938, _844934)), _844948 = _844946, _844944 = _844942, _844940 = _844938, _844936 = _844934], (4146 ^ _782435) ^ [_845235, _845237, _845239, _845241, _845243, _845245, _845247, _845249] : [-(c_New__Random__Sequence_Opos__bind(_845249, _845245, _845241, _845237) = c_New__Random__Sequence_Opos__bind(_845247, _845243, _845239, _845235)), _845249 = _845247, _845245 = _845243, _845241 = _845239, _845237 = _845235], (4164 ^ _782435) ^ [_845536, _845538, _845540, _845542] : [-(c_New__DSequence_Oneg__single(_845542, _845538) = c_New__DSequence_Oneg__single(_845540, _845536)), _845542 = _845540, _845538 = _845536], (4174 ^ _782435) ^ [_845685, _845687, _845689, _845691] : [-(c_Lazy__Sequence_Ohb__single(_845691, _845687) = c_Lazy__Sequence_Ohb__single(_845689, _845685)), _845691 = _845689, _845687 = _845685], (4184 ^ _782435) ^ [_845834, _845836] : [_845836 = _845834, -(c_New__Random__Sequence_Opos__single(_845836) = c_New__Random__Sequence_Opos__single(_845834))], (4190 ^ _782435) ^ [_845919, _845921, _845923, _845925] : [-(c_New__DSequence_Opos__single(_845925, _845921) = c_New__DSequence_Opos__single(_845923, _845919)), _845925 = _845923, _845921 = _845919], (4200 ^ _782435) ^ [_846068, _846070, _846072, _846074, _846076, _846078] : [-(c_List_Osplice(_846078, _846074, _846070) = c_List_Osplice(_846076, _846072, _846068)), _846078 = _846076, _846074 = _846072, _846070 = _846068], (4214 ^ _782435) ^ [_846289, _846291, _846293, _846295] : [-(c_Hilbert__Choice_OEps(_846295, _846291) = c_Hilbert__Choice_OEps(_846293, _846289)), _846295 = _846293, _846291 = _846289], (4224 ^ _782435) ^ [_846438, _846440] : [_846440 = _846438, -(c_Fun_Oid(_846440) = c_Fun_Oid(_846438))], (4230 ^ _782435) ^ [_846523, _846525, _846527, _846529, _846531, _846533] : [-(c_Set_Ovimage(_846533, _846529, _846525) = c_Set_Ovimage(_846531, _846527, _846523)), _846533 = _846531, _846529 = _846527, _846525 = _846523], (4244 ^ _782435) ^ [_846744, _846746, _846748, _846750, _846752, _846754] : [-(c_Set_Oimage(_846754, _846750, _846746) = c_Set_Oimage(_846752, _846748, _846744)), _846754 = _846752, _846750 = _846748, _846746 = _846744], (4258 ^ _782435) ^ [_846965, _846967, _846969, _846971, _846973, _846975, _846977, _846979] : [-(c_Hilbert__Choice_Oinv__into(_846979, _846975, _846971, _846967) = c_Hilbert__Choice_Oinv__into(_846977, _846973, _846969, _846965)), _846979 = _846977, _846975 = _846973, _846971 = _846969, _846967 = _846965], (4276 ^ _782435) ^ [_847266, _847268] : [_847268 = _847266, -(c_If(_847268) = c_If(_847266))], (4282 ^ _782435) ^ [_847351, _847353, _847355, _847357, _847359, _847361, _847363, _847365] : [-(c_Lazy__Sequence_Oproduct(_847365, _847361, _847357, _847353) = c_Lazy__Sequence_Oproduct(_847363, _847359, _847355, _847351)), _847365 = _847363, _847361 = _847359, _847357 = _847355, _847353 = _847351], (4300 ^ _782435) ^ [_847652, _847654, _847656, _847658, _847660, _847662] : [-(c_Predicate_Oconversep(_847662, _847658, _847654) = c_Predicate_Oconversep(_847660, _847656, _847652)), _847662 = _847660, _847658 = _847656, _847654 = _847652], (4314 ^ _782435) ^ [_847873, _847875, _847877, _847879, _847881, _847883, _847885, _847887, _847889, _847891, _847893, _847895] : [-(c_New__Random__Sequence_Opos__union(_847895, _847891, _847887, _847883, _847879, _847875) = c_New__Random__Sequence_Opos__union(_847893, _847889, _847885, _847881, _847877, _847873)), _847895 = _847893, _847891 = _847889, _847887 = _847885, _847883 = _847881, _847879 = _847877, _847875 = _847873], (4340 ^ _782435) ^ [_848358, _848360, _848362, _848364, _848366, _848368] : [-(c_New__DSequence_Opos__union(_848368, _848364, _848360) = c_New__DSequence_Opos__union(_848366, _848362, _848358)), _848368 = _848366, _848364 = _848362, _848360 = _848358], (4354 ^ _782435) ^ [_848579, _848581, _848583, _848585] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848585, _848581) = c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_848583, _848579)), _848585 = _848583, _848581 = _848579], (4364 ^ _782435) ^ [_848728, _848730] : [_848730 = _848728, -(c_Groups_Ouminus__class_Ouminus(_848730) = c_Groups_Ouminus__class_Ouminus(_848728))], (4370 ^ _782435) ^ [_848813, _848815] : [_848815 = _848813, -(c_Lazy__Sequence_Oempty(_848815) = c_Lazy__Sequence_Oempty(_848813))], (4376 ^ _782435) ^ [_848898, _848900] : [_848900 = _848898, -(c_Lazy__Sequence_Osingle(_848900) = c_Lazy__Sequence_Osingle(_848898))], (4382 ^ _782435) ^ [_848983, _848985, _848987, _848989] : [-(c_Lazy__Sequence_Osmall__lazy_H(_848989, _848985) = c_Lazy__Sequence_Osmall__lazy_H(_848987, _848983)), _848989 = _848987, _848985 = _848983], (4392 ^ _782435) ^ [_849132, _849134] : [_849134 = _849132, -(c_List_Otl(_849134) = c_List_Otl(_849132))], (4398 ^ _782435) ^ [_849217, _849219, _849221, _849223] : [-(c_List_Oconcat(_849223, _849219) = c_List_Oconcat(_849221, _849217)), _849223 = _849221, _849219 = _849217], (4408 ^ _782435) ^ [_849366, _849368] : [_849368 = _849366, -(c_List_Onth(_849368) = c_List_Onth(_849366))], (4414 ^ _782435) ^ [_849451, _849453, _849455, _849457] : [-(c_List_Ozip(_849457, _849453) = c_List_Ozip(_849455, _849451)), _849457 = _849455, _849453 = _849451], (4424 ^ _782435) ^ [_849600, _849602] : [_849602 = _849600, -(c_List_Odrop(_849602) = c_List_Odrop(_849600))], (4430 ^ _782435) ^ [_849685, _849687] : [_849687 = _849685, -(c_List_Ohd(_849687) = c_List_Ohd(_849685))], (4436 ^ _782435) ^ [_849770, _849772] : [_849772 = _849770, -(c_List_Otake(_849772) = c_List_Otake(_849770))], (4442 ^ _782435) ^ [_849855, _849857] : [_849857 = _849855, -(c_Orderings_Oord__class_Omin(_849857) = c_Orderings_Oord__class_Omin(_849855))], (4448 ^ _782435) ^ [_849940, _849942, _849944, _849946] : [-(c_List_Olast(_849946, _849942) = c_List_Olast(_849944, _849940)), _849946 = _849944, _849942 = _849940], (4458 ^ _782435) ^ [_850089, _850091] : [_850091 = _850089, -(c_List_Orev(_850091) = c_List_Orev(_850089))], (4464 ^ _782435) ^ [_850174, _850176, _850178, _850180] : [-(c_List_Ofilter(_850180, _850176) = c_List_Ofilter(_850178, _850174)), _850180 = _850178, _850176 = _850174], (4474 ^ _782435) ^ [_850323, _850325] : [_850325 = _850323, -(c_List_Oappend(_850325) = c_List_Oappend(_850323))], (4480 ^ _782435) ^ [_850408, _850410, _850412, _850414] : [-(c_List_Omap(_850414, _850410) = c_List_Omap(_850412, _850408)), _850414 = _850412, _850410 = _850408], (4490 ^ _782435) ^ [_850557, _850559, _850561, _850563, _850565, _850567] : [-(c_List_Oreplicate(_850567, _850563, _850559) = c_List_Oreplicate(_850565, _850561, _850557)), _850567 = _850565, _850563 = _850561, _850559 = _850557], (4504 ^ _782435) ^ [_850778, _850780, _850782, _850784] : [-(c_Wellfounded_Oaccp(_850784, _850780) = c_Wellfounded_Oaccp(_850782, _850778)), _850784 = _850782, _850780 = _850778], (4514 ^ _782435) ^ [_850927, _850929, _850931, _850933, _850935, _850937, _850939, _850941, _850943, _850945] : [-(c_Predicate_Opred__comp(_850945, _850941, _850937, _850933, _850929) = c_Predicate_Opred__comp(_850943, _850939, _850935, _850931, _850927)), _850945 = _850943, _850941 = _850939, _850937 = _850935, _850933 = _850931, _850929 = _850927], (4536 ^ _782435) ^ [_851316, _851318, _851320, _851322, _851324, _851326, _851328, _851330, _851332, _851334] : [-(c_Option_Ooption_Ooption__case(_851334, _851330, _851326, _851322, _851318) = c_Option_Ooption_Ooption__case(_851332, _851328, _851324, _851320, _851316)), _851334 = _851332, _851330 = _851328, _851326 = _851324, _851322 = _851320, _851318 = _851316], (4558 ^ _782435) ^ [_851705, _851707] : [_851707 = _851705, -(c_Lazy__Sequence_Oyieldn(_851707) = c_Lazy__Sequence_Oyieldn(_851705))], (4564 ^ _782435) ^ [_851790, _851792, _851794, _851796, _851798, _851800] : [-(c_Lazy__Sequence_Oanamorph(_851800, _851796, _851792) = c_Lazy__Sequence_Oanamorph(_851798, _851794, _851790)), _851800 = _851798, _851796 = _851794, _851792 = _851790], (4578 ^ _782435) ^ [_852011, _852013] : [_852013 = _852011, -(c_Lazy__Sequence_Oyield(_852013) = c_Lazy__Sequence_Oyield(_852011))], (4584 ^ _782435) ^ [_852096, _852098] : [_852098 = _852096, -(c_List_Olist_OCons(_852098) = c_List_Olist_OCons(_852096))], (4590 ^ _782435) ^ [_852181, _852183] : [_852183 = _852181, -(c_List_Olist_ONil(_852183) = c_List_Olist_ONil(_852181))], (4596 ^ _782435) ^ [_852266, _852268] : [_852268 = _852266, -(c_List_Omember(_852268) = c_List_Omember(_852266))], (4602 ^ _782435) ^ [_852351, _852353, _852355, _852357, _852359, _852361, _852363, _852365, _852367, _852369] : [-(c_Nitpick_Opair__box_Opair__box__size(_852369, _852365, _852361, _852357, _852353) = c_Nitpick_Opair__box_Opair__box__size(_852367, _852363, _852359, _852355, _852351)), _852369 = _852367, _852365 = _852363, _852361 = _852359, _852357 = _852355, _852353 = _852351], (4624 ^ _782435) ^ [_852740, _852742, _852744, _852746, _852748, _852750, _852752, _852754, _852756, _852758] : [-(c_Nitpick_Opair__box_Opair__box__rec(_852758, _852754, _852750, _852746, _852742) = c_Nitpick_Opair__box_Opair__box__rec(_852756, _852752, _852748, _852744, _852740)), _852758 = _852756, _852754 = _852752, _852750 = _852748, _852746 = _852744, _852742 = _852740], (4646 ^ _782435) ^ [_853129, _853131, _853133, _853135, _853137, _853139, _853141, _853143, _853145, _853147] : [-(c_Nitpick_Opair__box_Opair__box__case(_853147, _853143, _853139, _853135, _853131) = c_Nitpick_Opair__box_Opair__box__case(_853145, _853141, _853137, _853133, _853129)), _853147 = _853145, _853143 = _853141, _853139 = _853137, _853135 = _853133, _853131 = _853129], (4668 ^ _782435) ^ [_853518, _853520, _853522, _853524, _853526, _853528, _853530, _853532] : [-(c_Nitpick_Opair__box_OPairBox(_853532, _853528, _853524, _853520) = c_Nitpick_Opair__box_OPairBox(_853530, _853526, _853522, _853518)), _853532 = _853530, _853528 = _853526, _853524 = _853522, _853520 = _853518], (4686 ^ _782435) ^ [_853819, _853821, _853823, _853825] : [-(c_HOL_OThe(_853825, _853821) = c_HOL_OThe(_853823, _853819)), _853825 = _853823, _853821 = _853819], (4696 ^ _782435) ^ [_853968, _853970, _853972, _853974, _853976, _853978] : [-(c_FunDef_OTHE__default(_853978, _853974, _853970) = c_FunDef_OTHE__default(_853976, _853972, _853968)), _853978 = _853976, _853974 = _853972, _853970 = _853968], (4710 ^ _782435) ^ [_854189, _854191, _854193, _854195] : [-(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854195, _854191) = c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_854193, _854189)), _854195 = _854193, _854191 = _854189], (4720 ^ _782435) ^ [_854338, _854340] : [_854340 = _854338, -(c_Nat_Osize__class_Osize(_854340) = c_Nat_Osize__class_Osize(_854338))], (4726 ^ _782435) ^ [_854423, _854425, _854427, _854429, _854431, _854433, _854435, _854437, _854439, _854441] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854441, _854437, _854433, _854429, _854425) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_854439, _854435, _854431, _854427, _854423)), _854441 = _854439, _854437 = _854435, _854433 = _854431, _854429 = _854427, _854425 = _854423], (4748 ^ _782435) ^ [_854812, _854814, _854816, _854818] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854818, _854814) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_854816, _854812)), _854818 = _854816, _854814 = _854812], (4758 ^ _782435) ^ [_854961, _854963, _854965, _854967] : [-(c_List_Oupto(_854967, _854963) = c_List_Oupto(_854965, _854961)), _854967 = _854965, _854963 = _854961], (4768 ^ _782435) ^ [_855110, _855112, _855114, _855116, _855118, _855120] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_855120, _855116, _855112) = c_SetInterval_Oord__class_OatLeastAtMost(_855118, _855114, _855110)), _855120 = _855118, _855116 = _855114, _855112 = _855110], (4782 ^ _782435) ^ [_855331, _855333] : [_855333 = _855331, -(c_Code__Numeral_OSuc__code__numeral(_855333) = c_Code__Numeral_OSuc__code__numeral(_855331))], (4788 ^ _782435) ^ [_855416, _855418, _855420, _855422, _855424, _855426, _855428, _855430] : [-(c_Product__Type_Oscomp(_855430, _855426, _855422, _855418) = c_Product__Type_Oscomp(_855428, _855424, _855420, _855416)), _855430 = _855428, _855426 = _855424, _855422 = _855420, _855418 = _855416], (4806 ^ _782435) ^ [_855717, _855719, _855721, _855723, _855725, _855727, _855729, _855731] : [-(c_Random__Sequence_ORandom(_855731, _855727, _855723, _855719) = c_Random__Sequence_ORandom(_855729, _855725, _855721, _855717)), _855731 = _855729, _855727 = _855725, _855723 = _855721, _855719 = _855717], (4824 ^ _782435) ^ [_856018, _856020] : [_856020 = _856018, -(c_DSequence_Ounion(_856020) = c_DSequence_Ounion(_856018))], (4830 ^ _782435) ^ [_856103, _856105, _856107, _856109, _856111, _856113, _856115, _856117] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_856117, _856113, _856109, _856105) = c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_856115, _856111, _856107, _856103)), _856117 = _856115, _856113 = _856111, _856109 = _856107, _856105 = _856103], (4848 ^ _782435) ^ [_856404, _856406, _856408, _856410, _856412, _856414] : [-(c_Random__Sequence_Oempty(_856414, _856410, _856406) = c_Random__Sequence_Oempty(_856412, _856408, _856404)), _856414 = _856412, _856410 = _856408, _856406 = _856404], (4862 ^ _782435) ^ [_856625, _856627] : [_856627 = _856625, -(c_DSequence_Oempty(_856627) = c_DSequence_Oempty(_856625))], (4868 ^ _782435) ^ [_856710, _856712] : [_856712 = _856710, -(c_DSequence_Osingle(_856712) = c_DSequence_Osingle(_856710))], (4874 ^ _782435) ^ [_856795, _856797, _856799, _856801, _856803, _856805, _856807, _856809] : [-(c_Random__Sequence_Omap(_856809, _856805, _856801, _856797) = c_Random__Sequence_Omap(_856807, _856803, _856799, _856795)), _856809 = _856807, _856805 = _856803, _856801 = _856799, _856797 = _856795], (4892 ^ _782435) ^ [_857096, _857098, _857100, _857102, _857104, _857106, _857108, _857110] : [-(c_Random__Sequence_Obind(_857110, _857106, _857102, _857098) = c_Random__Sequence_Obind(_857108, _857104, _857100, _857096)), _857110 = _857108, _857106 = _857104, _857102 = _857100, _857098 = _857096], (4910 ^ _782435) ^ [_857397, _857399] : [_857399 = _857397, -(c_Random__Sequence_Osingle(_857399) = c_Random__Sequence_Osingle(_857397))], (4916 ^ _782435) ^ [_857482, _857484, _857486, _857488] : [-(c_Product__Type_Osnd(_857488, _857484) = c_Product__Type_Osnd(_857486, _857482)), _857488 = _857486, _857484 = _857482], (4926 ^ _782435) ^ [_857631, _857633, _857635, _857637] : [-(c_Product__Type_Ofst(_857637, _857633) = c_Product__Type_Ofst(_857635, _857631)), _857637 = _857635, _857633 = _857631], (4936 ^ _782435) ^ [_857780, _857782, _857784, _857786, _857788, _857790] : [-(c_Relation_OImage(_857790, _857786, _857782) = c_Relation_OImage(_857788, _857784, _857780)), _857790 = _857788, _857786 = _857784, _857782 = _857780], (4950 ^ _782435) ^ [_858001, _858003, _858005, _858007, _858009, _858011, _858013, _858015] : [-(c_Wellfounded_Olex__prod(_858015, _858011, _858007, _858003) = c_Wellfounded_Olex__prod(_858013, _858009, _858005, _858001)), _858015 = _858013, _858011 = _858009, _858007 = _858005, _858003 = _858001], (4968 ^ _782435) ^ [_858302, _858304] : [_858304 = _858302, -(c_Set_OBex(_858304) = c_Set_OBex(_858302))], (4974 ^ _782435) ^ [_858387, _858389, _858391, _858393] : [-(c_List_Olexord(_858393, _858389) = c_List_Olexord(_858391, _858387)), _858393 = _858391, _858389 = _858387], (4984 ^ _782435) ^ [_858536, _858538] : [_858538 = _858536, -(c_Wellfounded_Ofinite__psubset(_858538) = c_Wellfounded_Ofinite__psubset(_858536))], (4990 ^ _782435) ^ [_858621, _858623] : [_858623 = _858621, -(c_List_Oset(_858623) = c_List_Oset(_858621))], (4996 ^ _782435) ^ [_858706, _858708, _858710, _858712] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858712, _858708) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_858710, _858706)), _858712 = _858710, _858708 = _858706], (5006 ^ _782435) ^ [_858855, _858857, _858859, _858861] : [-(c_Complete__Lattice_OSup__class_OSup(_858861, _858857) = c_Complete__Lattice_OSup__class_OSup(_858859, _858855)), _858861 = _858859, _858857 = _858855], (5016 ^ _782435) ^ [_859004, _859006, _859008, _859010] : [-(c_Complete__Lattice_OInf__class_OInf(_859010, _859006) = c_Complete__Lattice_OInf__class_OInf(_859008, _859004)), _859010 = _859008, _859006 = _859004], (5026 ^ _782435) ^ [_859153, _859155, _859157, _859159, _859161, _859163, _859165, _859167, _859169, _859171, _859173, _859175] : [-(c_Partial__Function_Ofun__lub(_859175, _859171, _859167, _859163, _859159, _859155) = c_Partial__Function_Ofun__lub(_859173, _859169, _859165, _859161, _859157, _859153)), _859175 = _859173, _859171 = _859169, _859167 = _859165, _859163 = _859161, _859159 = _859157, _859155 = _859153], (5052 ^ _782435) ^ [_859638, _859640, _859642, _859644, _859646, _859648] : [-(c_Relation_Orel__comp(_859648, _859644, _859640) = c_Relation_Orel__comp(_859646, _859642, _859638)), _859648 = _859646, _859644 = _859642, _859640 = _859638], (5066 ^ _782435) ^ [_859859, _859861, _859863, _859865] : [-(c_Relation_Oinv__image(_859865, _859861) = c_Relation_Oinv__image(_859863, _859859)), _859865 = _859863, _859861 = _859859], (5076 ^ _782435) ^ [_860008, _860010, _860012, _860014] : [-(c_Relation_OId__on(_860014, _860010) = c_Relation_OId__on(_860012, _860008)), _860014 = _860012, _860010 = _860008], (5086 ^ _782435) ^ [_860157, _860159] : [_860159 = _860157, -(c_Relation_OId(_860159) = c_Relation_OId(_860157))], (5092 ^ _782435) ^ [_860242, _860244, _860246, _860248] : [-(c_List_Olistrel(_860248, _860244) = c_List_Olistrel(_860246, _860242)), _860248 = _860246, _860244 = _860242], (5102 ^ _782435) ^ [_860391, _860393] : [_860393 = _860391, -(c_Lattices_Osemilattice__sup__class_Osup(_860393) = c_Lattices_Osemilattice__sup__class_Osup(_860391))], (5108 ^ _782435) ^ [_860476, _860478, _860480, _860482] : [-(c_Relation_Oconverse(_860482, _860478) = c_Relation_Oconverse(_860480, _860476)), _860482 = _860480, _860478 = _860476], (5118 ^ _782435) ^ [_860625, _860627] : [_860627 = _860625, -(c_Set_OCollect(_860627) = c_Set_OCollect(_860625))], (5124 ^ _782435) ^ [_860710, _860712] : [_860712 = _860710, -(c_HOL_OEx(_860712) = c_HOL_OEx(_860710))], (5130 ^ _782435) ^ [_860795, _860797] : [_860797 = _860795, -(c_Lattices_Osemilattice__inf__class_Oinf(_860797) = c_Lattices_Osemilattice__inf__class_Oinf(_860795))], (5136 ^ _782435) ^ [_860880, _860882, _860884, _860886, _860888, _860890] : [-(c_Finite__Set_Ofold__image(_860890, _860886, _860882) = c_Finite__Set_Ofold__image(_860888, _860884, _860880)), _860890 = _860888, _860886 = _860884, _860882 = _860880], (5150 ^ _782435) ^ [_861101, _861103] : [_861103 = _861101, -(c_Orderings_Otop__class_Otop(_861103) = c_Orderings_Otop__class_Otop(_861101))], (5156 ^ _782435) ^ [_861186, _861188, _861190, _861192, _861194, _861196, _861198, _861200, _861202, _861204] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_861204, _861200, _861196, _861192, _861188) = c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_861202, _861198, _861194, _861190, _861186)), _861204 = _861202, _861200 = _861198, _861196 = _861194, _861192 = _861190, _861188 = _861186], (5178 ^ _782435) ^ [_861575, _861577, _861579, _861581] : [-(c_Orderings_Oord__class_OLeast(_861581, _861577) = c_Orderings_Oord__class_OLeast(_861579, _861575)), _861581 = _861579, _861577 = _861575], (5188 ^ _782435) ^ [_861724, _861726, _861728, _861730] : [-(c_Quickcheck_Obeyond(_861730, _861726) = c_Quickcheck_Obeyond(_861728, _861724)), _861730 = _861728, _861726 = _861724], (5198 ^ _782435) ^ [_861873, _861875, _861877, _861879] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861879, _861875) = c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_861877, _861873)), _861879 = _861877, _861875 = _861873], (5208 ^ _782435) ^ [_862022, _862024, _862026, _862028, _862030, _862032] : [-(c_Product__Type_Oprod_Oprod__case(_862032, _862028, _862024) = c_Product__Type_Oprod_Oprod__case(_862030, _862026, _862022)), _862032 = _862030, _862028 = _862026, _862024 = _862022], (5222 ^ _782435) ^ [_862243, _862245, _862247, _862249, _862251, _862253, _862255, _862257] : [-(c_Product__Type_Ocurry(_862257, _862253, _862249, _862245) = c_Product__Type_Ocurry(_862255, _862251, _862247, _862243)), _862257 = _862255, _862253 = _862251, _862249 = _862247, _862245 = _862243], (5240 ^ _782435) ^ [_862544, _862546, _862548, _862550] : [-(c_Transitive__Closure_Otrancl(_862550, _862546) = c_Transitive__Closure_Otrancl(_862548, _862544)), _862550 = _862548, _862546 = _862544], (5250 ^ _782435) ^ [_862693, _862695, _862697, _862699] : [-(c_Quotient_ORespects(_862699, _862695) = c_Quotient_ORespects(_862697, _862693)), _862699 = _862697, _862695 = _862693], (5260 ^ _782435) ^ [_862842, _862844, _862846, _862848, _862850, _862852, _862854, _862856] : [-(c_Quotient_OBabs(_862856, _862852, _862848, _862844) = c_Quotient_OBabs(_862854, _862850, _862846, _862842)), _862856 = _862854, _862852 = _862850, _862848 = _862846, _862844 = _862842], (5278 ^ _782435) ^ [_863143, _863145, _863147, _863149] : [-(c_Transitive__Closure_Ortrancl(_863149, _863145) = c_Transitive__Closure_Ortrancl(_863147, _863143)), _863149 = _863147, _863145 = _863143], (5288 ^ _782435) ^ [_863292, _863294, _863296, _863298] : [-(c_Product__Type_OPair(_863298, _863294) = c_Product__Type_OPair(_863296, _863292)), _863298 = _863296, _863294 = _863292], (5298 ^ _782435) ^ [_863441, _863443, _863445, _863447, _863449, _863451] : [-(c_Lazy__Sequence_Oappend(_863451, _863447, _863443) = c_Lazy__Sequence_Oappend(_863449, _863445, _863441)), _863451 = _863449, _863447 = _863445, _863443 = _863441], (5312 ^ _782435) ^ [_863662, _863664, _863666, _863668, _863670, _863672] : [-(c_Lazy__Sequence_Obind(_863672, _863668, _863664) = c_Lazy__Sequence_Obind(_863670, _863666, _863662)), _863672 = _863670, _863668 = _863666, _863664 = _863662], (5326 ^ _782435) ^ [_863883, _863885, _863887, _863889] : [-(c_Lazy__Sequence_Oflat(_863889, _863885) = c_Lazy__Sequence_Oflat(_863887, _863883)), _863889 = _863887, _863885 = _863883], (5336 ^ _782435) ^ [_864032, _864034, _864036, _864038] : [-(c_SetInterval_Oord__class_OatLeastLessThan(_864038, _864034) = c_SetInterval_Oord__class_OatLeastLessThan(_864036, _864032)), _864038 = _864036, _864034 = _864032], (5346 ^ _782435) ^ [_864181, _864183, _864185, _864187, _864189, _864191] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_864191, _864187, _864183) = c_Lazy__Sequence_Olazy__sequence_OInsert(_864189, _864185, _864181)), _864191 = _864189, _864187 = _864185, _864183 = _864181], (5360 ^ _782435) ^ [_864402, _864404] : [_864404 = _864402, -(c_Lazy__Sequence_Olazy__sequence_OEmpty(_864404) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_864402))], (5366 ^ _782435) ^ [_864487, _864489, _864491, _864493] : [-(c_List_Oupt(_864493, _864489) = c_List_Oupt(_864491, _864487)), _864493 = _864491, _864489 = _864487], (5376 ^ _782435) ^ [_864636, _864638, _864640, _864642, _864644, _864646, _864648, _864650] : [-(c_Fun_Ocomp(_864650, _864646, _864642, _864638) = c_Fun_Ocomp(_864648, _864644, _864640, _864636)), _864650 = _864648, _864646 = _864644, _864642 = _864640, _864638 = _864636], (5394 ^ _782435) ^ [_864937, _864939, _864941, _864943, _864945, _864947, _864949, _864951, _864953, _864955] : [-(c_New__DSequence_Opos__map(_864955, _864951, _864947, _864943, _864939) = c_New__DSequence_Opos__map(_864953, _864949, _864945, _864941, _864937)), _864955 = _864953, _864951 = _864949, _864947 = _864945, _864943 = _864941, _864939 = _864937], (5416 ^ _782435) ^ [_865326, _865328, _865330, _865332, _865334, _865336, _865338, _865340] : [-(c_Lazy__Sequence_Omap(_865340, _865336, _865332, _865328) = c_Lazy__Sequence_Omap(_865338, _865334, _865330, _865326)), _865340 = _865338, _865336 = _865334, _865332 = _865330, _865328 = _865326], (5434 ^ _782435) ^ [_865627, _865629] : [_865629 = _865627, -(c_member(_865629) = c_member(_865627))], (5440 ^ _782435) ^ [_865712, _865714] : [_865714 = _865712, -(c_Power_Opower__class_Opower(_865714) = c_Power_Opower__class_Opower(_865712))], (5446 ^ _782435) ^ [_865797, _865799] : [_865799 = _865797, -(c_Orderings_Oord__class_Oless(_865799) = c_Orderings_Oord__class_Oless(_865797))], (5452 ^ _782435) ^ [_865882, _865884] : [_865884 = _865882, -(c_Groups_Oone__class_Oone(_865884) = c_Groups_Oone__class_Oone(_865882))], (5458 ^ _782435) ^ [_865967, _865969] : [_865969 = _865967, -(c_Finite__Set_Ofinite(_865969) = c_Finite__Set_Ofinite(_865967))], (5464 ^ _782435) ^ [_866052, _866054, _866056, _866058, _866060, _866062] : [-(c_Finite__Set_Ofold1Set(_866062, _866058, _866054) = c_Finite__Set_Ofold1Set(_866060, _866056, _866052)), _866062 = _866060, _866058 = _866056, _866054 = _866052], (5478 ^ _782435) ^ [_866273, _866275] : [_866275 = _866273, -(c_Groups_Oplus__class_Oplus(_866275) = c_Groups_Oplus__class_Oplus(_866273))], (5484 ^ _782435) ^ [_866358, _866360] : [_866360 = _866358, -(c_Groups_Ominus__class_Ominus(_866360) = c_Groups_Ominus__class_Ominus(_866358))], (5490 ^ _782435) ^ [_866443, _866445] : [_866445 = _866443, -(c_Groups_Ozero__class_Ozero(_866445) = c_Groups_Ozero__class_Ozero(_866443))], (5496 ^ _782435) ^ [_866528, _866530] : [_866530 = _866528, -(c_Divides_Odiv__class_Odiv(_866530) = c_Divides_Odiv__class_Odiv(_866528))], (5502 ^ _782435) ^ [_866613, _866615] : [_866615 = _866613, -(c_Groups_Otimes__class_Otimes(_866615) = c_Groups_Otimes__class_Otimes(_866613))], (5508 ^ _782435) ^ [_866698, _866700, _866702, _866704, _866706, _866708, _866710, _866712] : [-(c_SetInterval_Oord_OatLeastAtMost(_866712, _866708, _866704, _866700) = c_SetInterval_Oord_OatLeastAtMost(_866710, _866706, _866702, _866698)), _866712 = _866710, _866708 = _866706, _866704 = _866702, _866700 = _866698], (5526 ^ _782435) ^ [_866999, _867001] : [_867001 = _866999, -(c_Set_Oinsert(_867001) = c_Set_Oinsert(_866999))], (5532 ^ _782435) ^ [_867084, _867086, _867088, _867090, _867092, _867094, _867096, _867098] : [-(c_SetInterval_Oord_OgreaterThanLessThan(_867098, _867094, _867090, _867086) = c_SetInterval_Oord_OgreaterThanLessThan(_867096, _867092, _867088, _867084)), _867098 = _867096, _867094 = _867092, _867090 = _867088, _867086 = _867084], (5550 ^ _782435) ^ [_867385, _867387, _867389, _867391, _867393, _867395, _867397, _867399, _867401, _867403] : [-(c_SetInterval_Oord_OatLeastLessThan(_867403, _867399, _867395, _867391, _867387) = c_SetInterval_Oord_OatLeastLessThan(_867401, _867397, _867393, _867389, _867385)), _867403 = _867401, _867399 = _867397, _867395 = _867393, _867391 = _867389, _867387 = _867385], (5572 ^ _782435) ^ [_867774, _867776] : [_867776 = _867774, -(c_Orderings_Obot__class_Obot(_867776) = c_Orderings_Obot__class_Obot(_867774))], (5578 ^ _782435) ^ [_867859, _867861, _867863, _867865, _867867, _867869, _867871, _867873, _867875, _867877] : [-(c_SetInterval_Oord_OgreaterThanAtMost(_867877, _867873, _867869, _867865, _867861) = c_SetInterval_Oord_OgreaterThanAtMost(_867875, _867871, _867867, _867863, _867859)), _867877 = _867875, _867873 = _867871, _867869 = _867867, _867865 = _867863, _867861 = _867859], (5600 ^ _782435) ^ [_868248, _868250] : [_868250 = _868248, -(c_Rings_Odvd__class_Odvd(_868250) = c_Rings_Odvd__class_Odvd(_868248))], (5606 ^ _782435) ^ [_868333, _868335] : [_868335 = _868333, -(tc_List_Olist(_868335) = tc_List_Olist(_868333))], (5612 ^ _782435) ^ [_868418, _868420, _868422, _868424] : [-(tc_sum(_868424, _868420) = tc_sum(_868422, _868418)), _868424 = _868422, _868420 = _868418], (5622 ^ _782435) ^ [_868567, _868569] : [_868569 = _868567, -(tc_Option_Ooption(_868569) = tc_Option_Ooption(_868567))], (5628 ^ _782435) ^ [_868652, _868654, _868656, _868658] : [-(tc_Nitpick_Opair__box(_868658, _868654) = tc_Nitpick_Opair__box(_868656, _868652)), _868658 = _868656, _868654 = _868652], (5638 ^ _782435) ^ [_868801, _868803, _868805, _868807] : [-(tc_prod(_868807, _868803) = tc_prod(_868805, _868801)), _868807 = _868805, _868803 = _868801], (5648 ^ _782435) ^ [_868950, _868952] : [_868952 = _868950, -(tc_Lazy__Sequence_Olazy__sequence(_868952) = tc_Lazy__Sequence_Olazy__sequence(_868950))], (5654 ^ _782435) ^ [_869035, _869037] : [_869037 = _869035, -(c_COMBI(_869037) = c_COMBI(_869035))], (5660 ^ _782435) ^ [_869120, _869122, _869124, _869126] : [-(c_COMBK(_869126, _869122) = c_COMBK(_869124, _869120)), _869126 = _869124, _869122 = _869120], (5670 ^ _782435) ^ [_869269, _869271, _869273, _869275, _869277, _869279] : [-(c_COMBB(_869279, _869275, _869271) = c_COMBB(_869277, _869273, _869269)), _869279 = _869277, _869275 = _869273, _869271 = _869269], (5684 ^ _782435) ^ [_869490, _869492, _869494, _869496, _869498, _869500] : [-(c_COMBC(_869500, _869496, _869492) = c_COMBC(_869498, _869494, _869490)), _869500 = _869498, _869496 = _869494, _869492 = _869490], (5698 ^ _782435) ^ [_869711, _869713, _869715, _869717, _869719, _869721] : [-(c_COMBS(_869721, _869717, _869713) = c_COMBS(_869719, _869715, _869711)), _869721 = _869719, _869717 = _869715, _869713 = _869711], (5712 ^ _782435) ^ [_869932, _869934, _869936, _869938] : [-(hAPP(_869938, _869934) = hAPP(_869936, _869932)), _869938 = _869936, _869934 = _869932], (5722 ^ _782435) ^ [_870081, _870083] : [_870083 = _870081, -(c_Orderings_Oord__class_Oless__eq(_870083) = c_Orderings_Oord__class_Oless__eq(_870081))], (5738 ^ _782435) ^ [_870311, _870313] : [_870313 = _870311, -(tc_Hoare__Mirabelle_Otriple(_870313) = tc_Hoare__Mirabelle_Otriple(_870311))], (5728 ^ _782435) ^ [_870166, _870168, _870170, _870172] : [-(tc_fun(_870172, _870168) = tc_fun(_870170, _870166)), _870172 = _870170, _870168 = _870166], (5744 ^ _782435) ^ [_873211, _873213] : [hAPP(_873211, 5745 ^ [_873211, _873213]) = hAPP(_873213, 5745 ^ [_873211, _873213]), -(_873211 = _873213)], (5751 ^ _782435) ^ [_873337, _873339, _873341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_873337), tc_HOL_Obool)), _873339), _873341)), -(c_Hoare__Mirabelle_Ohoare__derivs(_873337, _873341, _873339))], (5757 ^ _782435) ^ [_873442, _873444, _873446, _873448] : [c_Hoare__Mirabelle_Ohoare__derivs(_873442, _873444, _873446), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(_873442), tc_HOL_Obool)), _873448), _873446)), -(c_Hoare__Mirabelle_Ohoare__derivs(_873442, _873444, _873448))], (5767 ^ _782435) ^ [_873607, _873609, _873611, _873613] : [c_Hoare__Mirabelle_Ohoare__derivs(_873607, _873609, _873611), c_Hoare__Mirabelle_Ohoare__derivs(_873607, _873613, _873609), -(c_Hoare__Mirabelle_Ohoare__derivs(_873607, _873613, _873611))], (5777 ^ _782435) ^ [_873750, _873752, _873754] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873750, tc_HOL_Obool)), _873752), _873754)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_873750, tc_HOL_Obool)), _873754), _873752)), -(_873752 = _873754)], (5787 ^ _782435) ^ [_873923, _873925] : [class_Orderings_Opreorder(_873923), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_873923), _873925), _873925)))], (5793 ^ _782435) ^ [_874012, _874014, _874016, _874018] : [class_Orderings_Oord(_874012), 5796 ^ _782435 : [(5797 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874014, _874012)), _874016), _874018)), 5800 ^ _782435 : [(5801 ^ _782435) ^ [_874169] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874012), hAPP(_874016, _874169)), hAPP(_874018, _874169))))]]], (5803 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874012), hAPP(_874016, 5804 ^ [_874012, _874014, _874016, _874018])), hAPP(_874018, 5804 ^ [_874012, _874014, _874016, _874018]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874014, _874012)), _874016), _874018)))]]], (5810 ^ _782435) ^ [_874358, _874360, _874362, _874364, _874366] : [class_Orderings_Oord(_874358), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874360, _874358)), _874362), _874364)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874358), hAPP(_874362, _874366)), hAPP(_874364, _874366))))], (5820 ^ _782435) ^ [_874543, _874545, _874547, _874549, _874551] : [class_Orderings_Oord(_874543), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874545, _874543)), _874547), _874549)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_874543), hAPP(_874547, _874551)), hAPP(_874549, _874551))))], (5830 ^ _782435) ^ [_874728, _874730] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874728, tc_HOL_Obool)), _874730), _874730)))], (5832 ^ _782435) ^ [_874781, _874783, _874785] : [_874781 = _874783, 5835 ^ _782435 : [(5836 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874785, tc_HOL_Obool)), _874781), _874783)))], (5838 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874785, tc_HOL_Obool)), _874783), _874781)))]]], (5840 ^ _782435) ^ [_874922, _874924, _874926] : [-(_874922 = _874924), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874926, tc_HOL_Obool)), _874922), _874924)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_874926, tc_HOL_Obool)), _874924), _874922))], (5850 ^ _782435) ^ [_875097, _875099, _875101, _875103] : [hBOOL(hAPP(_875097, _875099)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875101, tc_HOL_Obool)), _875097), _875103)), -(hBOOL(hAPP(_875103, _875099)))], (5860 ^ _782435) ^ [_875262, _875264, _875266] : [_875262 = _875264, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875266, tc_HOL_Obool)), _875262), _875264)))], (5866 ^ _782435) ^ [_875361, _875363, _875365] : [_875361 = _875363, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875365, tc_HOL_Obool)), _875363), _875361)))], (5872 ^ _782435) ^ [_875460, _875462, _875464, _875466] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875460, tc_HOL_Obool)), _875462), _875464)), hBOOL(hAPP(_875462, _875466)), -(hBOOL(hAPP(_875464, _875466)))], (5882 ^ _782435) ^ [_875625, _875627, _875629, _875631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875625, tc_HOL_Obool)), _875627), _875629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875625, tc_HOL_Obool)), _875629), _875631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_875625, tc_HOL_Obool)), _875627), _875631)))], (5892 ^ _782435) ^ [_875822, _875824, _875826] : [class_Orderings_Olinorder(_875822), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875822), _875824), _875826))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875822), _875826), _875824)))], (5902 ^ _782435) ^ [_875942, _875944, _875946, _875948] : [class_Orderings_Oorder(_875942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875942), _875944), _875946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875942), _875948), _875944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_875942), _875948), _875946)))], (5916 ^ _782435) ^ [_876175, _876177, _876179] : [class_Orderings_Oorder(_876175), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876175), _876177), _876179)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876175), _876179), _876177)), -(_876179 = _876177)], (5930 ^ _782435) ^ [_876388, _876390, _876392, _876394] : [class_Orderings_Opreorder(_876388), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876388), _876390), _876392)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876388), _876392), _876394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876388), _876390), _876394)))], (5944 ^ _782435) ^ [_876621, _876623, _876625] : [class_Orderings_Oorder(_876621), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876621), _876623), _876625)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876621), _876625), _876623)), -(_876623 = _876625)], (5958 ^ _782435) ^ [_876834, _876836, _876838, _876840] : [class_Orderings_Oorder(_876834), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876834), _876836), _876838)), _876836 = _876840, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_876834), _876840), _876838)))], (5972 ^ _782435) ^ [_877053, _877055, _877057, _877059] : [class_Orderings_Oord(_877053), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877053), _877055), _877057)), _877057 = _877059, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877053), _877055), _877059)))], (5986 ^ _782435) ^ [_877272, _877274, _877276, _877278] : [class_Orderings_Oorder(_877272), _877274 = _877276, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877272), _877278), _877276)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877272), _877278), _877274)))], (6000 ^ _782435) ^ [_877491, _877493, _877495, _877497] : [class_Orderings_Oord(_877491), _877493 = _877495, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877491), _877495), _877497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877491), _877493), _877497)))], (6014 ^ _782435) ^ [_877710, _877712, _877714] : [class_Orderings_Oorder(_877710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877710), _877712), _877714)), 6021 ^ _782435 : [(6022 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877710), _877714), _877712)), -(_877714 = _877712)], (6028 ^ _782435) ^ [] : [_877714 = _877712, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_877710), _877714), _877712)))]]], (6034 ^ _782435) ^ [_878010, _878012, _878014] : [class_Orderings_Opreorder(_878010), _878012 = _878014, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878010), _878012), _878014)))], (6044 ^ _782435) ^ [_878155, _878157, _878159] : [class_Orderings_Oorder(_878155), 6047 ^ _782435 : [(6048 ^ _782435) ^ [] : [_878157 = _878159, 6051 ^ _782435 : [(6052 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878155), _878157), _878159)))], (6054 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878155), _878159), _878157)))]]], (6056 ^ _782435) ^ [] : [-(_878157 = _878159), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878155), _878157), _878159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878155), _878159), _878157))]]], (6066 ^ _782435) ^ [_878482, _878484, _878486] : [class_Orderings_Olinorder(_878482), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878482), _878484), _878486))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_878482), _878486), _878484)))], (6076 ^ _782435) ^ [_878600, _878602, _878604] : [_878600 = _878602, 6079 ^ _782435 : [(6080 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878604, tc_HOL_Obool)), _878600), _878602)))], (6082 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878604, tc_HOL_Obool)), _878602), _878600)))]]], (6084 ^ _782435) ^ [_878749, _878751, _878753] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878749, tc_HOL_Obool)), _878751), _878753)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_878749, tc_HOL_Obool), tc_HOL_Obool)), c_Predicate_OPowp(_878749, _878751)), c_Predicate_OPowp(_878749, _878753))))], (6090 ^ _782435) ^ [_878886, _878888, _878890, _878892] : [class_Orderings_Oorder(_878886), class_Enum_Oenum(_878888), 6097 ^ _782435 : [(6098 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878888, _878886)), _878890), _878892)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878888), hAPP(hAPP(c_COMBS(_878888, _878886, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878886, tc_fun(_878886, tc_HOL_Obool), _878888), c_Orderings_Oord__class_Oless__eq(_878886)), _878890)), _878892))))], (6104 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_878888), hAPP(hAPP(c_COMBS(_878888, _878886, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_878886, tc_fun(_878886, tc_HOL_Obool), _878888), c_Orderings_Oord__class_Oless__eq(_878886)), _878890)), _878892))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_878888, _878886)), _878890), _878892)))]]], (6110 ^ _782435) ^ [_879276, _879278, _879280] : [class_Orderings_Owellorder(_879276), hBOOL(hAPP(_879278, _879280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879276), c_Orderings_Oord__class_OLeast(_879276, _879278)), _879280)))], (6120 ^ _782435) ^ [_879431, _879433, _879435, _879437] : [class_Orderings_Oord(_879431), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879431), hAPP(_879433, 6125 ^ [_879431, _879433, _879435, _879437])), hAPP(_879435, 6125 ^ [_879431, _879433, _879435, _879437]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_879437, _879431)), _879433), _879435)))], (6131 ^ _782435) ^ [_879695, _879697, _879699, _879701, _879703, _879705] : [c_Predicate_Oinv__imagep(_879695, _879697, _879699, _879701, _879703, _879705), -(hBOOL(hAPP(hAPP(_879699, hAPP(_879701, _879703)), hAPP(_879701, _879705))))], (6137 ^ _782435) ^ [_879806, _879808, _879810, _879812, _879814, _879816] : [hBOOL(hAPP(hAPP(_879810, hAPP(_879812, _879814)), hAPP(_879812, _879816))), -(c_Predicate_Oinv__imagep(_879806, _879808, _879810, _879812, _879814, _879816))], (6143 ^ _782435) ^ [_879923, _879925, _879927, _879929, _879931] : [class_Orderings_Oorder(_879923), class_Orderings_Olinorder(_879925), c_Orderings_Oorder__class_Ostrict__mono(_879925, _879923, _879927), 6154 ^ _782435 : [(6155 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879923), hAPP(_879927, _879929)), hAPP(_879927, _879931))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879925), _879929), _879931)))], (6161 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879925), _879929), _879931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_879923), hAPP(_879927, _879929)), hAPP(_879927, _879931))))]]], (6167 ^ _782435) ^ [_880324, _880326, _880328] : [class_Orderings_Olinorder(_880324), 6170 ^ _782435 : [(6171 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880324, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880324), _880326)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880324), _880328))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880324), _880328), _880326)))], (6177 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880324), _880328), _880326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880324, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880324), _880326)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_880324), _880328))))]]], (6183 ^ _782435) ^ [_880616, _880618, _880620] : [class_Orderings_Olinorder(_880616), 6186 ^ _782435 : [(6187 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880616, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_880616), _880618)), hAPP(c_SetInterval_Oord__class_OlessThan(_880616), _880620))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880616), _880618), _880620)))], (6193 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880616), _880618), _880620)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880616, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_880616), _880618)), hAPP(c_SetInterval_Oord__class_OlessThan(_880616), _880620))))]]], (6199 ^ _782435) ^ [_880908, _880910, _880912] : [class_Orderings_Oorder(_880908), 6202 ^ _782435 : [(6203 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880908, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_880908), _880910)), hAPP(c_SetInterval_Oord__class_OatLeast(_880908), _880912))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880908), _880912), _880910)))], (6209 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_880908), _880912), _880910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_880908, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_880908), _880910)), hAPP(c_SetInterval_Oord__class_OatLeast(_880908), _880912))))]]], (6215 ^ _782435) ^ [_881200, _881202, _881204] : [class_Orderings_Oorder(_881200), 6218 ^ _782435 : [(6219 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881200, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_881200), _881202)), hAPP(c_SetInterval_Oord__class_OatMost(_881200), _881204))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881200), _881202), _881204)))], (6225 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881200), _881202), _881204)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881200, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_881200), _881202)), hAPP(c_SetInterval_Oord__class_OatMost(_881200), _881204))))]]], (6231 ^ _782435) ^ [_881492, _881494, _881496, _881498, _881500] : [class_Complete__Lattice_Ocomplete__lattice(_881492), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881494, tc_HOL_Obool)), _881496), _881498)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881492), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881494, _881492), _881496), _881500)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881494, _881492), _881498), _881500))))], (6241 ^ _782435) ^ [_881701, _881703, _881705, _881707, _881709] : [class_Complete__Lattice_Ocomplete__lattice(_881701), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_881703, tc_HOL_Obool)), _881705), _881707)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_881701), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_881703, _881701), _881707), _881709)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_881703, _881701), _881705), _881709))))], (6251 ^ _782435) ^ [_881910, _881912, _881914, _881916, _881918, _881920] : [class_Complete__Lattice_Ocomplete__lattice(_881910), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881912, tc_fun(_881914, _881910)), _881916), _881918), _881920) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_881912, _881910), _881916), hAPP(hAPP(c_COMBC(_881912, _881914, _881910), _881918), _881920)))], (6257 ^ _782435) ^ [_882061, _882063, _882065, _882067, _882069, _882071] : [class_Complete__Lattice_Ocomplete__lattice(_882061), -(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_882063, tc_fun(_882065, _882061)), _882067), _882069), _882071) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_882063, _882061), _882067), hAPP(hAPP(c_COMBC(_882063, _882065, _882061), _882069), _882071)))], (6263 ^ _782435) ^ [_882212, _882214, _882216] : [class_Orderings_Olinorder(_882212), 6266 ^ _782435 : [(6267 ^ _782435) ^ [] : [hAPP(c_SetInterval_Oord__class_OgreaterThan(_882212), _882214) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_882212), _882216), -(_882214 = _882216)], (6273 ^ _782435) ^ [] : [_882214 = _882216, -(hAPP(c_SetInterval_Oord__class_OgreaterThan(_882212), _882214) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_882212), _882216))]]], (6279 ^ _782435) ^ [_882453, _882455, _882457] : [class_Orderings_Olinorder(_882453), 6282 ^ _782435 : [(6283 ^ _782435) ^ [] : [hAPP(c_SetInterval_Oord__class_OlessThan(_882453), _882455) = hAPP(c_SetInterval_Oord__class_OlessThan(_882453), _882457), -(_882455 = _882457)], (6289 ^ _782435) ^ [] : [_882455 = _882457, -(hAPP(c_SetInterval_Oord__class_OlessThan(_882453), _882455) = hAPP(c_SetInterval_Oord__class_OlessThan(_882453), _882457))]]], (6295 ^ _782435) ^ [_882694, _882696, _882698] : [class_Orderings_Olinorder(_882694), 6298 ^ _782435 : [(6299 ^ _782435) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeast(_882694), _882696) = hAPP(c_SetInterval_Oord__class_OatLeast(_882694), _882698), -(_882696 = _882698)], (6305 ^ _782435) ^ [] : [_882696 = _882698, -(hAPP(c_SetInterval_Oord__class_OatLeast(_882694), _882696) = hAPP(c_SetInterval_Oord__class_OatLeast(_882694), _882698))]]], (6311 ^ _782435) ^ [_882935, _882937, _882939] : [class_Orderings_Olinorder(_882935), 6314 ^ _782435 : [(6315 ^ _782435) ^ [] : [hAPP(c_SetInterval_Oord__class_OatMost(_882935), _882937) = hAPP(c_SetInterval_Oord__class_OatMost(_882935), _882939), -(_882937 = _882939)], (6321 ^ _782435) ^ [] : [_882937 = _882939, -(hAPP(c_SetInterval_Oord__class_OatMost(_882935), _882937) = hAPP(c_SetInterval_Oord__class_OatMost(_882935), _882939))]]], (6327 ^ _782435) ^ [_883176, _883178, _883180, _883182, _883184, _883186] : [class_Complete__Lattice_Ocomplete__lattice(_883176), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883178, _883176), _883180), hAPP(hAPP(c_COMBB(tc_fun(_883182, _883176), _883176, _883178), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883182, _883176), _883184)), _883186)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883182, _883176), _883184), hAPP(hAPP(c_COMBB(tc_fun(_883178, _883176), _883176, _883182), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_883178, _883176), _883180)), hAPP(c_COMBC(_883178, _883182, _883176), _883186))))], (6333 ^ _782435) ^ [_883385, _883387, _883389, _883391, _883393, _883395] : [class_Complete__Lattice_Ocomplete__lattice(_883385), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883387, _883385), _883389), hAPP(hAPP(c_COMBB(tc_fun(_883391, _883385), _883385, _883387), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883391, _883385), _883393)), _883395)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883391, _883385), _883393), hAPP(hAPP(c_COMBB(tc_fun(_883387, _883385), _883385, _883391), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_883387, _883385), _883389)), hAPP(c_COMBC(_883387, _883391, _883385), _883395))))], (6339 ^ _782435) ^ [_883594, _883596] : [class_Enum_Oenum(_883594), 6342 ^ _782435 : [(6343 ^ _782435) ^ [] : [hBOOL(hAPP(_883596, 6344 ^ [_883594, _883596])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883594), _883596)))], (6350 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883594), _883596)), 6353 ^ _782435 : [(6354 ^ _782435) ^ [_883812] : [-(hBOOL(hAPP(_883596, _883812)))]]]]], (6356 ^ _782435) ^ [_883847, _883849] : [class_Enum_Oenum(_883847), 6359 ^ _782435 : [(6360 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883847), _883849)), 6363 ^ _782435 : [(6364 ^ _782435) ^ [_883973] : [-(hBOOL(hAPP(_883849, _883973)))]]], (6366 ^ _782435) ^ [] : [hBOOL(hAPP(_883849, 6367 ^ [_883847, _883849])), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_883847), _883849)))]]], (6373 ^ _782435) ^ [_884100, _884102] : [class_Orderings_Owellorder(_884100), 6378 ^ _782435 : [(6379 ^ _782435) ^ [_884194] : [hBOOL(hAPP(_884102, _884194))]], -(hBOOL(hAPP(_884102, c_Orderings_Oord__class_OLeast(_884100, _884102))))], (6383 ^ _782435) ^ [_884254, _884256, _884258, _884260, _884262] : [class_Orderings_Oorder(_884254), class_Orderings_Olinorder(_884256), c_Orderings_Oorder__class_Ostrict__mono(_884256, _884254, _884258), 6394 ^ _782435 : [(6395 ^ _782435) ^ [] : [hAPP(_884258, _884260) = hAPP(_884258, _884262), -(_884260 = _884262)], (6401 ^ _782435) ^ [] : [_884260 = _884262, -(hAPP(_884258, _884260) = hAPP(_884258, _884262))]]], (6417 ^ _782435) ^ [_884895, _884897, _884899, _884901, _884903] : [6419 ^ _782435 : [(6420 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_884899), 6418 ^ [_884895, _884897, _884899, _884901, _884903]), _884901)))], (6422 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884895, tc_HOL_Obool)), _884897), hAPP(_884903, 6418 ^ [_884895, _884897, _884899, _884901, _884903])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884895, tc_HOL_Obool)), _884897), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884899, tc_fun(_884895, tc_HOL_Obool)), _884901), _884903))))], (6407 ^ _782435) ^ [_884637, _884639, _884641, _884643, _884645] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884637, tc_HOL_Obool)), _884639), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_884641, tc_fun(_884637, tc_HOL_Obool)), _884643), _884645))), 6410 ^ _782435 : [(6411 ^ _782435) ^ [_884770] : [hBOOL(hAPP(hAPP(c_member(_884641), _884770), _884643)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_884637, tc_HOL_Obool)), _884639), hAPP(_884645, _884770))))]]], (6436 ^ _782435) ^ [_885440, _885442, _885444, _885446, _885448] : [6438 ^ _782435 : [(6439 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885442), 6437 ^ [_885440, _885442, _885444, _885446, _885448]), _885444)))], (6441 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885440, tc_HOL_Obool)), hAPP(_885446, 6437 ^ [_885440, _885442, _885444, _885446, _885448])), _885448))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885440, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_885442, tc_fun(_885440, tc_HOL_Obool)), _885444), _885446)), _885448)))], (6426 ^ _782435) ^ [_885182, _885184, _885186, _885188, _885190] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885182, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_885184, tc_fun(_885182, tc_HOL_Obool)), _885186), _885188)), _885190)), 6429 ^ _782435 : [(6430 ^ _782435) ^ [_885315] : [hBOOL(hAPP(hAPP(c_member(_885184), _885315), _885186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_885182, tc_HOL_Obool)), hAPP(_885188, _885315)), _885190)))]]], (6445 ^ _782435) ^ [_885703, _885705, _885707] : [class_Orderings_Owellorder(_885703), hBOOL(hAPP(_885705, _885707)), -(hBOOL(hAPP(_885705, c_Orderings_Oord__class_OLeast(_885703, _885705))))], (6455 ^ _782435) ^ [_885848, _885850, _885852, _885854, _885856] : [class_Complete__Lattice_Ocomplete__lattice(_885848), 6458 ^ _782435 : [(6469 ^ _782435) ^ [] : [6471 ^ _782435 : [(6472 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_885852), 6470 ^ [_885848, _885850, _885852, _885854, _885856]), _885854)))], (6474 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885848), _885850), hAPP(_885856, 6470 ^ [_885848, _885850, _885852, _885854, _885856])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885848), _885850), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_885852, _885848), _885854), _885856))))], (6459 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885848), _885850), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_885852, _885848), _885854), _885856))), 6462 ^ _782435 : [(6463 ^ _782435) ^ [_886029] : [hBOOL(hAPP(hAPP(c_member(_885852), _886029), _885854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_885848), _885850), hAPP(_885856, _886029))))]]]]], (6478 ^ _782435) ^ [_886342, _886344, _886346, _886348, _886350] : [class_Complete__Lattice_Ocomplete__lattice(_886342), 6481 ^ _782435 : [(6492 ^ _782435) ^ [] : [6494 ^ _782435 : [(6495 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_886344), 6493 ^ [_886342, _886344, _886346, _886348, _886350]), _886346)))], (6497 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886342), hAPP(_886348, 6493 ^ [_886342, _886344, _886346, _886348, _886350])), _886350))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_886344, _886342), _886346), _886348)), _886350)))], (6482 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886342), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_886344, _886342), _886346), _886348)), _886350)), 6485 ^ _782435 : [(6486 ^ _782435) ^ [_886523] : [hBOOL(hAPP(hAPP(c_member(_886344), _886523), _886346)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_886342), hAPP(_886348, _886523)), _886350)))]]]]], (6501 ^ _782435) ^ [_886863, _886865, _886867, _886869, _886871, _886873] : [c_Predicate_Oinv__imagep(_886863, _886865, _886867, _886869, _886871, _886873), -(hBOOL(hAPP(hAPP(_886867, hAPP(_886869, _886871)), hAPP(_886869, _886873))))], (6507 ^ _782435) ^ [_886974, _886976, _886978, _886980, _886982, _886984] : [hBOOL(hAPP(hAPP(_886978, hAPP(_886980, _886982)), hAPP(_886980, _886984))), -(c_Predicate_Oinv__imagep(_886974, _886976, _886978, _886980, _886982, _886984))], (6513 ^ _782435) ^ [_887091, _887093, _887095] : [class_Orderings_Oorder(_887091), hBOOL(hAPP(_887093, _887095)), 6523 ^ _782435 : [(6524 ^ _782435) ^ [] : [-(hBOOL(hAPP(_887093, 6522 ^ [_887091, _887093, _887095])))], (6526 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887091), _887095), 6522 ^ [_887091, _887093, _887095]))]], -(c_Orderings_Oord__class_OLeast(_887091, _887093) = _887095)], (6530 ^ _782435) ^ [_887380, _887382, _887384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887380, tc_HOL_Obool)), _887382), _887384)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887380, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_887380), _887382)), hAPP(c_Set_OPow(_887380), _887384))))], (6536 ^ _782435) ^ [_887525, _887527, _887529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_887525, tc_HOL_Obool), tc_HOL_Obool)), _887527), _887529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_887525, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_887525, tc_HOL_Obool), _887529)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_887525, tc_HOL_Obool), _887527))))], (6542 ^ _782435) ^ [_887674, _887676, _887678, _887680, _887682] : [class_Complete__Lattice_Ocomplete__lattice(_887674), hBOOL(hAPP(hAPP(c_member(_887676), _887678), _887680)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887674), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_887676, _887674), _887680), _887682)), hAPP(_887682, _887678))))], (6552 ^ _782435) ^ [_887865, _887867, _887869, _887871, _887873] : [class_Complete__Lattice_Ocomplete__lattice(_887865), hBOOL(hAPP(hAPP(c_member(_887867), _887869), _887871)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_887865), hAPP(_887873, _887869)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_887867, _887865), _887871), _887873))))], (6562 ^ _782435) ^ [_888056, _888058, _888060, _888062, _888064] : [class_Orderings_Olinorder(_888056), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888056, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_888056, _888058), _888060)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_888056, _888062), _888064))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888056), _888060), _888058))), 6573 ^ _782435 : [(6574 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888056), _888062), _888058)))], (6576 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888056), _888060), _888064)))]]], (6578 ^ _782435) ^ [_888337, _888339] : [class_Orderings_Olinorder(_888337), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888337, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_888337), _888339)) = hAPP(c_SetInterval_Oord__class_OatMost(_888337), _888339))], (6584 ^ _782435) ^ [_888448, _888450] : [class_Orderings_Olinorder(_888448), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_888448, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_888448), _888450)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_888448), _888450))], (6590 ^ _782435) ^ [_888559, _888561, _888563, _888565, _888567] : [class_Orderings_Oorder(_888559), 6593 ^ _782435 : [(6594 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888559, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_888559, _888561, _888563)), c_SetInterval_Oord__class_OatLeastAtMost(_888559, _888565, _888567))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888559), _888561), _888563)), 6601 ^ _782435 : [(6602 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888559), _888565), _888561)))], (6604 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888559), _888563), _888567)))]]], (6606 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_888559, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_888559, _888561, _888563)), c_SetInterval_Oord__class_OatLeastAtMost(_888559, _888565, _888567)))), 6607 ^ _782435 : [(6608 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888559), _888561), _888563)))], (6610 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888559), _888565), _888561)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_888559), _888563), _888567))]]]]], (6618 ^ _782435) ^ [_889062, _889064] : [class_Orderings_Olinorder(_889062), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_889062, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_889062), _889064)) = hAPP(c_SetInterval_Oord__class_OatLeast(_889062), _889064))], (6624 ^ _782435) ^ [_889173, _889175] : [class_Orderings_Olinorder(_889173), -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_889173, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_889173), _889175)) = hAPP(c_SetInterval_Oord__class_OlessThan(_889173), _889175))], (6630 ^ _782435) ^ [_889284, _889286, _889288] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_889284, tc_HOL_Obool), tc_HOL_Obool)), _889286), _889288)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_889284, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_889284, tc_HOL_Obool), _889286)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_889284, tc_HOL_Obool), _889288))))], (6636 ^ _782435) ^ [_889433, _889435, _889437, _889439] : [_889433 = _889435, 6641 ^ _782435 : [(6642 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889437), _889439), _889433)))], (6644 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_889437), _889439), _889435)))]], 6645 ^ _782435 : [(6646 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889437), _889439), _889433))], (6648 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_889437), _889439), _889435))]]], (6650 ^ _782435) ^ [_889696, _889698, _889700, _889702, _889704, _889706, _889708, _889710] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_889696, tc_fun(_889698, tc_fun(_889700, tc_HOL_Obool))), _889702), _889704), _889706), _889708)), -(hBOOL(hAPP(hAPP(hAPP(_889704, _889710), _889706), _889708))), hBOOL(hAPP(hAPP(c_member(_889696), _889710), _889702))], (6660 ^ _782435) ^ [_889923, _889925, _889927, _889929, _889931, _889933, _889935, _889937] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_889923, tc_fun(_889925, tc_fun(_889927, tc_HOL_Obool))), _889929), _889931), _889933), _889935)), hBOOL(hAPP(hAPP(c_member(_889923), _889937), _889929)), -(hBOOL(hAPP(hAPP(hAPP(_889931, _889937), _889933), _889935)))], (6670 ^ _782435) ^ [_890146, _890148, _890150, _890152, _890154, _890156, _890158, _890160] : [hBOOL(hAPP(hAPP(c_member(_890146), _890148), _890150)), hBOOL(hAPP(hAPP(hAPP(_890152, _890148), _890154), _890156)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_890146, tc_fun(_890158, tc_fun(_890160, tc_HOL_Obool))), _890150), _890152), _890154), _890156)))], (6680 ^ _782435) ^ [_890369, _890371, _890373, _890375] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_890369, tc_HOL_Obool)), _890371), _890373)), hBOOL(hAPP(hAPP(c_member(_890369), _890375), _890371)), -(hBOOL(hAPP(hAPP(c_member(_890369), _890375), _890373)))], (6690 ^ _782435) ^ [_890550, _890552, _890554] : [-(hBOOL(hAPP(hAPP(c_member(_890550), _890552), _890554))), -(hBOOL(hAPP(hAPP(c_member(_890550), _890552), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_890550, tc_HOL_Obool)), _890554))))], (6696 ^ _782435) ^ [_890610, _890612, _890614, _890616] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_890610, tc_HOL_Obool)), _890612), _890614)), hBOOL(hAPP(hAPP(c_member(_890610), _890616), _890612)), -(hBOOL(hAPP(hAPP(c_member(_890610), _890616), c_Complete__Lattice_OSup__class_OSup(tc_fun(_890610, tc_HOL_Obool), _890614))))], (6706 ^ _782435) ^ [_890807, _890809, _890811, _890813] : [hBOOL(hAPP(hAPP(c_member(_890807), _890809), c_Complete__Lattice_OInf__class_OInf(tc_fun(_890807, tc_HOL_Obool), _890811))), hBOOL(hAPP(hAPP(c_member(tc_fun(_890807, tc_HOL_Obool)), _890813), _890811)), -(hBOOL(hAPP(hAPP(c_member(_890807), _890809), _890813)))], (6716 ^ _782435) ^ [_891004, _891006, _891008, _891010] : [hBOOL(hAPP(hAPP(c_member(_891004), _891006), c_Complete__Lattice_OInf__class_OInf(tc_fun(_891004, tc_HOL_Obool), _891008))), hBOOL(hAPP(hAPP(c_member(tc_fun(_891004, tc_HOL_Obool)), _891010), _891008)), -(hBOOL(hAPP(hAPP(c_member(_891004), _891006), _891010)))], (6726 ^ _782435) ^ [_891201, _891203, _891205] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_891201, tc_HOL_Obool)), _891203), _891205)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_891201, tc_HOL_Obool)), _891203), hAPP(c_Set_OPow(_891201), _891205))))], (6732 ^ _782435) ^ [_891330, _891332, _891334, _891336, _891338, _891340] : [hBOOL(hAPP(hAPP(c_member(_891330), _891332), _891334)), hBOOL(hAPP(hAPP(c_member(_891336), _891338), hAPP(_891340, _891332))), -(hBOOL(hAPP(hAPP(c_member(_891336), _891338), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891330, tc_fun(_891336, tc_HOL_Obool)), _891334), _891340))))], (6742 ^ _782435) ^ [_891547, _891549, _891551, _891553, _891555, _891557] : [hBOOL(hAPP(hAPP(c_member(_891547), _891549), _891551)), hBOOL(hAPP(hAPP(_891553, _891549), _891555)), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_891547, tc_fun(_891557, tc_HOL_Obool)), _891551), _891553), _891555)))], (6752 ^ _782435) ^ [_891744, _891746, _891748, _891750, _891752, _891754] : [hBOOL(hAPP(hAPP(c_member(_891744), _891746), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891748, tc_fun(_891744, tc_HOL_Obool)), _891750), _891752))), hBOOL(hAPP(hAPP(c_member(_891748), _891754), _891750)), -(hBOOL(hAPP(hAPP(c_member(_891744), _891746), hAPP(_891752, _891754))))], (6762 ^ _782435) ^ [_891961, _891963, _891965, _891967, _891969, _891971] : [hBOOL(hAPP(hAPP(c_member(_891961), _891963), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_891965, tc_fun(_891961, tc_HOL_Obool)), _891967), _891969))), -(hBOOL(hAPP(hAPP(c_member(_891961), _891963), hAPP(_891969, _891971)))), hBOOL(hAPP(hAPP(c_member(_891965), _891971), _891967))], (6772 ^ _782435) ^ [_892182, _892184, _892186, _892188, _892190, _892192] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892182, tc_fun(_892184, tc_HOL_Obool)), _892186), _892188), _892190)), -(hBOOL(hAPP(hAPP(_892188, _892192), _892190))), hBOOL(hAPP(hAPP(c_member(_892182), _892192), _892186))], (6782 ^ _782435) ^ [_892383, _892385, _892387, _892389, _892391, _892393] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892383, tc_fun(_892385, tc_HOL_Obool)), _892387), _892389), _892391)), hBOOL(hAPP(hAPP(c_member(_892383), _892393), _892387)), -(hBOOL(hAPP(hAPP(_892389, _892393), _892391)))], (6792 ^ _782435) ^ [_892580, _892582, _892584, _892586, _892588, _892590] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892580, tc_fun(_892582, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892584, tc_fun(_892580, tc_HOL_Obool)), _892586), _892588)), _892590) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892584, tc_fun(_892582, tc_HOL_Obool)), _892586), hAPP(hAPP(c_COMBC(_892584, tc_fun(_892580, tc_fun(_892582, tc_HOL_Obool)), tc_fun(_892582, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892580, tc_HOL_Obool), tc_fun(tc_fun(_892580, tc_fun(_892582, tc_HOL_Obool)), tc_fun(_892582, tc_HOL_Obool)), _892584), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892580, tc_fun(_892582, tc_HOL_Obool))), _892588)), _892590)))], (6794 ^ _782435) ^ [_892699, _892701, _892703, _892705, _892707, _892709] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892699, tc_fun(_892701, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892703, tc_fun(_892699, tc_HOL_Obool)), _892705), _892707)), _892709) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892703, tc_fun(_892701, tc_HOL_Obool)), _892705), hAPP(hAPP(c_COMBC(_892703, tc_fun(_892699, tc_fun(_892701, tc_HOL_Obool)), tc_fun(_892701, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892699, tc_HOL_Obool), tc_fun(tc_fun(_892699, tc_fun(_892701, tc_HOL_Obool)), tc_fun(_892701, tc_HOL_Obool)), _892703), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892699, tc_fun(_892701, tc_HOL_Obool))), _892707)), _892709)))], (6796 ^ _782435) ^ [_892818, _892820, _892822, _892824, _892826, _892828] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892818, tc_fun(_892820, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892822, tc_fun(_892818, tc_HOL_Obool)), _892824), _892826)), _892828) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892822, tc_fun(_892820, tc_HOL_Obool)), _892824), hAPP(hAPP(c_COMBC(_892822, tc_fun(_892818, tc_fun(_892820, tc_HOL_Obool)), tc_fun(_892820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_892818, tc_HOL_Obool), tc_fun(tc_fun(_892818, tc_fun(_892820, tc_HOL_Obool)), tc_fun(_892820, tc_HOL_Obool)), _892822), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_892818, tc_fun(_892820, tc_HOL_Obool))), _892826)), _892828)))], (6815 ^ _782435) ^ [_893397, _893399, _893401, _893403, _893405] : [6817 ^ _782435 : [(6818 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893399), 6816 ^ [_893397, _893399, _893401, _893403, _893405]), _893401)))], (6821 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_893397), 6819 ^ [_893397, _893399, _893401, _893403, _893405]), hAPP(_893403, 6816 ^ [_893397, _893399, _893401, _893403, _893405]))))], (6823 ^ _782435) ^ [] : [hBOOL(hAPP(_893405, 6819 ^ [_893397, _893399, _893401, _893403, _893405]))]], 6824 ^ _782435 : [(6825 ^ _782435) ^ [_893707] : [hBOOL(hAPP(hAPP(c_member(_893397), _893707), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893399, tc_fun(_893397, tc_HOL_Obool)), _893401), _893403))), -(hBOOL(hAPP(_893405, _893707)))]]], (6798 ^ _782435) ^ [_892961, _892963, _892965, _892967, _892969] : [6800 ^ _782435 : [(6801 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_892961), 6799 ^ [_892961, _892963, _892965, _892967, _892969]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_892963, tc_fun(_892961, tc_HOL_Obool)), _892965), _892967))))], (6803 ^ _782435) ^ [] : [hBOOL(hAPP(_892969, 6799 ^ [_892961, _892963, _892965, _892967, _892969]))]], 6804 ^ _782435 : [(6805 ^ _782435) ^ [_893183] : [hBOOL(hAPP(hAPP(c_member(_892963), _893183), _892965)), 6808 ^ _782435 : [(6809 ^ _782435) ^ [_893280] : [hBOOL(hAPP(hAPP(c_member(_892961), _893280), hAPP(_892967, _893183))), -(hBOOL(hAPP(_892969, _893280)))]]]]], (6831 ^ _782435) ^ [_893842, _893844, _893846, _893848, _893850, _893852] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893842, tc_fun(_893844, tc_HOL_Obool)), _893846), hAPP(hAPP(c_COMBC(_893842, tc_fun(_893848, tc_fun(_893844, tc_HOL_Obool)), tc_fun(_893844, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_893848, tc_HOL_Obool), tc_fun(tc_fun(_893848, tc_fun(_893844, tc_HOL_Obool)), tc_fun(_893844, tc_HOL_Obool)), _893842), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893848, tc_fun(_893844, tc_HOL_Obool))), _893850)), _893852)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893848, tc_fun(_893844, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893842, tc_fun(_893848, tc_HOL_Obool)), _893846), _893850)), _893852))], (6833 ^ _782435) ^ [_893961, _893963, _893965, _893967, _893969, _893971] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893961, tc_fun(_893963, tc_HOL_Obool)), _893965), hAPP(hAPP(c_COMBC(_893961, tc_fun(_893967, tc_fun(_893963, tc_HOL_Obool)), tc_fun(_893963, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_893967, tc_HOL_Obool), tc_fun(tc_fun(_893967, tc_fun(_893963, tc_HOL_Obool)), tc_fun(_893963, tc_HOL_Obool)), _893961), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893967, tc_fun(_893963, tc_HOL_Obool))), _893969)), _893971)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_893967, tc_fun(_893963, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_893961, tc_fun(_893967, tc_HOL_Obool)), _893965), _893969)), _893971))], (6835 ^ _782435) ^ [_894080, _894082] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_894080, tc_HOL_Obool), hAPP(c_Set_OPow(_894080), _894082)) = _894082)], (6847 ^ _782435) ^ [_894358, _894360, _894362, _894364, _894366] : [6849 ^ _782435 : [(6850 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894358), 6848 ^ [_894358, _894360, _894362, _894364, _894366]), _894362)))], (6852 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_894364, 6848 ^ [_894358, _894360, _894362, _894364, _894366]), _894366))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894358, tc_fun(_894360, tc_HOL_Obool)), _894362), _894364), _894366)))], (6837 ^ _782435) ^ [_894140, _894142, _894144, _894146, _894148] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_894140, tc_fun(_894142, tc_HOL_Obool)), _894144), _894146), _894148)), 6840 ^ _782435 : [(6841 ^ _782435) ^ [_894249] : [hBOOL(hAPP(hAPP(c_member(_894140), _894249), _894144)), -(hBOOL(hAPP(hAPP(_894146, _894249), _894148)))]]], (6856 ^ _782435) ^ [_894605, _894607, _894609, _894611, _894613] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_894605, tc_fun(_894607, tc_HOL_Obool)), _894609), _894611), _894613)), 6860 ^ _782435 : [(6861 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_894605), 6859 ^ [_894605, _894607, _894609, _894611, _894613]), _894609)))], (6863 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_894611, 6859 ^ [_894605, _894607, _894609, _894611, _894613]), _894613)))]]], (6865 ^ _782435) ^ [_894793, _894795, _894797, _894799, _894801] : [-(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_894793, tc_fun(_894795, tc_HOL_Obool)), _894797), _894799), _894801))), 6866 ^ _782435 : [(6867 ^ _782435) ^ [_894865] : [hBOOL(hAPP(hAPP(c_member(_894793), _894865), _894797)), hBOOL(hAPP(hAPP(_894799, _894865), _894801))]]], (6875 ^ _782435) ^ [_895017, _895019, _895021] : [hBOOL(hAPP(hAPP(c_member(_895017), _895019), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895017, tc_HOL_Obool)), _895021))), hBOOL(hAPP(hAPP(c_member(_895017), _895019), _895021))], (6881 ^ _782435) ^ [_895141, _895143, _895145] : [hBOOL(hAPP(hAPP(c_member(_895141), _895143), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895141, tc_HOL_Obool)), _895145))), hBOOL(hAPP(hAPP(c_member(_895141), _895143), _895145))], (6887 ^ _782435) ^ [_895265, _895267, _895269, _895271] : [_895265 = _895267, hBOOL(hAPP(hAPP(c_member(_895269), _895267), _895271)), -(hBOOL(hAPP(hAPP(c_member(_895269), _895265), _895271)))], (6897 ^ _782435) ^ [_895430, _895432, _895434, _895436] : [_895430 = _895432, 6900 ^ _782435 : [(6901 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895434), _895430), _895436)), -(hBOOL(hAPP(hAPP(c_member(_895434), _895432), _895436)))], (6907 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895434), _895432), _895436)), -(hBOOL(hAPP(hAPP(c_member(_895434), _895430), _895436)))]]], (6913 ^ _782435) ^ [_895691, _895693, _895695, _895697] : [_895691 = _895693, 6916 ^ _782435 : [(6917 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895695), _895697), _895691)), -(hBOOL(hAPP(hAPP(c_member(_895695), _895697), _895693)))], (6923 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_895695), _895697), _895693)), -(hBOOL(hAPP(hAPP(c_member(_895695), _895697), _895691)))]]], (6929 ^ _782435) ^ [_895970, _895972, _895974] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895970, tc_HOL_Obool)), _895972) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_895970, tc_HOL_Obool)), _895974), -(_895972 = _895974)], (6935 ^ _782435) ^ [_896077, _896079, _896081] : [_896079 = _896081, -(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896077, tc_HOL_Obool)), _896079) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896077, tc_HOL_Obool)), _896081))], (6941 ^ _782435) ^ [_896208, _896210, _896212] : [hBOOL(hAPP(hAPP(c_member(_896208), _896210), hAPP(c_fequal, _896212))), -(_896210 = _896212)], (6947 ^ _782435) ^ [_896303, _896305, _896307] : [_896305 = _896307, -(hBOOL(hAPP(hAPP(c_member(_896303), _896305), hAPP(c_fequal, _896307))))], (6953 ^ _782435) ^ [_896422, _896424, _896426] : [hBOOL(hAPP(hAPP(c_member(_896422), _896424), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896422, tc_HOL_Obool)), _896426))), hBOOL(hAPP(hAPP(c_member(_896422), _896424), _896426))], (6959 ^ _782435) ^ [_896540, _896542, _896544] : [-(hBOOL(hAPP(hAPP(c_member(_896540), _896542), _896544))), -(hBOOL(hAPP(hAPP(c_member(_896540), _896542), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896540, tc_HOL_Obool)), _896544))))], (6965 ^ _782435) ^ [_896620, _896622, _896624] : [hBOOL(hAPP(hAPP(c_member(_896620), _896622), _896624)), -(hBOOL(hAPP(_896624, _896622)))], (6971 ^ _782435) ^ [_896713, _896715, _896717] : [hBOOL(hAPP(_896717, _896715)), -(hBOOL(hAPP(hAPP(c_member(_896713), _896715), _896717)))], (6977 ^ _782435) ^ [_896812, _896814] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896812, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_896812, tc_HOL_Obool)), _896814)) = _896814)], (6979 ^ _782435) ^ [_896853, _896855] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_896853, tc_HOL_Obool)), _896855), hAPP(c_Set_OPow(_896853), _896855))))], (6981 ^ _782435) ^ [_896893, _896895, _896897] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_896893, tc_HOL_Obool)), _896895), _896897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_896893, tc_HOL_Obool)), _896895), c_Complete__Lattice_OSup__class_OSup(tc_fun(_896893, tc_HOL_Obool), _896897))))], (6987 ^ _782435) ^ [_897024, _897026, _897028] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_897024, tc_HOL_Obool)), _897026), _897028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897024, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_897024, tc_HOL_Obool), _897028)), _897026)))], (6993 ^ _782435) ^ [_897155, _897157, _897159, _897161] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_897155, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897157, tc_fun(_897155, tc_HOL_Obool)), _897159), _897161)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897157, tc_fun(_897155, tc_HOL_Obool)), _897159), hAPP(hAPP(c_COMBB(tc_fun(_897155, tc_HOL_Obool), tc_fun(_897155, tc_HOL_Obool), _897157), c_Groups_Ouminus__class_Ouminus(tc_fun(_897155, tc_HOL_Obool))), _897161)))], (6995 ^ _782435) ^ [_897237, _897239, _897241, _897243] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_897237, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897239, tc_fun(_897237, tc_HOL_Obool)), _897241), _897243)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897239, tc_fun(_897237, tc_HOL_Obool)), _897241), hAPP(hAPP(c_COMBB(tc_fun(_897237, tc_HOL_Obool), tc_fun(_897237, tc_HOL_Obool), _897239), c_Groups_Ouminus__class_Ouminus(tc_fun(_897237, tc_HOL_Obool))), _897243)))], (6997 ^ _782435) ^ [_897319, _897321] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_897319, tc_HOL_Obool), _897321) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897319, tc_HOL_Obool), tc_fun(_897319, tc_HOL_Obool)), _897321), c_COMBI(tc_fun(_897319, tc_HOL_Obool))))], (6999 ^ _782435) ^ [_897370, _897372, _897374, _897376] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_897370, tc_HOL_Obool), tc_fun(_897372, tc_HOL_Obool)), _897374), hAPP(hAPP(c_COMBC(tc_fun(_897370, tc_HOL_Obool), tc_fun(_897370, tc_fun(_897372, tc_HOL_Obool)), tc_fun(_897372, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897370, tc_fun(_897372, tc_HOL_Obool))), _897376)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897370, tc_fun(_897372, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897370, tc_HOL_Obool), _897374)), _897376))], (7001 ^ _782435) ^ [_897460, _897462, _897464, _897466] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897460, tc_HOL_Obool), tc_fun(_897462, tc_HOL_Obool)), _897464), hAPP(hAPP(c_COMBC(tc_fun(_897460, tc_HOL_Obool), tc_fun(_897460, tc_fun(_897462, tc_HOL_Obool)), tc_fun(_897462, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897460, tc_fun(_897462, tc_HOL_Obool))), _897466)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897460, tc_fun(_897462, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897460, tc_HOL_Obool), _897464)), _897466))], (7003 ^ _782435) ^ [_897550, _897552, _897554, _897556] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897550, tc_fun(_897552, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897550, tc_HOL_Obool), _897554)), _897556) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_897550, tc_HOL_Obool), tc_fun(_897552, tc_HOL_Obool)), _897554), hAPP(hAPP(c_COMBC(tc_fun(_897550, tc_HOL_Obool), tc_fun(_897550, tc_fun(_897552, tc_HOL_Obool)), tc_fun(_897552, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_897550, tc_fun(_897552, tc_HOL_Obool))), _897556)))], (7005 ^ _782435) ^ [_897640, _897642, _897644, _897646] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897640, tc_fun(_897642, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_897640, tc_HOL_Obool), _897644)), _897646) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_897640, tc_HOL_Obool), tc_fun(_897642, tc_HOL_Obool)), _897644), hAPP(hAPP(c_COMBC(tc_fun(_897640, tc_HOL_Obool), tc_fun(_897640, tc_fun(_897642, tc_HOL_Obool)), tc_fun(_897642, tc_HOL_Obool)), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_897640, tc_fun(_897642, tc_HOL_Obool))), _897646)))], (7007 ^ _782435) ^ [_897748, _897750, _897752] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_897748, tc_HOL_Obool)), _897750), hAPP(c_Set_OPow(_897748), _897752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897748, tc_HOL_Obool)), _897750), _897752)))], (7013 ^ _782435) ^ [_897873, _897875, _897877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_897873, tc_HOL_Obool)), _897875), _897877)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_897873, tc_HOL_Obool)), _897875), hAPP(c_Set_OPow(_897873), _897877))))], (7019 ^ _782435) ^ [_898004, _898006, _898008] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_898004, tc_HOL_Obool)), _898006), hAPP(c_Set_OPow(_898004), _898008))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_898004, tc_HOL_Obool)), _898006), _898008)))], (7025 ^ _782435) ^ [_898151, _898153, _898155] : [hAPP(hAPP(c_COMBC(_898151, tc_fun(_898151, tc_HOL_Obool), tc_HOL_Obool), c_member(_898151)), _898153) = hAPP(hAPP(c_COMBC(_898151, tc_fun(_898151, tc_HOL_Obool), tc_HOL_Obool), c_member(_898151)), _898155), -(_898153 = _898155)], (7031 ^ _782435) ^ [_898286, _898288, _898290] : [_898288 = _898290, -(hAPP(hAPP(c_COMBC(_898286, tc_fun(_898286, tc_HOL_Obool), tc_HOL_Obool), c_member(_898286)), _898288) = hAPP(hAPP(c_COMBC(_898286, tc_fun(_898286, tc_HOL_Obool), tc_HOL_Obool), c_member(_898286)), _898290))], (7047 ^ _782435) ^ [_898694, _898696, _898698, _898700, _898702] : [7049 ^ _782435 : [(7050 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898698), 7048 ^ [_898694, _898696, _898698, _898700, _898702]), _898700)))], (7052 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_898694), _898696), hAPP(_898702, 7048 ^ [_898694, _898696, _898698, _898700, _898702])))]], -(hBOOL(hAPP(hAPP(c_member(_898694), _898696), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_898698, tc_fun(_898694, tc_HOL_Obool)), _898700), _898702))))], (7037 ^ _782435) ^ [_898451, _898453, _898455, _898457, _898459] : [hBOOL(hAPP(hAPP(c_member(_898451), _898453), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_898455, tc_fun(_898451, tc_HOL_Obool)), _898457), _898459))), 7040 ^ _782435 : [(7041 ^ _782435) ^ [_898575] : [hBOOL(hAPP(hAPP(c_member(_898455), _898575), _898457)), -(hBOOL(hAPP(hAPP(c_member(_898451), _898453), hAPP(_898459, _898575))))]]], (7056 ^ _782435) ^ [_898966, _898968, _898970, _898972, _898974] : [hBOOL(hAPP(hAPP(c_member(_898966), _898968), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_898970, tc_fun(_898966, tc_HOL_Obool)), _898972), _898974))), 7060 ^ _782435 : [(7061 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898970), 7059 ^ [_898966, _898968, _898970, _898972, _898974]), _898972)))], (7063 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_898966), _898968), hAPP(_898974, 7059 ^ [_898966, _898968, _898970, _898972, _898974]))))]]], (7065 ^ _782435) ^ [_899174, _899176, _899178, _899180, _899182] : [-(hBOOL(hAPP(hAPP(c_member(_899174), _899176), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_899178, tc_fun(_899174, tc_HOL_Obool)), _899180), _899182)))), 7066 ^ _782435 : [(7067 ^ _782435) ^ [_899256] : [hBOOL(hAPP(hAPP(c_member(_899178), _899256), _899180)), hBOOL(hAPP(hAPP(c_member(_899174), _899176), hAPP(_899182, _899256)))]]], (7075 ^ _782435) ^ [_899423, _899425, _899427] : [class_Complete__Lattice_Ocomplete__lattice(_899423), hBOOL(hAPP(hAPP(c_member(_899423), _899425), _899427)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899423), _899425), c_Complete__Lattice_OSup__class_OSup(_899423, _899427))))], (7085 ^ _782435) ^ [_899588, _899590, _899592] : [class_Complete__Lattice_Ocomplete__lattice(_899588), hBOOL(hAPP(hAPP(c_member(_899588), _899590), _899592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_899588), c_Complete__Lattice_OInf__class_OInf(_899588, _899592)), _899590)))], (7095 ^ _782435) ^ [_899753, _899755] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_899753, tc_HOL_Obool), _899755) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_899753, tc_HOL_Obool), tc_fun(_899753, tc_HOL_Obool)), _899755), c_COMBI(tc_fun(_899753, tc_HOL_Obool))))], (7097 ^ _782435) ^ [_899822, _899824, _899826] : [hBOOL(hAPP(c_Predicate_OPowp(_899822, hAPP(hAPP(c_COMBC(_899822, tc_fun(_899822, tc_HOL_Obool), tc_HOL_Obool), c_member(_899822)), _899824)), _899826)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_899822, tc_HOL_Obool)), _899826), hAPP(c_Set_OPow(_899822), _899824))))], (7103 ^ _782435) ^ [_899967, _899969, _899971] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_899967, tc_HOL_Obool)), _899971), hAPP(c_Set_OPow(_899967), _899969))), -(hBOOL(hAPP(c_Predicate_OPowp(_899967, hAPP(hAPP(c_COMBC(_899967, tc_fun(_899967, tc_HOL_Obool), tc_HOL_Obool), c_member(_899967)), _899969)), _899971)))], (7109 ^ _782435) ^ [_900118, _900120, _900122, _900124] : [-(hAPP(c_Set_OPow(_900118), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_900120, tc_fun(_900118, tc_HOL_Obool)), _900122), _900124)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_900120, tc_fun(tc_fun(_900118, tc_HOL_Obool), tc_HOL_Obool)), _900122), hAPP(hAPP(c_COMBB(tc_fun(_900118, tc_HOL_Obool), tc_fun(tc_fun(_900118, tc_HOL_Obool), tc_HOL_Obool), _900120), c_Set_OPow(_900118)), _900124)))], (7111 ^ _782435) ^ [_900200, _900202] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_900200, tc_HOL_Obool), tc_HOL_Obool)), _900202), hAPP(c_Set_OPow(_900200), c_Complete__Lattice_OSup__class_OSup(tc_fun(_900200, tc_HOL_Obool), _900202)))))], (7113 ^ _782435) ^ [_900249, _900251, _900253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900249, tc_HOL_Obool)), _900251), _900253)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900249, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900249, tc_HOL_Obool)), _900253)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900249, tc_HOL_Obool)), _900251))))], (7119 ^ _782435) ^ [_900418, _900420, _900422] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900418, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900418, tc_HOL_Obool)), _900420)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900418, tc_HOL_Obool)), _900422))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900418, tc_HOL_Obool)), _900422), _900420)))], (7125 ^ _782435) ^ [_900565, _900567, _900569] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900565, tc_HOL_Obool)), _900569), _900567)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900565, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900565, tc_HOL_Obool)), _900567)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_900565, tc_HOL_Obool)), _900569))))], (7131 ^ _782435) ^ [_900718, _900720, _900722, _900724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900718, tc_HOL_Obool)), _900720), _900722)), hBOOL(hAPP(hAPP(c_member(_900718), _900724), _900720)), -(hBOOL(hAPP(hAPP(c_member(_900718), _900724), _900722)))], (7141 ^ _782435) ^ [_900903, _900905, _900907, _900909] : [hBOOL(hAPP(hAPP(c_member(_900903), _900905), _900907)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_900903, tc_HOL_Obool)), _900907), _900909)), -(hBOOL(hAPP(hAPP(c_member(_900903), _900905), _900909)))], (7151 ^ _782435) ^ [_901088, _901090, _901092, _901094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901088, tc_HOL_Obool)), _901090), _901092)), hBOOL(hAPP(hAPP(c_member(_901088), _901094), _901090)), -(hBOOL(hAPP(hAPP(c_member(_901088), _901094), _901092)))], (7161 ^ _782435) ^ [_901291, _901293, _901295] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901291, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_901291, tc_fun(_901291, tc_HOL_Obool), tc_HOL_Obool), c_member(_901291)), _901293)), hAPP(hAPP(c_COMBC(_901291, tc_fun(_901291, tc_HOL_Obool), tc_HOL_Obool), c_member(_901291)), _901295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901291, tc_HOL_Obool)), _901293), _901295)))], (7167 ^ _782435) ^ [_901466, _901468, _901470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901466, tc_HOL_Obool)), _901468), _901470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901466, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_901466, tc_fun(_901466, tc_HOL_Obool), tc_HOL_Obool), c_member(_901466)), _901468)), hAPP(hAPP(c_COMBC(_901466, tc_fun(_901466, tc_HOL_Obool), tc_HOL_Obool), c_member(_901466)), _901470))))], (7173 ^ _782435) ^ [_901647, _901649, _901651, _901653, _901655] : [hBOOL(hAPP(hAPP(c_member(_901647), _901649), _901651)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901653, tc_HOL_Obool)), hAPP(_901655, _901649)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_901647, tc_fun(_901653, tc_HOL_Obool)), _901651), _901655))))], (7179 ^ _782435) ^ [_901794, _901796, _901798, _901800, _901802] : [hBOOL(hAPP(hAPP(c_member(_901794), _901796), _901798)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_901800, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_901794, tc_fun(_901800, tc_HOL_Obool)), _901798), _901802)), hAPP(_901802, _901796))))], (7185 ^ _782435) ^ [_901941, _901943, _901945] : [class_Complete__Lattice_Ocomplete__lattice(_901941), 7188 ^ _782435 : [(7199 ^ _782435) ^ [] : [7201 ^ _782435 : [(7202 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_901941), 7200 ^ [_901941, _901943, _901945]), _901943)))], (7204 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901941), 7200 ^ [_901941, _901943, _901945]), _901945))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901941), c_Complete__Lattice_OSup__class_OSup(_901941, _901943)), _901945)))], (7189 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901941), c_Complete__Lattice_OSup__class_OSup(_901941, _901943)), _901945)), 7192 ^ _782435 : [(7193 ^ _782435) ^ [_902099] : [hBOOL(hAPP(hAPP(c_member(_901941), _902099), _901943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_901941), _902099), _901945)))]]]]], (7208 ^ _782435) ^ [_902375, _902377, _902379] : [class_Complete__Lattice_Ocomplete__lattice(_902375), 7211 ^ _782435 : [(7222 ^ _782435) ^ [] : [7224 ^ _782435 : [(7225 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_902375), 7223 ^ [_902375, _902377, _902379]), _902379)))], (7227 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902375), _902377), 7223 ^ [_902375, _902377, _902379]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902375), _902377), c_Complete__Lattice_OInf__class_OInf(_902375, _902379))))], (7212 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902375), _902377), c_Complete__Lattice_OInf__class_OInf(_902375, _902379))), 7215 ^ _782435 : [(7216 ^ _782435) ^ [_902533] : [hBOOL(hAPP(hAPP(c_member(_902375), _902533), _902379)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902375), _902377), _902533)))]]]]], (7231 ^ _782435) ^ [_902809, _902811, _902813, _902815] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_902809, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_902811, tc_fun(tc_fun(_902809, tc_HOL_Obool), tc_HOL_Obool)), _902813), hAPP(hAPP(c_COMBB(tc_fun(_902809, tc_HOL_Obool), tc_fun(tc_fun(_902809, tc_HOL_Obool), tc_HOL_Obool), _902811), c_Set_OPow(_902809)), _902815))), hAPP(c_Set_OPow(_902809), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_902811, tc_fun(_902809, tc_HOL_Obool)), _902813), _902815)))))], (7233 ^ _782435) ^ [_902904, _902906, _902908] : [class_Orderings_Oord(_902904), 7236 ^ _782435 : [(7237 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_902904), _902906), hAPP(c_SetInterval_Oord__class_OatMost(_902904), _902908))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902904), _902906), _902908)))], (7243 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_902904), _902906), _902908)), -(hBOOL(hAPP(hAPP(c_member(_902904), _902906), hAPP(c_SetInterval_Oord__class_OatMost(_902904), _902908))))]]], (7249 ^ _782435) ^ [_903172, _903174, _903176] : [class_Orderings_Oord(_903172), 7252 ^ _782435 : [(7253 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_903172), _903174), hAPP(c_SetInterval_Oord__class_OatLeast(_903172), _903176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903172), _903176), _903174)))], (7259 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_903172), _903176), _903174)), -(hBOOL(hAPP(hAPP(c_member(_903172), _903174), hAPP(c_SetInterval_Oord__class_OatLeast(_903172), _903176))))]]], (7265 ^ _782435) ^ [_903440, _903442, _903444, _903446] : [class_Groups_Ouminus(_903440), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_903442, _903440)), _903444), _903446) = hAPP(c_Groups_Ouminus__class_Ouminus(_903440), hAPP(_903444, _903446)))], (7271 ^ _782435) ^ [_903557, _903559, _903561, _903563] : [class_Groups_Ouminus(_903557), -(hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_903559, _903557)), _903561), _903563) = hAPP(c_Groups_Ouminus__class_Ouminus(_903557), hAPP(_903561, _903563)))], (7277 ^ _782435) ^ [_903701, _903703, _903705, _903707, _903709, _903711] : [hBOOL(hAPP(hAPP(c_member(_903701), _903703), c_SetInterval_Oord_OgreaterThanAtMost(_903701, _903705, _903707, _903709, _903711))), 7280 ^ _782435 : [(7281 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_903707, _903709), _903703)))], (7283 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_903705, _903703), _903711)))]]], (7285 ^ _782435) ^ [_903854, _903856, _903858, _903860, _903862, _903864] : [-(hBOOL(hAPP(hAPP(c_member(_903854), _903856), c_SetInterval_Oord_OgreaterThanAtMost(_903854, _903858, _903860, _903862, _903864)))), hBOOL(hAPP(hAPP(_903860, _903862), _903856)), hBOOL(hAPP(hAPP(_903858, _903856), _903864))], (7295 ^ _782435) ^ [_904074, _904076, _904078, _904080, _904082, _904084] : [hBOOL(hAPP(hAPP(c_member(_904074), _904076), c_SetInterval_Oord_OatLeastLessThan(_904074, _904078, _904080, _904082, _904084))), 7298 ^ _782435 : [(7299 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_904078, _904082), _904076)))], (7301 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_904080, _904076), _904084)))]]], (7303 ^ _782435) ^ [_904227, _904229, _904231, _904233, _904235, _904237] : [-(hBOOL(hAPP(hAPP(c_member(_904227), _904229), c_SetInterval_Oord_OatLeastLessThan(_904227, _904231, _904233, _904235, _904237)))), hBOOL(hAPP(hAPP(_904231, _904235), _904229)), hBOOL(hAPP(hAPP(_904233, _904229), _904237))], (7313 ^ _782435) ^ [_904444, _904446, _904448, _904450, _904452] : [hBOOL(hAPP(hAPP(c_member(_904444), _904446), c_SetInterval_Oord_OgreaterThanLessThan(_904444, _904448, _904450, _904452))), 7316 ^ _782435 : [(7317 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_904448, _904450), _904446)))], (7319 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_904448, _904446), _904452)))]]], (7321 ^ _782435) ^ [_904593, _904595, _904597, _904599, _904601] : [-(hBOOL(hAPP(hAPP(c_member(_904593), _904595), c_SetInterval_Oord_OgreaterThanLessThan(_904593, _904597, _904599, _904601)))), hBOOL(hAPP(hAPP(_904597, _904599), _904595)), hBOOL(hAPP(hAPP(_904597, _904595), _904601))], (7331 ^ _782435) ^ [_904804, _904806, _904808, _904810, _904812] : [hBOOL(hAPP(hAPP(c_member(_904804), _904806), c_SetInterval_Oord_OatLeastAtMost(_904804, _904808, _904810, _904812))), 7334 ^ _782435 : [(7335 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_904808, _904810), _904806)))], (7337 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_904808, _904806), _904812)))]]], (7339 ^ _782435) ^ [_904953, _904955, _904957, _904959, _904961] : [-(hBOOL(hAPP(hAPP(c_member(_904953), _904955), c_SetInterval_Oord_OatLeastAtMost(_904953, _904957, _904959, _904961)))), hBOOL(hAPP(hAPP(_904957, _904959), _904955)), hBOOL(hAPP(hAPP(_904957, _904955), _904961))], (7349 ^ _782435) ^ [_905161, _905163, _905165, _905167] : [hBOOL(hAPP(hAPP(c_member(_905161), _905163), c_SetInterval_Oord_OgreaterThan(_905161, _905165, _905167))), -(hBOOL(hAPP(hAPP(_905165, _905167), _905163)))], (7355 ^ _782435) ^ [_905270, _905272, _905274, _905276] : [hBOOL(hAPP(hAPP(_905274, _905276), _905272)), -(hBOOL(hAPP(hAPP(c_member(_905270), _905272), c_SetInterval_Oord_OgreaterThan(_905270, _905274, _905276))))], (7361 ^ _782435) ^ [_905406, _905408, _905410, _905412] : [hBOOL(hAPP(hAPP(c_member(_905406), _905408), c_SetInterval_Oord_OlessThan(_905406, _905410, _905412))), -(hBOOL(hAPP(hAPP(_905410, _905408), _905412)))], (7367 ^ _782435) ^ [_905515, _905517, _905519, _905521] : [hBOOL(hAPP(hAPP(_905519, _905517), _905521)), -(hBOOL(hAPP(hAPP(c_member(_905515), _905517), c_SetInterval_Oord_OlessThan(_905515, _905519, _905521))))], (7373 ^ _782435) ^ [_905651, _905653, _905655, _905657] : [hBOOL(hAPP(hAPP(c_member(_905651), _905653), c_SetInterval_Oord_OatLeast(_905651, _905655, _905657))), -(hBOOL(hAPP(hAPP(_905655, _905657), _905653)))], (7379 ^ _782435) ^ [_905760, _905762, _905764, _905766] : [hBOOL(hAPP(hAPP(_905764, _905766), _905762)), -(hBOOL(hAPP(hAPP(c_member(_905760), _905762), c_SetInterval_Oord_OatLeast(_905760, _905764, _905766))))], (7385 ^ _782435) ^ [_905896, _905898, _905900, _905902] : [hBOOL(hAPP(hAPP(c_member(_905896), _905898), c_SetInterval_Oord_OatMost(_905896, _905900, _905902))), -(hBOOL(hAPP(hAPP(_905900, _905898), _905902)))], (7391 ^ _782435) ^ [_906005, _906007, _906009, _906011] : [hBOOL(hAPP(hAPP(_906009, _906007), _906011)), -(hBOOL(hAPP(hAPP(c_member(_906005), _906007), c_SetInterval_Oord_OatMost(_906005, _906009, _906011))))], (7397 ^ _782435) ^ [_906120, _906122, _906124] : [class_Lattices_Oboolean__algebra(_906120), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906120), _906122), _906124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906120), hAPP(c_Groups_Ouminus__class_Ouminus(_906120), _906124)), hAPP(c_Groups_Ouminus__class_Ouminus(_906120), _906122))))], (7407 ^ _782435) ^ [_906299, _906301, _906303] : [class_Groups_Oordered__ab__group__add(_906299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906299), _906301), _906303)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_906299), hAPP(c_Groups_Ouminus__class_Ouminus(_906299), _906303)), hAPP(c_Groups_Ouminus__class_Ouminus(_906299), _906301))))], (7417 ^ _782435) ^ [_906508, _906510, _906512, _906514, _906516, _906518, _906520] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_906508, tc_fun(_906510, tc_fun(_906512, tc_HOL_Obool))), _906514), _906516), _906518), _906520)), 7421 ^ _782435 : [(7422 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_906508), 7420 ^ [_906508, _906510, _906512, _906514, _906516, _906518, _906520]), _906514)))], (7424 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_906516, 7420 ^ [_906508, _906510, _906512, _906514, _906516, _906518, _906520]), _906518), _906520)))]]], (7426 ^ _782435) ^ [_906726, _906728, _906730, _906732, _906734, _906736, _906738] : [-(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_906726, tc_fun(_906728, tc_fun(_906730, tc_HOL_Obool))), _906732), _906734), _906736), _906738))), 7427 ^ _782435 : [(7428 ^ _782435) ^ [_906811] : [hBOOL(hAPP(hAPP(c_member(_906726), _906811), _906732)), hBOOL(hAPP(hAPP(hAPP(_906734, _906811), _906736), _906738))]]], (7446 ^ _782435) ^ [_907256, _907258, _907260, _907262, _907264, _907266, _907268] : [7448 ^ _782435 : [(7449 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_907256), 7447 ^ [_907256, _907258, _907260, _907262, _907264, _907266, _907268]), _907262)))], (7451 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_907264, 7447 ^ [_907256, _907258, _907260, _907262, _907264, _907266, _907268]), _907266), _907268))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_907256, tc_fun(_907258, tc_fun(_907260, tc_HOL_Obool))), _907262), _907264), _907266), _907268)))], (7436 ^ _782435) ^ [_907009, _907011, _907013, _907015, _907017, _907019, _907021] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_907009, tc_fun(_907011, tc_fun(_907013, tc_HOL_Obool))), _907015), _907017), _907019), _907021)), 7439 ^ _782435 : [(7440 ^ _782435) ^ [_907137] : [hBOOL(hAPP(hAPP(c_member(_907009), _907137), _907015)), -(hBOOL(hAPP(hAPP(hAPP(_907017, _907137), _907019), _907021)))]]], (7455 ^ _782435) ^ [_907516, _907518, _907520] : [class_Lattices_Oboolean__algebra(_907516), 7458 ^ _782435 : [(7459 ^ _782435) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907516), _907518) = hAPP(c_Groups_Ouminus__class_Ouminus(_907516), _907520), -(_907518 = _907520)], (7465 ^ _782435) ^ [] : [_907518 = _907520, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907516), _907518) = hAPP(c_Groups_Ouminus__class_Ouminus(_907516), _907520))]]], (7471 ^ _782435) ^ [_907757, _907759, _907761] : [class_Groups_Ogroup__add(_907757), 7474 ^ _782435 : [(7475 ^ _782435) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907757), _907759) = hAPP(c_Groups_Ouminus__class_Ouminus(_907757), _907761), -(_907759 = _907761)], (7481 ^ _782435) ^ [] : [_907759 = _907761, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907757), _907759) = hAPP(c_Groups_Ouminus__class_Ouminus(_907757), _907761))]]], (7487 ^ _782435) ^ [_907998, _908000, _908002] : [class_Groups_Ogroup__add(_907998), 7490 ^ _782435 : [(7491 ^ _782435) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907998), _908000) = _908002, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907998), _908002) = _908000)], (7497 ^ _782435) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_907998), _908002) = _908000, -(hAPP(c_Groups_Ouminus__class_Ouminus(_907998), _908000) = _908002)]]], (7503 ^ _782435) ^ [_908239, _908241, _908243] : [class_Groups_Ogroup__add(_908239), 7506 ^ _782435 : [(7507 ^ _782435) ^ [] : [_908241 = hAPP(c_Groups_Ouminus__class_Ouminus(_908239), _908243), -(_908243 = hAPP(c_Groups_Ouminus__class_Ouminus(_908239), _908241))], (7513 ^ _782435) ^ [] : [_908243 = hAPP(c_Groups_Ouminus__class_Ouminus(_908239), _908241), -(_908241 = hAPP(c_Groups_Ouminus__class_Ouminus(_908239), _908243))]]], (7519 ^ _782435) ^ [_908480, _908482] : [class_Lattices_Oboolean__algebra(_908480), -(hAPP(c_Groups_Ouminus__class_Ouminus(_908480), hAPP(c_Groups_Ouminus__class_Ouminus(_908480), _908482)) = _908482)], (7525 ^ _782435) ^ [_908575, _908577] : [class_Groups_Ogroup__add(_908575), -(hAPP(c_Groups_Ouminus__class_Ouminus(_908575), hAPP(c_Groups_Ouminus__class_Ouminus(_908575), _908577)) = _908577)], (7531 ^ _782435) ^ [_908670, _908672, _908674] : [class_Groups_Oordered__ab__group__add(_908670), 7534 ^ _782435 : [(7535 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908670), _908672), hAPP(c_Groups_Ouminus__class_Ouminus(_908670), _908674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908670), _908674), hAPP(c_Groups_Ouminus__class_Ouminus(_908670), _908672))))], (7541 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908670), _908674), hAPP(c_Groups_Ouminus__class_Ouminus(_908670), _908672))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908670), _908672), hAPP(c_Groups_Ouminus__class_Ouminus(_908670), _908674))))]]], (7547 ^ _782435) ^ [_908953, _908955, _908957] : [class_Groups_Oordered__ab__group__add(_908953), 7550 ^ _782435 : [(7551 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908953), hAPP(c_Groups_Ouminus__class_Ouminus(_908953), _908955)), _908957)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908953), hAPP(c_Groups_Ouminus__class_Ouminus(_908953), _908957)), _908955)))], (7557 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908953), hAPP(c_Groups_Ouminus__class_Ouminus(_908953), _908957)), _908955)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_908953), hAPP(c_Groups_Ouminus__class_Ouminus(_908953), _908955)), _908957)))]]], (7563 ^ _782435) ^ [_909236, _909238, _909240] : [class_Groups_Oordered__ab__group__add(_909236), 7566 ^ _782435 : [(7567 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909236), hAPP(c_Groups_Ouminus__class_Ouminus(_909236), _909238)), hAPP(c_Groups_Ouminus__class_Ouminus(_909236), _909240))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909236), _909240), _909238)))], (7573 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909236), _909240), _909238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909236), hAPP(c_Groups_Ouminus__class_Ouminus(_909236), _909238)), hAPP(c_Groups_Ouminus__class_Ouminus(_909236), _909240))))]]], (7579 ^ _782435) ^ [_909519, _909521, _909523] : [class_Lattices_Oboolean__algebra(_909519), 7582 ^ _782435 : [(7583 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909519), hAPP(c_Groups_Ouminus__class_Ouminus(_909519), _909521)), hAPP(c_Groups_Ouminus__class_Ouminus(_909519), _909523))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909519), _909523), _909521)))], (7589 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909519), _909523), _909521)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_909519), hAPP(c_Groups_Ouminus__class_Ouminus(_909519), _909521)), hAPP(c_Groups_Ouminus__class_Ouminus(_909519), _909523))))]]], (7595 ^ _782435) ^ [_909802, _909804, _909806] : [7597 ^ _782435 : [(7598 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_909802, tc_HOL_Obool)), 7596 ^ [_909802, _909804, _909806]), _909804)))], (7600 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_909802), _909806), 7596 ^ [_909802, _909804, _909806]))]], -(hBOOL(hAPP(hAPP(c_member(_909802), _909806), c_Complete__Lattice_OInf__class_OInf(tc_fun(_909802, tc_HOL_Obool), _909804))))], (7604 ^ _782435) ^ [_910018, _910020, _910022] : [hBOOL(hAPP(hAPP(c_member(_910018), _910020), c_Complete__Lattice_OSup__class_OSup(tc_fun(_910018, tc_HOL_Obool), _910022))), 7608 ^ _782435 : [(7609 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910018), _910020), 7607 ^ [_910018, _910020, _910022])))], (7611 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_910018, tc_HOL_Obool)), 7607 ^ [_910018, _910020, _910022]), _910022)))]]], (7613 ^ _782435) ^ [_910210, _910212, _910214, _910216, _910218, _910220, _910222] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_910210, tc_fun(_910212, tc_fun(_910214, tc_HOL_Obool))), _910216), _910218), _910220), _910222)), 7617 ^ _782435 : [(7618 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910210), 7616 ^ [_910210, _910212, _910214, _910216, _910218, _910220, _910222]), _910216)))], (7620 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(hAPP(_910218, 7616 ^ [_910210, _910212, _910214, _910216, _910218, _910220, _910222]), _910220), _910222)))]]], (7622 ^ _782435) ^ [_910436, _910438, _910440, _910442, _910444, _910446, _910448] : [7624 ^ _782435 : [(7625 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_910436), 7623 ^ [_910436, _910438, _910440, _910442, _910444, _910446, _910448]), _910438)))], (7627 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(hAPP(_910440, 7623 ^ [_910436, _910438, _910440, _910442, _910444, _910446, _910448]), _910442), _910444))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_910436, tc_fun(_910446, tc_fun(_910448, tc_HOL_Obool))), _910438), _910440), _910442), _910444)))], (7631 ^ _782435) ^ [_910694, _910696, _910698] : [class_Orderings_Olinorder(_910694), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910694), _910696), _910698)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910694, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_910694, _910696, _910698)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_910694), _910698)) = hAPP(c_SetInterval_Oord__class_OatLeast(_910694), _910696))], (7641 ^ _782435) ^ [_910889, _910891, _910893] : [class_Orderings_Olinorder(_910889), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_910889), _910891), _910893)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_910889, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_910889), _910891)), c_SetInterval_Oord__class_OatLeastAtMost(_910889, _910891, _910893)) = hAPP(c_SetInterval_Oord__class_OatMost(_910889), _910893))], (7651 ^ _782435) ^ [_911084, _911086, _911088, _911090, _911092] : [7653 ^ _782435 : [(7654 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911084), 7652 ^ [_911084, _911086, _911088, _911090, _911092]), _911086)))], (7656 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911088, tc_HOL_Obool)), _911090), hAPP(_911092, 7652 ^ [_911084, _911086, _911088, _911090, _911092])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911088, tc_HOL_Obool)), _911090), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911084, tc_fun(_911088, tc_HOL_Obool)), _911086), _911092))))], (7660 ^ _782435) ^ [_911345, _911347, _911349, _911351, _911353, _911355] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911345, tc_HOL_Obool)), _911347), _911349)), 7666 ^ _782435 : [(7667 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911345), 7665 ^ [_911345, _911347, _911349, _911351, _911353, _911355]), _911349)))], (7669 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911351, tc_HOL_Obool)), hAPP(_911353, 7665 ^ [_911345, _911347, _911349, _911351, _911353, _911355])), hAPP(_911355, 7665 ^ [_911345, _911347, _911349, _911351, _911353, _911355])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911351, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911345, tc_fun(_911351, tc_HOL_Obool)), _911349), _911353)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_911345, tc_fun(_911351, tc_HOL_Obool)), _911349), _911355))))], (7673 ^ _782435) ^ [_911742, _911744, _911746, _911748, _911750] : [7675 ^ _782435 : [(7676 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_911742), 7674 ^ [_911742, _911744, _911746, _911748, _911750]), _911744)))], (7678 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911746, tc_HOL_Obool)), hAPP(_911748, 7674 ^ [_911742, _911744, _911746, _911748, _911750])), _911750))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_911746, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_911742, tc_fun(_911746, tc_HOL_Obool)), _911744), _911748)), _911750)))], (7682 ^ _782435) ^ [_912003, _912005, _912007, _912009, _912011, _912013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912003, tc_HOL_Obool)), _912005), _912007)), 7688 ^ _782435 : [(7689 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912003), 7687 ^ [_912003, _912005, _912007, _912009, _912011, _912013]), _912005)))], (7691 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912009, tc_HOL_Obool)), hAPP(_912011, 7687 ^ [_912003, _912005, _912007, _912009, _912011, _912013])), hAPP(_912013, 7687 ^ [_912003, _912005, _912007, _912009, _912011, _912013])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_912009, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_912003, tc_fun(_912009, tc_HOL_Obool)), _912005), _912011)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_912003, tc_fun(_912009, tc_HOL_Obool)), _912007), _912013))))], (7695 ^ _782435) ^ [_912400, _912402, _912404, _912406, _912408] : [class_Complete__Lattice_Ocomplete__lattice(_912400), 7701 ^ _782435 : [(7702 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_912402), 7700 ^ [_912400, _912402, _912404, _912406, _912408]), _912404)))], (7704 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912400), _912406), hAPP(_912408, 7700 ^ [_912400, _912402, _912404, _912406, _912408])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_912400), _912406), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_912402, _912400), _912404), _912408))))], (7708 ^ _782435) ^ [_912696, _912698, _912700, _912702] : [7709 ^ _782435 : [(7710 ^ _782435) ^ [] : [hBOOL(hAPP(_912696, _912698))], (7712 ^ _782435) ^ [] : [hBOOL(hAPP(_912700, _912698))]], -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912702, tc_HOL_Obool)), _912700), _912696), _912698)))], (7716 ^ _782435) ^ [_912851, _912853, _912855, _912857] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912851, tc_HOL_Obool)), _912853), _912855), _912857)), -(hBOOL(hAPP(_912853, _912857))), -(hBOOL(hAPP(_912855, _912857)))], (7726 ^ _782435) ^ [_912981, _912983, _912985, _912987] : [7727 ^ _782435 : [(7728 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912981), _912983), _912985))], (7730 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_912981), _912983), _912987))]], -(hBOOL(hAPP(hAPP(c_member(_912981), _912983), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_912981, tc_HOL_Obool)), _912987), _912985))))], (7734 ^ _782435) ^ [_913166, _913168, _913170, _913172] : [hBOOL(hAPP(hAPP(c_member(_913166), _913168), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913166, tc_HOL_Obool)), _913170), _913172))), -(hBOOL(hAPP(hAPP(c_member(_913166), _913168), _913170))), -(hBOOL(hAPP(hAPP(c_member(_913166), _913168), _913172)))], (7744 ^ _782435) ^ [_913326, _913328, _913330, _913332, _913334] : [class_Lattices_Olattice(_913326), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_913328, _913326)), _913330), _913332), _913334) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913326), hAPP(_913330, _913334)), hAPP(_913332, _913334)))], (7750 ^ _782435) ^ [_913463, _913465, _913467, _913469] : [class_Lattices_Osemilattice__sup(_913463), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913463), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913463), _913465), _913467)), _913469) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913463), _913465), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913463), _913467), _913469)))], (7756 ^ _782435) ^ [_913606, _913608, _913610, _913612] : [class_Lattices_Olattice(_913606), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913606), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913606), _913608), _913610)), _913612) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913606), _913608), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913606), _913610), _913612)))], (7762 ^ _782435) ^ [_913749, _913751, _913753, _913755] : [class_Lattices_Osemilattice__sup(_913749), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913749), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913749), _913751), _913753)), _913755) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913749), _913751), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913749), _913753), _913755)))], (7768 ^ _782435) ^ [_913892, _913894, _913896, _913898] : [class_Lattices_Osemilattice__sup(_913892), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913892), _913894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913892), _913896), _913898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913892), _913896), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_913892), _913894), _913898)))], (7774 ^ _782435) ^ [_914035, _914037, _914039, _914041] : [class_Lattices_Olattice(_914035), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914035), _914037), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914035), _914039), _914041)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914035), _914039), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914035), _914037), _914041)))], (7780 ^ _782435) ^ [_914178, _914180, _914182, _914184] : [class_Lattices_Osemilattice__sup(_914178), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914178), _914180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914178), _914182), _914184)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914178), _914182), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914178), _914180), _914184)))], (7786 ^ _782435) ^ [_914321, _914323, _914325] : [class_Lattices_Osemilattice__sup(_914321), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914321), _914323), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914321), _914323), _914325)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914321), _914323), _914325))], (7792 ^ _782435) ^ [_914446, _914448, _914450] : [class_Lattices_Olattice(_914446), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914446), _914448), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914446), _914448), _914450)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914446), _914448), _914450))], (7798 ^ _782435) ^ [_914571, _914573, _914575] : [class_Lattices_Osemilattice__sup(_914571), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914571), _914573), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914571), _914573), _914575)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914571), _914573), _914575))], (7804 ^ _782435) ^ [_914696, _914698, _914700] : [class_Lattices_Osemilattice__sup(_914696), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914696), _914698), _914700) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914696), _914700), _914698))], (7810 ^ _782435) ^ [_914805, _914807, _914809] : [class_Lattices_Olattice(_914805), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914805), _914807), _914809) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914805), _914809), _914807))], (7816 ^ _782435) ^ [_914914, _914916, _914918] : [class_Lattices_Osemilattice__sup(_914914), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914914), _914916), _914918) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_914914), _914918), _914916))], (7822 ^ _782435) ^ [_915023, _915025, _915027, _915029, _915031] : [class_Lattices_Olattice(_915023), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915025, _915023)), _915027), _915029), _915031) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915023), hAPP(_915027, _915031)), hAPP(_915029, _915031)))], (7828 ^ _782435) ^ [_915160, _915162] : [class_Lattices_Osemilattice__sup(_915160), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915160), _915162), _915162) = _915162)], (7834 ^ _782435) ^ [_915251, _915253] : [class_Lattices_Osemilattice__sup(_915251), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_915251), _915253), _915253) = _915253)], (7840 ^ _782435) ^ [_915342, _915344, _915346, _915348] : [hBOOL(hAPP(_915342, _915344)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915346, tc_HOL_Obool)), _915348), _915342), _915344)))], (7846 ^ _782435) ^ [_915453, _915455, _915457, _915459] : [hBOOL(hAPP(_915453, _915455)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915457, tc_HOL_Obool)), _915453), _915459), _915455)))], (7871 ^ _782435) ^ [_916007, _916009, _916011, _916013] : [7875 ^ _782435 : [(7876 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916007), 7874 ^ [_916007, _916009, _916011, _916013]), _916009)))], (7878 ^ _782435) ^ [] : [hBOOL(hAPP(_916013, 7874 ^ [_916007, _916009, _916011, _916013]))]], 7880 ^ _782435 : [(7881 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916007), 7879 ^ [_916007, _916009, _916011, _916013]), _916011)))], (7883 ^ _782435) ^ [] : [hBOOL(hAPP(_916013, 7879 ^ [_916007, _916009, _916011, _916013]))]], 7884 ^ _782435 : [(7885 ^ _782435) ^ [_916340] : [hBOOL(hAPP(hAPP(c_member(_916007), _916340), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916007, tc_HOL_Obool)), _916009), _916011))), -(hBOOL(hAPP(_916013, _916340)))]]], (7852 ^ _782435) ^ [_915585, _915587, _915589, _915591] : [7854 ^ _782435 : [(7855 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_915585), 7853 ^ [_915585, _915587, _915589, _915591]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_915585, tc_HOL_Obool)), _915587), _915589))))], (7857 ^ _782435) ^ [] : [hBOOL(hAPP(_915591, 7853 ^ [_915585, _915587, _915589, _915591]))]], 7858 ^ _782435 : [(7859 ^ _782435) ^ [_915805] : [hBOOL(hAPP(hAPP(c_member(_915585), _915805), _915587)), -(hBOOL(hAPP(_915591, _915805)))], (7865 ^ _782435) ^ [_915902] : [hBOOL(hAPP(hAPP(c_member(_915585), _915902), _915589)), -(hBOOL(hAPP(_915591, _915902)))]]], (7891 ^ _782435) ^ [_916492, _916494, _916496, _916498] : [7892 ^ _782435 : [(7893 ^ _782435) ^ [_916602] : [hBOOL(hAPP(hAPP(c_member(_916492), _916602), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916492, tc_HOL_Obool)), _916494), _916496))), hBOOL(hAPP(_916498, _916602))]], 7901 ^ _782435 : [(7902 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916492), 7900 ^ [_916492, _916494, _916496, _916498]), _916494)))], (7904 ^ _782435) ^ [] : [-(hBOOL(hAPP(_916498, 7900 ^ [_916492, _916494, _916496, _916498])))]], 7906 ^ _782435 : [(7907 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916492), 7905 ^ [_916492, _916494, _916496, _916498]), _916496)))], (7909 ^ _782435) ^ [] : [-(hBOOL(hAPP(_916498, 7905 ^ [_916492, _916494, _916496, _916498])))]]], (7911 ^ _782435) ^ [_916891, _916893, _916895, _916897] : [7925 ^ _782435 : [(7926 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_916891), 7924 ^ [_916891, _916893, _916895, _916897]), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_916891, tc_HOL_Obool)), _916893), _916895))))], (7928 ^ _782435) ^ [] : [-(hBOOL(hAPP(_916897, 7924 ^ [_916891, _916893, _916895, _916897])))]], 7912 ^ _782435 : [(7913 ^ _782435) ^ [_917004] : [hBOOL(hAPP(hAPP(c_member(_916891), _917004), _916893)), hBOOL(hAPP(_916897, _917004))], (7919 ^ _782435) ^ [_917100] : [hBOOL(hAPP(hAPP(c_member(_916891), _917100), _916895)), hBOOL(hAPP(_916897, _917100))]]], (7930 ^ _782435) ^ [_917294, _917296, _917298, _917300] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917294, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917294, tc_HOL_Obool)), _917296), _917298)), _917300) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917294, tc_HOL_Obool)), _917296), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917294, tc_HOL_Obool)), _917298), _917300)))], (7932 ^ _782435) ^ [_917367, _917369, _917371, _917373] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917367, tc_HOL_Obool)), _917369), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917367, tc_HOL_Obool)), _917371), _917373)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917367, tc_HOL_Obool)), _917371), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917367, tc_HOL_Obool)), _917369), _917373)))], (7934 ^ _782435) ^ [_917440, _917442, _917444] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917440, tc_HOL_Obool)), _917442), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917440, tc_HOL_Obool)), _917442), _917444)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917440, tc_HOL_Obool)), _917442), _917444))], (7936 ^ _782435) ^ [_917500, _917502, _917504] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917500, tc_HOL_Obool)), _917502), _917504) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917500, tc_HOL_Obool)), _917504), _917502))], (7938 ^ _782435) ^ [_917549, _917551] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917549, tc_HOL_Obool)), _917551), _917551) = _917551)], (7940 ^ _782435) ^ [_917585, _917587, _917589] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_917585, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_917585, tc_HOL_Obool), tc_HOL_Obool)), _917587), _917589)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_917585, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917585, tc_HOL_Obool), _917587)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_917585, tc_HOL_Obool), _917589)))], (7942 ^ _782435) ^ [_917655, _917657, _917659, _917661] : [class_Lattices_Osemilattice__sup(_917655), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917655), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917655), _917657), _917659)), _917661)), 7949 ^ _782435 : [(7950 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917655), _917657), _917661)))], (7952 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917655), _917659), _917661)))]]], (7954 ^ _782435) ^ [_917878, _917880, _917882, _917884, _917886] : [class_Lattices_Osemilattice__sup(_917878), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917878), _917880), _917882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917878), _917884), _917886)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_917878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917878), _917880), _917884)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_917878), _917882), _917886))))], (7968 ^ _782435) ^ [_918149, _918151, _918153, _918155] : [class_Lattices_Osemilattice__sup(_918149), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918149), _918151), _918153)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918149), _918155), _918153)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918149), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918149), _918151), _918155)), _918153)))], (7982 ^ _782435) ^ [_918398, _918400, _918402, _918404] : [class_Lattices_Osemilattice__sup(_918398), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918398), _918400), _918402)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918398), _918404), _918402)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918398), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918398), _918400), _918404)), _918402)))], (7996 ^ _782435) ^ [_918647, _918649, _918651] : [class_Lattices_Osemilattice__sup(_918647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918647), _918649), _918651)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918647), _918651), _918649) = _918651)], (8006 ^ _782435) ^ [_918808, _918810, _918812] : [class_Lattices_Osemilattice__sup(_918808), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918808), _918810), _918812)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918808), _918810), _918812) = _918812)], (8016 ^ _782435) ^ [_918969, _918971, _918973, _918975] : [class_Lattices_Osemilattice__sup(_918969), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918969), _918971), _918973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_918969), _918971), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_918969), _918975), _918973))))], (8026 ^ _782435) ^ [_919148, _919150, _919152, _919154] : [class_Lattices_Osemilattice__sup(_919148), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919148), _919150), _919152)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919148), _919150), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919148), _919152), _919154))))], (8036 ^ _782435) ^ [_919327, _919329, _919331, _919333] : [class_Lattices_Osemilattice__sup(_919327), 8039 ^ _782435 : [(8040 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919327), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919327), _919329), _919331)), _919333)), 8043 ^ _782435 : [(8044 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919327), _919329), _919333)))], (8046 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919327), _919331), _919333)))]]], (8048 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919327), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919327), _919329), _919331)), _919333))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919327), _919329), _919333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919327), _919331), _919333))]]], (8058 ^ _782435) ^ [_919707, _919709, _919711] : [class_Lattices_Osemilattice__sup(_919707), 8061 ^ _782435 : [(8062 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919707), _919709), _919711)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919707), _919709), _919711) = _919711)], (8068 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919707), _919709), _919711) = _919711, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919707), _919709), _919711)))]]], (8074 ^ _782435) ^ [_919963, _919965, _919967] : [class_Lattices_Osemilattice__sup(_919963), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_919963), _919965), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_919963), _919967), _919965))))], (8080 ^ _782435) ^ [_920070, _920072, _920074] : [class_Lattices_Olattice(_920070), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920070), _920072), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920070), _920074), _920072))))], (8086 ^ _782435) ^ [_920177, _920179, _920181] : [class_Lattices_Osemilattice__sup(_920177), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920177), _920179), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920177), _920179), _920181))))], (8092 ^ _782435) ^ [_920284, _920286, _920288] : [class_Lattices_Olattice(_920284), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_920284), _920286), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_920284), _920286), _920288))))], (8098 ^ _782435) ^ [_920391, _920393, _920395, _920397] : [hBOOL(hAPP(hAPP(c_member(_920391), _920393), _920395)), -(hBOOL(hAPP(hAPP(c_member(_920391), _920393), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920391, tc_HOL_Obool)), _920397), _920395))))], (8104 ^ _782435) ^ [_920522, _920524, _920526, _920528] : [hBOOL(hAPP(hAPP(c_member(_920522), _920524), _920526)), -(hBOOL(hAPP(hAPP(c_member(_920522), _920524), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920522, tc_HOL_Obool)), _920526), _920528))))], (8120 ^ _782435) ^ [_920828, _920830, _920832, _920834] : [8121 ^ _782435 : [(8122 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920828), _920830), _920832))], (8124 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_920828), _920830), _920834))]], -(hBOOL(hAPP(hAPP(c_member(_920828), _920830), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920828, tc_HOL_Obool)), _920832), _920834))))], (8110 ^ _782435) ^ [_920674, _920676, _920678, _920680] : [hBOOL(hAPP(hAPP(c_member(_920674), _920676), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_920674, tc_HOL_Obool)), _920678), _920680))), -(hBOOL(hAPP(hAPP(c_member(_920674), _920676), _920678))), -(hBOOL(hAPP(hAPP(c_member(_920674), _920676), _920680)))], (8128 ^ _782435) ^ [_921013, _921015, _921017, _921019, _921021] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921013, tc_HOL_Obool)), _921015), _921017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921013, tc_HOL_Obool)), _921019), _921021)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921013, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921013, tc_HOL_Obool)), _921015), _921019)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921013, tc_HOL_Obool)), _921017), _921021))))], (8138 ^ _782435) ^ [_921258, _921260, _921262, _921264] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921258, tc_HOL_Obool)), _921260), _921262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921258, tc_HOL_Obool)), _921264), _921262)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921258, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921258, tc_HOL_Obool)), _921260), _921264)), _921262)))], (8148 ^ _782435) ^ [_921477, _921479, _921481] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921477, tc_HOL_Obool)), _921479), _921481)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921477, tc_HOL_Obool)), _921481), _921479) = _921481)], (8154 ^ _782435) ^ [_921598, _921600, _921602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921598, tc_HOL_Obool)), _921600), _921602)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921598, tc_HOL_Obool)), _921600), _921602) = _921602)], (8160 ^ _782435) ^ [_921737, _921739, _921741] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921737, tc_HOL_Obool)), _921739), _921741)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921737, tc_HOL_Obool)), _921739), _921741) = _921741)], (8166 ^ _782435) ^ [_921854, _921856, _921858] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921854, tc_HOL_Obool)), _921856), _921858) = _921858, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921854, tc_HOL_Obool)), _921856), _921858)))], (8172 ^ _782435) ^ [_921977, _921979, _921981] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_921977, tc_HOL_Obool)), _921979), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_921977, tc_HOL_Obool)), _921981), _921979))))], (8174 ^ _782435) ^ [_922025, _922027, _922029] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_922025, tc_HOL_Obool)), _922027), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922025, tc_HOL_Obool)), _922027), _922029))))], (8176 ^ _782435) ^ [_922073, _922075, _922077] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_922073, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_922073, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_922073), _922075)), hAPP(c_Set_OPow(_922073), _922077))), hAPP(c_Set_OPow(_922073), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922073, tc_HOL_Obool)), _922075), _922077)))))], (8178 ^ _782435) ^ [_922174, _922176, _922178, _922180] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922174, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922174, tc_fun(_922174, tc_HOL_Obool), tc_HOL_Obool), c_member(_922174)), _922176)), hAPP(hAPP(c_COMBC(_922174, tc_fun(_922174, tc_HOL_Obool), tc_HOL_Obool), c_member(_922174)), _922178)), _922180)), -(hBOOL(hAPP(hAPP(c_member(_922174), _922180), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922174, tc_HOL_Obool)), _922176), _922178))))], (8184 ^ _782435) ^ [_922373, _922375, _922377, _922379] : [hBOOL(hAPP(hAPP(c_member(_922373), _922379), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922373, tc_HOL_Obool)), _922375), _922377))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922373, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_922373, tc_fun(_922373, tc_HOL_Obool), tc_HOL_Obool), c_member(_922373)), _922375)), hAPP(hAPP(c_COMBC(_922373, tc_fun(_922373, tc_HOL_Obool), tc_HOL_Obool), c_member(_922373)), _922377)), _922379)))], (8190 ^ _782435) ^ [_922578, _922580, _922582, _922584, _922586] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922578, tc_fun(_922580, tc_HOL_Obool)), _922582), hAPP(hAPP(c_COMBS(_922578, tc_fun(_922580, tc_HOL_Obool), tc_fun(_922580, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_922580, tc_HOL_Obool), tc_fun(tc_fun(_922580, tc_HOL_Obool), tc_fun(_922580, tc_HOL_Obool)), _922578), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922580, tc_HOL_Obool))), _922584)), _922586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922580, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922578, tc_fun(_922580, tc_HOL_Obool)), _922582), _922584)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922578, tc_fun(_922580, tc_HOL_Obool)), _922582), _922586)))], (8192 ^ _782435) ^ [_922699, _922701, _922703, _922705, _922707] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922699, tc_fun(_922701, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922699, tc_HOL_Obool)), _922703), _922705)), _922707) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922701, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922699, tc_fun(_922701, tc_HOL_Obool)), _922703), _922707)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_922699, tc_fun(_922701, tc_HOL_Obool)), _922705), _922707)))], (8194 ^ _782435) ^ [_922788, _922790, _922792, _922794, _922796] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922788, tc_fun(_922790, tc_HOL_Obool)), _922792), hAPP(hAPP(c_COMBB(tc_fun(_922790, tc_HOL_Obool), tc_fun(_922790, tc_HOL_Obool), _922788), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922790, tc_HOL_Obool)), _922794)), _922796)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922790, tc_HOL_Obool)), _922794), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922788, tc_fun(_922790, tc_HOL_Obool)), _922792), _922796)))], (8196 ^ _782435) ^ [_922878, _922880, _922882, _922884, _922886] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922878, tc_fun(_922880, tc_HOL_Obool)), _922882), hAPP(hAPP(c_COMBC(_922878, tc_fun(_922880, tc_HOL_Obool), tc_fun(_922880, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_922880, tc_HOL_Obool), tc_fun(tc_fun(_922880, tc_HOL_Obool), tc_fun(_922880, tc_HOL_Obool)), _922878), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922880, tc_HOL_Obool))), _922884)), _922886)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922880, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922878, tc_fun(_922880, tc_HOL_Obool)), _922882), _922884)), _922886))], (8198 ^ _782435) ^ [_922987, _922989, _922991, _922993, _922995] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922987, tc_HOL_Obool)), _922989), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922991, tc_fun(_922987, tc_HOL_Obool)), _922993), _922995)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_922991, tc_fun(_922987, tc_HOL_Obool)), _922993), hAPP(hAPP(c_COMBB(tc_fun(_922987, tc_HOL_Obool), tc_fun(_922987, tc_HOL_Obool), _922991), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_922987, tc_HOL_Obool)), _922989)), _922995)))], (8200 ^ _782435) ^ [_923077, _923079, _923081, _923083, _923085] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923077, tc_HOL_Obool)), _923079), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923081, tc_fun(_923077, tc_HOL_Obool)), _923083), _923085)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923081, tc_fun(_923077, tc_HOL_Obool)), _923083), hAPP(hAPP(c_COMBB(tc_fun(_923077, tc_HOL_Obool), tc_fun(_923077, tc_HOL_Obool), _923081), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923077, tc_HOL_Obool)), _923079)), _923085)))], (8202 ^ _782435) ^ [_923167, _923169, _923171, _923173, _923175] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923167, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923169, tc_fun(_923167, tc_HOL_Obool)), _923171), _923173)), _923175) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923169, tc_fun(_923167, tc_HOL_Obool)), _923171), hAPP(hAPP(c_COMBC(_923169, tc_fun(_923167, tc_HOL_Obool), tc_fun(_923167, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_923167, tc_HOL_Obool), tc_fun(tc_fun(_923167, tc_HOL_Obool), tc_fun(_923167, tc_HOL_Obool)), _923169), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923167, tc_HOL_Obool))), _923173)), _923175)))], (8204 ^ _782435) ^ [_923276, _923278, _923280, _923282, _923284, _923286, _923288] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923276, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923278, tc_fun(_923276, tc_HOL_Obool)), _923280), _923282)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923284, tc_fun(_923276, tc_HOL_Obool)), _923286), _923288)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923278, tc_fun(_923276, tc_HOL_Obool)), _923280), hAPP(hAPP(c_COMBB(tc_fun(_923284, tc_fun(_923276, tc_HOL_Obool)), tc_fun(_923276, tc_HOL_Obool), _923278), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_923284, tc_fun(_923276, tc_HOL_Obool)), _923286)), hAPP(hAPP(c_COMBC(_923278, tc_fun(_923284, tc_fun(_923276, tc_HOL_Obool)), tc_fun(_923284, tc_fun(_923276, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_923276, tc_HOL_Obool), tc_fun(_923276, tc_HOL_Obool)), tc_fun(tc_fun(_923284, tc_fun(_923276, tc_HOL_Obool)), tc_fun(_923284, tc_fun(_923276, tc_HOL_Obool))), _923278), c_COMBB(tc_fun(_923276, tc_HOL_Obool), tc_fun(_923276, tc_HOL_Obool), _923284)), hAPP(hAPP(c_COMBB(tc_fun(_923276, tc_HOL_Obool), tc_fun(tc_fun(_923276, tc_HOL_Obool), tc_fun(_923276, tc_HOL_Obool)), _923278), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923276, tc_HOL_Obool))), _923282))), _923288))))], (8206 ^ _782435) ^ [_923479, _923481, _923483, _923485] : [class_Orderings_Olinorder(_923479), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923479), _923481), _923483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923479), _923483), _923485)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923479, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923479, _923481), _923483)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923479, _923483), _923485)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923479, _923481), _923485))], (8220 ^ _782435) ^ [_923756, _923758, _923760, _923762, _923764] : [hBOOL(hAPP(hAPP(c_member(_923756), _923758), _923760)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923762, tc_HOL_Obool)), hAPP(_923764, _923758)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_923756, tc_fun(_923762, tc_HOL_Obool)), _923760), _923764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_923756, tc_fun(_923762, tc_HOL_Obool)), _923760), _923764))], (8226 ^ _782435) ^ [_923929, _923931, _923933, _923935] : [class_Orderings_Olinorder(_923929), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923929), _923931), _923933)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_923929), _923933), _923935)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_923929, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_923929, _923931), _923933)), c_SetInterval_Oord__class_OatLeastAtMost(_923929, _923933, _923935)) = c_SetInterval_Oord__class_OatLeastAtMost(_923929, _923931, _923935))], (8240 ^ _782435) ^ [_924198, _924200, _924202] : [class_Orderings_Olinorder(_924198), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924198), _924200), _924202)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924198, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_924198), _924200)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_924198, _924200), _924202)) = hAPP(c_SetInterval_Oord__class_OlessThan(_924198), _924202))], (8250 ^ _782435) ^ [_924397, _924399, _924401] : [class_Orderings_Olinorder(_924397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924397), _924399), _924401)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924397, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_924397, _924399), _924401)), hAPP(c_SetInterval_Oord__class_OatLeast(_924397), _924401)) = hAPP(c_SetInterval_Oord__class_OatLeast(_924397), _924399))], (8260 ^ _782435) ^ [_924596, _924598, _924600] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924596, tc_HOL_Obool)), _924598), c_Complete__Lattice_OInf__class_OInf(tc_fun(_924596, tc_HOL_Obool), _924600)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(_924596, tc_HOL_Obool), tc_fun(_924596, tc_HOL_Obool)), _924600), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924596, tc_HOL_Obool)), _924598)))], (8262 ^ _782435) ^ [_924663, _924665, _924667] : [class_Orderings_Olinorder(_924663), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924663), _924665), _924667)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924663, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_924663, _924665, _924667)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_924663), _924667)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_924663), _924665))], (8272 ^ _782435) ^ [_924858, _924860, _924862] : [class_Orderings_Olinorder(_924858), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_924858), _924860), _924862)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_924858, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_924858), _924860)), c_SetInterval_Oord__class_OgreaterThanAtMost(_924858, _924860, _924862)) = hAPP(c_SetInterval_Oord__class_OatMost(_924858), _924862))], (8282 ^ _782435) ^ [_925053, _925055, _925057, _925059, _925061] : [class_Complete__Lattice_Ocomplete__lattice(_925053), 8288 ^ _782435 : [(8289 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_925055), 8287 ^ [_925053, _925055, _925057, _925059, _925061]), _925057)))], (8291 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925053), hAPP(_925059, 8287 ^ [_925053, _925055, _925057, _925059, _925061])), _925061))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925053), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_925055, _925053), _925057), _925059)), _925061)))], (8295 ^ _782435) ^ [_925349, _925351, _925353, _925355] : [class_Orderings_Olinorder(_925349), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925349), _925351), _925353)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_925349), _925353), _925355)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_925349, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_925349, _925351, _925353)), c_SetInterval_Oord__class_OgreaterThanAtMost(_925349, _925353, _925355)) = c_SetInterval_Oord__class_OatLeastAtMost(_925349, _925351, _925355))], (8309 ^ _782435) ^ [_925614, _925616, _925618] : [8311 ^ _782435 : [(8312 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_925614, tc_HOL_Obool)), 8310 ^ [_925614, _925616, _925618]), _925616)))], (8314 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925614, tc_HOL_Obool)), _925618), 8310 ^ [_925614, _925616, _925618]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925614, tc_HOL_Obool)), _925618), c_Complete__Lattice_OInf__class_OInf(tc_fun(_925614, tc_HOL_Obool), _925616))))], (8318 ^ _782435) ^ [_925845, _925847, _925849] : [8320 ^ _782435 : [(8321 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_925845, tc_HOL_Obool)), 8319 ^ [_925845, _925847, _925849]), _925847)))], (8323 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925845, tc_HOL_Obool)), 8319 ^ [_925845, _925847, _925849]), _925849))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_925845, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_925845, tc_HOL_Obool), _925847)), _925849)))], (8327 ^ _782435) ^ [_926076, _926078, _926080, _926082, _926084] : [8329 ^ _782435 : [(8330 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926076), 8328 ^ [_926076, _926078, _926080, _926082, _926084]), _926078)))], (8332 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_926080, 8328 ^ [_926076, _926078, _926080, _926082, _926084]), _926082))]], -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_926076, tc_fun(_926084, tc_HOL_Obool)), _926078), _926080), _926082)))], (8336 ^ _782435) ^ [_926297, _926299, _926301, _926303, _926305] : [8338 ^ _782435 : [(8339 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926297), 8337 ^ [_926297, _926299, _926301, _926303, _926305]), _926299)))], (8341 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_926301), _926303), hAPP(_926305, 8337 ^ [_926297, _926299, _926301, _926303, _926305])))]], -(hBOOL(hAPP(hAPP(c_member(_926301), _926303), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_926297, tc_fun(_926301, tc_HOL_Obool)), _926299), _926305))))], (8345 ^ _782435) ^ [_926543, _926545, _926547, _926549, _926551] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_926543, tc_fun(_926545, tc_HOL_Obool)), _926547), _926549), _926551)), 8349 ^ _782435 : [(8350 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926543), 8348 ^ [_926543, _926545, _926547, _926549, _926551]), _926547)))], (8352 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_926549, 8348 ^ [_926543, _926545, _926547, _926549, _926551]), _926551)))]]], (8354 ^ _782435) ^ [_926739, _926741, _926743, _926745, _926747] : [hBOOL(hAPP(hAPP(c_member(_926739), _926741), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_926743, tc_fun(_926739, tc_HOL_Obool)), _926745), _926747))), 8358 ^ _782435 : [(8359 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926743), 8357 ^ [_926739, _926741, _926743, _926745, _926747]), _926745)))], (8361 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926739), _926741), hAPP(_926747, 8357 ^ [_926739, _926741, _926743, _926745, _926747]))))]]], (8363 ^ _782435) ^ [_926955, _926957, _926959] : [class_Complete__Lattice_Ocomplete__lattice(_926955), 8369 ^ _782435 : [(8370 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_926955), 8368 ^ [_926955, _926957, _926959]), _926957)))], (8372 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926955), _926959), 8368 ^ [_926955, _926957, _926959]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_926955), _926959), c_Complete__Lattice_OInf__class_OInf(_926955, _926957))))], (8376 ^ _782435) ^ [_927211, _927213, _927215, _927217] : [class_Orderings_Olinorder(_927211), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927211), _927213), _927215)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927211), _927215), _927217)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927211, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_927211, _927213, _927215)), c_SetInterval_Oord__class_OgreaterThanAtMost(_927211, _927215, _927217)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_927211, _927213, _927217))], (8390 ^ _782435) ^ [_927476, _927478, _927480] : [class_Complete__Lattice_Ocomplete__lattice(_927476), 8396 ^ _782435 : [(8397 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927476), 8395 ^ [_927476, _927478, _927480]), _927478)))], (8399 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927476), 8395 ^ [_927476, _927478, _927480]), _927480))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_927476), c_Complete__Lattice_OSup__class_OSup(_927476, _927478)), _927480)))], (8403 ^ _782435) ^ [_927732, _927734] : [class_Lattices_Olattice(_927732), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_927732), _927734), _927734) = _927734)], (8409 ^ _782435) ^ [_927823, _927825, _927827, _927829, _927831] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_927823, tc_fun(_927825, tc_HOL_Obool)), _927827), hAPP(hAPP(c_COMBS(_927823, tc_fun(_927825, tc_HOL_Obool), tc_fun(_927825, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_927825, tc_HOL_Obool), tc_fun(tc_fun(_927825, tc_HOL_Obool), tc_fun(_927825, tc_HOL_Obool)), _927823), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927825, tc_HOL_Obool))), _927829)), _927831)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_927825, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_927825, tc_HOL_Obool), hAPP(c_Set_Oimage(_927823, tc_fun(_927825, tc_HOL_Obool), _927829), _927827))), c_Complete__Lattice_OSup__class_OSup(tc_fun(_927825, tc_HOL_Obool), hAPP(c_Set_Oimage(_927823, tc_fun(_927825, tc_HOL_Obool), _927831), _927827))))], (8411 ^ _782435) ^ [_927952, _927954, _927956] : [8413 ^ _782435 : [(8414 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_927952), 8412 ^ [_927952, _927954, _927956]), _927954)))], (8416 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_927952), 8412 ^ [_927952, _927954, _927956]), _927956))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_927952, tc_HOL_Obool)), _927954), _927956)))], (8420 ^ _782435) ^ [_928156, _928158, _928160] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_928156, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_928156, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928156, tc_HOL_Obool), _928158)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928156, tc_HOL_Obool), _928160))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_928156, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_928156, tc_HOL_Obool), tc_HOL_Obool)), _928158), _928160)))))], (8422 ^ _782435) ^ [_928236, _928238] : [class_Groups_Oordered__ab__group__add(_928236), -(hAPP(c_Set_Oimage(_928236, _928236, c_Groups_Ouminus__class_Ouminus(_928236)), hAPP(c_SetInterval_Oord__class_OatLeast(_928236), _928238)) = hAPP(c_SetInterval_Oord__class_OatMost(_928236), hAPP(c_Groups_Ouminus__class_Ouminus(_928236), _928238)))], (8428 ^ _782435) ^ [_928359, _928361] : [class_Groups_Oordered__ab__group__add(_928359), -(hAPP(c_Set_Oimage(_928359, _928359, c_Groups_Ouminus__class_Ouminus(_928359)), hAPP(c_SetInterval_Oord__class_OatMost(_928359), _928361)) = hAPP(c_SetInterval_Oord__class_OatLeast(_928359), hAPP(c_Groups_Ouminus__class_Ouminus(_928359), _928361)))], (8434 ^ _782435) ^ [_928482, _928484] : [class_Groups_Oordered__ab__group__add(_928482), -(hAPP(c_Set_Oimage(_928482, _928482, c_Groups_Ouminus__class_Ouminus(_928482)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_928482), _928484)) = hAPP(c_SetInterval_Oord__class_OlessThan(_928482), hAPP(c_Groups_Ouminus__class_Ouminus(_928482), _928484)))], (8440 ^ _782435) ^ [_928605, _928607] : [class_Groups_Oordered__ab__group__add(_928605), -(hAPP(c_Set_Oimage(_928605, _928605, c_Groups_Ouminus__class_Ouminus(_928605)), hAPP(c_SetInterval_Oord__class_OlessThan(_928605), _928607)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_928605), hAPP(c_Groups_Ouminus__class_Ouminus(_928605), _928607)))], (8446 ^ _782435) ^ [_928728, _928730, _928732, _928734, _928736, _928738] : [_928728 = _928730, 8452 ^ _782435 : [(8453 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_928732), 8451 ^ [_928728, _928730, _928732, _928734, _928736, _928738]), _928730)))], (8455 ^ _782435) ^ [] : [hAPP(_928734, 8451 ^ [_928728, _928730, _928732, _928734, _928736, _928738]) = hAPP(_928736, 8451 ^ [_928728, _928730, _928732, _928734, _928736, _928738])]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_928732, tc_fun(_928738, tc_HOL_Obool)), _928728), _928734) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_928732, tc_fun(_928738, tc_HOL_Obool)), _928730), _928736))], (8459 ^ _782435) ^ [_929055, _929057] : [class_Lattices_Oboolean__algebra(_929055), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_929055), _929057), hAPP(c_Groups_Ouminus__class_Ouminus(_929055), _929057)) = c_Orderings_Otop__class_Otop(_929055))], (8465 ^ _782435) ^ [_929160, _929162] : [-(hBOOL(hAPP(hAPP(c_member(_929160), _929162), c_Orderings_Otop__class_Otop(tc_fun(_929160, tc_HOL_Obool)))))], (8467 ^ _782435) ^ [_929197, _929199, _929201, _929203] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929197, tc_HOL_Obool)), _929199), _929201), _929203)), 8470 ^ _782435 : [(8471 ^ _782435) ^ [] : [-(hBOOL(hAPP(_929199, _929203)))], (8473 ^ _782435) ^ [] : [-(hBOOL(hAPP(_929201, _929203)))]]], (8475 ^ _782435) ^ [_929342, _929344, _929346, _929348] : [hBOOL(hAPP(_929342, _929344)), hBOOL(hAPP(_929346, _929344)), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929348, tc_HOL_Obool)), _929342), _929346), _929344)))], (8485 ^ _782435) ^ [_929513, _929515, _929517, _929519, _929521, _929523] : [_929513 = hAPP(_929515, _929517), hBOOL(hAPP(hAPP(c_member(_929519), _929517), _929521)), -(hBOOL(hAPP(hAPP(c_member(_929523), _929513), hAPP(c_Set_Oimage(_929519, _929523, _929515), _929521))))], (8495 ^ _782435) ^ [_929706, _929708, _929710, _929712] : [hBOOL(hAPP(hAPP(c_member(_929706), _929708), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929706, tc_HOL_Obool)), _929710), _929712))), 8498 ^ _782435 : [(8499 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929706), _929708), _929710)))], (8501 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_929706), _929708), _929712)))]]], (8503 ^ _782435) ^ [_929881, _929883, _929885, _929887] : [hBOOL(hAPP(hAPP(c_member(_929881), _929883), _929885)), hBOOL(hAPP(hAPP(c_member(_929881), _929883), _929887)), -(hBOOL(hAPP(hAPP(c_member(_929881), _929883), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_929881, tc_HOL_Obool)), _929885), _929887))))], (8513 ^ _782435) ^ [_930082, _930084, _930086, _930088] : [-(hBOOL(hAPP(hAPP(c_member(_930082), hAPP(_930084, _930086)), hAPP(c_Set_Oimage(_930088, _930082, _930084), c_Orderings_Otop__class_Otop(tc_fun(_930088, tc_HOL_Obool))))))], (8515 ^ _782435) ^ [_930133, _930135, _930137, _930139, _930141] : [_930133 = hAPP(_930135, _930137), -(hBOOL(hAPP(hAPP(c_member(_930139), _930133), hAPP(c_Set_Oimage(_930141, _930139, _930135), c_Orderings_Otop__class_Otop(tc_fun(_930141, tc_HOL_Obool))))))], (8521 ^ _782435) ^ [_930260, _930262, _930264, _930266, _930268] : [class_Lattices_Olattice(_930260), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_930262, _930260)), _930264), _930266), _930268) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930260), hAPP(_930264, _930268)), hAPP(_930266, _930268)))], (8527 ^ _782435) ^ [_930397, _930399, _930401, _930403] : [class_Lattices_Osemilattice__inf(_930397), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930397), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930397), _930399), _930401)), _930403) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930397), _930399), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930397), _930401), _930403)))], (8533 ^ _782435) ^ [_930540, _930542, _930544, _930546] : [class_Lattices_Olattice(_930540), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930540), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930540), _930542), _930544)), _930546) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930540), _930542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930540), _930544), _930546)))], (8539 ^ _782435) ^ [_930683, _930685, _930687, _930689] : [class_Lattices_Osemilattice__inf(_930683), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930683), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930683), _930685), _930687)), _930689) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930683), _930685), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930683), _930687), _930689)))], (8545 ^ _782435) ^ [_930826, _930828, _930830] : [class_Lattices_Obounded__lattice__top(_930826), 8548 ^ _782435 : [(8549 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930826), _930828), _930830) = c_Orderings_Otop__class_Otop(_930826), 8552 ^ _782435 : [(8553 ^ _782435) ^ [] : [-(_930828 = c_Orderings_Otop__class_Otop(_930826))], (8555 ^ _782435) ^ [] : [-(_930830 = c_Orderings_Otop__class_Otop(_930826))]]], (8557 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_930826), _930828), _930830) = c_Orderings_Otop__class_Otop(_930826)), _930828 = c_Orderings_Otop__class_Otop(_930826), _930830 = c_Orderings_Otop__class_Otop(_930826)]]], (8567 ^ _782435) ^ [_931153, _931155, _931157, _931159] : [class_Lattices_Osemilattice__inf(_931153), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931153), _931155), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931153), _931157), _931159)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931153), _931157), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931153), _931155), _931159)))], (8573 ^ _782435) ^ [_931296, _931298, _931300, _931302] : [class_Lattices_Olattice(_931296), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931296), _931298), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931296), _931300), _931302)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931296), _931300), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931296), _931298), _931302)))], (8579 ^ _782435) ^ [_931439, _931441, _931443, _931445] : [class_Lattices_Osemilattice__inf(_931439), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931439), _931441), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931439), _931443), _931445)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931439), _931443), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931439), _931441), _931445)))], (8585 ^ _782435) ^ [_931582, _931584, _931586] : [class_Lattices_Osemilattice__inf(_931582), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931582), _931584), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931582), _931584), _931586)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931582), _931584), _931586))], (8591 ^ _782435) ^ [_931707, _931709, _931711] : [class_Lattices_Olattice(_931707), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931707), _931709), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931707), _931709), _931711)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931707), _931709), _931711))], (8597 ^ _782435) ^ [_931832, _931834, _931836] : [class_Lattices_Osemilattice__inf(_931832), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931832), _931834), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931832), _931834), _931836)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931832), _931834), _931836))], (8603 ^ _782435) ^ [_931957, _931959, _931961] : [class_Lattices_Osemilattice__inf(_931957), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931957), _931959), _931961) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_931957), _931961), _931959))], (8609 ^ _782435) ^ [_932066, _932068, _932070] : [class_Lattices_Olattice(_932066), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932066), _932068), _932070) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932066), _932070), _932068))], (8615 ^ _782435) ^ [_932175, _932177, _932179] : [class_Lattices_Osemilattice__inf(_932175), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932175), _932177), _932179) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932175), _932179), _932177))], (8621 ^ _782435) ^ [_932284, _932286, _932288, _932290, _932292] : [class_Lattices_Olattice(_932284), -(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932286, _932284)), _932288), _932290), _932292) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932284), hAPP(_932288, _932292)), hAPP(_932290, _932292)))], (8627 ^ _782435) ^ [_932421, _932423] : [class_Lattices_Osemilattice__inf(_932421), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932421), _932423), _932423) = _932423)], (8633 ^ _782435) ^ [_932512, _932514] : [class_Lattices_Osemilattice__inf(_932512), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932512), _932514), _932514) = _932514)], (8639 ^ _782435) ^ [_932603, _932605] : [class_Lattices_Obounded__lattice__top(_932603), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932603), _932605), c_Orderings_Otop__class_Otop(_932603)) = _932605)], (8645 ^ _782435) ^ [_932698, _932700] : [class_Lattices_Obounded__lattice__top(_932698), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932698), c_Orderings_Otop__class_Otop(_932698)), _932700) = _932700)], (8651 ^ _782435) ^ [_932793, _932795] : [class_Lattices_Olattice(_932793), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_932793), _932795), _932795) = _932795)], (8657 ^ _782435) ^ [_932884, _932886, _932888, _932890] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932884, tc_HOL_Obool)), _932886), _932888), _932890)), -(hBOOL(hAPP(_932888, _932890)))], (8663 ^ _782435) ^ [_932995, _932997, _932999, _933001] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_932995, tc_HOL_Obool)), _932997), _932999), _933001)), -(hBOOL(hAPP(_932997, _933001)))], (8669 ^ _782435) ^ [_933106, _933108, _933110, _933112] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933106, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933106, tc_HOL_Obool)), _933108), _933110)), _933112) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933106, tc_HOL_Obool)), _933108), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933106, tc_HOL_Obool)), _933110), _933112)))], (8671 ^ _782435) ^ [_933179, _933181, _933183, _933185, _933187] : [-(hAPP(c_Set_Oimage(_933179, _933181, hAPP(hAPP(c_COMBB(_933183, _933181, _933179), _933185), _933187)), c_Orderings_Otop__class_Otop(tc_fun(_933179, tc_HOL_Obool))) = hAPP(c_Set_Oimage(_933183, _933181, _933185), hAPP(c_Set_Oimage(_933179, _933183, _933187), c_Orderings_Otop__class_Otop(tc_fun(_933179, tc_HOL_Obool)))))], (8673 ^ _782435) ^ [_933251, _933253, _933255, _933257] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933251, tc_HOL_Obool)), _933253), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933251, tc_HOL_Obool)), _933255), _933257)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933251, tc_HOL_Obool)), _933255), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933251, tc_HOL_Obool)), _933253), _933257)))], (8675 ^ _782435) ^ [_933324, _933326, _933328] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933324, tc_HOL_Obool)), _933326), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933324, tc_HOL_Obool)), _933326), _933328)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933324, tc_HOL_Obool)), _933326), _933328))], (8677 ^ _782435) ^ [_933384, _933386, _933388] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933384, tc_HOL_Obool)), _933386), _933388) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933384, tc_HOL_Obool)), _933388), _933386))], (8679 ^ _782435) ^ [_933433, _933435] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933433, tc_HOL_Obool)), _933435), _933435) = _933435)], (8681 ^ _782435) ^ [_933469, _933471] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933469, tc_HOL_Obool)), _933471), c_Orderings_Otop__class_Otop(tc_fun(_933469, tc_HOL_Obool))) = _933471)], (8683 ^ _782435) ^ [_933510, _933512] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933510, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_933510, tc_HOL_Obool))), _933512) = _933512)], (8685 ^ _782435) ^ [_933551, _933553, _933555] : [class_Orderings_Otop(_933551), -(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_933553, _933551)), _933555) = c_Orderings_Otop__class_Otop(_933551))], (8691 ^ _782435) ^ [_933648, _933650, _933652, _933654, _933656] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_933648, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933650, _933648, _933652), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933650, tc_HOL_Obool)), _933654), _933656))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933648, tc_HOL_Obool)), hAPP(c_Set_Oimage(_933650, _933648, _933652), _933654)), hAPP(c_Set_Oimage(_933650, _933648, _933652), _933656)))))], (8693 ^ _782435) ^ [_933732, _933734, _933736, _933738, _933740, _933742] : [-(hAPP(c_Set_Oimage(_933732, _933734, _933736), hAPP(c_Set_Oimage(_933738, _933732, _933740), _933742)) = hAPP(c_Set_Oimage(_933738, _933734, hAPP(hAPP(c_COMBB(_933732, _933734, _933738), _933736), _933740)), _933742))], (8695 ^ _782435) ^ [_933796, _933798, _933800, _933802, _933804] : [hAPP(c_Set_Oimage(_933796, _933798, _933800), _933802) = _933804, -(hAPP(c_Set_Oimage(tc_fun(_933796, tc_HOL_Obool), tc_fun(_933798, tc_HOL_Obool), c_Set_Oimage(_933796, _933798, _933800)), hAPP(c_Set_OPow(_933796), _933802)) = hAPP(c_Set_OPow(_933798), _933804))], (8701 ^ _782435) ^ [_933947, _933949, _933951] : [-(hAPP(c_Set_OPow(_933947), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_933947, tc_HOL_Obool)), _933949), _933951)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_933947, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_933947), _933949)), hAPP(c_Set_OPow(_933947), _933951)))], (8703 ^ _782435) ^ [_934014] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_934014, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_934014, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_934014, tc_HOL_Obool)))], (8705 ^ _782435) ^ [_934056] : [-(hAPP(c_Set_OPow(_934056), c_Orderings_Otop__class_Otop(tc_fun(_934056, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_934056, tc_HOL_Obool), tc_HOL_Obool)))], (8707 ^ _782435) ^ [_934097] : [class_Complete__Lattice_Ocomplete__lattice(_934097), -(c_Complete__Lattice_OSup__class_OSup(_934097, c_Orderings_Otop__class_Otop(tc_fun(_934097, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_934097))], (8713 ^ _782435) ^ [_934190, _934192, _934194, _934196, _934198, _934200] : [hBOOL(hAPP(hAPP(c_member(_934190), _934192), _934194)), _934196 = hAPP(_934198, _934192), -(hBOOL(hAPP(hAPP(c_member(_934200), _934196), hAPP(c_Set_Oimage(_934190, _934200, _934198), _934194))))], (8723 ^ _782435) ^ [_934383, _934385, _934387, _934389, _934391] : [hBOOL(hAPP(hAPP(c_member(_934383), _934385), _934387)), -(hBOOL(hAPP(hAPP(c_member(_934389), hAPP(_934391, _934385)), hAPP(c_Set_Oimage(_934383, _934389, _934391), _934387))))], (8729 ^ _782435) ^ [_934538, _934540, _934542, _934544, _934546] : [hBOOL(hAPP(hAPP(c_member(_934538), _934540), hAPP(c_Set_Oimage(_934542, _934538, _934544), _934546))), 8733 ^ _782435 : [(8734 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_934542), 8732 ^ [_934538, _934540, _934542, _934544, _934546]), _934546)))], (8736 ^ _782435) ^ [] : [-(_934540 = hAPP(_934544, 8732 ^ [_934538, _934540, _934542, _934544, _934546]))]]], (8738 ^ _782435) ^ [_934722, _934724, _934726, _934728, _934730] : [-(hBOOL(hAPP(hAPP(c_member(_934722), _934724), hAPP(c_Set_Oimage(_934726, _934722, _934728), _934730)))), 8739 ^ _782435 : [(8740 ^ _782435) ^ [_934792] : [hBOOL(hAPP(hAPP(c_member(_934726), _934792), _934730)), _934724 = hAPP(_934728, _934792)]]], (8748 ^ _782435) ^ [_934940, _934942, _934944] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_934940, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934940, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(_934940, tc_HOL_Obool), tc_HOL_Obool)), _934942), _934944))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_934940, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934940, tc_HOL_Obool), _934942)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_934940, tc_HOL_Obool), _934944)))))], (8750 ^ _782435) ^ [_935020, _935022, _935024, _935026] : [class_Lattices_Osemilattice__inf(_935020), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935020), _935022), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935020), _935024), _935026))), 8757 ^ _782435 : [(8758 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935020), _935022), _935024)))], (8760 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935020), _935022), _935026)))]]], (8762 ^ _782435) ^ [_935243, _935245, _935247, _935249, _935251] : [class_Lattices_Osemilattice__inf(_935243), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935243), _935245), _935247)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935243), _935249), _935251)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935243), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935243), _935245), _935249)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935243), _935247), _935251))))], (8776 ^ _782435) ^ [_935514, _935516, _935518, _935520] : [class_Lattices_Osemilattice__inf(_935514), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935514), _935516), _935518)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935514), _935516), _935520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935514), _935516), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935514), _935518), _935520))))], (8790 ^ _782435) ^ [_935763, _935765, _935767, _935769] : [class_Lattices_Osemilattice__inf(_935763), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935763), _935765), _935767)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935763), _935765), _935769)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_935763), _935765), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_935763), _935767), _935769))))], (8804 ^ _782435) ^ [_936012, _936014, _936016] : [class_Lattices_Osemilattice__inf(_936012), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936012), _936014), _936016)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936012), _936016), _936014) = _936014)], (8814 ^ _782435) ^ [_936173, _936175, _936177] : [class_Lattices_Osemilattice__inf(_936173), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936173), _936175), _936177)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936173), _936175), _936177) = _936175)], (8824 ^ _782435) ^ [_936334, _936336, _936338, _936340] : [class_Lattices_Osemilattice__inf(_936334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936334), _936336), _936338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936334), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936334), _936340), _936336)), _936338)))], (8834 ^ _782435) ^ [_936513, _936515, _936517, _936519] : [class_Lattices_Osemilattice__inf(_936513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936513), _936515), _936517)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936513), _936515), _936519)), _936517)))], (8844 ^ _782435) ^ [_936692, _936694, _936696, _936698] : [class_Lattices_Osemilattice__inf(_936692), 8847 ^ _782435 : [(8848 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936692), _936694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936692), _936696), _936698))), 8851 ^ _782435 : [(8852 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936692), _936694), _936696)))], (8854 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936692), _936694), _936698)))]]], (8856 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936692), _936694), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_936692), _936696), _936698)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936692), _936694), _936696)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_936692), _936694), _936698))]]], (8866 ^ _782435) ^ [_937072, _937074, _937076] : [class_Lattices_Osemilattice__inf(_937072), 8869 ^ _782435 : [(8870 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937072), _937074), _937076)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937072), _937074), _937076) = _937074)], (8876 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937072), _937074), _937076) = _937074, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937072), _937074), _937076)))]]], (8882 ^ _782435) ^ [_937328, _937330, _937332] : [class_Lattices_Osemilattice__inf(_937328), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937328), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937328), _937330), _937332)), _937332)))], (8888 ^ _782435) ^ [_937435, _937437, _937439] : [class_Lattices_Olattice(_937435), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937435), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937435), _937437), _937439)), _937439)))], (8894 ^ _782435) ^ [_937542, _937544, _937546] : [class_Lattices_Osemilattice__inf(_937542), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937542), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937542), _937544), _937546)), _937544)))], (8900 ^ _782435) ^ [_937649, _937651, _937653] : [class_Lattices_Olattice(_937649), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_937649), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_937649), _937651), _937653)), _937651)))], (8906 ^ _782435) ^ [_937756, _937758, _937760, _937762, _937764] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937756, tc_HOL_Obool)), _937758), _937760)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937762, tc_HOL_Obool)), hAPP(c_Set_Oimage(_937756, _937762, _937764), _937758)), hAPP(c_Set_Oimage(_937756, _937762, _937764), _937760))))], (8912 ^ _782435) ^ [_937931, _937933, _937935, _937937, _937939] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937931, tc_HOL_Obool)), _937933), hAPP(c_Set_Oimage(_937935, _937931, _937937), _937939))), 8916 ^ _782435 : [(8917 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_937935, tc_HOL_Obool)), 8915 ^ [_937931, _937933, _937935, _937937, _937939]), _937939)))], (8919 ^ _782435) ^ [] : [-(_937933 = hAPP(c_Set_Oimage(_937935, _937931, _937937), 8915 ^ [_937931, _937933, _937935, _937937, _937939]))]]], (8921 ^ _782435) ^ [_938135, _938137, _938139, _938141, _938143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938135, tc_HOL_Obool)), _938137), hAPP(c_Set_Oimage(_938139, _938135, _938141), _938143)))), 8922 ^ _782435 : [(8923 ^ _782435) ^ [_938215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_938139, tc_HOL_Obool)), _938215), _938143)), _938137 = hAPP(c_Set_Oimage(_938139, _938135, _938141), _938215)]]], (8931 ^ _782435) ^ [_938380, _938382, _938384, _938386, _938388] : [-(hAPP(c_Set_Oimage(_938380, _938382, _938384), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938380, tc_HOL_Obool)), _938386), _938388)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_938382, tc_HOL_Obool)), hAPP(c_Set_Oimage(_938380, _938382, _938384), _938386)), hAPP(c_Set_Oimage(_938380, _938382, _938384), _938388)))], (8933 ^ _782435) ^ [_938454, _938456, _938458, _938460] : [class_Lattices_Odistrib__lattice(_938454), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938454), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938454), _938456), _938458)), _938460) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938454), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938454), _938456), _938460)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938454), _938458), _938460)))], (8939 ^ _782435) ^ [_938613, _938615, _938617, _938619] : [class_Lattices_Odistrib__lattice(_938613), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938613), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938613), _938615), _938617)), _938619) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938613), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938613), _938615), _938619)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938613), _938617), _938619)))], (8945 ^ _782435) ^ [_938772, _938774, _938776, _938778] : [class_Lattices_Odistrib__lattice(_938772), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938772), _938774), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938772), _938776), _938778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938772), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938772), _938774), _938776)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938772), _938774), _938778)))], (8951 ^ _782435) ^ [_938931, _938933, _938935, _938937] : [class_Lattices_Odistrib__lattice(_938931), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938931), _938933), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938931), _938935), _938937)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_938931), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938931), _938933), _938935)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_938931), _938933), _938937)))], (8957 ^ _782435) ^ [_939090, _939092, _939094] : [class_Lattices_Olattice(_939090), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939090), _939092), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939090), _939092), _939094)) = _939092)], (8963 ^ _782435) ^ [_939199, _939201, _939203] : [class_Lattices_Olattice(_939199), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_939199), _939201), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_939199), _939201), _939203)) = _939201)], (8969 ^ _782435) ^ [_939308, _939310, _939312, _939314] : [hBOOL(hAPP(hAPP(c_member(_939308), _939310), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939308, tc_HOL_Obool)), _939312), _939314))), -(hBOOL(hAPP(hAPP(c_member(_939308), _939310), _939314)))], (8975 ^ _782435) ^ [_939439, _939441, _939443, _939445] : [hBOOL(hAPP(hAPP(c_member(_939439), _939441), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939439, tc_HOL_Obool)), _939443), _939445))), -(hBOOL(hAPP(hAPP(c_member(_939439), _939441), _939443)))], (8981 ^ _782435) ^ [_939591, _939593, _939595, _939597] : [hBOOL(hAPP(hAPP(c_member(_939591), _939593), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939591, tc_HOL_Obool)), _939595), _939597))), 8984 ^ _782435 : [(8985 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939591), _939593), _939595)))], (8987 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_939591), _939593), _939597)))]]], (8989 ^ _782435) ^ [_939758, _939760, _939762, _939764] : [-(hBOOL(hAPP(hAPP(c_member(_939758), _939760), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939758, tc_HOL_Obool)), _939762), _939764)))), hBOOL(hAPP(hAPP(c_member(_939758), _939760), _939762)), hBOOL(hAPP(hAPP(c_member(_939758), _939760), _939764))], (8999 ^ _782435) ^ [_939961, _939963, _939965, _939967, _939969] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939961, tc_HOL_Obool)), _939963), _939965)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939961, tc_HOL_Obool)), _939967), _939969)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_939961, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939961, tc_HOL_Obool)), _939963), _939967)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_939961, tc_HOL_Obool)), _939965), _939969))))], (9009 ^ _782435) ^ [_940206, _940208, _940210, _940212] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940206, tc_HOL_Obool)), _940208), _940210)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940206, tc_HOL_Obool)), _940208), _940212)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940206, tc_HOL_Obool)), _940208), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940206, tc_HOL_Obool)), _940210), _940212))))], (9019 ^ _782435) ^ [_940425, _940427, _940429] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940425, tc_HOL_Obool)), _940427), _940429)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940425, tc_HOL_Obool)), _940429), _940427) = _940427)], (9025 ^ _782435) ^ [_940546, _940548, _940550] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940546, tc_HOL_Obool)), _940548), _940550)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940546, tc_HOL_Obool)), _940548), _940550) = _940548)], (9031 ^ _782435) ^ [_940667, _940669, _940671] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940667, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940667, tc_HOL_Obool)), _940669), _940671)), _940671)))], (9033 ^ _782435) ^ [_940715, _940717, _940719] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_940715, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940715, tc_HOL_Obool)), _940717), _940719)), _940717)))], (9035 ^ _782435) ^ [_940763, _940765, _940767, _940769] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940763, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940763, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940763, tc_HOL_Obool)), _940765), _940767)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940763, tc_HOL_Obool)), _940767), _940769))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940763, tc_HOL_Obool)), _940769), _940765)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940763, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940763, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940763, tc_HOL_Obool)), _940765), _940767)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940763, tc_HOL_Obool)), _940767), _940769))), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940763, tc_HOL_Obool)), _940769), _940765)))], (9037 ^ _782435) ^ [_940902, _940904, _940906, _940908] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940902, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940902, tc_HOL_Obool)), _940904), _940906)), _940908) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940902, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940902, tc_HOL_Obool)), _940904), _940908)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940902, tc_HOL_Obool)), _940906), _940908)))], (9039 ^ _782435) ^ [_940986, _940988, _940990, _940992] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940986, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940986, tc_HOL_Obool)), _940988), _940990)), _940992) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_940986, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940986, tc_HOL_Obool)), _940988), _940992)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_940986, tc_HOL_Obool)), _940990), _940992)))], (9041 ^ _782435) ^ [_941070, _941072, _941074, _941076] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941070, tc_HOL_Obool)), _941072), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941070, tc_HOL_Obool)), _941074), _941076)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941070, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941070, tc_HOL_Obool)), _941072), _941074)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941070, tc_HOL_Obool)), _941072), _941076)))], (9043 ^ _782435) ^ [_941154, _941156, _941158, _941160] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941154, tc_HOL_Obool)), _941156), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941154, tc_HOL_Obool)), _941158), _941160)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941154, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941154, tc_HOL_Obool)), _941156), _941158)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941154, tc_HOL_Obool)), _941156), _941160)))], (9045 ^ _782435) ^ [_941238, _941240] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_941238, tc_HOL_Obool)), _941240), c_Orderings_Otop__class_Otop(tc_fun(_941238, tc_HOL_Obool)))))], (9047 ^ _782435) ^ [_941278, _941280] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941278, tc_HOL_Obool)), _941280), c_Orderings_Otop__class_Otop(tc_fun(_941278, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_941278, tc_HOL_Obool)))], (9049 ^ _782435) ^ [_941324, _941326] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_941324, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_941324, tc_HOL_Obool))), _941326) = c_Orderings_Otop__class_Otop(tc_fun(_941324, tc_HOL_Obool)))], (9051 ^ _782435) ^ [_941370, _941372, _941374, _941376, _941378] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941370, tc_fun(_941372, tc_HOL_Obool)), _941374), hAPP(hAPP(c_COMBS(_941370, tc_fun(_941372, tc_HOL_Obool), tc_fun(_941372, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_941372, tc_HOL_Obool), tc_fun(tc_fun(_941372, tc_HOL_Obool), tc_fun(_941372, tc_HOL_Obool)), _941370), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941372, tc_HOL_Obool))), _941376)), _941378)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941372, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_941372, tc_HOL_Obool), hAPP(c_Set_Oimage(_941370, tc_fun(_941372, tc_HOL_Obool), _941376), _941374))), c_Complete__Lattice_OInf__class_OInf(tc_fun(_941372, tc_HOL_Obool), hAPP(c_Set_Oimage(_941370, tc_fun(_941372, tc_HOL_Obool), _941378), _941374))))], (9053 ^ _782435) ^ [_941499, _941501, _941503, _941505, _941507, _941509] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941499, tc_fun(_941501, tc_HOL_Obool)), _941503), hAPP(hAPP(c_COMBB(_941505, tc_fun(_941501, tc_HOL_Obool), _941499), _941507), _941509)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941505, tc_fun(_941501, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941499, _941505, _941509), _941503)), _941507))], (9055 ^ _782435) ^ [_941576, _941578, _941580, _941582, _941584, _941586] : [-(hAPP(c_Set_Oimage(_941576, _941578, _941580), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941582, tc_fun(_941576, tc_HOL_Obool)), _941584), _941586)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941582, tc_fun(_941578, tc_HOL_Obool)), _941584), hAPP(hAPP(c_COMBB(tc_fun(_941576, tc_HOL_Obool), tc_fun(_941578, tc_HOL_Obool), _941582), c_Set_Oimage(_941576, _941578, _941580)), _941586)))], (9057 ^ _782435) ^ [_941660, _941662, _941664, _941666, _941668, _941670] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941660, tc_fun(_941662, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941664, _941660, _941666), _941668)), _941670) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_941664, tc_fun(_941662, tc_HOL_Obool)), _941668), hAPP(hAPP(c_COMBB(_941660, tc_fun(_941662, tc_HOL_Obool), _941664), _941670), _941666)))], (9059 ^ _782435) ^ [_941737, _941739, _941741, _941743, _941745, _941747] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941737, tc_fun(_941739, tc_HOL_Obool)), _941741), hAPP(hAPP(c_COMBB(_941743, tc_fun(_941739, tc_HOL_Obool), _941737), _941745), _941747)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941743, tc_fun(_941739, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941737, _941743, _941747), _941741)), _941745))], (9061 ^ _782435) ^ [_941814, _941816, _941818, _941820, _941822, _941824] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941814, tc_fun(_941816, tc_HOL_Obool)), hAPP(c_Set_Oimage(_941818, _941814, _941820), _941822)), _941824) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_941818, tc_fun(_941816, tc_HOL_Obool)), _941822), hAPP(hAPP(c_COMBB(_941814, tc_fun(_941816, tc_HOL_Obool), _941818), _941824), _941820)))], (9063 ^ _782435) ^ [_941912, _941914, _941916, _941918] : [hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941912, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_941912, tc_fun(_941912, tc_HOL_Obool), tc_HOL_Obool), c_member(_941912)), _941914)), hAPP(hAPP(c_COMBC(_941912, tc_fun(_941912, tc_HOL_Obool), tc_HOL_Obool), c_member(_941912)), _941916)), _941918)), -(hBOOL(hAPP(hAPP(c_member(_941912), _941918), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_941912, tc_HOL_Obool)), _941914), _941916))))], (9069 ^ _782435) ^ [_942111, _942113, _942115, _942117] : [hBOOL(hAPP(hAPP(c_member(_942111), _942117), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942111, tc_HOL_Obool)), _942113), _942115))), -(hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942111, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_942111, tc_fun(_942111, tc_HOL_Obool), tc_HOL_Obool), c_member(_942111)), _942113)), hAPP(hAPP(c_COMBC(_942111, tc_fun(_942111, tc_HOL_Obool), tc_HOL_Obool), c_member(_942111)), _942115)), _942117)))], (9075 ^ _782435) ^ [_942316, _942318, _942320, _942322, _942324] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942316, tc_fun(_942318, tc_HOL_Obool)), _942320), hAPP(hAPP(c_COMBB(tc_fun(_942318, tc_HOL_Obool), tc_fun(_942318, tc_HOL_Obool), _942316), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942318, tc_HOL_Obool)), _942322)), _942324)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942318, tc_HOL_Obool)), _942322), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942316, tc_fun(_942318, tc_HOL_Obool)), _942320), _942324)))], (9077 ^ _782435) ^ [_942406, _942408, _942410, _942412, _942414] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942406, tc_fun(_942408, tc_HOL_Obool)), _942410), hAPP(hAPP(c_COMBC(_942406, tc_fun(_942408, tc_HOL_Obool), tc_fun(_942408, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_942408, tc_HOL_Obool), tc_fun(tc_fun(_942408, tc_HOL_Obool), tc_fun(_942408, tc_HOL_Obool)), _942406), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942408, tc_HOL_Obool))), _942412)), _942414)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942408, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942406, tc_fun(_942408, tc_HOL_Obool)), _942410), _942412)), _942414))], (9079 ^ _782435) ^ [_942515, _942517, _942519, _942521, _942523] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942515, tc_HOL_Obool)), _942517), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942519, tc_fun(_942515, tc_HOL_Obool)), _942521), _942523)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942519, tc_fun(_942515, tc_HOL_Obool)), _942521), hAPP(hAPP(c_COMBB(tc_fun(_942515, tc_HOL_Obool), tc_fun(_942515, tc_HOL_Obool), _942519), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942515, tc_HOL_Obool)), _942517)), _942523)))], (9081 ^ _782435) ^ [_942605, _942607, _942609, _942611, _942613] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942605, tc_HOL_Obool)), _942607), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942609, tc_fun(_942605, tc_HOL_Obool)), _942611), _942613)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942609, tc_fun(_942605, tc_HOL_Obool)), _942611), hAPP(hAPP(c_COMBB(tc_fun(_942605, tc_HOL_Obool), tc_fun(_942605, tc_HOL_Obool), _942609), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942605, tc_HOL_Obool)), _942607)), _942613)))], (9083 ^ _782435) ^ [_942695, _942697, _942699, _942701, _942703] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942695, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942697, tc_fun(_942695, tc_HOL_Obool)), _942699), _942701)), _942703) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942697, tc_fun(_942695, tc_HOL_Obool)), _942699), hAPP(hAPP(c_COMBC(_942697, tc_fun(_942695, tc_HOL_Obool), tc_fun(_942695, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_942695, tc_HOL_Obool), tc_fun(tc_fun(_942695, tc_HOL_Obool), tc_fun(_942695, tc_HOL_Obool)), _942697), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942695, tc_HOL_Obool))), _942701)), _942703)))], (9085 ^ _782435) ^ [_942804, _942806, _942808, _942810, _942812, _942814, _942816] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942804, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942806, tc_fun(_942804, tc_HOL_Obool)), _942808), _942810)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942812, tc_fun(_942804, tc_HOL_Obool)), _942814), _942816)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942806, tc_fun(_942804, tc_HOL_Obool)), _942808), hAPP(hAPP(c_COMBB(tc_fun(_942812, tc_fun(_942804, tc_HOL_Obool)), tc_fun(_942804, tc_HOL_Obool), _942806), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_942812, tc_fun(_942804, tc_HOL_Obool)), _942814)), hAPP(hAPP(c_COMBC(_942806, tc_fun(_942812, tc_fun(_942804, tc_HOL_Obool)), tc_fun(_942812, tc_fun(_942804, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_942804, tc_HOL_Obool), tc_fun(_942804, tc_HOL_Obool)), tc_fun(tc_fun(_942812, tc_fun(_942804, tc_HOL_Obool)), tc_fun(_942812, tc_fun(_942804, tc_HOL_Obool))), _942806), c_COMBB(tc_fun(_942804, tc_HOL_Obool), tc_fun(_942804, tc_HOL_Obool), _942812)), hAPP(hAPP(c_COMBB(tc_fun(_942804, tc_HOL_Obool), tc_fun(tc_fun(_942804, tc_HOL_Obool), tc_fun(_942804, tc_HOL_Obool)), _942806), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_942804, tc_HOL_Obool))), _942810))), _942816))))], (9087 ^ _782435) ^ [_943007, _943009, _943011, _943013, _943015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_943007, tc_HOL_Obool)), hAPP(c_Set_Oimage(_943009, _943007, _943011), _943013)), _943015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(_943007, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_fun(_943009, tc_HOL_Obool), tc_fun(_943007, tc_HOL_Obool), c_Set_Oimage(_943009, _943007, _943011)), hAPP(c_Set_OPow(_943009), _943013))), hAPP(c_Set_OPow(_943007), _943015))))], (9093 ^ _782435) ^ [_943204, _943206, _943208, _943210, _943212] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943204, tc_fun(_943206, tc_HOL_Obool)), _943208), hAPP(hAPP(c_COMBS(_943204, tc_fun(_943206, tc_HOL_Obool), tc_fun(_943206, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_943206, tc_HOL_Obool), tc_fun(tc_fun(_943206, tc_HOL_Obool), tc_fun(_943206, tc_HOL_Obool)), _943204), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943206, tc_HOL_Obool))), _943210)), _943212)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_943206, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943204, tc_fun(_943206, tc_HOL_Obool)), _943208), _943210)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943204, tc_fun(_943206, tc_HOL_Obool)), _943208), _943212)))], (9105 ^ _782435) ^ [_943575, _943577, _943579, _943581] : [9107 ^ _782435 : [(9108 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_943577), 9106 ^ [_943575, _943577, _943579, _943581]), _943579)))], (9110 ^ _782435) ^ [] : [hAPP(_943581, 9106 ^ [_943575, _943577, _943579, _943581]) = c_Orderings_Otop__class_Otop(tc_fun(_943575, tc_HOL_Obool))]], -(c_Orderings_Otop__class_Otop(tc_fun(_943575, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943577, tc_fun(_943575, tc_HOL_Obool)), _943579), _943581))], (9095 ^ _782435) ^ [_943346, _943348, _943350, _943352] : [c_Orderings_Otop__class_Otop(tc_fun(_943346, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943348, tc_fun(_943346, tc_HOL_Obool)), _943350), _943352), 9098 ^ _782435 : [(9099 ^ _782435) ^ [_943462] : [hBOOL(hAPP(hAPP(c_member(_943348), _943462), _943350)), -(hAPP(_943352, _943462) = c_Orderings_Otop__class_Otop(tc_fun(_943346, tc_HOL_Obool)))]]], (9124 ^ _782435) ^ [_944055, _944057, _944059, _944061] : [9126 ^ _782435 : [(9127 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_944055), 9125 ^ [_944055, _944057, _944059, _944061]), _944059)))], (9129 ^ _782435) ^ [] : [hAPP(_944061, 9125 ^ [_944055, _944057, _944059, _944061]) = c_Orderings_Otop__class_Otop(tc_fun(_944057, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_944055, tc_fun(_944057, tc_HOL_Obool)), _944059), _944061) = c_Orderings_Otop__class_Otop(tc_fun(_944057, tc_HOL_Obool)))], (9114 ^ _782435) ^ [_943826, _943828, _943830, _943832] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_943826, tc_fun(_943828, tc_HOL_Obool)), _943830), _943832) = c_Orderings_Otop__class_Otop(tc_fun(_943828, tc_HOL_Obool)), 9117 ^ _782435 : [(9118 ^ _782435) ^ [_943942] : [hBOOL(hAPP(hAPP(c_member(_943826), _943942), _943830)), -(hAPP(_943832, _943942) = c_Orderings_Otop__class_Otop(tc_fun(_943828, tc_HOL_Obool)))]]], (9133 ^ _782435) ^ [_944285, _944287] : [class_Orderings_Otop(_944285), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944285), _944287), c_Orderings_Otop__class_Otop(_944285))))], (9139 ^ _782435) ^ [_944378, _944380] : [class_Lattices_Obounded__lattice__top(_944378), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944378), _944380), c_Orderings_Otop__class_Otop(_944378)) = c_Orderings_Otop__class_Otop(_944378))], (9145 ^ _782435) ^ [_944477, _944479] : [class_Lattices_Obounded__lattice__top(_944477), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944477), c_Orderings_Otop__class_Otop(_944477)), _944479) = c_Orderings_Otop__class_Otop(_944477))], (9151 ^ _782435) ^ [_944576, _944578, _944580, _944582] : [class_Lattices_Olattice(_944576), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944576), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944576), _944578), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944576), _944580), _944582))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944576), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944576), _944578), _944580)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944576), _944578), _944582)))))], (9157 ^ _782435) ^ [_944749, _944751, _944753, _944755] : [class_Lattices_Olattice(_944749), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_944749), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944749), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944749), _944751), _944753)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944749), _944751), _944755))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944749), _944751), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944749), _944753), _944755)))))], (9163 ^ _782435) ^ [_944922, _944924, _944926] : [class_Lattices_Oboolean__algebra(_944922), -(hAPP(c_Groups_Ouminus__class_Ouminus(_944922), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_944922), _944924), _944926)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_944922), hAPP(c_Groups_Ouminus__class_Ouminus(_944922), _944924)), hAPP(c_Groups_Ouminus__class_Ouminus(_944922), _944926)))], (9169 ^ _782435) ^ [_945061, _945063, _945065] : [class_Lattices_Oboolean__algebra(_945061), -(hAPP(c_Groups_Ouminus__class_Ouminus(_945061), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_945061), _945063), _945065)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_945061), hAPP(c_Groups_Ouminus__class_Ouminus(_945061), _945063)), hAPP(c_Groups_Ouminus__class_Ouminus(_945061), _945065)))], (9175 ^ _782435) ^ [_945200, _945202, _945204] : [class_Groups_Oordered__ab__group__add(_945200), -(hAPP(c_Set_Oimage(_945200, _945200, c_Groups_Ouminus__class_Ouminus(_945200)), c_SetInterval_Oord__class_OatLeastAtMost(_945200, _945202, _945204)) = c_SetInterval_Oord__class_OatLeastAtMost(_945200, hAPP(c_Groups_Ouminus__class_Ouminus(_945200), _945204), hAPP(c_Groups_Ouminus__class_Ouminus(_945200), _945202)))], (9181 ^ _782435) ^ [_945352, _945354, _945356, _945358] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945352, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945352, tc_HOL_Obool)), _945354), _945356)), _945358) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945352, tc_HOL_Obool)), _945354), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945352, tc_HOL_Obool)), _945356), _945358)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945352, tc_HOL_Obool)), _945358), _945354)))], (9187 ^ _782435) ^ [_945537, _945539, _945541, _945543] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_945537, tc_HOL_Obool)), _945543), _945539)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945537, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945537, tc_HOL_Obool)), _945539), _945541)), _945543) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945537, tc_HOL_Obool)), _945539), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945537, tc_HOL_Obool)), _945541), _945543)))], (9193 ^ _782435) ^ [_945728, _945730, _945732] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945728, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945728, tc_HOL_Obool)), _945730), _945732)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945728, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945728, tc_HOL_Obool)), _945730)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945728, tc_HOL_Obool)), _945732)))], (9195 ^ _782435) ^ [_945801, _945803, _945805] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945801, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_945801, tc_HOL_Obool)), _945803), _945805)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945801, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945801, tc_HOL_Obool)), _945803)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945801, tc_HOL_Obool)), _945805)))], (9197 ^ _782435) ^ [_945874, _945876] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945874, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945874, tc_HOL_Obool)), _945876)), _945876) = c_Orderings_Otop__class_Otop(tc_fun(_945874, tc_HOL_Obool)))], (9199 ^ _782435) ^ [_945923, _945925] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_945923, tc_HOL_Obool)), _945925), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_945923, tc_HOL_Obool)), _945925)) = c_Orderings_Otop__class_Otop(tc_fun(_945923, tc_HOL_Obool)))], (9201 ^ _782435) ^ [_945972, _945974, _945976, _945978] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_945972, tc_fun(_945974, tc_HOL_Obool)), _945976), _945978) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_945974, tc_HOL_Obool), hAPP(c_Set_Oimage(_945972, tc_fun(_945974, tc_HOL_Obool), _945978), _945976)))], (9203 ^ _782435) ^ [_946029, _946031, _946033, _946035] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_946029, tc_HOL_Obool), hAPP(c_Set_Oimage(_946031, tc_fun(_946029, tc_HOL_Obool), _946033), _946035)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946031, tc_fun(_946029, tc_HOL_Obool)), _946035), _946033))], (9205 ^ _782435) ^ [_946086, _946088, _946090, _946092, _946094] : [hBOOL(hAPP(hAPP(c_member(_946086), _946088), _946090)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946092, tc_HOL_Obool)), hAPP(_946094, _946088)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946086, tc_fun(_946092, tc_HOL_Obool)), _946090), _946094)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946086, tc_fun(_946092, tc_HOL_Obool)), _946090), _946094))], (9211 ^ _782435) ^ [_946259, _946261, _946263, _946265] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946259, tc_fun(_946261, tc_HOL_Obool)), _946263), _946265) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_946261, tc_HOL_Obool), hAPP(c_Set_Oimage(_946259, tc_fun(_946261, tc_HOL_Obool), _946265), _946263)))], (9213 ^ _782435) ^ [_946316, _946318, _946320, _946322] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_946316, tc_HOL_Obool), hAPP(c_Set_Oimage(_946318, tc_fun(_946316, tc_HOL_Obool), _946320), _946322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946318, tc_fun(_946316, tc_HOL_Obool)), _946322), _946320))], (9215 ^ _782435) ^ [_946373, _946375, _946377, _946379, _946381] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946373, tc_fun(_946375, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_946373, tc_HOL_Obool)), _946377), _946379)), _946381) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_946375, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946373, tc_fun(_946375, tc_HOL_Obool)), _946377), _946381)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946373, tc_fun(_946375, tc_HOL_Obool)), _946379), _946381)))], (9217 ^ _782435) ^ [_946483, _946485, _946487, _946489] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946483, tc_fun(_946485, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946483, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946485, tc_HOL_Obool), tc_fun(_946485, tc_HOL_Obool), _946483), hAPP(c_COMBC(_946485, tc_fun(_946485, tc_HOL_Obool), tc_HOL_Obool), c_member(_946485))), _946487)), _946489)), -(hBOOL(hAPP(hAPP(c_member(_946485), _946489), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946483, tc_fun(_946485, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946483, tc_HOL_Obool))), _946487))))], (9223 ^ _782435) ^ [_946702, _946704, _946706, _946708] : [hBOOL(hAPP(hAPP(c_member(_946704), _946708), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946702, tc_fun(_946704, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946702, tc_HOL_Obool))), _946706))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_946702, tc_fun(_946704, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946702, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946704, tc_HOL_Obool), tc_fun(_946704, tc_HOL_Obool), _946702), hAPP(c_COMBC(_946704, tc_fun(_946704, tc_HOL_Obool), tc_HOL_Obool), c_member(_946704))), _946706)), _946708)))], (9229 ^ _782435) ^ [_946948, _946950, _946952, _946954] : [hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946948, tc_fun(_946950, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946948, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_946950, tc_HOL_Obool), tc_fun(_946950, tc_HOL_Obool), _946948), hAPP(c_COMBC(_946950, tc_fun(_946950, tc_HOL_Obool), tc_HOL_Obool), c_member(_946950))), _946952)), _946954)), -(hBOOL(hAPP(hAPP(c_member(_946950), _946954), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_946948, tc_fun(_946950, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_946948, tc_HOL_Obool))), _946952))))], (9235 ^ _782435) ^ [_947167, _947169, _947171, _947173] : [hBOOL(hAPP(hAPP(c_member(_947169), _947173), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_947167, tc_fun(_947169, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_947167, tc_HOL_Obool))), _947171))), -(hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_947167, tc_fun(_947169, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_947167, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_947169, tc_HOL_Obool), tc_fun(_947169, tc_HOL_Obool), _947167), hAPP(c_COMBC(_947169, tc_fun(_947169, tc_HOL_Obool), tc_HOL_Obool), c_member(_947169))), _947171)), _947173)))], (9241 ^ _782435) ^ [_947392, _947394, _947396, _947398] : [-(hAPP(c_Set_Oimage(_947392, _947394, _947396), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947392, tc_HOL_Obool), _947398)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947392, tc_HOL_Obool), tc_fun(_947394, tc_HOL_Obool)), _947398), c_Set_Oimage(_947392, _947394, _947396)))], (9243 ^ _782435) ^ [_947453, _947455, _947457] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_947453, tc_HOL_Obool), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_947453, tc_HOL_Obool), tc_HOL_Obool)), _947455), _947457)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947453, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_947453, tc_HOL_Obool), _947455)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_947453, tc_HOL_Obool), _947457)))], (9245 ^ _782435) ^ [_947523, _947525, _947527] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947523, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947523, tc_HOL_Obool), _947525)), _947527) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947523, tc_HOL_Obool), tc_fun(_947523, tc_HOL_Obool)), _947525), hAPP(hAPP(c_COMBC(tc_fun(_947523, tc_HOL_Obool), tc_fun(_947523, tc_HOL_Obool), tc_fun(_947523, tc_HOL_Obool)), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947523, tc_HOL_Obool))), _947527)))], (9247 ^ _782435) ^ [_947606, _947608, _947610] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947606, tc_HOL_Obool)), _947608), c_Complete__Lattice_OSup__class_OSup(tc_fun(_947606, tc_HOL_Obool), _947610)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_947606, tc_HOL_Obool), tc_fun(_947606, tc_HOL_Obool)), _947610), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_947606, tc_HOL_Obool)), _947608)))], (9249 ^ _782435) ^ [_947673, _947675, _947677] : [class_Groups_Oordered__ab__group__add(_947673), -(hAPP(c_Set_Oimage(_947673, _947673, c_Groups_Ouminus__class_Ouminus(_947673)), c_SetInterval_Oord__class_OgreaterThanAtMost(_947673, _947675, _947677)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_947673, hAPP(c_Groups_Ouminus__class_Ouminus(_947673), _947677)), hAPP(c_Groups_Ouminus__class_Ouminus(_947673), _947675)))], (9255 ^ _782435) ^ [_947808, _947810, _947812] : [class_Groups_Oordered__ab__group__add(_947808), -(hAPP(c_Set_Oimage(_947808, _947808, c_Groups_Ouminus__class_Ouminus(_947808)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_947808, _947810), _947812)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_947808, hAPP(c_Groups_Ouminus__class_Ouminus(_947808), _947812), hAPP(c_Groups_Ouminus__class_Ouminus(_947808), _947810)))], (9261 ^ _782435) ^ [_947943, _947945] : [class_Lattices_Oboolean__algebra(_947943), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_947943), hAPP(c_Groups_Ouminus__class_Ouminus(_947943), _947945)), _947945) = c_Orderings_Otop__class_Otop(_947943))], (9267 ^ _782435) ^ [_948048, _948050, _948052, _948054] : [hAPP(c_Set_Oimage(_948048, _948050, _948052), c_Orderings_Otop__class_Otop(tc_fun(_948048, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_948050, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_948050, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_948050, tc_HOL_Obool)), hAPP(c_Set_Oimage(_948048, _948050, _948052), _948054))), hAPP(c_Set_Oimage(_948048, _948050, _948052), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_948048, tc_HOL_Obool)), _948054)))))], (9273 ^ _782435) ^ [_948259, _948261, _948263] : [hAPP(c_Set_Oimage(_948261, tc_fun(_948261, tc_HOL_Obool), _948259), _948263) = hAPP(c_Set_OPow(_948261), _948263)], (9275 ^ _782435) ^ [_948301, _948303, _948305, _948307] : [class_Orderings_Oorder(_948301), class_Orderings_Oorder(_948303), c_Orderings_Oorder__class_Omono(_948303, _948301, _948305), -(c_Orderings_Oord__class_OLeast(_948301, hAPP(hAPP(c_COMBC(_948301, tc_fun(_948301, tc_HOL_Obool), tc_HOL_Obool), c_member(_948301)), hAPP(c_Set_Oimage(_948303, _948301, _948305), _948307))) = hAPP(_948305, c_Orderings_Oord__class_OLeast(_948303, hAPP(hAPP(c_COMBC(_948303, tc_fun(_948303, tc_HOL_Obool), tc_HOL_Obool), c_member(_948303)), _948307)))), 9288 ^ _782435 : [(9289 ^ _782435) ^ [_948585] : [hBOOL(hAPP(hAPP(c_member(_948303), _948585), _948307)), 9293 ^ _782435 : [(9294 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_948303), 9292 ^ [_948301, _948303, _948305, _948307, _948585]), _948307)))], (9296 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_948303), _948585), 9292 ^ [_948301, _948303, _948305, _948307, _948585]))]]]]], (9300 ^ _782435) ^ [_948878, _948880, _948882] : [class_Lattices_Oboolean__algebra(_948878), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_948878), _948880), _948882) = c_Orderings_Obot__class_Obot(_948878), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_948878), _948880), _948882) = c_Orderings_Otop__class_Otop(_948878), -(hAPP(c_Groups_Ouminus__class_Ouminus(_948878), _948880) = _948882)], (9314 ^ _782435) ^ [_949113, _949115] : [-(hAPP(c_Set_Oimage(_949113, _949113, c_COMBI(_949113)), _949115) = _949115)], (9316 ^ _782435) ^ [_949147, _949149, _949151, _949153, _949155] : [hBOOL(hAPP(hAPP(c_member(_949147), _949149), hAPP(c_Set_Oimage(_949151, _949147, _949153), _949155))), 9320 ^ _782435 : [(9321 ^ _782435) ^ [] : [-(_949149 = hAPP(_949153, 9319 ^ [_949147, _949149, _949151, _949153, _949155]))], (9323 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_949151), 9319 ^ [_949147, _949149, _949151, _949153, _949155]), _949155)))]]], (9325 ^ _782435) ^ [_949339, _949341, _949343, _949345, _949347] : [9327 ^ _782435 : [(9328 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_949339), 9326 ^ [_949339, _949341, _949343, _949345, _949347]), _949341)))], (9330 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_949343), hAPP(_949345, 9326 ^ [_949339, _949341, _949343, _949345, _949347])), _949347))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_949343, tc_HOL_Obool)), hAPP(c_Set_Oimage(_949339, _949343, _949345), _949341)), _949347)))], (9334 ^ _782435) ^ [_949581, _949583, _949585] : [class_Orderings_Oorder(_949581), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949581, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949581, _949583, _949585)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949581), _949585)) = c_Orderings_Obot__class_Obot(tc_fun(_949581, tc_HOL_Obool)))], (9340 ^ _782435) ^ [_949708, _949710, _949712] : [class_Orderings_Oorder(_949708), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949708, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_949708), _949710)), c_SetInterval_Oord__class_OgreaterThanAtMost(_949708, _949710, _949712)) = c_Orderings_Obot__class_Obot(tc_fun(_949708, tc_HOL_Obool)))], (9346 ^ _782435) ^ [_949835, _949837, _949839] : [class_Orderings_Oorder(_949835), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949835, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_949835, _949837, _949839)), hAPP(c_SetInterval_Oord__class_OgreaterThan(_949835), _949839)) = c_Orderings_Obot__class_Obot(tc_fun(_949835, tc_HOL_Obool)))], (9352 ^ _782435) ^ [_949962, _949964, _949966] : [class_Orderings_Oorder(_949962), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_949962, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_949962, _949964), _949966)), hAPP(c_SetInterval_Oord__class_OatLeast(_949962), _949966)) = c_Orderings_Obot__class_Obot(tc_fun(_949962, tc_HOL_Obool)))], (9358 ^ _782435) ^ [_950093, _950095] : [-(hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(_950093, tc_HOL_Obool)), _950095)))], (9360 ^ _782435) ^ [_950137, _950139] : [hBOOL(hAPP(hAPP(c_member(_950137), _950139), c_Orderings_Obot__class_Obot(tc_fun(_950137, tc_HOL_Obool))))], (9362 ^ _782435) ^ [_950174, _950176] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_950174, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_950174, tc_HOL_Obool))), _950176)))], (9364 ^ _782435) ^ [_950223] : [c_Orderings_Otop__class_Otop(tc_fun(_950223, tc_HOL_Obool)) = c_Orderings_Obot__class_Obot(tc_fun(_950223, tc_HOL_Obool))], (9366 ^ _782435) ^ [_950256, _950258, _950260] : [class_Orderings_Obot(_950256), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_950258, _950256)), _950260) = c_Orderings_Obot__class_Obot(_950256))], (9372 ^ _782435) ^ [_950353, _950355, _950357] : [class_Orderings_Obot(_950353), -(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_950355, _950353)), _950357) = c_Orderings_Obot__class_Obot(_950353))], (9378 ^ _782435) ^ [_950450] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_950450, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_950450, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_950450, tc_HOL_Obool)))], (9380 ^ _782435) ^ [_950492] : [class_Complete__Lattice_Ocomplete__lattice(_950492), -(c_Complete__Lattice_OSup__class_OSup(_950492, c_Orderings_Obot__class_Obot(tc_fun(_950492, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_950492))], (9386 ^ _782435) ^ [_950594, _950596] : [-(hBOOL(hAPP(hAPP(c_member(_950594), 9387 ^ [_950594, _950596]), _950596))), -(_950596 = c_Orderings_Obot__class_Obot(tc_fun(_950594, tc_HOL_Obool)))], (9393 ^ _782435) ^ [_950645, _950647] : [_950647 = c_Orderings_Obot__class_Obot(tc_fun(_950645, tc_HOL_Obool)), 9396 ^ _782435 : [(9397 ^ _782435) ^ [_950725] : [hBOOL(hAPP(hAPP(c_member(_950645), _950725), _950647))]]], (9399 ^ _782435) ^ [_950776, _950778] : [9400 ^ _782435 : [(9401 ^ _782435) ^ [_950829] : [hBOOL(hAPP(hAPP(c_member(_950776), _950829), _950778))]], _950778 = c_Orderings_Obot__class_Obot(tc_fun(_950776, tc_HOL_Obool))], (9405 ^ _782435) ^ [_950885, _950887] : [-(_950887 = c_Orderings_Obot__class_Obot(tc_fun(_950885, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_950885), 9408 ^ [_950885, _950887]), _950887)))], (9412 ^ _782435) ^ [_950954, _950956] : [hBOOL(hAPP(hAPP(c_member(_950954), _950956), c_Orderings_Obot__class_Obot(tc_fun(_950954, tc_HOL_Obool))))], (9414 ^ _782435) ^ [_950991, _950993, _950995] : [_950991 = c_Orderings_Obot__class_Obot(tc_fun(_950993, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(_950993), _950995), _950991))], (9420 ^ _782435) ^ [_951110, _951112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951110, tc_HOL_Obool)), _951112), c_Orderings_Obot__class_Obot(tc_fun(_951110, tc_HOL_Obool)))), -(_951112 = c_Orderings_Obot__class_Obot(tc_fun(_951110, tc_HOL_Obool)))], (9426 ^ _782435) ^ [_951223, _951225] : [_951225 = c_Orderings_Obot__class_Obot(tc_fun(_951223, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_951223, tc_HOL_Obool)), _951225), c_Orderings_Obot__class_Obot(tc_fun(_951223, tc_HOL_Obool)))))], (9432 ^ _782435) ^ [_951363, _951365, _951367, _951369] : [c_Orderings_Obot__class_Obot(tc_fun(_951363, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_951365, _951363, _951367), _951369), -(_951369 = c_Orderings_Obot__class_Obot(tc_fun(_951365, tc_HOL_Obool)))], (9438 ^ _782435) ^ [_951474, _951476, _951478, _951480] : [_951480 = c_Orderings_Obot__class_Obot(tc_fun(_951476, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(_951474, tc_HOL_Obool)) = hAPP(c_Set_Oimage(_951476, _951474, _951478), _951480))], (9444 ^ _782435) ^ [_951591, _951593, _951595] : [-(hAPP(c_Set_Oimage(_951591, _951593, _951595), c_Orderings_Obot__class_Obot(tc_fun(_951591, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_951593, tc_HOL_Obool)))], (9446 ^ _782435) ^ [_951656, _951658, _951660, _951662] : [hAPP(c_Set_Oimage(_951656, _951658, _951660), _951662) = c_Orderings_Obot__class_Obot(tc_fun(_951658, tc_HOL_Obool)), -(_951662 = c_Orderings_Obot__class_Obot(tc_fun(_951656, tc_HOL_Obool)))], (9452 ^ _782435) ^ [_951767, _951769, _951771, _951773] : [_951773 = c_Orderings_Obot__class_Obot(tc_fun(_951767, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_951767, _951769, _951771), _951773) = c_Orderings_Obot__class_Obot(tc_fun(_951769, tc_HOL_Obool)))], (9458 ^ _782435) ^ [_951884, _951886] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951884, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_951884, tc_HOL_Obool))), _951886) = _951886)], (9460 ^ _782435) ^ [_951925, _951927] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951925, tc_HOL_Obool)), _951927), c_Orderings_Obot__class_Obot(tc_fun(_951925, tc_HOL_Obool))) = _951927)], (9462 ^ _782435) ^ [_951984, _951986, _951988] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_951984, tc_HOL_Obool)), _951986), _951988) = c_Orderings_Obot__class_Obot(tc_fun(_951984, tc_HOL_Obool)), 9465 ^ _782435 : [(9466 ^ _782435) ^ [] : [-(_951986 = c_Orderings_Obot__class_Obot(tc_fun(_951984, tc_HOL_Obool)))], (9468 ^ _782435) ^ [] : [-(_951988 = c_Orderings_Obot__class_Obot(tc_fun(_951984, tc_HOL_Obool)))]]], (9470 ^ _782435) ^ [_952137, _952139, _952141] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_952137, tc_HOL_Obool)), _952139), _952141) = c_Orderings_Obot__class_Obot(tc_fun(_952137, tc_HOL_Obool))), _952139 = c_Orderings_Obot__class_Obot(tc_fun(_952137, tc_HOL_Obool)), _952141 = c_Orderings_Obot__class_Obot(tc_fun(_952137, tc_HOL_Obool))], (9480 ^ _782435) ^ [_952324, _952326] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952324, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_952324, tc_HOL_Obool))), _952326) = c_Orderings_Obot__class_Obot(tc_fun(_952324, tc_HOL_Obool)))], (9482 ^ _782435) ^ [_952370, _952372] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952370, tc_HOL_Obool)), _952372), c_Orderings_Obot__class_Obot(tc_fun(_952370, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_952370, tc_HOL_Obool)))], (9498 ^ _782435) ^ [_952748, _952750, _952752] : [9500 ^ _782435 : [(9501 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952748), 9499 ^ [_952748, _952750, _952752]), _952750)))], (9504 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_952748), 9502 ^ [_952748, _952750, _952752]), _952752)))], (9506 ^ _782435) ^ [] : [-(9499 ^ [_952748, _952750, _952752] = 9502 ^ [_952748, _952750, _952752])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952748, tc_HOL_Obool)), _952750), _952752) = c_Orderings_Obot__class_Obot(tc_fun(_952748, tc_HOL_Obool)))], (9484 ^ _782435) ^ [_952434, _952436, _952438] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_952434, tc_HOL_Obool)), _952436), _952438) = c_Orderings_Obot__class_Obot(tc_fun(_952434, tc_HOL_Obool)), 9487 ^ _782435 : [(9488 ^ _782435) ^ [_952558] : [hBOOL(hAPP(hAPP(c_member(_952434), _952558), _952436)), 9491 ^ _782435 : [(9492 ^ _782435) ^ [_952648] : [hBOOL(hAPP(hAPP(c_member(_952434), _952648), _952438)), _952558 = _952648]]]]], (9510 ^ _782435) ^ [_952909] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952909, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_952909, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_952909, tc_HOL_Obool)))], (9512 ^ _782435) ^ [_952950] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_952950, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_952950, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_952950, tc_HOL_Obool)))], (9514 ^ _782435) ^ [_952991, _952993] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_952991, _952993, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_952991), tc_HOL_Obool))))], (9516 ^ _782435) ^ [_953024, _953026] : [-(c_Hoare__Mirabelle_Ohoare__derivs(_953024, _953026, c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_953024), tc_HOL_Obool))))], (9518 ^ _782435) ^ [_953069, _953071] : [hAPP(c_Set_OPow(_953069), _953071) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_953069, tc_HOL_Obool), tc_HOL_Obool))], (9520 ^ _782435) ^ [_953107] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_953107, tc_HOL_Obool), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_953107, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_953107, tc_HOL_Obool)))], (9522 ^ _782435) ^ [_953149] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_953149, tc_HOL_Obool), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_953149, tc_HOL_Obool), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_953149, tc_HOL_Obool)))], (9524 ^ _782435) ^ [_953191, _953193, _953195, _953197, _953199] : [class_Orderings_Oorder(_953191), class_Orderings_Oorder(_953193), c_Orderings_Oorder__class_Omono(_953193, _953191, _953195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953193), _953197), _953199)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953191), hAPP(_953195, _953197)), hAPP(_953195, _953199))))], (9542 ^ _782435) ^ [_953503, _953505] : [hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_953503, tc_HOL_Obool)), _953505)), -(hBOOL(hAPP(hAPP(c_member(_953503), _953505), c_Orderings_Obot__class_Obot(tc_fun(_953503, tc_HOL_Obool)))))], (9548 ^ _782435) ^ [_953614, _953616] : [hBOOL(hAPP(hAPP(c_member(_953614), _953616), c_Orderings_Obot__class_Obot(tc_fun(_953614, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_953614, tc_HOL_Obool)), _953616)))], (9554 ^ _782435) ^ [_953731, _953733] : [class_Orderings_Obot(_953731), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_953731), c_Orderings_Obot__class_Obot(_953731)), _953733)))], (9560 ^ _782435) ^ [_953824, _953826, _953828, _953830] : [class_Complete__Lattice_Ocomplete__lattice(_953824), -(_953826 = c_Orderings_Obot__class_Obot(tc_fun(_953828, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_953828, _953824), _953826), hAPP(c_COMBK(_953824, _953828), _953830)) = _953830)], (9580 ^ _782435) ^ [_954208, _954210, _954212, _954214] : [9582 ^ _782435 : [(9583 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954208), 9581 ^ [_954208, _954210, _954212, _954214]), _954212)))], (9585 ^ _782435) ^ [] : [hAPP(_954214, 9581 ^ [_954208, _954210, _954212, _954214]) = c_Orderings_Obot__class_Obot(tc_fun(_954210, tc_HOL_Obool))]], -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954208, tc_fun(_954210, tc_HOL_Obool)), _954212), _954214) = c_Orderings_Obot__class_Obot(tc_fun(_954210, tc_HOL_Obool)))], (9570 ^ _782435) ^ [_953979, _953981, _953983, _953985] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_953979, tc_fun(_953981, tc_HOL_Obool)), _953983), _953985) = c_Orderings_Obot__class_Obot(tc_fun(_953981, tc_HOL_Obool)), 9573 ^ _782435 : [(9574 ^ _782435) ^ [_954095] : [hBOOL(hAPP(hAPP(c_member(_953979), _954095), _953983)), -(hAPP(_953985, _954095) = c_Orderings_Obot__class_Obot(tc_fun(_953981, tc_HOL_Obool)))]]], (9589 ^ _782435) ^ [_954453, _954455, _954457, _954459] : [_954453 = c_Orderings_Obot__class_Obot(tc_fun(_954455, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954455, tc_fun(_954457, tc_HOL_Obool)), _954453), hAPP(c_COMBK(tc_fun(_954457, tc_HOL_Obool), _954455), _954459)) = c_Orderings_Obot__class_Obot(tc_fun(_954457, tc_HOL_Obool)))], (9595 ^ _782435) ^ [_954590, _954592, _954594, _954596] : [-(_954590 = c_Orderings_Obot__class_Obot(tc_fun(_954592, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954592, tc_fun(_954594, tc_HOL_Obool)), _954590), hAPP(c_COMBK(tc_fun(_954594, tc_HOL_Obool), _954592), _954596)) = _954596)], (9601 ^ _782435) ^ [_954658, _954660, _954662] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954658, tc_fun(_954660, tc_HOL_Obool)), _954662), hAPP(c_COMBK(tc_fun(_954660, tc_HOL_Obool), _954658), c_Orderings_Obot__class_Obot(tc_fun(_954660, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_954660, tc_HOL_Obool)))], (9613 ^ _782435) ^ [_954966, _954968, _954970, _954972] : [9615 ^ _782435 : [(9616 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_954968), 9614 ^ [_954966, _954968, _954970, _954972]), _954970)))], (9618 ^ _782435) ^ [] : [hAPP(_954972, 9614 ^ [_954966, _954968, _954970, _954972]) = c_Orderings_Obot__class_Obot(tc_fun(_954966, tc_HOL_Obool))]], -(c_Orderings_Obot__class_Obot(tc_fun(_954966, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954968, tc_fun(_954966, tc_HOL_Obool)), _954970), _954972))], (9603 ^ _782435) ^ [_954737, _954739, _954741, _954743] : [c_Orderings_Obot__class_Obot(tc_fun(_954737, tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_954739, tc_fun(_954737, tc_HOL_Obool)), _954741), _954743), 9606 ^ _782435 : [(9607 ^ _782435) ^ [_954853] : [hBOOL(hAPP(hAPP(c_member(_954739), _954853), _954741)), -(hAPP(_954743, _954853) = c_Orderings_Obot__class_Obot(tc_fun(_954737, tc_HOL_Obool)))]]], (9622 ^ _782435) ^ [_955196, _955198, _955200, _955202] : [class_Complete__Lattice_Ocomplete__lattice(_955196), -(_955198 = c_Orderings_Obot__class_Obot(tc_fun(_955200, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955200, _955196), _955198), hAPP(c_COMBK(_955196, _955200), _955202)) = _955202)], (9632 ^ _782435) ^ [_955330, _955332, _955334] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955330, tc_fun(_955332, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_955330, tc_HOL_Obool))), _955334) = c_Orderings_Otop__class_Otop(tc_fun(_955332, tc_HOL_Obool)))], (9634 ^ _782435) ^ [_955394, _955396, _955398, _955400] : [_955394 = c_Orderings_Obot__class_Obot(tc_fun(_955396, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955396, tc_fun(_955398, tc_HOL_Obool)), _955394), hAPP(c_COMBK(tc_fun(_955398, tc_HOL_Obool), _955396), _955400)) = c_Orderings_Otop__class_Otop(tc_fun(_955398, tc_HOL_Obool)))], (9640 ^ _782435) ^ [_955531, _955533, _955535, _955537] : [-(_955531 = c_Orderings_Obot__class_Obot(tc_fun(_955533, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_955533, tc_fun(_955535, tc_HOL_Obool)), _955531), hAPP(c_COMBK(tc_fun(_955535, tc_HOL_Obool), _955533), _955537)) = _955537)], (9646 ^ _782435) ^ [_955599, _955601] : [class_Lattices_Obounded__lattice__bot(_955599), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955599), c_Orderings_Obot__class_Obot(_955599)), _955601) = _955601)], (9652 ^ _782435) ^ [_955694, _955696] : [class_Lattices_Obounded__lattice__bot(_955694), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955694), _955696), c_Orderings_Obot__class_Obot(_955694)) = _955696)], (9658 ^ _782435) ^ [_955789, _955791, _955793] : [class_Lattices_Obounded__lattice__bot(_955789), 9661 ^ _782435 : [(9662 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955789), _955791), _955793) = c_Orderings_Obot__class_Obot(_955789), 9665 ^ _782435 : [(9666 ^ _782435) ^ [] : [-(_955791 = c_Orderings_Obot__class_Obot(_955789))], (9668 ^ _782435) ^ [] : [-(_955793 = c_Orderings_Obot__class_Obot(_955789))]]], (9670 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_955789), _955791), _955793) = c_Orderings_Obot__class_Obot(_955789)), _955791 = c_Orderings_Obot__class_Obot(_955789), _955793 = c_Orderings_Obot__class_Obot(_955789)]]], (9680 ^ _782435) ^ [_956116, _956118] : [class_Lattices_Obounded__lattice__bot(_956116), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956116), c_Orderings_Obot__class_Obot(_956116)), _956118) = c_Orderings_Obot__class_Obot(_956116))], (9686 ^ _782435) ^ [_956215, _956217] : [class_Lattices_Obounded__lattice__bot(_956215), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_956215), _956217), c_Orderings_Obot__class_Obot(_956215)) = c_Orderings_Obot__class_Obot(_956215))], (9692 ^ _782435) ^ [_956314] : [class_Complete__Lattice_Ocomplete__lattice(_956314), -(c_Complete__Lattice_OInf__class_OInf(_956314, c_Orderings_Otop__class_Otop(tc_fun(_956314, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(_956314))], (9698 ^ _782435) ^ [_956407, _956409, _956411] : [class_Orderings_Oorder(_956407), class_Orderings_Oorder(_956409), c_Orderings_Oorder__class_Ostrict__mono(_956409, _956407, _956411), -(c_Orderings_Oorder__class_Omono(_956409, _956407, _956411))], (9712 ^ _782435) ^ [_956596, _956598, _956600] : [class_Orderings_Oorder(_956596), 9715 ^ _782435 : [(9716 ^ _782435) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_956596, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_956596, _956598, _956600), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956596), _956598), _956600))], (9722 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956596), _956598), _956600))), -(c_Orderings_Obot__class_Obot(tc_fun(_956596, tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(_956596, _956598, _956600))]]], (9728 ^ _782435) ^ [_956815, _956817, _956819] : [class_Orderings_Oorder(_956815), 9731 ^ _782435 : [(9732 ^ _782435) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_956815, _956817, _956819) = c_Orderings_Obot__class_Obot(tc_fun(_956815, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956815), _956817), _956819))], (9738 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_956815), _956817), _956819))), -(c_SetInterval_Oord__class_OatLeastAtMost(_956815, _956817, _956819) = c_Orderings_Obot__class_Obot(tc_fun(_956815, tc_HOL_Obool)))]]], (9744 ^ _782435) ^ [_957034, _957036, _957038] : [class_Orderings_Oorder(_957034), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957034), _957036), _957038)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957034, _957038), _957036) = c_Orderings_Obot__class_Obot(tc_fun(_957034, tc_HOL_Obool)))], (9754 ^ _782435) ^ [_957201, _957203, _957205, _957207] : [class_Orderings_Oorder(_957201), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957201, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957201, _957203), _957205)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_957201, _957205), _957207)) = c_Orderings_Obot__class_Obot(tc_fun(_957201, tc_HOL_Obool)))], (9760 ^ _782435) ^ [_957351, _957353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957351, tc_HOL_Obool)), _957353), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957351, tc_HOL_Obool)), _957353))), -(_957353 = c_Orderings_Obot__class_Obot(tc_fun(_957351, tc_HOL_Obool)))], (9766 ^ _782435) ^ [_957470, _957472] : [_957472 = c_Orderings_Obot__class_Obot(tc_fun(_957470, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_957470, tc_HOL_Obool)), _957472), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957470, tc_HOL_Obool)), _957472))))], (9772 ^ _782435) ^ [_957595, _957597] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957595, tc_HOL_Obool)), _957597), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957595, tc_HOL_Obool)), _957597)) = c_Orderings_Obot__class_Obot(tc_fun(_957595, tc_HOL_Obool)))], (9774 ^ _782435) ^ [_957644, _957646] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957644, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_957644, tc_HOL_Obool)), _957646)), _957646) = c_Orderings_Obot__class_Obot(tc_fun(_957644, tc_HOL_Obool)))], (9776 ^ _782435) ^ [_957693, _957695, _957697] : [class_Orderings_Oorder(_957693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_957693), _957695), _957697)), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_957693, _957697, _957695) = c_Orderings_Obot__class_Obot(tc_fun(_957693, tc_HOL_Obool)))], (9786 ^ _782435) ^ [_957856] : [class_Complete__Lattice_Ocomplete__lattice(_957856), -(c_Complete__Lattice_OInf__class_OInf(_957856, c_Orderings_Obot__class_Obot(tc_fun(_957856, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(_957856))], (9802 ^ _782435) ^ [_958235, _958237, _958239] : [9804 ^ _782435 : [(9805 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_958235, tc_HOL_Obool)), 9803 ^ [_958235, _958237, _958239]), _958237)))], (9807 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958235, tc_HOL_Obool)), 9803 ^ [_958235, _958237, _958239]), _958239) = c_Orderings_Obot__class_Obot(tc_fun(_958235, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958235, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_958235, tc_HOL_Obool), _958237)), _958239) = c_Orderings_Obot__class_Obot(tc_fun(_958235, tc_HOL_Obool)))], (9792 ^ _782435) ^ [_957967, _957969, _957971] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957967, tc_HOL_Obool)), c_Complete__Lattice_OSup__class_OSup(tc_fun(_957967, tc_HOL_Obool), _957969)), _957971) = c_Orderings_Obot__class_Obot(tc_fun(_957967, tc_HOL_Obool)), 9795 ^ _782435 : [(9796 ^ _782435) ^ [_958102] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_957967, tc_HOL_Obool)), _958102), _957969)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_957967, tc_HOL_Obool)), _958102), _957971) = c_Orderings_Obot__class_Obot(tc_fun(_957967, tc_HOL_Obool)))]]], (9811 ^ _782435) ^ [_958498, _958500] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_958498, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_958498, tc_HOL_Obool))), hAPP(c_Set_OPow(_958498), _958500))))], (9813 ^ _782435) ^ [_958543, _958545, _958547, _958549] : [class_Orderings_Oorder(_958543), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958543, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_958543, _958545, _958547)), c_SetInterval_Oord__class_OgreaterThanAtMost(_958543, _958547, _958549)) = c_Orderings_Obot__class_Obot(tc_fun(_958543, tc_HOL_Obool)))], (9819 ^ _782435) ^ [_958670, _958672, _958674, _958676, _958678] : [c_Orderings_Oorder__class_Omono(tc_fun(_958670, tc_HOL_Obool), tc_fun(_958672, tc_HOL_Obool), _958674), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958672, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958672, tc_HOL_Obool)), hAPP(_958674, _958676)), hAPP(_958674, _958678))), hAPP(_958674, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_958670, tc_HOL_Obool)), _958676), _958678)))))], (9825 ^ _782435) ^ [_958849, _958851, _958853, _958855, _958857] : [c_Orderings_Oorder__class_Omono(tc_fun(_958849, tc_HOL_Obool), tc_fun(_958851, tc_HOL_Obool), _958853), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_958851, tc_HOL_Obool)), hAPP(_958853, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958849, tc_HOL_Obool)), _958855), _958857))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_958851, tc_HOL_Obool)), hAPP(_958853, _958855)), hAPP(_958853, _958857)))))], (9831 ^ _782435) ^ [_959046, _959048, _959050, _959052, _959054] : [_959046 = c_Orderings_Obot__class_Obot(tc_fun(_959048, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959048, tc_fun(_959050, tc_HOL_Obool)), _959046), hAPP(hAPP(c_COMBB(tc_fun(_959050, tc_HOL_Obool), tc_fun(_959050, tc_HOL_Obool), _959048), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959050, tc_HOL_Obool)), _959052)), _959054)) = c_Orderings_Obot__class_Obot(tc_fun(_959050, tc_HOL_Obool)))], (9837 ^ _782435) ^ [_959215, _959217, _959219, _959221, _959223] : [-(_959215 = c_Orderings_Obot__class_Obot(tc_fun(_959217, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959217, tc_fun(_959219, tc_HOL_Obool)), _959215), hAPP(hAPP(c_COMBB(tc_fun(_959219, tc_HOL_Obool), tc_fun(_959219, tc_HOL_Obool), _959217), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959219, tc_HOL_Obool)), _959221)), _959223)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959219, tc_HOL_Obool)), _959221), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959217, tc_fun(_959219, tc_HOL_Obool)), _959215), _959223)))], (9843 ^ _782435) ^ [_959341, _959343, _959345, _959347, _959349] : [_959341 = c_Orderings_Obot__class_Obot(tc_fun(_959343, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959343, tc_fun(_959345, tc_HOL_Obool)), _959341), hAPP(hAPP(c_COMBC(_959343, tc_fun(_959345, tc_HOL_Obool), tc_fun(_959345, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_959345, tc_HOL_Obool), tc_fun(tc_fun(_959345, tc_HOL_Obool), tc_fun(_959345, tc_HOL_Obool)), _959343), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959345, tc_HOL_Obool))), _959347)), _959349)) = c_Orderings_Obot__class_Obot(tc_fun(_959345, tc_HOL_Obool)))], (9849 ^ _782435) ^ [_959548, _959550, _959552, _959554, _959556] : [-(_959548 = c_Orderings_Obot__class_Obot(tc_fun(_959550, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959550, tc_fun(_959552, tc_HOL_Obool)), _959548), hAPP(hAPP(c_COMBC(_959550, tc_fun(_959552, tc_HOL_Obool), tc_fun(_959552, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_959552, tc_HOL_Obool), tc_fun(tc_fun(_959552, tc_HOL_Obool), tc_fun(_959552, tc_HOL_Obool)), _959550), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959552, tc_HOL_Obool))), _959554)), _959556)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959552, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959550, tc_fun(_959552, tc_HOL_Obool)), _959548), _959554)), _959556))], (9855 ^ _782435) ^ [_959693, _959695, _959697, _959699, _959701] : [_959693 = c_Orderings_Obot__class_Obot(tc_fun(_959695, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959697, tc_HOL_Obool)), _959699), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959695, tc_fun(_959697, tc_HOL_Obool)), _959693), _959701)) = _959699)], (9861 ^ _782435) ^ [_959826, _959828, _959830, _959832, _959834] : [-(_959826 = c_Orderings_Obot__class_Obot(tc_fun(_959828, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959830, tc_HOL_Obool)), _959832), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959828, tc_fun(_959830, tc_HOL_Obool)), _959826), _959834)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959828, tc_fun(_959830, tc_HOL_Obool)), _959826), hAPP(hAPP(c_COMBB(tc_fun(_959830, tc_HOL_Obool), tc_fun(_959830, tc_HOL_Obool), _959828), hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959830, tc_HOL_Obool)), _959832)), _959834)))], (9867 ^ _782435) ^ [_959952, _959954, _959956, _959958, _959960] : [_959952 = c_Orderings_Obot__class_Obot(tc_fun(_959954, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_959956, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_959954, tc_fun(_959956, tc_HOL_Obool)), _959952), _959958)), _959960) = _959960)], (9873 ^ _782435) ^ [_960085, _960087, _960089, _960091, _960093] : [-(_960085 = c_Orderings_Obot__class_Obot(tc_fun(_960087, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960089, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_960087, tc_fun(_960089, tc_HOL_Obool)), _960085), _960091)), _960093) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_960087, tc_fun(_960089, tc_HOL_Obool)), _960085), hAPP(hAPP(c_COMBC(_960087, tc_fun(_960089, tc_HOL_Obool), tc_fun(_960089, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960089, tc_HOL_Obool), tc_fun(tc_fun(_960089, tc_HOL_Obool), tc_fun(_960089, tc_HOL_Obool)), _960087), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_960089, tc_HOL_Obool))), _960091)), _960093)))], (9879 ^ _782435) ^ [_960230, _960232, _960234, _960236, _960238] : [_960230 = c_Orderings_Obot__class_Obot(tc_fun(_960232, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960234, tc_HOL_Obool)), _960236), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960232, tc_fun(_960234, tc_HOL_Obool)), _960230), _960238)) = _960236)], (9885 ^ _782435) ^ [_960363, _960365, _960367, _960369, _960371] : [-(_960363 = c_Orderings_Obot__class_Obot(tc_fun(_960365, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960367, tc_HOL_Obool)), _960369), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960365, tc_fun(_960367, tc_HOL_Obool)), _960363), _960371)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960365, tc_fun(_960367, tc_HOL_Obool)), _960363), hAPP(hAPP(c_COMBB(tc_fun(_960367, tc_HOL_Obool), tc_fun(_960367, tc_HOL_Obool), _960365), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960367, tc_HOL_Obool)), _960369)), _960371)))], (9891 ^ _782435) ^ [_960489, _960491, _960493, _960495, _960497] : [_960489 = c_Orderings_Obot__class_Obot(tc_fun(_960491, tc_HOL_Obool)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960493, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960491, tc_fun(_960493, tc_HOL_Obool)), _960489), _960495)), _960497) = _960497)], (9897 ^ _782435) ^ [_960622, _960624, _960626, _960628, _960630] : [-(_960622 = c_Orderings_Obot__class_Obot(tc_fun(_960624, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960626, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960624, tc_fun(_960626, tc_HOL_Obool)), _960622), _960628)), _960630) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960624, tc_fun(_960626, tc_HOL_Obool)), _960622), hAPP(hAPP(c_COMBC(_960624, tc_fun(_960626, tc_HOL_Obool), tc_fun(_960626, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960626, tc_HOL_Obool), tc_fun(tc_fun(_960626, tc_HOL_Obool), tc_fun(_960626, tc_HOL_Obool)), _960624), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960626, tc_HOL_Obool))), _960628)), _960630)))], (9903 ^ _782435) ^ [_960767, _960769, _960771, _960773, _960775] : [_960767 = c_Orderings_Obot__class_Obot(tc_fun(_960769, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960769, tc_fun(_960771, tc_HOL_Obool)), _960767), hAPP(hAPP(c_COMBC(_960769, tc_fun(_960771, tc_HOL_Obool), tc_fun(_960771, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960771, tc_HOL_Obool), tc_fun(tc_fun(_960771, tc_HOL_Obool), tc_fun(_960771, tc_HOL_Obool)), _960769), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960771, tc_HOL_Obool))), _960773)), _960775)) = c_Orderings_Otop__class_Otop(tc_fun(_960771, tc_HOL_Obool)))], (9909 ^ _782435) ^ [_960974, _960976, _960978, _960980, _960982] : [-(_960974 = c_Orderings_Obot__class_Obot(tc_fun(_960976, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960976, tc_fun(_960978, tc_HOL_Obool)), _960974), hAPP(hAPP(c_COMBC(_960976, tc_fun(_960978, tc_HOL_Obool), tc_fun(_960978, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_960978, tc_HOL_Obool), tc_fun(tc_fun(_960978, tc_HOL_Obool), tc_fun(_960978, tc_HOL_Obool)), _960976), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960978, tc_HOL_Obool))), _960980)), _960982)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_960978, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_960976, tc_fun(_960978, tc_HOL_Obool)), _960974), _960980)), _960982))], (9915 ^ _782435) ^ [_961119, _961121, _961123, _961125, _961127] : [_961119 = c_Orderings_Obot__class_Obot(tc_fun(_961121, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961121, tc_fun(_961123, tc_HOL_Obool)), _961119), hAPP(hAPP(c_COMBB(tc_fun(_961123, tc_HOL_Obool), tc_fun(_961123, tc_HOL_Obool), _961121), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961123, tc_HOL_Obool)), _961125)), _961127)) = c_Orderings_Otop__class_Otop(tc_fun(_961123, tc_HOL_Obool)))], (9921 ^ _782435) ^ [_961288, _961290, _961292, _961294, _961296] : [-(_961288 = c_Orderings_Obot__class_Obot(tc_fun(_961290, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961290, tc_fun(_961292, tc_HOL_Obool)), _961288), hAPP(hAPP(c_COMBB(tc_fun(_961292, tc_HOL_Obool), tc_fun(_961292, tc_HOL_Obool), _961290), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961292, tc_HOL_Obool)), _961294)), _961296)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_961292, tc_HOL_Obool)), _961294), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_961290, tc_fun(_961292, tc_HOL_Obool)), _961288), _961296)))], (9927 ^ _782435) ^ [_961396, _961398, _961400, _961402, _961404] : [class_Lattices_Osemilattice__sup(_961396), class_Lattices_Osemilattice__sup(_961398), c_Orderings_Oorder__class_Omono(_961398, _961396, _961400), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961396), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961396), hAPP(_961400, _961402)), hAPP(_961400, _961404))), hAPP(_961400, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_961398), _961402), _961404)))))], (9941 ^ _782435) ^ [_961659, _961661, _961663, _961665, _961667] : [class_Lattices_Osemilattice__inf(_961659), class_Lattices_Osemilattice__inf(_961661), c_Orderings_Oorder__class_Omono(_961661, _961659, _961663), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_961659), hAPP(_961663, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961661), _961665), _961667))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961659), hAPP(_961663, _961665)), hAPP(_961663, _961667)))))], (9955 ^ _782435) ^ [_961922, _961924] : [class_Lattices_Oboolean__algebra(_961922), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_961922), _961924), hAPP(c_Groups_Ouminus__class_Ouminus(_961922), _961924)) = c_Orderings_Obot__class_Obot(_961922))], (9961 ^ _782435) ^ [_962027, _962029] : [class_Lattices_Oboolean__algebra(_962027), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_962027), hAPP(c_Groups_Ouminus__class_Ouminus(_962027), _962029)), _962029) = c_Orderings_Obot__class_Obot(_962027))], (9967 ^ _782435) ^ [_962132] : [class_Lattices_Oboolean__algebra(_962132), -(hAPP(c_Groups_Ouminus__class_Ouminus(_962132), c_Orderings_Otop__class_Otop(_962132)) = c_Orderings_Obot__class_Obot(_962132))], (9973 ^ _782435) ^ [_962223] : [class_Lattices_Oboolean__algebra(_962223), -(hAPP(c_Groups_Ouminus__class_Ouminus(_962223), c_Orderings_Obot__class_Obot(_962223)) = c_Orderings_Otop__class_Otop(_962223))], (9979 ^ _782435) ^ [_962332, _962334, _962336] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962332, tc_HOL_Obool)), _962334), _962336) = c_Orderings_Obot__class_Obot(tc_fun(_962332, tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962332, tc_HOL_Obool)), _962334), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962332, tc_HOL_Obool)), _962336))))], (9985 ^ _782435) ^ [_962475, _962477, _962479] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_962475, tc_HOL_Obool)), _962477), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_962475, tc_HOL_Obool)), _962479))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962475, tc_HOL_Obool)), _962477), _962479) = c_Orderings_Obot__class_Obot(tc_fun(_962475, tc_HOL_Obool)))], (9991 ^ _782435) ^ [_962624, _962626, _962628, _962630] : [class_Orderings_Oorder(_962624), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962624, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962624, _962626), _962628)), c_SetInterval_Oord__class_OatLeastAtMost(_962624, _962628, _962630)) = c_Orderings_Obot__class_Obot(tc_fun(_962624, tc_HOL_Obool)))], (9997 ^ _782435) ^ [_962755, _962757, _962759] : [class_Orderings_Oorder(_962755), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962755, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_962755), _962757)), c_SetInterval_Oord__class_OatLeastAtMost(_962755, _962757, _962759)) = c_Orderings_Obot__class_Obot(tc_fun(_962755, tc_HOL_Obool)))], (10003 ^ _782435) ^ [_962882, _962884, _962886] : [class_Orderings_Oorder(_962882), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_962882, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_962882), _962884)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_962882, _962884), _962886)) = c_Orderings_Obot__class_Obot(tc_fun(_962882, tc_HOL_Obool)))], (10009 ^ _782435) ^ [_963013, _963015, _963017, _963019] : [class_Orderings_Oorder(_963013), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963013, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_963013, _963015, _963017)), c_SetInterval_Oord__class_OgreaterThanAtMost(_963013, _963017, _963019)) = c_Orderings_Obot__class_Obot(tc_fun(_963013, tc_HOL_Obool)))], (10015 ^ _782435) ^ [_963140, _963142] : [-(hBOOL(hAPP(hAPP(c_member(_963140), _963142), c_Orderings_Otop__class_Otop(tc_fun(_963140, tc_HOL_Obool)))))], (10017 ^ _782435) ^ [_963177, _963179, _963181] : [class_Orderings_Olinorder(_963177), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963177), _963179), _963181)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963177, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_963177), _963179), c_Orderings_Obot__class_Obot(tc_fun(_963177, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanAtMost(_963177, _963179, _963181)) = c_SetInterval_Oord__class_OatLeastAtMost(_963177, _963179, _963181))], (10027 ^ _782435) ^ [_963386, _963388, _963390] : [class_Orderings_Olinorder(_963386), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_963386), _963388), _963390)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963386, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_963386, _963388), _963390)), hAPP(hAPP(c_Set_Oinsert(_963386), _963390), c_Orderings_Obot__class_Obot(tc_fun(_963386, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(_963386, _963388, _963390))], (10037 ^ _782435) ^ [_963599, _963601, _963603, _963605, _963607] : [class_Orderings_Oorder(_963599), c_Orderings_Oorder__class_Omono(_963599, tc_fun(_963601, tc_HOL_Obool), _963603), -(c_Orderings_Oorder__class_Omono(_963599, tc_fun(_963601, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_963599, tc_fun(_963601, tc_HOL_Obool), tc_fun(_963601, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_963601, tc_HOL_Obool), tc_fun(tc_fun(_963601, tc_HOL_Obool), tc_fun(_963601, tc_HOL_Obool)), _963599), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963601, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_963599, tc_fun(_963601, tc_HOL_Obool), tc_fun(_963601, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_963601, tc_HOL_Obool), tc_fun(tc_fun(_963601, tc_HOL_Obool), tc_fun(_963601, tc_HOL_Obool)), _963599), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_963601, tc_HOL_Obool))), _963603)), _963605))), _963607)))], (10047 ^ _782435) ^ [_963926, _963928, _963930] : [class_Orderings_Oorder(_963926), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_963926, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_963926, _963928, _963930)), hAPP(c_SetInterval_Oord__class_OatLeast(_963926), _963930)) = c_Orderings_Obot__class_Obot(tc_fun(_963926, tc_HOL_Obool)))], (10053 ^ _782435) ^ [_964053, _964055, _964057] : [class_Orderings_Oorder(_964053), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964053, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_964053), _964055)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964053, _964055, _964057)) = c_Orderings_Obot__class_Obot(tc_fun(_964053, tc_HOL_Obool)))], (10059 ^ _782435) ^ [_964180, _964182, _964184, _964186] : [class_Orderings_Oorder(_964180), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964180, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_964180, _964182, _964184)), c_SetInterval_Oord__class_OgreaterThanLessThan(_964180, _964184, _964186)) = c_Orderings_Obot__class_Obot(tc_fun(_964180, tc_HOL_Obool)))], (10065 ^ _782435) ^ [_964307, _964309] : [class_Orderings_Olinorder(_964307), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_964307, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_964307), _964309), c_Orderings_Obot__class_Obot(tc_fun(_964307, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OgreaterThan(_964307), _964309)) = hAPP(c_SetInterval_Oord__class_OatLeast(_964307), _964309))], (10071 ^ _782435) ^ [_964468, _964470, _964472, _964474, _964476] : [_964468 = c_Orderings_Obot__class_Obot(tc_fun(_964470, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_964470, tc_fun(_964472, tc_HOL_Obool)), _964468), hAPP(hAPP(c_COMBB(tc_fun(_964472, tc_HOL_Obool), tc_fun(_964472, tc_HOL_Obool), _964470), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964472, tc_HOL_Obool)), _964474)), _964476)) = c_Orderings_Otop__class_Otop(tc_fun(_964472, tc_HOL_Obool)))], (10077 ^ _782435) ^ [_964637, _964639, _964641, _964643, _964645] : [-(_964637 = c_Orderings_Obot__class_Obot(tc_fun(_964639, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_964639, tc_fun(_964641, tc_HOL_Obool)), _964637), hAPP(hAPP(c_COMBB(tc_fun(_964641, tc_HOL_Obool), tc_fun(_964641, tc_HOL_Obool), _964639), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964641, tc_HOL_Obool)), _964643)), _964645)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_964641, tc_HOL_Obool)), _964643), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_964639, tc_fun(_964641, tc_HOL_Obool)), _964637), _964645)))], (10083 ^ _782435) ^ [_964745, _964747] : [class_Orderings_Oorder(_964745), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_964745, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_964745), _964747)), hAPP(c_SetInterval_Oord__class_OatLeast(_964745), _964747)) = hAPP(hAPP(c_Set_Oinsert(_964745), _964747), c_Orderings_Obot__class_Obot(tc_fun(_964745, tc_HOL_Obool))))], (10089 ^ _782435) ^ [_964888, _964890, _964892, _964894] : [10090 ^ _782435 : [(10091 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_964888), _964890), _964892))], (10093 ^ _782435) ^ [] : [_964890 = _964894]], -(hBOOL(hAPP(hAPP(c_member(_964888), _964890), hAPP(hAPP(c_Set_Oinsert(_964888), _964894), _964892))))], (10097 ^ _782435) ^ [_965053, _965055, _965057, _965059] : [hBOOL(hAPP(hAPP(c_member(_965053), _965055), hAPP(hAPP(c_Set_Oinsert(_965053), _965057), _965059))), -(_965055 = _965057), -(hBOOL(hAPP(hAPP(c_member(_965053), _965055), _965059)))], (10107 ^ _782435) ^ [_965193, _965195, _965197, _965199] : [hBOOL(hAPP(hAPP(c_member(_965193), _965195), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965193, tc_HOL_Obool)), _965197), _965199))), 10110 ^ _782435 : [(10111 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_965193), _965195), _965197)))], (10113 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_965193), _965195), _965199))]]], (10115 ^ _782435) ^ [_965372, _965374, _965376, _965378] : [hBOOL(hAPP(hAPP(c_member(_965372), _965374), _965376)), -(hBOOL(hAPP(hAPP(c_member(_965372), _965374), _965378))), -(hBOOL(hAPP(hAPP(c_member(_965372), _965374), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965372, tc_HOL_Obool)), _965376), _965378))))], (10125 ^ _782435) ^ [_965532, _965534, _965536, _965538] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965532, tc_HOL_Obool)), _965534), hAPP(hAPP(c_Set_Oinsert(_965532), _965536), _965538)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965532, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965532, tc_HOL_Obool)), _965534), _965538)), hAPP(hAPP(c_Set_Oinsert(_965532), _965536), c_Orderings_Obot__class_Obot(tc_fun(_965532, tc_HOL_Obool)))))], (10127 ^ _782435) ^ [_965615, _965617, _965619, _965621] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965615, tc_HOL_Obool)), _965617), hAPP(hAPP(c_Set_Oinsert(_965615), _965619), _965621)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965615, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965615, tc_HOL_Obool)), _965617), hAPP(hAPP(c_Set_Oinsert(_965615), _965619), c_Orderings_Obot__class_Obot(tc_fun(_965615, tc_HOL_Obool))))), _965621))], (10129 ^ _782435) ^ [_965698, _965700, _965702] : [-(hAPP(hAPP(c_Set_Oinsert(_965698), _965700), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965698, tc_HOL_Obool)), _965702), hAPP(hAPP(c_Set_Oinsert(_965698), _965700), c_Orderings_Obot__class_Obot(tc_fun(_965698, tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(_965698), _965700), _965702))], (10131 ^ _782435) ^ [_965780, _965782, _965784, _965786] : [hBOOL(hAPP(hAPP(c_member(_965780), _965782), _965784)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965780, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_965780), _965782), _965786)), _965784) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965780, tc_HOL_Obool)), _965786), _965784))], (10137 ^ _782435) ^ [_965929, _965931, _965933, _965935] : [-(hBOOL(hAPP(hAPP(c_member(_965929), _965931), _965933))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965929, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_965929), _965931), _965935)), _965933) = hAPP(hAPP(c_Set_Oinsert(_965929), _965931), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_965929, tc_HOL_Obool)), _965935), _965933)))], (10143 ^ _782435) ^ [_966016, _966018, _966020, _966022] : [hBOOL(hAPP(hAPP(c_member(_966016), _966018), _966020)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966016, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_966016), _966018), _966022)), _966020) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966016, tc_HOL_Obool)), _966022), _966020))], (10149 ^ _782435) ^ [_966171, _966173, _966175, _966177, _966179] : [class_Groups_Oab__group__add(_966171), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966171), _966173), _966175) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966171), _966177), _966179), 10156 ^ _782435 : [(10157 ^ _782435) ^ [] : [_966173 = _966175, -(_966177 = _966179)], (10163 ^ _782435) ^ [] : [_966177 = _966179, -(_966173 = _966175)]]], (10169 ^ _782435) ^ [_966484, _966486, _966488, _966490, _966492] : [class_Groups_Ominus(_966484), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966486, _966484)), _966488), _966490), _966492) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966484), hAPP(_966488, _966492)), hAPP(_966490, _966492)))], (10175 ^ _782435) ^ [_966621, _966623, _966625, _966627, _966629] : [class_Groups_Ominus(_966621), -(hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_966623, _966621)), _966625), _966627), _966629) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_966621), hAPP(_966625, _966629)), hAPP(_966627, _966629)))], (10191 ^ _782435) ^ [_966893, _966895, _966897, _966899] : [10192 ^ _782435 : [(10193 ^ _782435) ^ [] : [_966895 = _966899], (10195 ^ _782435) ^ [] : [hBOOL(hAPP(_966897, _966899))]], -(hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_966893), _966895), _966897), _966899)))], (10181 ^ _782435) ^ [_966779, _966781, _966783, _966785] : [hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(_966779), _966781), _966783), _966785)), -(_966781 = _966785), -(hBOOL(hAPP(_966783, _966785)))], (10199 ^ _782435) ^ [_967038, _967040, _967042] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967038, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967038, tc_HOL_Obool)), _967040), _967042)), _967042) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967038, tc_HOL_Obool)), _967040), _967042))], (10201 ^ _782435) ^ [_967098, _967100, _967102, _967104] : [-(hAPP(hAPP(c_Set_Oinsert(_967098), _967100), hAPP(hAPP(c_Set_Oinsert(_967098), _967102), _967104)) = hAPP(hAPP(c_Set_Oinsert(_967098), _967102), hAPP(hAPP(c_Set_Oinsert(_967098), _967100), _967104)))], (10203 ^ _782435) ^ [_967159, _967161, _967163] : [-(hAPP(hAPP(c_Set_Oinsert(_967159), _967161), hAPP(hAPP(c_Set_Oinsert(_967159), _967161), _967163)) = hAPP(hAPP(c_Set_Oinsert(_967159), _967161), _967163))], (10205 ^ _782435) ^ [_967210, _967212, _967214] : [hBOOL(hAPP(hAPP(c_member(_967210), _967212), _967214)), -(hAPP(hAPP(c_Set_Oinsert(_967210), _967212), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967210, tc_HOL_Obool)), _967214), hAPP(hAPP(c_Set_Oinsert(_967210), _967212), c_Orderings_Obot__class_Obot(tc_fun(_967210, tc_HOL_Obool))))) = _967214)], (10211 ^ _782435) ^ [_967363, _967365, _967367] : [-(hBOOL(hAPP(hAPP(c_member(_967363), _967365), _967367))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967363, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_967363), _967365), _967367)), hAPP(hAPP(c_Set_Oinsert(_967363), _967365), c_Orderings_Obot__class_Obot(tc_fun(_967363, tc_HOL_Obool)))) = _967367)], (10217 ^ _782435) ^ [_967440, _967442, _967444, _967446, _967448] : [class_Groups_Oordered__ab__group__add(_967440), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967440), _967442), _967444) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967440), _967446), _967448), 10224 ^ _782435 : [(10225 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967440), _967442), _967444)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967440), _967446), _967448)))], (10231 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967440), _967446), _967448)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_967440), _967442), _967444)))]]], (10237 ^ _782435) ^ [_967795, _967797] : [class_Orderings_Oorder(_967795), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_967795, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_967795), _967797), c_Orderings_Obot__class_Obot(tc_fun(_967795, tc_HOL_Obool)))), hAPP(c_SetInterval_Oord__class_OlessThan(_967795), _967797)) = hAPP(hAPP(c_Set_Oinsert(_967795), _967797), c_Orderings_Obot__class_Obot(tc_fun(_967795, tc_HOL_Obool))))], (10243 ^ _782435) ^ [_967954, _967956, _967958] : [class_Groups_Oab__group__add(_967954), -(hAPP(c_Groups_Ouminus__class_Ouminus(_967954), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967954), _967956), _967958)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_967954), _967958), _967956))], (10249 ^ _782435) ^ [_968073, _968075, _968077, _968079] : [hBOOL(hAPP(hAPP(c_member(_968073), _968075), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968073, tc_HOL_Obool)), _968077), _968079))), hBOOL(hAPP(hAPP(c_member(_968073), _968075), _968079))], (10255 ^ _782435) ^ [_968205, _968207, _968209, _968211] : [hBOOL(hAPP(hAPP(c_member(_968205), _968207), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968205, tc_HOL_Obool)), _968209), _968211))), -(hBOOL(hAPP(hAPP(c_member(_968205), _968207), _968209)))], (10261 ^ _782435) ^ [_968357, _968359, _968361, _968363] : [hBOOL(hAPP(hAPP(c_member(_968357), _968359), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968357, tc_HOL_Obool)), _968361), _968363))), 10264 ^ _782435 : [(10265 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_968357), _968359), _968361)))], (10267 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_968357), _968359), _968363))]]], (10269 ^ _782435) ^ [_968532, _968534, _968536, _968538] : [-(hBOOL(hAPP(hAPP(c_member(_968532), _968534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_968532, tc_HOL_Obool)), _968536), _968538)))), hBOOL(hAPP(hAPP(c_member(_968532), _968534), _968536)), -(hBOOL(hAPP(hAPP(c_member(_968532), _968534), _968538)))], (10279 ^ _782435) ^ [_968738, _968740, _968742] : [hBOOL(hAPP(hAPP(c_member(_968738), _968740), _968742)), -(hAPP(hAPP(c_Set_Oinsert(_968738), _968740), _968742) = _968742)], (10285 ^ _782435) ^ [_968847, _968849, _968851, _968853] : [hBOOL(hAPP(hAPP(c_member(_968847), _968849), _968851)), -(hBOOL(hAPP(hAPP(c_member(_968847), _968849), hAPP(hAPP(c_Set_Oinsert(_968847), _968853), _968851))))], (10291 ^ _782435) ^ [_968971, _968973, _968975, _968977] : [-(hBOOL(hAPP(hAPP(c_member(_968971), _968973), _968975))), -(hBOOL(hAPP(hAPP(c_member(_968971), _968973), _968977))), 10298 ^ _782435 : [(10299 ^ _782435) ^ [] : [hAPP(hAPP(c_Set_Oinsert(_968971), _968973), _968975) = hAPP(hAPP(c_Set_Oinsert(_968971), _968973), _968977), -(_968975 = _968977)], (10305 ^ _782435) ^ [] : [_968975 = _968977, -(hAPP(hAPP(c_Set_Oinsert(_968971), _968973), _968975) = hAPP(hAPP(c_Set_Oinsert(_968971), _968973), _968977))]]], (10321 ^ _782435) ^ [_969471, _969473, _969475, _969477] : [10322 ^ _782435 : [(10323 ^ _782435) ^ [] : [_969473 = _969475], (10325 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_969471), _969473), _969477))]], -(hBOOL(hAPP(hAPP(c_member(_969471), _969473), hAPP(hAPP(c_Set_Oinsert(_969471), _969475), _969477))))], (10311 ^ _782435) ^ [_969337, _969339, _969341, _969343] : [hBOOL(hAPP(hAPP(c_member(_969337), _969339), hAPP(hAPP(c_Set_Oinsert(_969337), _969341), _969343))), -(_969339 = _969341), -(hBOOL(hAPP(hAPP(c_member(_969337), _969339), _969343)))], (10329 ^ _782435) ^ [_969636, _969638, _969640] : [-(hBOOL(hAPP(hAPP(c_member(_969636), _969638), hAPP(hAPP(c_Set_Oinsert(_969636), _969638), _969640))))], (10331 ^ _782435) ^ [_969678, _969680] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969678, tc_HOL_Obool)), _969680), _969680) = c_Orderings_Obot__class_Obot(tc_fun(_969678, tc_HOL_Obool)))], (10333 ^ _782435) ^ [_969719, _969721] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969719, tc_HOL_Obool)), _969721), c_Orderings_Obot__class_Obot(tc_fun(_969719, tc_HOL_Obool))) = _969721)], (10335 ^ _782435) ^ [_969760, _969762] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_969760, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_969760, tc_HOL_Obool))), _969762) = c_Orderings_Obot__class_Obot(tc_fun(_969760, tc_HOL_Obool)))], (10337 ^ _782435) ^ [_969806, _969808, _969810] : [hAPP(hAPP(c_Set_Oinsert(_969806), _969808), c_Orderings_Obot__class_Obot(tc_fun(_969806, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(_969806), _969810), c_Orderings_Obot__class_Obot(tc_fun(_969806, tc_HOL_Obool))), -(_969808 = _969810)], (10343 ^ _782435) ^ [_969961, _969963, _969965, _969967, _969969] : [hAPP(hAPP(c_Set_Oinsert(_969961), _969963), hAPP(hAPP(c_Set_Oinsert(_969961), _969965), c_Orderings_Obot__class_Obot(tc_fun(_969961, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_969961), _969967), hAPP(hAPP(c_Set_Oinsert(_969961), _969969), c_Orderings_Obot__class_Obot(tc_fun(_969961, tc_HOL_Obool)))), 10348 ^ _782435 : [(10349 ^ _782435) ^ [] : [-(_969963 = _969967)], (10351 ^ _782435) ^ [] : [-(_969965 = _969969)]], 10352 ^ _782435 : [(10353 ^ _782435) ^ [] : [-(_969963 = _969969)], (10355 ^ _782435) ^ [] : [-(_969965 = _969967)]]], (10357 ^ _782435) ^ [_970223, _970225, _970227, _970229, _970231] : [-(hAPP(hAPP(c_Set_Oinsert(_970223), _970225), hAPP(hAPP(c_Set_Oinsert(_970223), _970227), c_Orderings_Obot__class_Obot(tc_fun(_970223, tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(_970223), _970229), hAPP(hAPP(c_Set_Oinsert(_970223), _970231), c_Orderings_Obot__class_Obot(tc_fun(_970223, tc_HOL_Obool))))), 10358 ^ _782435 : [(10359 ^ _782435) ^ [] : [_970225 = _970229, _970227 = _970231], (10365 ^ _782435) ^ [] : [_970225 = _970231, _970227 = _970229]]], (10373 ^ _782435) ^ [_970554, _970556, _970558] : [hAPP(hAPP(c_Set_Oinsert(_970554), _970556), _970558) = c_Orderings_Obot__class_Obot(tc_fun(_970554, tc_HOL_Obool))], (10375 ^ _782435) ^ [_970609, _970611, _970613] : [c_Orderings_Obot__class_Obot(tc_fun(_970609, tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(_970609), _970611), _970613)], (10377 ^ _782435) ^ [_970649, _970651, _970653, _970655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970649, tc_HOL_Obool)), _970651), _970653)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970649, tc_HOL_Obool)), _970653), _970655)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970649, tc_HOL_Obool)), _970653), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970649, tc_HOL_Obool)), _970655), _970651)) = _970651)], (10387 ^ _782435) ^ [_970870, _970872, _970874, _970876, _970878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970870, tc_HOL_Obool)), _970872), _970874)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970870, tc_HOL_Obool)), _970876), _970878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_970870, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970870, tc_HOL_Obool)), _970872), _970878)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_970870, tc_HOL_Obool)), _970874), _970876))))], (10397 ^ _782435) ^ [_971115, _971117, _971119] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971115, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971115, tc_HOL_Obool)), _971117), _971119)), _971117)))], (10399 ^ _782435) ^ [_971163, _971165, _971167, _971169] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971163, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971163, tc_HOL_Obool)), _971165), _971167)), _971169) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971163, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971163, tc_HOL_Obool)), _971165), _971169)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971163, tc_HOL_Obool)), _971167), _971169)))], (10401 ^ _782435) ^ [_971247, _971249, _971251] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971247, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971247, tc_HOL_Obool)), _971249), _971251)), _971251) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971247, tc_HOL_Obool)), _971249), _971251))], (10403 ^ _782435) ^ [_971307, _971309, _971311] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971307, tc_HOL_Obool)), _971309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971307, tc_HOL_Obool)), _971311), _971309)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_971307, tc_HOL_Obool)), _971309), _971311))], (10405 ^ _782435) ^ [_971367, _971369, _971371, _971373] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971367, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971367, tc_HOL_Obool)), _971369), _971371)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971367, tc_HOL_Obool)), _971373), _971371)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971367, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971367, tc_HOL_Obool)), _971369), _971371)), _971373))], (10407 ^ _782435) ^ [_971451, _971453, _971455, _971457] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971451, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971451, tc_HOL_Obool)), _971453), _971455)), _971457) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971451, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971451, tc_HOL_Obool)), _971453), _971457)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971451, tc_HOL_Obool)), _971455), _971457)))], (10409 ^ _782435) ^ [_971535, _971537, _971539, _971541] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971535, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971535, tc_HOL_Obool)), _971537), _971539)), _971541) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971535, tc_HOL_Obool)), _971537), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971535, tc_HOL_Obool)), _971539), _971541)))], (10411 ^ _782435) ^ [_971608, _971610, _971612, _971614] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971608, tc_HOL_Obool)), _971610), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971608, tc_HOL_Obool)), _971612), _971614)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_971608, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971608, tc_HOL_Obool)), _971610), _971612)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_971608, tc_HOL_Obool)), _971610), _971614)))], (10413 ^ _782435) ^ [_971692, _971694, _971696, _971698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971692, tc_HOL_Obool)), _971694), _971696)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971692, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_971692), _971698), _971694)), hAPP(hAPP(c_Set_Oinsert(_971692), _971698), _971696))))], (10419 ^ _782435) ^ [_971845, _971847, _971849, _971851] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971845, tc_HOL_Obool)), _971847), _971849)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971845, tc_HOL_Obool)), _971847), hAPP(hAPP(c_Set_Oinsert(_971845), _971851), _971849))))], (10425 ^ _782435) ^ [_971982, _971984, _971986] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_971982, tc_HOL_Obool)), _971984), hAPP(hAPP(c_Set_Oinsert(_971982), _971986), _971984))))], (10427 ^ _782435) ^ [_972027, _972029, _972031, _972033, _972035] : [-(hAPP(c_Set_Oimage(_972027, _972029, _972031), hAPP(hAPP(c_Set_Oinsert(_972027), _972033), _972035)) = hAPP(hAPP(c_Set_Oinsert(_972029), hAPP(_972031, _972033)), hAPP(c_Set_Oimage(_972027, _972029, _972031), _972035)))], (10429 ^ _782435) ^ [_972091, _972093, _972095, _972097] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972091, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_972091), _972093), _972095)), _972097) = hAPP(hAPP(c_Set_Oinsert(_972091), _972093), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972091, tc_HOL_Obool)), _972095), _972097)))], (10431 ^ _782435) ^ [_972158, _972160, _972162, _972164] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972158, tc_HOL_Obool)), _972160), hAPP(hAPP(c_Set_Oinsert(_972158), _972162), _972164)) = hAPP(hAPP(c_Set_Oinsert(_972158), _972162), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_972158, tc_HOL_Obool)), _972160), _972164)))], (10433 ^ _782435) ^ [_972225, _972227, _972229, _972231] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972225, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_972225), _972227), _972229)), hAPP(hAPP(c_Set_Oinsert(_972225), _972227), _972231)) = hAPP(hAPP(c_Set_Oinsert(_972225), _972227), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_972225, tc_HOL_Obool)), _972229), _972231)))], (10435 ^ _782435) ^ [_972300, _972302, _972304, _972306] : [c_Hoare__Mirabelle_Ohoare__derivs(_972300, _972302, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_972300)), _972304), c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(_972300), tc_HOL_Obool)))), c_Hoare__Mirabelle_Ohoare__derivs(_972300, _972302, _972306), -(c_Hoare__Mirabelle_Ohoare__derivs(_972300, _972302, hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(_972300)), _972304), _972306)))], (10461 ^ _782435) ^ [_972850, _972852, _972854, _972856] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972850, tc_HOL_Obool)), _972852), hAPP(hAPP(c_Set_Oinsert(_972850), _972854), _972856)))), 10464 ^ _782435 : [(10465 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972850), _972854), _972852)))], (10467 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972850, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972850, tc_HOL_Obool)), _972852), hAPP(hAPP(c_Set_Oinsert(_972850), _972854), c_Orderings_Obot__class_Obot(tc_fun(_972850, tc_HOL_Obool))))), _972856))]], 10468 ^ _782435 : [(10469 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972850), _972854), _972852))], (10471 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972850, tc_HOL_Obool)), _972852), _972856))]]], (10445 ^ _782435) ^ [_972518, _972520, _972522, _972524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972518, tc_HOL_Obool)), _972520), hAPP(hAPP(c_Set_Oinsert(_972518), _972522), _972524))), 10448 ^ _782435 : [(10449 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_972518), _972522), _972520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972518, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_972518, tc_HOL_Obool)), _972520), hAPP(hAPP(c_Set_Oinsert(_972518), _972522), c_Orderings_Obot__class_Obot(tc_fun(_972518, tc_HOL_Obool))))), _972524)))], (10455 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_972518), _972522), _972520))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_972518, tc_HOL_Obool)), _972520), _972524)))]]], (10475 ^ _782435) ^ [_973214, _973216, _973218, _973220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973214, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973214, tc_HOL_Obool)), _973216), hAPP(hAPP(c_Set_Oinsert(_973214), _973218), c_Orderings_Obot__class_Obot(tc_fun(_973214, tc_HOL_Obool))))), _973220)), hBOOL(hAPP(hAPP(c_member(_973214), _973218), _973216)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_973214, tc_HOL_Obool)), _973216), hAPP(hAPP(c_Set_Oinsert(_973214), _973218), _973220))))], (10485 ^ _782435) ^ [_973469, _973471, _973473, _973475, _973477] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973469, tc_fun(_973471, tc_HOL_Obool)), _973473), hAPP(hAPP(c_COMBC(_973469, tc_fun(_973471, tc_HOL_Obool), tc_fun(_973471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_973471, tc_HOL_Obool), tc_fun(tc_fun(_973471, tc_HOL_Obool), tc_fun(_973471, tc_HOL_Obool)), _973469), c_Groups_Ominus__class_Ominus(tc_fun(_973471, tc_HOL_Obool))), _973475)), _973477)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973471, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973469, tc_fun(_973471, tc_HOL_Obool)), _973473), _973475)), _973477))], (10487 ^ _782435) ^ [_973578, _973580, _973582, _973584, _973586] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_973578, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973580, tc_fun(_973578, tc_HOL_Obool)), _973582), _973584)), _973586) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_973580, tc_fun(_973578, tc_HOL_Obool)), _973582), hAPP(hAPP(c_COMBC(_973580, tc_fun(_973578, tc_HOL_Obool), tc_fun(_973578, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_973578, tc_HOL_Obool), tc_fun(tc_fun(_973578, tc_HOL_Obool), tc_fun(_973578, tc_HOL_Obool)), _973580), c_Groups_Ominus__class_Ominus(tc_fun(_973578, tc_HOL_Obool))), _973584)), _973586)))], (10489 ^ _782435) ^ [_973687, _973689, _973691, _973693, _973695] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973687, tc_fun(_973689, tc_HOL_Obool)), _973691), hAPP(hAPP(c_COMBB(tc_fun(_973689, tc_HOL_Obool), tc_fun(_973689, tc_HOL_Obool), _973687), hAPP(c_Set_Oinsert(_973689), _973693)), _973695)) = hAPP(hAPP(c_Set_Oinsert(_973689), _973693), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973687, tc_fun(_973689, tc_HOL_Obool)), _973691), _973695)))], (10491 ^ _782435) ^ [_973771, _973773, _973775, _973777, _973779] : [-(hAPP(hAPP(c_Set_Oinsert(_973771), _973773), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973775, tc_fun(_973771, tc_HOL_Obool)), _973777), _973779)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_973775, tc_fun(_973771, tc_HOL_Obool)), _973777), hAPP(hAPP(c_COMBB(tc_fun(_973771, tc_HOL_Obool), tc_fun(_973771, tc_HOL_Obool), _973775), hAPP(c_Set_Oinsert(_973771), _973773)), _973779)))], (10493 ^ _782435) ^ [_973855, _973857, _973859] : [class_Lattices_Oboolean__algebra(_973855), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_973855), _973857), _973859) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_973855), _973857), hAPP(c_Groups_Ouminus__class_Ouminus(_973855), _973859)))], (10499 ^ _782435) ^ [_973974, _973976, _973978] : [hBOOL(hAPP(hAPP(c_member(_973974), _973976), hAPP(hAPP(c_Set_Oinsert(_973974), _973978), c_Orderings_Obot__class_Obot(tc_fun(_973974, tc_HOL_Obool))))), -(_973976 = _973978)], (10505 ^ _782435) ^ [_974111, _974113, _974115] : [hBOOL(hAPP(hAPP(c_member(_974111), _974113), hAPP(hAPP(c_Set_Oinsert(_974111), _974115), c_Orderings_Obot__class_Obot(tc_fun(_974111, tc_HOL_Obool))))), -(_974113 = _974115)], (10511 ^ _782435) ^ [_974226, _974228, _974230] : [_974228 = _974230, -(hBOOL(hAPP(hAPP(c_member(_974226), _974228), hAPP(hAPP(c_Set_Oinsert(_974226), _974230), c_Orderings_Obot__class_Obot(tc_fun(_974226, tc_HOL_Obool))))))], (10517 ^ _782435) ^ [_974368, _974370, _974372, _974374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974368, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_974368), _974370), _974372)), _974374)), 10520 ^ _782435 : [(10521 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_974368), _974370), _974374)))], (10523 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974368, tc_HOL_Obool)), _974372), _974374)))]]], (10525 ^ _782435) ^ [_974541, _974543, _974545, _974547] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974541, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_974541), _974543), _974545)), _974547))), hBOOL(hAPP(hAPP(c_member(_974541), _974543), _974547)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974541, tc_HOL_Obool)), _974545), _974547))], (10535 ^ _782435) ^ [_974749, _974751, _974753, _974755] : [-(hBOOL(hAPP(hAPP(c_member(_974749), _974751), _974753))), 10538 ^ _782435 : [(10539 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974749, tc_HOL_Obool)), _974753), hAPP(hAPP(c_Set_Oinsert(_974749), _974751), _974755))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974749, tc_HOL_Obool)), _974753), _974755)))], (10545 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974749, tc_HOL_Obool)), _974753), _974755)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_974749, tc_HOL_Obool)), _974753), hAPP(hAPP(c_Set_Oinsert(_974749), _974751), _974755))))]]], (10551 ^ _782435) ^ [_975057, _975059, _975061, _975063, _975065] : [hBOOL(hAPP(hAPP(c_member(_975057), _975059), _975061)), -(hAPP(hAPP(c_Set_Oinsert(_975063), hAPP(_975065, _975059)), hAPP(c_Set_Oimage(_975057, _975063, _975065), _975061)) = hAPP(c_Set_Oimage(_975057, _975063, _975065), _975061))], (10557 ^ _782435) ^ [_975204, _975206] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_975204, tc_HOL_Obool)), _975206), c_Orderings_Otop__class_Otop(tc_fun(_975204, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_975204, tc_HOL_Obool)))], (10559 ^ _782435) ^ [_975250, _975252, _975254, _975256] : [hBOOL(hAPP(hAPP(c_member(_975250), _975252), _975254)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975250, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975250), _975252), _975256)), _975254) = hAPP(hAPP(c_Set_Oinsert(_975250), _975252), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975250, tc_HOL_Obool)), _975256), _975254)))], (10565 ^ _782435) ^ [_975421, _975423, _975425, _975427] : [hBOOL(hAPP(hAPP(c_member(_975421), _975423), _975425)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975421, tc_HOL_Obool)), _975425), hAPP(hAPP(c_Set_Oinsert(_975421), _975423), _975427)) = hAPP(hAPP(c_Set_Oinsert(_975421), _975423), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975421, tc_HOL_Obool)), _975425), _975427)))], (10571 ^ _782435) ^ [_975588, _975590, _975592, _975594] : [-(hBOOL(hAPP(hAPP(c_member(_975588), _975590), _975592))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975588, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975588), _975590), _975594)), _975592) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975588, tc_HOL_Obool)), _975594), _975592))], (10577 ^ _782435) ^ [_975661, _975663, _975665, _975667] : [-(hBOOL(hAPP(hAPP(c_member(_975661), _975663), _975665))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975661, tc_HOL_Obool)), _975665), hAPP(hAPP(c_Set_Oinsert(_975661), _975663), _975667)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975661, tc_HOL_Obool)), _975665), _975667))], (10583 ^ _782435) ^ [_975753, _975755, _975757, _975759] : [hBOOL(hAPP(hAPP(c_member(_975753), _975755), _975757)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975753, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975753), _975755), _975759)), _975757) = hAPP(hAPP(c_Set_Oinsert(_975753), _975755), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975753, tc_HOL_Obool)), _975759), _975757)))], (10589 ^ _782435) ^ [_975918, _975920, _975922, _975924] : [-(hBOOL(hAPP(hAPP(c_member(_975918), _975920), _975922))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975918, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_975918), _975920), _975924)), _975922) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_975918, tc_HOL_Obool)), _975924), _975922))], (10595 ^ _782435) ^ [_976012, _976014, _976016, _976018] : [hBOOL(hAPP(hAPP(c_member(_976012), _976014), _976016)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976012, tc_HOL_Obool)), _976016), hAPP(hAPP(c_Set_Oinsert(_976012), _976014), _976018)) = hAPP(hAPP(c_Set_Oinsert(_976012), _976014), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976012, tc_HOL_Obool)), _976016), _976018)))], (10601 ^ _782435) ^ [_976177, _976179, _976181, _976183] : [-(hBOOL(hAPP(hAPP(c_member(_976177), _976179), _976181))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976177, tc_HOL_Obool)), _976181), hAPP(hAPP(c_Set_Oinsert(_976177), _976179), _976183)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976177, tc_HOL_Obool)), _976181), _976183))], (10607 ^ _782435) ^ [_976256, _976258, _976260] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976256, tc_HOL_Obool)), _976258), _976260) = c_Orderings_Obot__class_Obot(tc_fun(_976256, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976256, tc_HOL_Obool)), _976258), _976260) = _976258)], (10613 ^ _782435) ^ [_976389, _976391, _976393] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_976389, tc_HOL_Obool)), _976391), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976389, tc_HOL_Obool)), _976393), _976391)) = c_Orderings_Obot__class_Obot(tc_fun(_976389, tc_HOL_Obool)))], (10615 ^ _782435) ^ [_976443, _976445, _976447, _976449, _976451] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976443, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976443, tc_HOL_Obool)), hAPP(c_Set_Oimage(_976445, _976443, _976447), _976449)), hAPP(c_Set_Oimage(_976445, _976443, _976447), _976451))), hAPP(c_Set_Oimage(_976445, _976443, _976447), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976445, tc_HOL_Obool)), _976449), _976451)))))], (10617 ^ _782435) ^ [_976527, _976529, _976531] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976527, tc_HOL_Obool)), _976529), hAPP(hAPP(c_Set_Oinsert(_976527), _976531), c_Orderings_Obot__class_Obot(tc_fun(_976527, tc_HOL_Obool))))), -(_976529 = c_Orderings_Obot__class_Obot(tc_fun(_976527, tc_HOL_Obool))), -(_976529 = hAPP(hAPP(c_Set_Oinsert(_976527), _976531), c_Orderings_Obot__class_Obot(tc_fun(_976527, tc_HOL_Obool))))], (10627 ^ _782435) ^ [_976722, _976724, _976726, _976728] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976722, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976722, tc_HOL_Obool)), _976724), _976726)), _976728)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976722, tc_HOL_Obool)), _976724), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976722, tc_HOL_Obool)), _976726), _976728))))], (10633 ^ _782435) ^ [_976883, _976885, _976887, _976889] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976883, tc_HOL_Obool)), _976885), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_976883, tc_HOL_Obool)), _976887), _976889))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_976883, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_976883, tc_HOL_Obool)), _976885), _976887)), _976889)))], (10639 ^ _782435) ^ [_977050, _977052, _977054] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_977050, tc_HOL_Obool)), _977052), _977054)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977050, tc_HOL_Obool)), _977052), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977050, tc_HOL_Obool)), _977054), _977052)) = _977054)], (10645 ^ _782435) ^ [_977193, _977195, _977197] : [-(hAPP(hAPP(c_Set_Oinsert(_977193), _977195), _977197) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977193, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_977193), _977195), c_Orderings_Obot__class_Obot(tc_fun(_977193, tc_HOL_Obool)))), _977197))], (10647 ^ _782435) ^ [_977252, _977254, _977256] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977252, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977252, tc_HOL_Obool)), _977254), _977256)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977252, tc_HOL_Obool)), _977254), _977256)) = _977254)], (10649 ^ _782435) ^ [_977312, _977314, _977316, _977318] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977312, tc_HOL_Obool)), _977314), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977312, tc_HOL_Obool)), _977316), _977318)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977312, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977312, tc_HOL_Obool)), _977314), _977316)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977312, tc_HOL_Obool)), _977314), _977318)))], (10651 ^ _782435) ^ [_977396, _977398, _977400, _977402] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977396, tc_HOL_Obool)), _977398), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_977396, tc_HOL_Obool)), _977400), _977402)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_977396, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977396, tc_HOL_Obool)), _977398), _977400)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977396, tc_HOL_Obool)), _977398), _977402)))], (10653 ^ _782435) ^ [_977480, _977482, _977484, _977486] : [class_Orderings_Olinorder(_977480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_977480), _977482), _977484)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_977480, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977480, _977482), _977486)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977480, _977482), _977484)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_977480, _977484), _977486))], (10663 ^ _782435) ^ [_977687, _977689, _977691] : [class_Orderings_Oorder(_977687), _977689 = _977691, -(c_SetInterval_Oord__class_OatLeastAtMost(_977687, _977689, _977691) = hAPP(hAPP(c_Set_Oinsert(_977687), _977689), c_Orderings_Obot__class_Obot(tc_fun(_977687, tc_HOL_Obool))))], (10673 ^ _782435) ^ [_977852, _977854, _977856, _977858] : [class_Orderings_Oorder(_977852), 10676 ^ _782435 : [(10677 ^ _782435) ^ [] : [c_SetInterval_Oord__class_OatLeastAtMost(_977852, _977854, _977856) = hAPP(hAPP(c_Set_Oinsert(_977852), _977858), c_Orderings_Obot__class_Obot(tc_fun(_977852, tc_HOL_Obool))), 10680 ^ _782435 : [(10681 ^ _782435) ^ [] : [-(_977854 = _977856)], (10683 ^ _782435) ^ [] : [-(_977856 = _977858)]]], (10685 ^ _782435) ^ [] : [-(c_SetInterval_Oord__class_OatLeastAtMost(_977852, _977854, _977856) = hAPP(hAPP(c_Set_Oinsert(_977852), _977858), c_Orderings_Obot__class_Obot(tc_fun(_977852, tc_HOL_Obool)))), _977854 = _977856, _977856 = _977858]]], (10695 ^ _782435) ^ [_978196, _978198] : [class_Orderings_Oorder(_978196), -(c_SetInterval_Oord__class_OatLeastAtMost(_978196, _978198, _978198) = hAPP(hAPP(c_Set_Oinsert(_978196), _978198), c_Orderings_Obot__class_Obot(tc_fun(_978196, tc_HOL_Obool))))], (10701 ^ _782435) ^ [_978305, _978307] : [class_Complete__Lattice_Ocomplete__lattice(_978305), -(c_Complete__Lattice_OSup__class_OSup(_978305, hAPP(hAPP(c_Set_Oinsert(_978305), _978307), c_Orderings_Obot__class_Obot(tc_fun(_978305, tc_HOL_Obool)))) = _978307)], (10707 ^ _782435) ^ [_978412, _978414, _978416] : [class_Complete__Lattice_Ocomplete__lattice(_978412), -(c_Complete__Lattice_OSup__class_OSup(_978412, hAPP(hAPP(c_Set_Oinsert(_978412), _978414), _978416)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_978412), _978414), c_Complete__Lattice_OSup__class_OSup(_978412, _978416)))], (10713 ^ _782435) ^ [_978533, _978535] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978533, tc_HOL_Obool)), _978535) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978533, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_978533, tc_HOL_Obool))), _978535))], (10715 ^ _782435) ^ [_978582, _978584, _978586] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978582, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978582, tc_HOL_Obool)), _978584), _978586)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978582, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978582, tc_HOL_Obool)), _978584)), _978586))], (10717 ^ _782435) ^ [_978647, _978649, _978651] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978647, tc_HOL_Obool)), _978649), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978647, tc_HOL_Obool)), _978651)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978647, tc_HOL_Obool)), _978649), _978651))], (10719 ^ _782435) ^ [_978704, _978706, _978708] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_978704, tc_HOL_Obool)), _978706), _978708) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_978704, tc_HOL_Obool)), _978706), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_978704, tc_HOL_Obool)), _978708)))], (10721 ^ _782435) ^ [_978761, _978763] : [class_Complete__Lattice_Ocomplete__lattice(_978761), -(c_Complete__Lattice_OInf__class_OInf(_978761, hAPP(hAPP(c_Set_Oinsert(_978761), _978763), c_Orderings_Obot__class_Obot(tc_fun(_978761, tc_HOL_Obool)))) = _978763)], (10727 ^ _782435) ^ [_978868, _978870, _978872] : [class_Complete__Lattice_Ocomplete__lattice(_978868), -(c_Complete__Lattice_OInf__class_OInf(_978868, hAPP(hAPP(c_Set_Oinsert(_978868), _978870), _978872)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_978868), _978870), c_Complete__Lattice_OInf__class_OInf(_978868, _978872)))], (10733 ^ _782435) ^ [_978989, _978991, _978993] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_978989, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_978989, tc_HOL_Obool)), _978991), _978993)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_978989, tc_HOL_Obool)), _978991), c_Complete__Lattice_OSup__class_OSup(tc_fun(_978989, tc_HOL_Obool), _978993)))], (10735 ^ _782435) ^ [_979050, _979052, _979054] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_979050, tc_HOL_Obool)), _979052), _979054) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_979050, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979050, tc_HOL_Obool)), _979052), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979050, tc_HOL_Obool)), _979054), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979050, tc_HOL_Obool), tc_HOL_Obool))))))], (10737 ^ _782435) ^ [_979124] : [-(hAPP(c_Set_OPow(_979124), c_Orderings_Obot__class_Obot(tc_fun(_979124, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_979124, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_979124, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979124, tc_HOL_Obool), tc_HOL_Obool))))], (10739 ^ _782435) ^ [_979181, _979183, _979185] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_979181, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979181, tc_HOL_Obool)), _979183), _979185)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979181, tc_HOL_Obool)), _979183), c_Complete__Lattice_OInf__class_OInf(tc_fun(_979181, tc_HOL_Obool), _979185)))], (10741 ^ _782435) ^ [_979242, _979244, _979246] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_979242, tc_HOL_Obool)), _979244), _979246) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_979242, tc_HOL_Obool), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979242, tc_HOL_Obool)), _979244), hAPP(hAPP(c_Set_Oinsert(tc_fun(_979242, tc_HOL_Obool)), _979246), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_979242, tc_HOL_Obool), tc_HOL_Obool))))))], (10743 ^ _782435) ^ [_979316, _979318, _979320, _979322, _979324, _979326] : [hBOOL(hAPP(hAPP(c_member(_979316), _979318), _979320)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979316, tc_fun(_979322, tc_HOL_Obool)), _979320), hAPP(hAPP(c_COMBB(tc_fun(_979322, tc_HOL_Obool), tc_fun(_979322, tc_HOL_Obool), _979316), hAPP(c_Set_Oinsert(_979322), _979324)), _979326)) = hAPP(hAPP(c_Set_Oinsert(_979322), _979324), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979316, tc_fun(_979322, tc_HOL_Obool)), _979320), _979326)))], (10749 ^ _782435) ^ [_979536, _979538, _979540, _979542] : [_979536 = c_Orderings_Obot__class_Obot(tc_fun(_979538, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_979538, _979540, hAPP(c_COMBK(_979540, _979538), _979542)), _979536) = c_Orderings_Obot__class_Obot(tc_fun(_979540, tc_HOL_Obool)))], (10755 ^ _782435) ^ [_979657, _979659, _979661, _979663] : [-(_979657 = c_Orderings_Obot__class_Obot(tc_fun(_979659, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_979659, _979661, hAPP(c_COMBK(_979661, _979659), _979663)), _979657) = hAPP(hAPP(c_Set_Oinsert(_979661), _979663), c_Orderings_Obot__class_Obot(tc_fun(_979661, tc_HOL_Obool))))], (10761 ^ _782435) ^ [_979748, _979750, _979752, _979754, _979756] : [_979748 = c_Orderings_Obot__class_Obot(tc_fun(_979750, tc_HOL_Obool)), -(hAPP(hAPP(c_Set_Oinsert(_979752), _979754), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979750, tc_fun(_979752, tc_HOL_Obool)), _979748), _979756)) = hAPP(hAPP(c_Set_Oinsert(_979752), _979754), c_Orderings_Obot__class_Obot(tc_fun(_979752, tc_HOL_Obool))))], (10767 ^ _782435) ^ [_979901, _979903, _979905, _979907, _979909] : [-(_979901 = c_Orderings_Obot__class_Obot(tc_fun(_979903, tc_HOL_Obool))), -(hAPP(hAPP(c_Set_Oinsert(_979905), _979907), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979903, tc_fun(_979905, tc_HOL_Obool)), _979901), _979909)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_979903, tc_fun(_979905, tc_HOL_Obool)), _979901), hAPP(hAPP(c_COMBB(tc_fun(_979905, tc_HOL_Obool), tc_fun(_979905, tc_HOL_Obool), _979903), hAPP(c_Set_Oinsert(_979905), _979907)), _979909)))], (10773 ^ _782435) ^ [_980003, _980005] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980003, tc_fun(_980003, tc_HOL_Obool)), _980005), hAPP(hAPP(c_COMBC(_980003, tc_fun(_980003, tc_HOL_Obool), tc_fun(_980003, tc_HOL_Obool)), c_Set_Oinsert(_980003)), c_Orderings_Obot__class_Obot(tc_fun(_980003, tc_HOL_Obool)))) = _980005)], (10775 ^ _782435) ^ [_980081, _980083, _980085, _980087, _980089] : [_980081 = c_Orderings_Obot__class_Obot(tc_fun(_980083, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980083, tc_fun(_980085, tc_HOL_Obool)), _980081), hAPP(hAPP(c_COMBB(tc_fun(_980085, tc_HOL_Obool), tc_fun(_980085, tc_HOL_Obool), _980083), hAPP(c_Set_Oinsert(_980085), _980087)), _980089)) = c_Orderings_Obot__class_Obot(tc_fun(_980085, tc_HOL_Obool)))], (10781 ^ _782435) ^ [_980244, _980246, _980248, _980250, _980252] : [-(_980244 = c_Orderings_Obot__class_Obot(tc_fun(_980246, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980246, tc_fun(_980248, tc_HOL_Obool)), _980244), hAPP(hAPP(c_COMBB(tc_fun(_980248, tc_HOL_Obool), tc_fun(_980248, tc_HOL_Obool), _980246), hAPP(c_Set_Oinsert(_980248), _980250)), _980252)) = hAPP(hAPP(c_Set_Oinsert(_980248), _980250), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980246, tc_fun(_980248, tc_HOL_Obool)), _980244), _980252)))], (10787 ^ _782435) ^ [_980346, _980348, _980350, _980352, _980354, _980356] : [hBOOL(hAPP(hAPP(c_member(_980346), _980348), _980350)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980346, tc_fun(_980352, tc_HOL_Obool)), _980350), hAPP(hAPP(c_COMBB(tc_fun(_980352, tc_HOL_Obool), tc_fun(_980352, tc_HOL_Obool), _980346), hAPP(c_Set_Oinsert(_980352), _980354)), _980356)) = hAPP(hAPP(c_Set_Oinsert(_980352), _980354), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980346, tc_fun(_980352, tc_HOL_Obool)), _980350), _980356)))], (10793 ^ _782435) ^ [_980551, _980553, _980555, _980557, _980559] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980551, tc_fun(_980553, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980551), _980555), _980557)), _980559) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_980553, tc_HOL_Obool)), hAPP(_980559, _980555)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980551, tc_fun(_980553, tc_HOL_Obool)), _980557), _980559)))], (10795 ^ _782435) ^ [_980628, _980630, _980632, _980634, _980636] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980628, tc_fun(_980630, tc_HOL_Obool)), _980632), hAPP(hAPP(c_COMBB(tc_fun(_980630, tc_HOL_Obool), tc_fun(_980630, tc_HOL_Obool), _980628), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980630, tc_HOL_Obool)), _980634)), _980636)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980630, tc_HOL_Obool)), _980634), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980628, tc_fun(_980630, tc_HOL_Obool)), _980632), _980636)))], (10797 ^ _782435) ^ [_980718, _980720, _980722, _980724, _980726] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980718, tc_HOL_Obool)), _980720), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980722, tc_fun(_980718, tc_HOL_Obool)), _980724), _980726)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_980722, tc_fun(_980718, tc_HOL_Obool)), _980724), hAPP(hAPP(c_COMBB(tc_fun(_980718, tc_HOL_Obool), tc_fun(_980718, tc_HOL_Obool), _980722), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_980718, tc_HOL_Obool)), _980720)), _980726)))], (10799 ^ _782435) ^ [_980808, _980810, _980812, _980814, _980816] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980808, tc_fun(_980810, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_980808), _980812), _980814)), _980816) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_980810, tc_HOL_Obool)), hAPP(_980816, _980812)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_980808, tc_fun(_980810, tc_HOL_Obool)), _980814), _980816)))], (10801 ^ _782435) ^ [_980885, _980887, _980889] : [class_Orderings_Oorder(_980885), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_980885), _980887), _980889)), -(c_SetInterval_Oord__class_OgreaterThanLessThan(_980885, _980889, _980887) = c_Orderings_Obot__class_Obot(tc_fun(_980885, tc_HOL_Obool)))], (10811 ^ _782435) ^ [_981048, _981050, _981052] : [class_Groups_Oordered__ab__group__add(_981048), -(hAPP(c_Set_Oimage(_981048, _981048, c_Groups_Ouminus__class_Ouminus(_981048)), c_SetInterval_Oord__class_OgreaterThanLessThan(_981048, _981050, _981052)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_981048, hAPP(c_Groups_Ouminus__class_Ouminus(_981048), _981052), hAPP(c_Groups_Ouminus__class_Ouminus(_981048), _981050)))], (10817 ^ _782435) ^ [_981179, _981181, _981183] : [class_Complete__Lattice_Ocomplete__lattice(_981179), -(c_Complete__Lattice_OSup__class_OSup(_981179, hAPP(hAPP(c_Set_Oinsert(_981179), _981181), hAPP(hAPP(c_Set_Oinsert(_981179), _981183), c_Orderings_Obot__class_Obot(tc_fun(_981179, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_981179), _981181), _981183))], (10823 ^ _782435) ^ [_981320, _981322, _981324] : [class_Complete__Lattice_Ocomplete__lattice(_981320), -(c_Complete__Lattice_OInf__class_OInf(_981320, hAPP(hAPP(c_Set_Oinsert(_981320), _981322), hAPP(hAPP(c_Set_Oinsert(_981320), _981324), c_Orderings_Obot__class_Obot(tc_fun(_981320, tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_981320), _981322), _981324))], (10829 ^ _782435) ^ [_981461, _981463, _981465, _981467, _981469] : [hBOOL(hAPP(hAPP(c_member(_981461), _981463), _981465)), -(hAPP(c_Set_Oimage(_981461, _981467, hAPP(c_COMBK(_981467, _981461), _981469)), _981465) = hAPP(hAPP(c_Set_Oinsert(_981467), _981469), c_Orderings_Obot__class_Obot(tc_fun(_981467, tc_HOL_Obool))))], (10835 ^ _782435) ^ [_981628, _981630, _981632, _981634, _981636] : [_981628 = c_Orderings_Obot__class_Obot(tc_fun(_981630, tc_HOL_Obool)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981630, tc_fun(_981632, tc_HOL_Obool)), _981628), hAPP(hAPP(c_COMBC(_981630, tc_fun(_981632, tc_HOL_Obool), tc_fun(_981632, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_981632, tc_HOL_Obool), tc_fun(tc_fun(_981632, tc_HOL_Obool), tc_fun(_981632, tc_HOL_Obool)), _981630), c_Groups_Ominus__class_Ominus(tc_fun(_981632, tc_HOL_Obool))), _981634)), _981636)) = c_Orderings_Otop__class_Otop(tc_fun(_981632, tc_HOL_Obool)))], (10841 ^ _782435) ^ [_981835, _981837, _981839, _981841, _981843] : [-(_981835 = c_Orderings_Obot__class_Obot(tc_fun(_981837, tc_HOL_Obool))), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981837, tc_fun(_981839, tc_HOL_Obool)), _981835), hAPP(hAPP(c_COMBC(_981837, tc_fun(_981839, tc_HOL_Obool), tc_fun(_981839, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_981839, tc_HOL_Obool), tc_fun(tc_fun(_981839, tc_HOL_Obool), tc_fun(_981839, tc_HOL_Obool)), _981837), c_Groups_Ominus__class_Ominus(tc_fun(_981839, tc_HOL_Obool))), _981841)), _981843)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981839, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981837, tc_fun(_981839, tc_HOL_Obool)), _981835), _981841)), _981843))], (10847 ^ _782435) ^ [_981980, _981982, _981984, _981986, _981988] : [_981980 = c_Orderings_Obot__class_Obot(tc_fun(_981982, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981984, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_981982, tc_fun(_981984, tc_HOL_Obool)), _981980), _981986)), _981988) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_981984, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_981984, tc_HOL_Obool))), _981988))], (10853 ^ _782435) ^ [_982145, _982147, _982149, _982151, _982153] : [-(_982145 = c_Orderings_Obot__class_Obot(tc_fun(_982147, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982149, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982147, tc_fun(_982149, tc_HOL_Obool)), _982145), _982151)), _982153) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982147, tc_fun(_982149, tc_HOL_Obool)), _982145), hAPP(hAPP(c_COMBC(_982147, tc_fun(_982149, tc_HOL_Obool), tc_fun(_982149, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_982149, tc_HOL_Obool), tc_fun(tc_fun(_982149, tc_HOL_Obool), tc_fun(_982149, tc_HOL_Obool)), _982147), c_Groups_Ominus__class_Ominus(tc_fun(_982149, tc_HOL_Obool))), _982151)), _982153)))], (10859 ^ _782435) ^ [_982272, _982274, _982276, _982278] : [-(hAPP(c_Set_Oimage(_982272, _982274, _982276), _982278) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982272, tc_fun(_982274, tc_HOL_Obool)), _982278), hAPP(hAPP(c_COMBC(_982272, tc_fun(_982274, tc_HOL_Obool), tc_fun(_982274, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_982274, tc_fun(tc_fun(_982274, tc_HOL_Obool), tc_fun(_982274, tc_HOL_Obool)), _982272), c_Set_Oinsert(_982274)), _982276)), c_Orderings_Obot__class_Obot(tc_fun(_982274, tc_HOL_Obool)))))], (10861 ^ _782435) ^ [_982380, _982382, _982384, _982386, _982388] : [_982380 = c_Orderings_Obot__class_Obot(tc_fun(_982382, tc_HOL_Obool)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982384, tc_HOL_Obool)), _982386), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982382, tc_fun(_982384, tc_HOL_Obool)), _982380), _982388)) = _982386)], (10867 ^ _782435) ^ [_982513, _982515, _982517, _982519, _982521] : [-(_982513 = c_Orderings_Obot__class_Obot(tc_fun(_982515, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982517, tc_HOL_Obool)), _982519), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_982515, tc_fun(_982517, tc_HOL_Obool)), _982513), _982521)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_982515, tc_fun(_982517, tc_HOL_Obool)), _982513), hAPP(hAPP(c_COMBB(tc_fun(_982517, tc_HOL_Obool), tc_fun(_982517, tc_HOL_Obool), _982515), hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_982517, tc_HOL_Obool)), _982519)), _982521)))], (10873 ^ _782435) ^ [_982621, _982623, _982625] : [-(hAPP(c_Set_OPow(_982621), hAPP(hAPP(c_Set_Oinsert(_982621), _982623), _982625)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(_982621, tc_HOL_Obool), tc_HOL_Obool)), hAPP(c_Set_OPow(_982621), _982625)), hAPP(c_Set_Oimage(tc_fun(_982621, tc_HOL_Obool), tc_fun(_982621, tc_HOL_Obool), hAPP(c_Set_Oinsert(_982621), _982623)), hAPP(c_Set_OPow(_982621), _982625))))], (10875 ^ _782435) ^ [_982703, _982705, _982707, _982709] : [class_Orderings_Oorder(_982703), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982703, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_982703, _982705, _982707)), c_SetInterval_Oord__class_OgreaterThanLessThan(_982703, _982707, _982709)) = c_Orderings_Obot__class_Obot(tc_fun(_982703, tc_HOL_Obool)))], (10881 ^ _782435) ^ [_982830, _982832, _982834, _982836] : [class_Orderings_Oorder(_982830), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_982830, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_982830, _982832, _982834)), c_SetInterval_Oord__class_OatLeastAtMost(_982830, _982834, _982836)) = c_Orderings_Obot__class_Obot(tc_fun(_982830, tc_HOL_Obool)))], (10887 ^ _782435) ^ [_982957, _982959] : [class_Orderings_Olinorder(_982957), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_982957, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_982957), _982959)), hAPP(hAPP(c_Set_Oinsert(_982957), _982959), c_Orderings_Obot__class_Obot(tc_fun(_982957, tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(_982957), _982959))], (10893 ^ _782435) ^ [_983100, _983102, _983104, _983106] : [class_Orderings_Oorder(_983100), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_983100, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_983100, _983102, _983104)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_983100, _983104), _983106)) = c_Orderings_Obot__class_Obot(tc_fun(_983100, tc_HOL_Obool)))], (10899 ^ _782435) ^ [_983231, _983233] : [-(c_Set_Othe__elem(_983231, hAPP(hAPP(c_Set_Oinsert(_983231), _983233), c_Orderings_Obot__class_Obot(tc_fun(_983231, tc_HOL_Obool)))) = _983233)], (10901 ^ _782435) ^ [_983293, _983295, _983297, _983299, _983301, _983303] : [hBOOL(hAPP(hAPP(c_member(_983293), _983295), _983297)), -(hAPP(c_Set_Oimage(_983293, _983299, c_Fun_Ofun__upd(_983293, _983299, _983301, _983295, _983303)), _983297) = hAPP(hAPP(c_Set_Oinsert(_983299), _983303), hAPP(c_Set_Oimage(_983293, _983299, _983301), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_983293, tc_HOL_Obool)), _983297), hAPP(hAPP(c_Set_Oinsert(_983293), _983295), c_Orderings_Obot__class_Obot(tc_fun(_983293, tc_HOL_Obool)))))))], (10907 ^ _782435) ^ [_983490, _983492, _983494, _983496, _983498, _983500] : [-(hBOOL(hAPP(hAPP(c_member(_983490), _983492), _983494))), -(hAPP(c_Set_Oimage(_983490, _983496, c_Fun_Ofun__upd(_983490, _983496, _983498, _983492, _983500)), _983494) = hAPP(c_Set_Oimage(_983490, _983496, _983498), _983494))], (10913 ^ _782435) ^ [_983563, _983565, _983567] : [10915 ^ _782435 : [(10916 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_983563, tc_HOL_Obool)), 10914 ^ [_983563, _983565, _983567]), _983565)))], (10918 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983563, tc_HOL_Obool)), 10914 ^ [_983563, _983565, _983567]), _983567))]], -(_983565 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_983563, tc_HOL_Obool), tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_983563, tc_HOL_Obool)), c_Complete__Lattice_OInf__class_OInf(tc_fun(_983563, tc_HOL_Obool), _983565)), _983567)))], (10926 ^ _782435) ^ [_983825, _983827, _983829, _983831] : [class_Orderings_Olinorder(_983825), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_983825), _983827), _983829)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_983825), _983829), _983831)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_983825, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_983825, _983827, _983829)), c_SetInterval_Oord__class_OatLeastAtMost(_983825, _983829, _983831)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_983825, _983827, _983831))], (10940 ^ _782435) ^ [_984090, _984092, _984094] : [class_Orderings_Olinorder(_984090), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984090), _984092), _984094)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984090, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_984090, _984092, _984094)), hAPP(hAPP(c_Set_Oinsert(_984090), _984094), c_Orderings_Obot__class_Obot(tc_fun(_984090, tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(_984090, _984092, _984094))], (10950 ^ _782435) ^ [_984299, _984301, _984303, _984305] : [class_Orderings_Olinorder(_984299), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_984299), _984301), _984303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984299), _984303), _984305)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984299, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_984299, _984301, _984303)), c_SetInterval_Oord__class_OgreaterThanLessThan(_984299, _984303, _984305)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_984299, _984301), _984305))], (10964 ^ _782435) ^ [_984568, _984570, _984572] : [class_Orderings_Olinorder(_984568), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_984568), _984570), _984572)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984568, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_984568), _984570), c_Orderings_Obot__class_Obot(tc_fun(_984568, tc_HOL_Obool)))), c_SetInterval_Oord__class_OgreaterThanLessThan(_984568, _984570, _984572)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_984568, _984570), _984572))], (10974 ^ _782435) ^ [_984781, _984783, _984785, _984787] : [c_Orderings_Oorder__class_Omono(tc_fun(_984781, tc_HOL_Obool), tc_fun(_984781, tc_HOL_Obool), _984783), hBOOL(hAPP(hAPP(c_member(_984781), _984785), _984787)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_984781, tc_HOL_Obool)), _984787), hAPP(_984783, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_984781, tc_HOL_Obool)), _984787), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_984781, tc_HOL_Obool), _984783))))), -(hBOOL(hAPP(hAPP(c_member(_984781), _984785), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_984781, tc_HOL_Obool), _984783))))], (10988 ^ _782435) ^ [_985088, _985090, _985092, _985094, _985096] : [_985088 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_985090, tc_HOL_Obool), _985092), c_Orderings_Oorder__class_Omono(tc_fun(_985090, tc_HOL_Obool), tc_fun(_985090, tc_HOL_Obool), _985092), hBOOL(hAPP(hAPP(c_member(_985090), _985094), _985096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_985090, tc_HOL_Obool)), _985096), hAPP(_985092, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_985090, tc_HOL_Obool)), _985096), _985088)))), -(hBOOL(hAPP(hAPP(c_member(_985090), _985094), _985088)))], (11006 ^ _782435) ^ [_985447, _985449, _985451, _985453] : [-(c_Fun_Ofun__upd(_985447, _985449, _985451, _985453, hAPP(_985451, _985453)) = _985451)], (11008 ^ _782435) ^ [_985485, _985487] : [class_Orderings_Opreorder(_985485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985485), _985487), _985487))], (11014 ^ _782435) ^ [_985575, _985577, _985579] : [class_Orderings_Olinorder(_985575), 11017 ^ _782435 : [(11028 ^ _782435) ^ [] : [11029 ^ _782435 : [(11030 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985575), _985577), _985579))], (11032 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985575), _985579), _985577))]], _985577 = _985579], (11018 ^ _782435) ^ [] : [-(_985577 = _985579), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985575), _985577), _985579))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985575), _985579), _985577)))]]], (11036 ^ _782435) ^ [_985829, _985831, _985833] : [class_Orderings_Olinorder(_985829), 11039 ^ _782435 : [(11050 ^ _782435) ^ [] : [11051 ^ _782435 : [(11052 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985829), _985833), _985831))], (11054 ^ _782435) ^ [] : [_985831 = _985833]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985829), _985831), _985833))], (11040 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985829), _985831), _985833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_985829), _985833), _985831))), -(_985831 = _985833)]]], (11058 ^ _782435) ^ [_986083, _986085, _986087] : [class_Orderings_Olinorder(_986083), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986083), _986085), _986087))), -(_986085 = _986087), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986083), _986087), _986085)))], (11072 ^ _782435) ^ [_986214, _986216, _986218] : [class_Orderings_Olinorder(_986214), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986214), _986216), _986218))), 11079 ^ _782435 : [(11080 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986214), _986218), _986216))), -(_986218 = _986216)], (11086 ^ _782435) ^ [] : [_986218 = _986216, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986214), _986218), _986216))]]], (11092 ^ _782435) ^ [_986473, _986475, _986477] : [class_Orderings_Olinorder(_986473), -(_986475 = _986477), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986473), _986475), _986477))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986473), _986477), _986475)))], (11106 ^ _782435) ^ [_986608, _986610, _986612] : [class_Orderings_Oorder(_986608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986608), _986610), _986612)), _986610 = _986612], (11116 ^ _782435) ^ [_986754, _986756, _986758] : [class_Orderings_Opreorder(_986754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986754), _986756), _986758)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986754), _986758), _986756))], (11126 ^ _782435) ^ [_986914, _986916, _986918] : [class_Orderings_Opreorder(_986914), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986914), _986916), _986918)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_986914), _986918), _986916))], (11136 ^ _782435) ^ [_987074, _987076, _987078] : [class_Orderings_Oorder(_987074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987074), _987076), _987078)), _987076 = _987078], (11146 ^ _782435) ^ [_987220, _987222, _987224] : [class_Orderings_Oorder(_987220), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987220), _987222), _987224)), _987224 = _987222], (11156 ^ _782435) ^ [_987366, _987368, _987370] : [class_Orderings_Opreorder(_987366), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987366), _987368), _987370)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987366), _987370), _987368))], (11166 ^ _782435) ^ [_987526, _987528, _987530] : [class_Orderings_Oorder(_987526), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987526), _987528), _987530)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987526), _987530), _987528))], (11176 ^ _782435) ^ [_987686, _987688, _987690, _987692] : [class_Orderings_Oord(_987686), _987688 = _987690, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987686), _987690), _987692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987686), _987688), _987692)))], (11190 ^ _782435) ^ [_987905, _987907, _987909, _987911] : [class_Orderings_Oorder(_987905), _987907 = _987909, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987905), _987911), _987909)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_987905), _987911), _987907)))], (11204 ^ _782435) ^ [_988124, _988126, _988128, _988130] : [class_Orderings_Oord(_988124), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988124), _988126), _988128)), _988128 = _988130, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988124), _988126), _988130)))], (11218 ^ _782435) ^ [_988343, _988345, _988347, _988349] : [class_Orderings_Oorder(_988343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988343), _988345), _988347)), _988345 = _988349, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988343), _988349), _988347)))], (11232 ^ _782435) ^ [_988562, _988564, _988566, _988568] : [class_Orderings_Opreorder(_988562), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988562), _988564), _988566)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988562), _988566), _988568)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988562), _988564), _988568)))], (11246 ^ _782435) ^ [_988795, _988797, _988799, _988801] : [class_Orderings_Oorder(_988795), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988795), _988797), _988799)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988795), _988801), _988797)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_988795), _988801), _988799)))], (11260 ^ _782435) ^ [_989028, _989030, _989032] : [class_Orderings_Opreorder(_989028), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989028), _989030), _989032)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989028), _989032), _989030))], (11270 ^ _782435) ^ [_989188, _989190, _989192] : [class_Orderings_Olinorder(_989188), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989188), _989190), _989192))), -(_989190 = _989192), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_989188), _989192), _989190)))], (11284 ^ _782435) ^ [_989347, _989349, _989351, _989353, _989355] : [c_Fun_Ofun__upd(_989347, _989349, _989351, _989353, _989355) = _989351, -(hAPP(_989351, _989353) = _989355)], (11290 ^ _782435) ^ [_989444, _989446, _989448, _989450, _989452] : [hAPP(_989448, _989450) = _989452, -(c_Fun_Ofun__upd(_989444, _989446, _989448, _989450, _989452) = _989448)], (11296 ^ _782435) ^ [_989547, _989549, _989551, _989553, _989555, _989557] : [-(c_Fun_Ofun__upd(_989547, _989549, c_Fun_Ofun__upd(_989547, _989549, _989551, _989553, _989555), _989553, _989557) = c_Fun_Ofun__upd(_989547, _989549, _989551, _989553, _989557))], (11298 ^ _782435) ^ [_989598, _989600, _989602, _989604, _989606] : [-(hAPP(c_Fun_Ofun__upd(_989598, _989600, _989602, _989604, _989606), _989604) = _989606)], (11300 ^ _782435) ^ [_989659, _989661, _989663, _989665, _989667, _989669] : [_989659 = _989661, -(hAPP(c_Fun_Ofun__upd(_989663, _989665, _989667, _989661, _989669), _989659) = _989669)], (11306 ^ _782435) ^ [_989756, _989758, _989760, _989762, _989764, _989766] : [-(_989756 = _989758), -(hAPP(c_Fun_Ofun__upd(_989760, _989762, _989764, _989758, _989766), _989756) = hAPP(_989764, _989756))], (11312 ^ _782435) ^ [_989810, _989812, _989814, _989816, _989818, _989820, _989822] : [-(_989810 = _989812), -(c_Fun_Ofun__upd(_989814, _989816, c_Fun_Ofun__upd(_989814, _989816, _989818, _989810, _989820), _989812, _989822) = c_Fun_Ofun__upd(_989814, _989816, c_Fun_Ofun__upd(_989814, _989816, _989818, _989812, _989822), _989810, _989820))], (11318 ^ _782435) ^ [_989876, _989878, _989880, _989882, _989884, _989886] : [-(_989876 = _989878), -(hAPP(c_Fun_Ofun__upd(_989880, _989882, _989884, _989878, _989886), _989876) = hAPP(_989884, _989876))], (11324 ^ _782435) ^ [_989932, _989934, _989936, _989938, _989940] : [hAPP(_989932, _989934) = _989936, -(c_Fun_Ofun__upd(_989938, _989940, _989932, _989934, _989936) = _989932)], (11330 ^ _782435) ^ [_990033, _990035, _990037] : [class_Orderings_Olinorder(_990033), 11333 ^ _782435 : [(11334 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990033, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_990033), _990035)), hAPP(c_SetInterval_Oord__class_OlessThan(_990033), _990037))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990033), _990035), _990037)))], (11340 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990033), _990035), _990037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990033, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OlessThan(_990033), _990035)), hAPP(c_SetInterval_Oord__class_OlessThan(_990033), _990037))))]]], (11346 ^ _782435) ^ [_990346, _990348, _990350, _990352, _990354, _990356] : [_990346 = _990348, -(hAPP(c_Fun_Ofun__upd(_990350, _990352, _990354, _990348, _990356), _990346) = _990356)], (11352 ^ _782435) ^ [_990443, _990445, _990447, _990449, _990451, _990453] : [-(_990443 = _990445), -(hAPP(c_Fun_Ofun__upd(_990447, _990449, _990451, _990445, _990453), _990443) = hAPP(_990451, _990443))], (11358 ^ _782435) ^ [_990501, _990503, _990505, _990507, _990509] : [class_Orderings_Oorder(_990501), 11361 ^ _782435 : [(11362 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990501, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_990501, _990503, _990505)), c_SetInterval_Oord__class_OatLeastAtMost(_990501, _990507, _990509))), 11365 ^ _782435 : [(11380 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990507), _990509)))], (11366 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990503), _990505)), 11369 ^ _782435 : [(11370 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990507), _990503)))], (11372 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990505), _990509)))], (11374 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990501), _990507), _990503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990501), _990505), _990509)))]]]]], (11382 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_990501, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_990501, _990503, _990505)), c_SetInterval_Oord__class_OatLeastAtMost(_990501, _990507, _990509)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990507), _990509)), 11385 ^ _782435 : [(11386 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990503), _990505)))], (11388 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990507), _990503)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_990501), _990505), _990509)), 11395 ^ _782435 : [(11396 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990501), _990507), _990503))], (11398 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_990501), _990505), _990509))]]]]]]], (11404 ^ _782435) ^ [_991272, _991274, _991276, _991278] : [class_Orderings_Oord(_991272), 11407 ^ _782435 : [(11408 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991274, _991272)), _991276), _991278)), 11411 ^ _782435 : [(11412 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991274, _991272)), _991276), _991278)))], (11414 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991274, _991272)), _991278), _991276))]]], (11416 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_991274, _991272)), _991276), _991278))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991274, _991272)), _991276), _991278)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_991274, _991272)), _991278), _991276)))]]], (11426 ^ _782435) ^ [_991664, _991666, _991668] : [class_Orderings_Olinorder(_991664), 11429 ^ _782435 : [(11430 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991664), _991666), _991668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991664), _991668), _991666)))], (11436 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991664), _991668), _991666)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991664), _991666), _991668))]]], (11442 ^ _782435) ^ [_991873, _991875, _991877] : [class_Orderings_Olinorder(_991873), 11445 ^ _782435 : [(11446 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991873), _991875), _991877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991873), _991877), _991875)))], (11452 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_991873), _991877), _991875)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_991873), _991875), _991877))]]], (11458 ^ _782435) ^ [_992082, _992084, _992086] : [class_Orderings_Olinorder(_992082), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992082), _992084), _992086))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992082), _992086), _992084)))], (11468 ^ _782435) ^ [_992200, _992202, _992204] : [class_Orderings_Oorder(_992200), 11471 ^ _782435 : [(11472 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992200), _992202), _992204)), 11475 ^ _782435 : [(11476 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992200), _992202), _992204)))], (11478 ^ _782435) ^ [] : [_992202 = _992204]]], (11480 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992200), _992202), _992204))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992200), _992202), _992204)), -(_992202 = _992204)]]], (11490 ^ _782435) ^ [_992536, _992538, _992540] : [class_Orderings_Opreorder(_992536), 11493 ^ _782435 : [(11494 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992536), _992538), _992540)), 11497 ^ _782435 : [(11498 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992536), _992538), _992540)))], (11500 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992536), _992540), _992538))]]], (11502 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992536), _992538), _992540))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992536), _992538), _992540)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992536), _992540), _992538)))]]], (11512 ^ _782435) ^ [_992893, _992895, _992897] : [class_Orderings_Oorder(_992893), 11515 ^ _782435 : [(11526 ^ _782435) ^ [] : [11527 ^ _782435 : [(11528 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992893), _992895), _992897))], (11530 ^ _782435) ^ [] : [_992895 = _992897]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992893), _992895), _992897)))], (11516 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_992893), _992895), _992897)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_992893), _992895), _992897))), -(_992895 = _992897)]]], (11534 ^ _782435) ^ [_993191, _993193, _993195] : [class_Orderings_Olinorder(_993191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993191), _993193), _993195))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993191), _993195), _993193)))], (11544 ^ _782435) ^ [_993311, _993313, _993315] : [class_Orderings_Olinorder(_993311), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993311), _993313), _993315))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993311), _993315), _993313)))], (11554 ^ _782435) ^ [_993431, _993433, _993435] : [class_Orderings_Olinorder(_993431), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993431), _993433), _993435))), 11561 ^ _782435 : [(11562 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993431), _993433), _993435)), -(_993433 = _993435)], (11568 ^ _782435) ^ [] : [_993433 = _993435, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993431), _993433), _993435)))]]], (11574 ^ _782435) ^ [_993734, _993736, _993738] : [class_Orderings_Oorder(_993734), -(_993736 = _993738), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993734), _993736), _993738)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993734), _993736), _993738)))], (11588 ^ _782435) ^ [_993950, _993952, _993954] : [class_Orderings_Oorder(_993950), -(_993952 = _993954), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_993950), _993954), _993952)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_993950), _993954), _993952)))], (11602 ^ _782435) ^ [_994166, _994168, _994170] : [class_Orderings_Olinorder(_994166), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994166), _994168), _994170)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994166), _994170), _994168))], (11612 ^ _782435) ^ [_994326, _994328, _994330] : [class_Orderings_Opreorder(_994326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994326), _994328), _994330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994326), _994328), _994330)))], (11622 ^ _782435) ^ [_994485, _994487, _994489] : [class_Orderings_Olinorder(_994485), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994485), _994487), _994489)), 11629 ^ _782435 : [(11630 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994485), _994487), _994489))), -(_994487 = _994489)], (11636 ^ _782435) ^ [] : [_994487 = _994489, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994485), _994487), _994489))]]], (11642 ^ _782435) ^ [_994741, _994743, _994745] : [class_Orderings_Oorder(_994741), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994741), _994743), _994745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994741), _994743), _994745))), -(_994743 = _994745)], (11656 ^ _782435) ^ [_994913, _994915, _994917] : [class_Orderings_Oorder(_994913), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_994913), _994915), _994917)), -(_994915 = _994917), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_994913), _994915), _994917)))], (11670 ^ _782435) ^ [_995087, _995089, _995091] : [class_Orderings_Oorder(_995087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995087), _995089), _995091)), -(_995091 = _995089), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995087), _995089), _995091)))], (11684 ^ _782435) ^ [_995261, _995263, _995265, _995267] : [class_Orderings_Opreorder(_995261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995261), _995263), _995265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995261), _995265), _995267)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995261), _995263), _995267)))], (11698 ^ _782435) ^ [_995494, _995496, _995498, _995500] : [class_Orderings_Oorder(_995494), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995494), _995496), _995498)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995494), _995500), _995496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995494), _995500), _995498)))], (11712 ^ _782435) ^ [_995727, _995729, _995731, _995733] : [class_Orderings_Opreorder(_995727), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995727), _995729), _995731)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995727), _995731), _995733)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995727), _995729), _995733)))], (11726 ^ _782435) ^ [_995960, _995962, _995964, _995966] : [class_Orderings_Oorder(_995960), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_995960), _995962), _995964)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995960), _995966), _995962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_995960), _995966), _995964)))], (11740 ^ _782435) ^ [_996193, _996195, _996197, _996199] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_996193, tc_HOL_Obool)), _996195), _996197)), hBOOL(hAPP(hAPP(c_member(_996193), _996199), _996195)), -(hBOOL(hAPP(hAPP(c_member(_996193), _996199), _996197)))], (11750 ^ _782435) ^ [_996390, _996392] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_996390, tc_HOL_Obool)), _996392), c_Orderings_Obot__class_Obot(tc_fun(_996390, tc_HOL_Obool))))], (11752 ^ _782435) ^ [_996430, _996432, _996434, _996436, _996438] : [class_Groups_Oordered__ab__group__add(_996430), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_996430), _996432), _996434) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_996430), _996436), _996438), 11759 ^ _782435 : [(11760 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996430), _996432), _996434)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996430), _996436), _996438)))], (11766 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996430), _996436), _996438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996430), _996432), _996434)))]]], (11772 ^ _782435) ^ [_996785, _996787, _996789, _996791] : [class_Lattices_Osemilattice__sup(_996785), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996785), _996787), _996789)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996785), _996787), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996785), _996789), _996791))))], (11782 ^ _782435) ^ [_996964, _996966, _996968, _996970] : [class_Lattices_Osemilattice__sup(_996964), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996964), _996966), _996968)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_996964), _996966), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_996964), _996970), _996968))))], (11792 ^ _782435) ^ [_997143, _997145, _997147, _997149] : [class_Lattices_Osemilattice__inf(_997143), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997143), _997145), _997147)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997143), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_997143), _997145), _997149)), _997147)))], (11802 ^ _782435) ^ [_997322, _997324, _997326, _997328] : [class_Lattices_Osemilattice__inf(_997322), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997322), _997324), _997326)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997322), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_997322), _997328), _997324)), _997326)))], (11812 ^ _782435) ^ [_997501, _997503, _997505] : [class_Groups_Oordered__ab__group__add(_997501), 11815 ^ _782435 : [(11816 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997501), hAPP(c_Groups_Ouminus__class_Ouminus(_997501), _997503)), hAPP(c_Groups_Ouminus__class_Ouminus(_997501), _997505))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997501), _997505), _997503)))], (11822 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997501), _997505), _997503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997501), hAPP(c_Groups_Ouminus__class_Ouminus(_997501), _997503)), hAPP(c_Groups_Ouminus__class_Ouminus(_997501), _997505))))]]], (11828 ^ _782435) ^ [_997784, _997786, _997788] : [class_Groups_Oordered__ab__group__add(_997784), 11831 ^ _782435 : [(11832 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997784), hAPP(c_Groups_Ouminus__class_Ouminus(_997784), _997786)), _997788)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997784), hAPP(c_Groups_Ouminus__class_Ouminus(_997784), _997788)), _997786)))], (11838 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997784), hAPP(c_Groups_Ouminus__class_Ouminus(_997784), _997788)), _997786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_997784), hAPP(c_Groups_Ouminus__class_Ouminus(_997784), _997786)), _997788)))]]], (11844 ^ _782435) ^ [_998067, _998069, _998071] : [class_Groups_Oordered__ab__group__add(_998067), 11847 ^ _782435 : [(11848 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998067), _998069), hAPP(c_Groups_Ouminus__class_Ouminus(_998067), _998071))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998067), _998071), hAPP(c_Groups_Ouminus__class_Ouminus(_998067), _998069))))], (11854 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998067), _998071), hAPP(c_Groups_Ouminus__class_Ouminus(_998067), _998069))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_998067), _998069), hAPP(c_Groups_Ouminus__class_Ouminus(_998067), _998071))))]]], (11860 ^ _782435) ^ [_998368, _998370, _998372] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998368, tc_HOL_Obool)), _998370), _998372)), 11863 ^ _782435 : [(11864 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998368, tc_HOL_Obool)), _998370), _998372)))], (11866 ^ _782435) ^ [] : [_998370 = _998372]]], (11868 ^ _782435) ^ [_998517, _998519, _998521] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998517, tc_HOL_Obool)), _998519), _998521))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998517, tc_HOL_Obool)), _998519), _998521)), -(_998519 = _998521)], (11888 ^ _782435) ^ [_998841, _998843, _998845] : [11889 ^ _782435 : [(11890 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998841, tc_HOL_Obool)), _998843), _998845))], (11892 ^ _782435) ^ [] : [_998843 = _998845]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998841, tc_HOL_Obool)), _998843), _998845)))], (11878 ^ _782435) ^ [_998713, _998715, _998717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_998713, tc_HOL_Obool)), _998715), _998717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_998713, tc_HOL_Obool)), _998715), _998717))), -(_998715 = _998717)], (11896 ^ _782435) ^ [_999000, _999002, _999004] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999000, tc_HOL_Obool)), _999002), _999004)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999000, tc_HOL_Obool)), _999002), _999004)))], (11902 ^ _782435) ^ [_999119, _999121, _999123, _999125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999119, tc_HOL_Obool)), _999121), _999123)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999119, tc_HOL_Obool)), _999123), _999125)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999119, tc_HOL_Obool)), _999121), _999125)))], (11912 ^ _782435) ^ [_999316, _999318, _999320, _999322] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_999316, tc_HOL_Obool)), _999318), _999320)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999316, tc_HOL_Obool)), _999320), _999322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_999316, tc_HOL_Obool)), _999318), _999322)))], (11922 ^ _782435) ^ [_999513, _999515, _999517, _999519, _999521] : [class_Orderings_Olinorder(_999513), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999513), _999515), _999517)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999513), _999519), _999521)), 11933 ^ _782435 : [(11934 ^ _782435) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999513, _999515), _999517) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999513, _999519), _999521), 11937 ^ _782435 : [(11938 ^ _782435) ^ [] : [-(_999515 = _999519)], (11940 ^ _782435) ^ [] : [-(_999517 = _999521)]]], (11942 ^ _782435) ^ [] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999513, _999515), _999517) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999513, _999519), _999521)), _999515 = _999519, _999517 = _999521]]], (11952 ^ _782435) ^ [_999994, _999996, _999998, _1000000, _1000002] : [class_Orderings_Olinorder(_999994), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999994, _999996), _999998) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_999994, _1000000), _1000002), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999994), _999996), _999998)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_999994), _1000000), _1000002)), -(_999996 = _1000000)], (11970 ^ _782435) ^ [_1000301, _1000303, _1000305, _1000307, _1000309] : [class_Orderings_Olinorder(_1000301), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000301, _1000303), _1000305) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1000301, _1000307), _1000309), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000301), _1000303), _1000305)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000301), _1000307), _1000309)), -(_1000305 = _1000309)], (11988 ^ _782435) ^ [_1000608, _1000610, _1000612] : [class_Complete__Lattice_Ocomplete__lattice(_1000608), class_Orderings_Olinorder(_1000608), 11995 ^ _782435 : [(11996 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000608), _1000610), c_Complete__Lattice_OSup__class_OSup(_1000608, _1000612))), 12000 ^ _782435 : [(12001 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1000608), 11999 ^ [_1000608, _1000610, _1000612]), _1000612)))], (12003 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000608), _1000610), 11999 ^ [_1000608, _1000610, _1000612])))]]], (12005 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000608), _1000610), c_Complete__Lattice_OSup__class_OSup(_1000608, _1000612)))), 12006 ^ _782435 : [(12007 ^ _782435) ^ [_1000914] : [hBOOL(hAPP(hAPP(c_member(_1000608), _1000914), _1000612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1000608), _1000610), _1000914))]]]]], (12015 ^ _782435) ^ [_1001068, _1001070, _1001072] : [class_Complete__Lattice_Ocomplete__lattice(_1001068), class_Orderings_Olinorder(_1001068), 12022 ^ _782435 : [(12023 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001068), c_Complete__Lattice_OInf__class_OInf(_1001068, _1001070)), _1001072)), 12027 ^ _782435 : [(12028 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001068), 12026 ^ [_1001068, _1001070, _1001072]), _1001070)))], (12030 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001068), 12026 ^ [_1001068, _1001070, _1001072]), _1001072)))]]], (12032 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001068), c_Complete__Lattice_OInf__class_OInf(_1001068, _1001070)), _1001072))), 12033 ^ _782435 : [(12034 ^ _782435) ^ [_1001374] : [hBOOL(hAPP(hAPP(c_member(_1001068), _1001374), _1001070)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001068), _1001374), _1001072))]]]]], (12042 ^ _782435) ^ [_1001528, _1001530, _1001532, _1001534, _1001536] : [class_Complete__Lattice_Ocomplete__lattice(_1001528), class_Orderings_Olinorder(_1001528), 12049 ^ _782435 : [(12050 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001528), _1001530), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001532, _1001528), _1001534), _1001536))), 12054 ^ _782435 : [(12055 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1001532), 12053 ^ [_1001528, _1001530, _1001532, _1001534, _1001536]), _1001534)))], (12057 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001528), _1001530), hAPP(_1001536, 12053 ^ [_1001528, _1001530, _1001532, _1001534, _1001536]))))]]], (12059 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001528), _1001530), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1001532, _1001528), _1001534), _1001536)))), 12060 ^ _782435 : [(12061 ^ _782435) ^ [_1001876] : [hBOOL(hAPP(hAPP(c_member(_1001532), _1001876), _1001534)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1001528), _1001530), hAPP(_1001536, _1001876)))]]]]], (12069 ^ _782435) ^ [_1002046, _1002048, _1002050, _1002052, _1002054] : [class_Complete__Lattice_Ocomplete__lattice(_1002046), class_Orderings_Olinorder(_1002046), 12076 ^ _782435 : [(12077 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002046), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1002048, _1002046), _1002050), _1002052)), _1002054)), 12081 ^ _782435 : [(12082 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1002048), 12080 ^ [_1002046, _1002048, _1002050, _1002052, _1002054]), _1002050)))], (12084 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002046), hAPP(_1002052, 12080 ^ [_1002046, _1002048, _1002050, _1002052, _1002054])), _1002054)))]]], (12086 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002046), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1002048, _1002046), _1002050), _1002052)), _1002054))), 12087 ^ _782435 : [(12088 ^ _782435) ^ [_1002394] : [hBOOL(hAPP(hAPP(c_member(_1002048), _1002394), _1002050)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002046), hAPP(_1002052, _1002394)), _1002054))]]]]], (12096 ^ _782435) ^ [_1002564, _1002566, _1002568] : [class_Complete__Lattice_Ocomplete__lattice(_1002564), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002564), _1002566), hAPP(_1002568, _1002566))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1002564), _1002566), c_Inductive_Ocomplete__lattice__class_Ogfp(_1002564, _1002568))))], (12106 ^ _782435) ^ [_1002735, _1002737, _1002739, _1002741, _1002743] : [class_Orderings_Oorder(_1002735), class_Orderings_Olinorder(_1002737), c_Orderings_Oorder__class_Ostrict__mono(_1002737, _1002735, _1002739), 12117 ^ _782435 : [(12118 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002735), hAPP(_1002739, _1002741)), hAPP(_1002739, _1002743))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002737), _1002741), _1002743)))], (12124 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002737), _1002741), _1002743)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1002735), hAPP(_1002739, _1002741)), hAPP(_1002739, _1002743))))]]], (12130 ^ _782435) ^ [_1003136, _1003138, _1003140, _1003142, _1003144] : [class_Orderings_Oorder(_1003136), class_Orderings_Oorder(_1003138), c_Orderings_Oorder__class_Ostrict__mono(_1003138, _1003136, _1003140), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003138), _1003142), _1003144)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003136), hAPP(_1003140, _1003142)), hAPP(_1003140, _1003144))))], (12148 ^ _782435) ^ [_1003433, _1003435, _1003437] : [class_Orderings_Owellorder(_1003433), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003433), _1003435), c_Orderings_Oord__class_OLeast(_1003433, _1003437))), hBOOL(hAPP(_1003437, _1003435))], (12158 ^ _782435) ^ [_1003589, _1003591, _1003593] : [class_Complete__Lattice_Ocomplete__lattice(_1003589), _1003591 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1003589, _1003593), c_Orderings_Oorder__class_Omono(_1003589, _1003589, _1003593), -(_1003591 = hAPP(_1003593, _1003591))], (12172 ^ _782435) ^ [_1003788, _1003790] : [class_Complete__Lattice_Ocomplete__lattice(_1003788), c_Orderings_Oorder__class_Omono(_1003788, _1003788, _1003790), -(c_Inductive_Ocomplete__lattice__class_Ogfp(_1003788, _1003790) = hAPP(_1003790, c_Inductive_Ocomplete__lattice__class_Ogfp(_1003788, _1003790)))], (12182 ^ _782435) ^ [_1003935, _1003937, _1003939] : [class_Orderings_Oorder(_1003935), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1003935), _1003937), _1003939)), -(c_SetInterval_Oord__class_OatLeastAtMost(_1003935, _1003939, _1003937) = c_Orderings_Obot__class_Obot(tc_fun(_1003935, tc_HOL_Obool)))], (12192 ^ _782435) ^ [_1004098, _1004100, _1004102] : [class_Orderings_Oorder(_1004098), 12195 ^ _782435 : [(12196 ^ _782435) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1004098, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004098, _1004100), _1004102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004098), _1004100), _1004102))], (12202 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004098), _1004100), _1004102))), -(c_Orderings_Obot__class_Obot(tc_fun(_1004098, tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004098, _1004100), _1004102))]]], (12208 ^ _782435) ^ [_1004323, _1004325, _1004327] : [class_Orderings_Oorder(_1004323), 12211 ^ _782435 : [(12212 ^ _782435) ^ [] : [hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004323, _1004325), _1004327) = c_Orderings_Obot__class_Obot(tc_fun(_1004323, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004323), _1004325), _1004327))], (12218 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004323), _1004325), _1004327))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1004323, _1004325), _1004327) = c_Orderings_Obot__class_Obot(tc_fun(_1004323, tc_HOL_Obool)))]]], (12224 ^ _782435) ^ [_1004548, _1004550, _1004552] : [class_Orderings_Oord(_1004548), 12227 ^ _782435 : [(12228 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1004548), _1004550), hAPP(c_SetInterval_Oord__class_OlessThan(_1004548), _1004552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004548), _1004550), _1004552)))], (12234 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004548), _1004550), _1004552)), -(hBOOL(hAPP(hAPP(c_member(_1004548), _1004550), hAPP(c_SetInterval_Oord__class_OlessThan(_1004548), _1004552))))]]], (12240 ^ _782435) ^ [_1004816, _1004818, _1004820] : [class_Orderings_Oorder(_1004816), 12243 ^ _782435 : [(12244 ^ _782435) ^ [] : [c_Orderings_Obot__class_Obot(tc_fun(_1004816, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1004816, _1004818, _1004820), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004816), _1004818), _1004820))], (12250 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1004816), _1004818), _1004820))), -(c_Orderings_Obot__class_Obot(tc_fun(_1004816, tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1004816, _1004818, _1004820))]]], (12256 ^ _782435) ^ [_1005035, _1005037, _1005039] : [class_Orderings_Oorder(_1005035), 12259 ^ _782435 : [(12260 ^ _782435) ^ [] : [c_SetInterval_Oord__class_OgreaterThanAtMost(_1005035, _1005037, _1005039) = c_Orderings_Obot__class_Obot(tc_fun(_1005035, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005035), _1005037), _1005039))], (12266 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005035), _1005037), _1005039))), -(c_SetInterval_Oord__class_OgreaterThanAtMost(_1005035, _1005037, _1005039) = c_Orderings_Obot__class_Obot(tc_fun(_1005035, tc_HOL_Obool)))]]], (12272 ^ _782435) ^ [_1005254, _1005256, _1005258] : [class_Orderings_Oord(_1005254), 12275 ^ _782435 : [(12276 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1005254), _1005256), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1005254), _1005258))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005254), _1005258), _1005256)))], (12282 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1005254), _1005258), _1005256)), -(hBOOL(hAPP(hAPP(c_member(_1005254), _1005256), hAPP(c_SetInterval_Oord__class_OgreaterThan(_1005254), _1005258))))]]], (12288 ^ _782435) ^ [_1005522, _1005524, _1005526, _1005528] : [hBOOL(hAPP(hAPP(c_member(_1005522), _1005524), _1005526)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1005522, tc_HOL_Obool)), _1005526), hAPP(_1005528, _1005526))), -(hBOOL(hAPP(hAPP(c_member(_1005522), _1005524), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1005522, tc_HOL_Obool), _1005528))))], (12298 ^ _782435) ^ [_1005725, _1005727] : [class_Complete__Lattice_Ocomplete__lattice(_1005725), c_Orderings_Oorder__class_Omono(_1005725, _1005725, _1005727), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005725), hAPP(_1005727, c_Inductive_Ocomplete__lattice__class_Ogfp(_1005725, _1005727))), c_Inductive_Ocomplete__lattice__class_Ogfp(_1005725, _1005727))))], (12308 ^ _782435) ^ [_1005886, _1005888] : [class_Complete__Lattice_Ocomplete__lattice(_1005886), c_Orderings_Oorder__class_Omono(_1005886, _1005886, _1005888), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1005886), c_Inductive_Ocomplete__lattice__class_Ogfp(_1005886, _1005888)), hAPP(_1005888, c_Inductive_Ocomplete__lattice__class_Ogfp(_1005886, _1005888)))))], (12318 ^ _782435) ^ [_1006047, _1006049, _1006051, _1006053, _1006055, _1006057] : [hBOOL(hAPP(hAPP(c_member(_1006047), _1006049), _1006051)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1006053, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1006047, _1006053, _1006055), _1006051)), hAPP(_1006057, hAPP(c_Set_Oimage(_1006047, _1006053, _1006055), _1006051)))), -(hBOOL(hAPP(hAPP(c_member(_1006053), hAPP(_1006055, _1006049)), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1006053, tc_HOL_Obool), _1006057))))], (12328 ^ _782435) ^ [_1006292, _1006294, _1006296, _1006298] : [c_Orderings_Oorder__class_Omono(tc_fun(_1006292, tc_HOL_Obool), tc_fun(_1006292, tc_HOL_Obool), _1006294), hBOOL(hAPP(hAPP(c_member(_1006292), _1006296), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1006292, tc_HOL_Obool), _1006294))), -(hBOOL(hAPP(hAPP(c_member(_1006292), _1006296), hAPP(_1006294, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006292, tc_HOL_Obool)), _1006298), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1006292, tc_HOL_Obool), _1006294))))))], (12338 ^ _782435) ^ [_1006523, _1006525, _1006527, _1006529] : [class_Orderings_Olinorder(_1006523), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006523), _1006525), _1006527)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006523), _1006527), _1006529)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006523, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1006523, _1006525, _1006527)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1006523, _1006527), _1006529)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1006523, _1006525, _1006529))], (12352 ^ _782435) ^ [_1006792, _1006794, _1006796, _1006798] : [class_Orderings_Olinorder(_1006792), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1006792), _1006794), _1006796)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1006792), _1006796), _1006798)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1006792, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1006792, _1006794, _1006796)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1006792, _1006796, _1006798)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1006792, _1006794, _1006798))], (12366 ^ _782435) ^ [_1007057, _1007059, _1007061, _1007063] : [class_Complete__Lattice_Ocomplete__lattice(_1007057), _1007059 = c_Inductive_Ocomplete__lattice__class_Ogfp(_1007057, _1007061), c_Orderings_Oorder__class_Omono(_1007057, _1007057, _1007061), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007057), _1007063), hAPP(_1007061, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007057), _1007063), _1007059)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007057), _1007063), _1007059)))], (12384 ^ _782435) ^ [_1007362, _1007364, _1007366] : [class_Complete__Lattice_Ocomplete__lattice(_1007362), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007362), _1007364), hAPP(_1007366, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007362), _1007364), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007362, _1007366))))), c_Orderings_Oorder__class_Omono(_1007362, _1007362, _1007366), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007362), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007362), _1007364), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007362, _1007366))), hAPP(_1007366, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007362), _1007364), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007362, _1007366))))))], (12398 ^ _782435) ^ [_1007655, _1007657, _1007659] : [class_Complete__Lattice_Ocomplete__lattice(_1007655), c_Orderings_Oorder__class_Omono(_1007655, _1007655, _1007657), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007655), _1007659), hAPP(_1007657, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1007655), _1007659), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007655, _1007657))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1007655), _1007659), c_Inductive_Ocomplete__lattice__class_Ogfp(_1007655, _1007657))))], (12412 ^ _782435) ^ [_1007904, _1007906, _1007908] : [class_Orderings_Olinorder(_1007904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1007904), _1007906), _1007908)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1007904, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1007904), _1007906)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1007904, _1007906, _1007908)) = hAPP(c_SetInterval_Oord__class_OlessThan(_1007904), _1007908))], (12422 ^ _782435) ^ [_1008099, _1008101, _1008103] : [class_Orderings_Olinorder(_1008099), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1008099), _1008101), _1008103)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1008099, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1008099, _1008101, _1008103)), hAPP(c_SetInterval_Oord__class_OatLeast(_1008099), _1008103)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(_1008099), _1008101))], (12458 ^ _782435) ^ [_1008842, _1008844, _1008846, _1008848] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008842, tc_HOL_Obool)), _1008844), hAPP(hAPP(c_Set_Oinsert(_1008842), _1008846), _1008848)))), 12461 ^ _782435 : [(12462 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008842), _1008846), _1008848)))], (12464 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008842, tc_HOL_Obool)), _1008844), _1008848))]], 12465 ^ _782435 : [(12466 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008842), _1008846), _1008848))], (12468 ^ _782435) ^ [] : [12469 ^ _782435 : [(12470 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008842), _1008846), _1008844)))], (12472 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008842, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008842, tc_HOL_Obool)), _1008844), hAPP(hAPP(c_Set_Oinsert(_1008842), _1008846), c_Orderings_Obot__class_Obot(tc_fun(_1008842, tc_HOL_Obool))))), _1008848))]], 12473 ^ _782435 : [(12474 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008842), _1008846), _1008844))], (12476 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008842, tc_HOL_Obool)), _1008844), _1008848))]]]]], (12432 ^ _782435) ^ [_1008315, _1008317, _1008319, _1008321] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008315, tc_HOL_Obool)), _1008317), hAPP(hAPP(c_Set_Oinsert(_1008315), _1008319), _1008321))), 12435 ^ _782435 : [(12436 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008315), _1008319), _1008321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008315, tc_HOL_Obool)), _1008317), _1008321)))], (12442 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008315), _1008319), _1008321))), 12445 ^ _782435 : [(12446 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1008315), _1008319), _1008317)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1008315, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1008315, tc_HOL_Obool)), _1008317), hAPP(hAPP(c_Set_Oinsert(_1008315), _1008319), c_Orderings_Obot__class_Obot(tc_fun(_1008315, tc_HOL_Obool))))), _1008321)))], (12452 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1008315), _1008319), _1008317))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1008315, tc_HOL_Obool)), _1008317), _1008321)))]]]]], (12480 ^ _782435) ^ [_1009381, _1009383, _1009385, _1009387] : [c_Orderings_Oorder__class_Omono(tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool), _1009383), hBOOL(hAPP(hAPP(c_member(_1009381), _1009385), _1009387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009381, tc_HOL_Obool)), _1009387), hAPP(_1009383, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1009381, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009381, tc_HOL_Obool), tc_fun(tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool)), tc_fun(_1009381, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009381, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009381, tc_HOL_Obool), tc_fun(tc_fun(_1009381, tc_HOL_Obool), tc_fun(_1009381, tc_HOL_Obool)), tc_fun(_1009381, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009381, tc_HOL_Obool))), _1009383)), _1009387))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1009381, tc_HOL_Obool), _1009383)))))), -(hBOOL(hAPP(hAPP(c_member(_1009381), _1009385), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1009381, tc_HOL_Obool), _1009383))))], (12494 ^ _782435) ^ [_1009874, _1009876, _1009878, _1009880, _1009882] : [_1009874 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1009876, tc_HOL_Obool), _1009878), c_Orderings_Oorder__class_Omono(tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool), _1009878), hBOOL(hAPP(hAPP(c_member(_1009876), _1009880), _1009882)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1009876, tc_HOL_Obool)), _1009882), hAPP(_1009878, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1009876, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009876, tc_HOL_Obool), tc_fun(tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool)), tc_fun(_1009876, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009876, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1009876, tc_HOL_Obool), tc_fun(tc_fun(_1009876, tc_HOL_Obool), tc_fun(_1009876, tc_HOL_Obool)), tc_fun(_1009876, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1009876, tc_HOL_Obool))), _1009878)), _1009882))), _1009874))))), -(hBOOL(hAPP(hAPP(c_member(_1009876), _1009880), _1009874)))], (12512 ^ _782435) ^ [_1010419, _1010421, _1010423] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010419, tc_HOL_Obool)), _1010421), hAPP(_1010423, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010419, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010419, tc_HOL_Obool), tc_fun(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), tc_fun(_1010419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010419, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010419, tc_HOL_Obool), tc_fun(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), tc_fun(_1010419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010419, tc_HOL_Obool))), _1010423)), _1010421))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010419, tc_HOL_Obool), _1010423)))))), c_Orderings_Oorder__class_Omono(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), _1010423), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1010419, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010419, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010419, tc_HOL_Obool), tc_fun(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), tc_fun(_1010419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010419, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010419, tc_HOL_Obool), tc_fun(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), tc_fun(_1010419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010419, tc_HOL_Obool))), _1010423)), _1010421))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010419, tc_HOL_Obool), _1010423)))), hAPP(_1010423, c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1010419, tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010419, tc_HOL_Obool), tc_fun(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), tc_fun(_1010419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010419, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1010419, tc_HOL_Obool), tc_fun(tc_fun(_1010419, tc_HOL_Obool), tc_fun(_1010419, tc_HOL_Obool)), tc_fun(_1010419, tc_HOL_Obool)), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1010419, tc_HOL_Obool))), _1010423)), _1010421))), c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1010419, tc_HOL_Obool), _1010423)))))))], (12522 ^ _782435) ^ [_1011278, _1011280] : [-(c_Set_Othe__elem(_1011278, _1011280) = c_HOL_OThe(_1011278, hAPP(hAPP(c_COMBB(tc_fun(_1011278, tc_HOL_Obool), tc_HOL_Obool, _1011278), hAPP(c_fequal, _1011280)), hAPP(hAPP(c_COMBC(_1011278, tc_fun(_1011278, tc_HOL_Obool), tc_fun(_1011278, tc_HOL_Obool)), c_Set_Oinsert(_1011278)), c_Orderings_Obot__class_Obot(tc_fun(_1011278, tc_HOL_Obool))))))], (12524 ^ _782435) ^ [_1011348, _1011350, _1011352, _1011354, _1011356, _1011358, _1011360] : [hBOOL(hAPP(hAPP(c_member(_1011348), _1011350), _1011352)), c_Nitpick_Ofold__graph_H(_1011348, _1011354, _1011356, _1011358, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1011348, tc_HOL_Obool)), _1011352), hAPP(hAPP(c_Set_Oinsert(_1011348), _1011350), c_Orderings_Obot__class_Obot(tc_fun(_1011348, tc_HOL_Obool)))), _1011360), -(c_Nitpick_Ofold__graph_H(_1011348, _1011354, _1011356, _1011358, _1011352, hAPP(hAPP(_1011356, _1011350), _1011360)))], (12534 ^ _782435) ^ [_1011586, _1011588, _1011590] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011586, tc_HOL_Obool)), _1011588), _1011590))), 12540 ^ _782435 : [(12541 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011586, tc_HOL_Obool)), 12539 ^ [_1011586, _1011588, _1011590]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1011586, tc_HOL_Obool)), _1011588), _1011590))))], (12544 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1011586, tc_HOL_Obool)), 12542 ^ [_1011586, _1011588, _1011590]), hAPP(hAPP(c_Set_Oinsert(tc_fun(_1011586, tc_HOL_Obool)), _1011588), _1011590))))], (12546 ^ _782435) ^ [] : [12539 ^ [_1011586, _1011588, _1011590] = 12542 ^ [_1011586, _1011588, _1011590]], (12548 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011586, tc_HOL_Obool)), 12539 ^ [_1011586, _1011588, _1011590]), 12542 ^ [_1011586, _1011588, _1011590]) = c_Orderings_Obot__class_Obot(tc_fun(_1011586, tc_HOL_Obool))]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1011586, tc_HOL_Obool)), _1011588), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1011586, tc_HOL_Obool), _1011590)) = c_Orderings_Obot__class_Obot(tc_fun(_1011586, tc_HOL_Obool)))], (12552 ^ _782435) ^ [_1012180, _1012182, _1012184, _1012186] : [class_Complete__Lattice_Ocomplete__lattice(_1012180), _1012182 = c_Inductive_Ocomplete__lattice__class_Olfp(_1012180, _1012184), c_Orderings_Oorder__class_Omono(_1012180, _1012180, _1012184), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012180), hAPP(_1012184, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012180), _1012182), _1012186))), _1012186)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012180), _1012182), _1012186)))], (12570 ^ _782435) ^ [_1012485, _1012487, _1012489] : [class_Complete__Lattice_Ocomplete__lattice(_1012485), c_Orderings_Oorder__class_Omono(_1012485, _1012485, _1012487), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012485), hAPP(_1012487, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1012485), c_Inductive_Ocomplete__lattice__class_Olfp(_1012485, _1012487)), _1012489))), _1012489)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1012485), c_Inductive_Ocomplete__lattice__class_Olfp(_1012485, _1012487)), _1012489)))], (12584 ^ _782435) ^ [_1012758, _1012760, _1012762, _1012764, _1012766] : [c_Fun_Oinj__on(_1012758, _1012760, _1012762, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1012758, tc_HOL_Obool)), _1012764), _1012766)), 12587 ^ _782435 : [(12588 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1012758, _1012760, _1012762, _1012764))], (12590 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1012758, _1012760, _1012762, _1012766))], (12592 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1012760, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1012758, _1012760, _1012762), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012758, tc_HOL_Obool)), _1012764), _1012766))), hAPP(c_Set_Oimage(_1012758, _1012760, _1012762), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1012758, tc_HOL_Obool)), _1012766), _1012764))) = c_Orderings_Obot__class_Obot(tc_fun(_1012760, tc_HOL_Obool)))]]], (12594 ^ _782435) ^ [_1013025, _1013027, _1013029, _1013031, _1013033] : [-(c_Fun_Oinj__on(_1013025, _1013027, _1013029, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1013025, tc_HOL_Obool)), _1013031), _1013033))), c_Fun_Oinj__on(_1013025, _1013027, _1013029, _1013031), c_Fun_Oinj__on(_1013025, _1013027, _1013029, _1013033), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1013027, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1013025, _1013027, _1013029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013025, tc_HOL_Obool)), _1013031), _1013033))), hAPP(c_Set_Oimage(_1013025, _1013027, _1013029), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1013025, tc_HOL_Obool)), _1013033), _1013031))) = c_Orderings_Obot__class_Obot(tc_fun(_1013027, tc_HOL_Obool))], (12608 ^ _782435) ^ [_1013364, _1013366, _1013368] : [-(c_Fun_Oinj__on(_1013364, _1013366, _1013368, c_Orderings_Obot__class_Obot(tc_fun(_1013364, tc_HOL_Obool))))], (12610 ^ _782435) ^ [_1013398, _1013400] : [class_Groups_Oordered__ab__group__add(_1013398), -(c_Fun_Oinj__on(_1013398, _1013398, c_Groups_Ouminus__class_Ouminus(_1013398), _1013400))], (12616 ^ _782435) ^ [_1013481, _1013483, _1013485, _1013487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013481, tc_HOL_Obool)), _1013483), _1013485)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013481, tc_HOL_Obool)), _1013485), _1013487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1013481, tc_HOL_Obool)), _1013483), _1013487)))], (12626 ^ _782435) ^ [_1013678, _1013680, _1013682, _1013684] : [c_Fun_Oinj__on(_1013678, _1013680, _1013682, c_Orderings_Otop__class_Otop(tc_fun(_1013678, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1013678, tc_fun(_1013684, _1013680), hAPP(hAPP(c_COMBB(_1013680, tc_fun(_1013684, _1013680), _1013678), c_COMBK(_1013680, _1013684)), _1013682), c_Orderings_Otop__class_Otop(tc_fun(_1013678, tc_HOL_Obool))))], (12650 ^ _782435) ^ [_1014231, _1014233, _1014235, _1014237] : [12652 ^ _782435 : [(12653 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014231), 12651 ^ [_1014231, _1014233, _1014235, _1014237]), _1014237)))], (12656 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1014231), 12654 ^ [_1014231, _1014233, _1014235, _1014237]), _1014237)))], (12658 ^ _782435) ^ [] : [-(hAPP(_1014235, 12651 ^ [_1014231, _1014233, _1014235, _1014237]) = hAPP(_1014235, 12654 ^ [_1014231, _1014233, _1014235, _1014237]))], (12660 ^ _782435) ^ [] : [12651 ^ [_1014231, _1014233, _1014235, _1014237] = 12654 ^ [_1014231, _1014233, _1014235, _1014237]]], -(c_Fun_Oinj__on(_1014231, _1014233, _1014235, _1014237))], (12632 ^ _782435) ^ [_1013846, _1013848, _1013850, _1013852] : [c_Fun_Oinj__on(_1013846, _1013848, _1013850, _1013852), 12635 ^ _782435 : [(12636 ^ _782435) ^ [_1013954] : [hBOOL(hAPP(hAPP(c_member(_1013846), _1013954), _1013852)), 12639 ^ _782435 : [(12640 ^ _782435) ^ [_1014056] : [hBOOL(hAPP(hAPP(c_member(_1013846), _1014056), _1013852)), hAPP(_1013850, _1013954) = hAPP(_1013850, _1014056), -(_1013954 = _1014056)]]]]], (12664 ^ _782435) ^ [_1014623, _1014625] : [-(c_Fun_Oinj__on(_1014623, _1014623, c_COMBI(_1014623), _1014625))], (12666 ^ _782435) ^ [_1014652, _1014654] : [class_Complete__Lattice_Ocomplete__lattice(_1014652), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1014652, hAPP(c_COMBK(_1014652, _1014652), _1014654)) = _1014654)], (12672 ^ _782435) ^ [_1014745, _1014747, _1014749, _1014751, _1014753, _1014755] : [c_Fun_Oinj__on(_1014745, _1014747, _1014749, _1014751), -(_1014753 = _1014755), hBOOL(hAPP(hAPP(c_member(_1014745), _1014753), _1014751)), hBOOL(hAPP(hAPP(c_member(_1014745), _1014755), _1014751)), hAPP(_1014749, _1014753) = hAPP(_1014749, _1014755)], (12690 ^ _782435) ^ [_1015058, _1015060, _1015062, _1015064, _1015066, _1015068] : [c_Fun_Oinj__on(_1015058, _1015060, _1015062, _1015064), hBOOL(hAPP(hAPP(c_member(_1015058), _1015066), _1015064)), hBOOL(hAPP(hAPP(c_member(_1015058), _1015068), _1015064)), 12701 ^ _782435 : [(12702 ^ _782435) ^ [] : [hAPP(_1015062, _1015066) = hAPP(_1015062, _1015068), -(_1015066 = _1015068)], (12708 ^ _782435) ^ [] : [_1015066 = _1015068, -(hAPP(_1015062, _1015066) = hAPP(_1015062, _1015068))]]], (12714 ^ _782435) ^ [_1015459, _1015461, _1015463, _1015465, _1015467, _1015469] : [c_Fun_Oinj__on(_1015459, _1015461, _1015463, _1015465), hAPP(_1015463, _1015467) = hAPP(_1015463, _1015469), hBOOL(hAPP(hAPP(c_member(_1015459), _1015467), _1015465)), hBOOL(hAPP(hAPP(c_member(_1015459), _1015469), _1015465)), -(_1015467 = _1015469)], (12732 ^ _782435) ^ [_1015768, _1015770, _1015772, _1015774, _1015776] : [c_Fun_Oinj__on(_1015768, _1015770, _1015772, _1015774), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1015768, tc_HOL_Obool)), _1015776), _1015774)), -(c_Fun_Oinj__on(_1015768, _1015770, _1015772, _1015776))], (12742 ^ _782435) ^ [_1015937, _1015939, _1015941, _1015943, _1015945] : [c_Fun_Oinj__on(_1015937, _1015939, _1015941, c_Orderings_Otop__class_Otop(tc_fun(_1015937, tc_HOL_Obool))), hAPP(_1015941, _1015943) = hAPP(_1015941, _1015945), -(_1015943 = _1015945)], (12752 ^ _782435) ^ [_1016104, _1016106, _1016108, _1016110, _1016112] : [c_Fun_Oinj__on(_1016104, _1016106, _1016108, c_Orderings_Otop__class_Otop(tc_fun(_1016104, tc_HOL_Obool))), 12755 ^ _782435 : [(12756 ^ _782435) ^ [] : [hAPP(_1016108, _1016110) = hAPP(_1016108, _1016112), -(_1016110 = _1016112)], (12762 ^ _782435) ^ [] : [_1016110 = _1016112, -(hAPP(_1016108, _1016110) = hAPP(_1016108, _1016112))]]], (12768 ^ _782435) ^ [_1016361, _1016363, _1016365, _1016367, _1016369] : [c_Fun_Oinj__on(_1016361, _1016363, _1016365, _1016367), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1016361, tc_HOL_Obool)), _1016369), _1016367)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1016363, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1016361, _1016363, _1016365), _1016369)), hAPP(c_Set_Oimage(_1016361, _1016363, _1016365), _1016367))))], (12778 ^ _782435) ^ [_1016574, _1016576, _1016578, _1016580, _1016582] : [c_Fun_Oinj__on(_1016574, _1016576, _1016578, _1016580), c_Fun_Oinj__on(_1016574, _1016576, _1016578, _1016582), -(c_Fun_Oinj__on(_1016574, _1016576, _1016578, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1016574, tc_HOL_Obool)), _1016580), _1016582)))], (12788 ^ _782435) ^ [_1016749, _1016751, _1016753, _1016755, _1016757] : [c_Fun_Oinj__on(_1016749, _1016751, _1016753, _1016755), -(c_Fun_Oinj__on(_1016749, _1016751, _1016753, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1016749, tc_HOL_Obool)), _1016755), _1016757)))], (12794 ^ _782435) ^ [_1016862, _1016864, _1016866, _1016868] : [-(c_Nitpick_Ofold__graph_H(_1016862, _1016864, _1016866, _1016868, c_Orderings_Obot__class_Obot(tc_fun(_1016862, tc_HOL_Obool)), _1016868))], (12796 ^ _782435) ^ [_1016900, _1016902, _1016904, _1016906] : [-(c_Nitpick_Ofold__graph_H(_1016900, _1016902, _1016904, _1016906, c_Orderings_Obot__class_Obot(tc_fun(_1016900, tc_HOL_Obool)), _1016906))], (12798 ^ _782435) ^ [_1016938, _1016940, _1016942, _1016944] : [class_Orderings_Oorder(_1016938), class_Orderings_Olinorder(_1016940), c_Orderings_Oorder__class_Ostrict__mono(_1016940, _1016938, _1016942), -(c_Fun_Oinj__on(_1016940, _1016938, _1016942, _1016944))], (12812 ^ _782435) ^ [_1017135, _1017137, _1017139] : [class_Complete__Lattice_Ocomplete__lattice(_1017135), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017135), hAPP(_1017137, _1017139)), _1017139)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1017135), c_Inductive_Ocomplete__lattice__class_Olfp(_1017135, _1017137)), _1017139)))], (12822 ^ _782435) ^ [_1017306, _1017308, _1017310, _1017312, _1017314] : [c_Fun_Oinj__on(_1017306, _1017308, _1017310, c_Orderings_Otop__class_Otop(tc_fun(_1017306, tc_HOL_Obool))), 12825 ^ _782435 : [(12826 ^ _782435) ^ [] : [hAPP(c_Set_Oimage(_1017306, _1017308, _1017310), _1017312) = hAPP(c_Set_Oimage(_1017306, _1017308, _1017310), _1017314), -(_1017312 = _1017314)], (12832 ^ _782435) ^ [] : [_1017312 = _1017314, -(hAPP(c_Set_Oimage(_1017306, _1017308, _1017310), _1017312) = hAPP(c_Set_Oimage(_1017306, _1017308, _1017310), _1017314))]]], (12838 ^ _782435) ^ [_1017587, _1017589, _1017591, _1017593, _1017595] : [c_Fun_Oinj__on(_1017587, _1017589, _1017591, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1017587, tc_HOL_Obool)), _1017593), _1017595)), 12841 ^ _782435 : [(12842 ^ _782435) ^ [] : [hAPP(c_Set_Oimage(_1017587, _1017589, _1017591), _1017593) = hAPP(c_Set_Oimage(_1017587, _1017589, _1017591), _1017595), -(_1017593 = _1017595)], (12848 ^ _782435) ^ [] : [_1017593 = _1017595, -(hAPP(c_Set_Oimage(_1017587, _1017589, _1017591), _1017593) = hAPP(c_Set_Oimage(_1017587, _1017589, _1017591), _1017595))]]], (12854 ^ _782435) ^ [_1017880, _1017882] : [class_Complete__Lattice_Ocomplete__lattice(_1017880), c_Orderings_Oorder__class_Omono(_1017880, _1017880, _1017882), -(c_Inductive_Ocomplete__lattice__class_Olfp(_1017880, _1017882) = hAPP(_1017882, c_Inductive_Ocomplete__lattice__class_Olfp(_1017880, _1017882)))], (12864 ^ _782435) ^ [_1018027, _1018029, _1018031] : [class_Complete__Lattice_Ocomplete__lattice(_1018027), _1018029 = c_Inductive_Ocomplete__lattice__class_Olfp(_1018027, _1018031), c_Orderings_Oorder__class_Omono(_1018027, _1018027, _1018031), -(_1018029 = hAPP(_1018031, _1018029))], (12878 ^ _782435) ^ [_1018226, _1018228, _1018230, _1018232] : [c_Fun_Oinj__on(_1018226, _1018228, _1018230, c_Orderings_Otop__class_Otop(tc_fun(_1018226, tc_HOL_Obool))), 12881 ^ _782435 : [(12882 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018228), _1018232), hAPP(c_Set_Oimage(_1018226, _1018228, _1018230), c_Orderings_Otop__class_Otop(tc_fun(_1018226, tc_HOL_Obool))))), 12886 ^ _782435 : [(12887 ^ _782435) ^ [] : [-(_1018232 = hAPP(_1018230, 12885 ^ [_1018226, _1018228, _1018230, _1018232]))], (12889 ^ _782435) ^ [_1018491] : [_1018232 = hAPP(_1018230, _1018491), -(_1018491 = 12885 ^ [_1018226, _1018228, _1018230, _1018232])]]], (12895 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1018228), _1018232), hAPP(c_Set_Oimage(_1018226, _1018228, _1018230), c_Orderings_Otop__class_Otop(tc_fun(_1018226, tc_HOL_Obool)))))), 12896 ^ _782435 : [(12897 ^ _782435) ^ [_1018629] : [_1018232 = hAPP(_1018230, _1018629), 12901 ^ _782435 : [(12902 ^ _782435) ^ [] : [-(_1018232 = hAPP(_1018230, 12900 ^ [_1018226, _1018228, _1018230, _1018232, _1018629]))], (12904 ^ _782435) ^ [] : [12900 ^ [_1018226, _1018228, _1018230, _1018232, _1018629] = _1018629]]]]]]], (12908 ^ _782435) ^ [_1018857, _1018859, _1018861, _1018863, _1018865] : [c_Fun_Oinj__on(_1018857, _1018859, _1018861, c_Orderings_Otop__class_Otop(tc_fun(_1018857, tc_HOL_Obool))), 12911 ^ _782435 : [(12912 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018859), hAPP(_1018861, _1018863)), hAPP(c_Set_Oimage(_1018857, _1018859, _1018861), _1018865))), -(hBOOL(hAPP(hAPP(c_member(_1018857), _1018863), _1018865)))], (12918 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1018857), _1018863), _1018865)), -(hBOOL(hAPP(hAPP(c_member(_1018859), hAPP(_1018861, _1018863)), hAPP(c_Set_Oimage(_1018857, _1018859, _1018861), _1018865))))]]], (12924 ^ _782435) ^ [_1019168, _1019170, _1019172, _1019174, _1019176] : [c_Fun_Oinj__on(_1019168, _1019170, _1019172, c_Orderings_Otop__class_Otop(tc_fun(_1019168, tc_HOL_Obool))), 12927 ^ _782435 : [(12928 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019170, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019168, _1019170, _1019172), _1019174)), hAPP(c_Set_Oimage(_1019168, _1019170, _1019172), _1019176))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019168, tc_HOL_Obool)), _1019174), _1019176)))], (12934 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019168, tc_HOL_Obool)), _1019174), _1019176)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019170, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019168, _1019170, _1019172), _1019174)), hAPP(c_Set_Oimage(_1019168, _1019170, _1019172), _1019176))))]]], (12940 ^ _782435) ^ [_1019509, _1019511, _1019513, _1019515, _1019517, _1019519] : [c_Fun_Oinj__on(_1019509, _1019511, _1019513, _1019515), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019509, tc_HOL_Obool)), _1019517), _1019515)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1019509, tc_HOL_Obool)), _1019519), _1019515)), -(hAPP(c_Set_Oimage(_1019509, _1019511, _1019513), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019509, tc_HOL_Obool)), _1019517), _1019519)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019511, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019509, _1019511, _1019513), _1019517)), hAPP(c_Set_Oimage(_1019509, _1019511, _1019513), _1019519)))], (12954 ^ _782435) ^ [_1019844, _1019846, _1019848, _1019850, _1019852] : [c_Fun_Oinj__on(_1019844, _1019846, _1019848, c_Orderings_Otop__class_Otop(tc_fun(_1019844, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1019844, _1019846, _1019848), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019844, tc_HOL_Obool)), _1019850), _1019852)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1019846, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1019844, _1019846, _1019848), _1019850)), hAPP(c_Set_Oimage(_1019844, _1019846, _1019848), _1019852)))], (12960 ^ _782435) ^ [_1020027, _1020029, _1020031, _1020033, _1020035, _1020037] : [c_Fun_Oinj__on(_1020027, _1020029, _1020031, _1020033), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020027, tc_HOL_Obool)), _1020035), _1020033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1020027, tc_HOL_Obool)), _1020037), _1020033)), -(hAPP(c_Set_Oimage(_1020027, _1020029, _1020031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020027, tc_HOL_Obool)), _1020035), _1020037)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020029, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1020027, _1020029, _1020031), _1020035)), hAPP(c_Set_Oimage(_1020027, _1020029, _1020031), _1020037)))], (12974 ^ _782435) ^ [_1020362, _1020364, _1020366, _1020368, _1020370] : [c_Fun_Oinj__on(_1020362, _1020364, _1020366, c_Orderings_Otop__class_Otop(tc_fun(_1020362, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1020362, _1020364, _1020366), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020362, tc_HOL_Obool)), _1020368), _1020370)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1020364, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1020362, _1020364, _1020366), _1020368)), hAPP(c_Set_Oimage(_1020362, _1020364, _1020366), _1020370)))], (12980 ^ _782435) ^ [_1020545, _1020547, _1020549, _1020551, _1020553, _1020555] : [c_Fun_Oinj__on(_1020545, _1020547, _1020549, _1020551), -(hBOOL(hAPP(hAPP(c_member(_1020547), _1020553), hAPP(c_Set_Oimage(_1020545, _1020547, _1020549), _1020551)))), -(c_Fun_Oinj__on(_1020545, _1020547, c_Fun_Ofun__upd(_1020545, _1020547, _1020549, _1020555, _1020553), _1020551))], (12990 ^ _782435) ^ [_1020693] : [-(c_Fun_Oinj__on(_1020693, tc_fun(_1020693, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1020693, tc_fun(_1020693, tc_HOL_Obool), tc_fun(_1020693, tc_HOL_Obool)), c_Set_Oinsert(_1020693)), c_Orderings_Obot__class_Obot(tc_fun(_1020693, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1020693, tc_HOL_Obool))))], (12992 ^ _782435) ^ [_1020749, _1020751] : [class_Complete__Lattice_Ocomplete__lattice(_1020749), c_Orderings_Oorder__class_Omono(_1020749, _1020749, _1020751), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020749), c_Inductive_Ocomplete__lattice__class_Olfp(_1020749, _1020751)), hAPP(_1020751, c_Inductive_Ocomplete__lattice__class_Olfp(_1020749, _1020751)))))], (13002 ^ _782435) ^ [_1020910, _1020912] : [class_Complete__Lattice_Ocomplete__lattice(_1020910), c_Orderings_Oorder__class_Omono(_1020910, _1020910, _1020912), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1020910), hAPP(_1020912, c_Inductive_Ocomplete__lattice__class_Olfp(_1020910, _1020912))), c_Inductive_Ocomplete__lattice__class_Olfp(_1020910, _1020912))))], (13012 ^ _782435) ^ [_1021071, _1021073, _1021075, _1021077] : [c_Fun_Oinj__on(_1021071, _1021073, _1021075, c_Orderings_Otop__class_Otop(tc_fun(_1021071, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021073, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021071, _1021073, _1021075), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021071, tc_HOL_Obool)), _1021077))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1021073, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021071, _1021073, _1021075), _1021077)))))], (13018 ^ _782435) ^ [_1021270, _1021272, _1021274, _1021276, _1021278] : [c_Fun_Oinj__on(_1021270, _1021272, _1021274, hAPP(hAPP(c_Set_Oinsert(_1021270), _1021276), _1021278)), 13021 ^ _782435 : [(13022 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1021270, _1021272, _1021274, _1021278))], (13024 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1021272), hAPP(_1021274, _1021276)), hAPP(c_Set_Oimage(_1021270, _1021272, _1021274), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021270, tc_HOL_Obool)), _1021278), hAPP(hAPP(c_Set_Oinsert(_1021270), _1021276), c_Orderings_Obot__class_Obot(tc_fun(_1021270, tc_HOL_Obool)))))))]]], (13026 ^ _782435) ^ [_1021489, _1021491, _1021493, _1021495, _1021497] : [-(c_Fun_Oinj__on(_1021489, _1021491, _1021493, hAPP(hAPP(c_Set_Oinsert(_1021489), _1021495), _1021497))), c_Fun_Oinj__on(_1021489, _1021491, _1021493, _1021497), -(hBOOL(hAPP(hAPP(c_member(_1021491), hAPP(_1021493, _1021495)), hAPP(c_Set_Oimage(_1021489, _1021491, _1021493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1021489, tc_HOL_Obool)), _1021497), hAPP(hAPP(c_Set_Oinsert(_1021489), _1021495), c_Orderings_Obot__class_Obot(tc_fun(_1021489, tc_HOL_Obool))))))))], (13036 ^ _782435) ^ [_1021740, _1021742, _1021744, _1021746] : [-(_1021740 = c_Orderings_Obot__class_Obot(tc_fun(_1021742, tc_HOL_Obool))), 13039 ^ _782435 : [(13051 ^ _782435) ^ [] : [13052 ^ _782435 : [(13053 ^ _782435) ^ [_1022073] : [hAPP(c_Set_Oimage(_1021744, _1021742, _1022073), _1021746) = _1021740]], 13055 ^ _782435 : [(13056 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1021742, _1021744, 13054 ^ [_1021740, _1021742, _1021744, _1021746], _1021740))], (13058 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021744, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021742, _1021744, 13054 ^ [_1021740, _1021742, _1021744, _1021746]), _1021740)), _1021746)))]]], (13040 ^ _782435) ^ [] : [-(hAPP(c_Set_Oimage(_1021744, _1021742, 13047 ^ [_1021740, _1021742, _1021744, _1021746]), _1021746) = _1021740), 13041 ^ _782435 : [(13042 ^ _782435) ^ [_1021881] : [c_Fun_Oinj__on(_1021742, _1021744, _1021881, _1021740), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1021744, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1021742, _1021744, _1021881), _1021740)), _1021746))]]]]], (13060 ^ _782435) ^ [_1022198, _1022200] : [-(c_Enum_Oenum__the(_1022198, _1022200) = c_HOL_OThe(_1022198, _1022200))], (13062 ^ _782435) ^ [_1022241, _1022243, _1022245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022241, tc_HOL_Obool)), _1022243), hAPP(hAPP(c_Set_Oinsert(_1022241), _1022245), c_Orderings_Obot__class_Obot(tc_fun(_1022241, tc_HOL_Obool))))), -(c_Partial__Function_Oflat__lub(_1022241, _1022245, _1022243) = _1022245)], (13068 ^ _782435) ^ [_1022368, _1022370, _1022372] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1022368, tc_HOL_Obool)), _1022370), hAPP(hAPP(c_Set_Oinsert(_1022368), _1022372), c_Orderings_Obot__class_Obot(tc_fun(_1022368, tc_HOL_Obool)))))), -(c_Partial__Function_Oflat__lub(_1022368, _1022372, _1022370) = c_HOL_OThe(_1022368, hAPP(hAPP(c_COMBC(_1022368, tc_fun(_1022368, tc_HOL_Obool), tc_HOL_Obool), c_member(_1022368)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022368, tc_HOL_Obool)), _1022370), hAPP(hAPP(c_Set_Oinsert(_1022368), _1022372), c_Orderings_Obot__class_Obot(tc_fun(_1022368, tc_HOL_Obool)))))))], (13074 ^ _782435) ^ [_1022507, _1022509, _1022511, _1022513, _1022515, _1022517, _1022519] : [c_Nitpick_Ofold__graph_H(_1022507, _1022509, _1022511, _1022513, _1022515, hAPP(hAPP(_1022511, _1022517), _1022519)), 13079 ^ _782435 : [(13080 ^ _782435) ^ [] : [-(_1022515 = c_Orderings_Obot__class_Obot(tc_fun(_1022507, tc_HOL_Obool)))], (13082 ^ _782435) ^ [] : [-(hAPP(hAPP(_1022511, _1022517), _1022519) = _1022513)]], 13085 ^ _782435 : [(13086 ^ _782435) ^ [] : [-(hAPP(hAPP(_1022511, _1022517), _1022519) = hAPP(hAPP(_1022511, 13083 ^ [_1022507, _1022509, _1022511, _1022513, _1022515, _1022517, _1022519]), 13084 ^ [_1022507, _1022509, _1022511, _1022513, _1022515, _1022517, _1022519]))], (13088 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1022507), 13083 ^ [_1022507, _1022509, _1022511, _1022513, _1022515, _1022517, _1022519]), _1022515)))], (13090 ^ _782435) ^ [] : [-(c_Nitpick_Ofold__graph_H(_1022507, _1022509, _1022511, _1022513, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022507, tc_HOL_Obool)), _1022515), hAPP(hAPP(c_Set_Oinsert(_1022507), 13083 ^ [_1022507, _1022509, _1022511, _1022513, _1022515, _1022517, _1022519]), c_Orderings_Obot__class_Obot(tc_fun(_1022507, tc_HOL_Obool)))), 13084 ^ [_1022507, _1022509, _1022511, _1022513, _1022515, _1022517, _1022519]))]]], (13092 ^ _782435) ^ [_1022944, _1022946, _1022948, _1022950, _1022952, _1022954, _1022956] : [-(c_Nitpick_Ofold__graph_H(_1022944, _1022946, _1022948, _1022950, _1022952, hAPP(hAPP(_1022948, _1022954), _1022956))), 13093 ^ _782435 : [(13094 ^ _782435) ^ [] : [_1022952 = c_Orderings_Obot__class_Obot(tc_fun(_1022944, tc_HOL_Obool)), hAPP(hAPP(_1022948, _1022954), _1022956) = _1022950], (13100 ^ _782435) ^ [_1023173, _1023175] : [hAPP(hAPP(_1022948, _1022954), _1022956) = hAPP(hAPP(_1022948, _1023175), _1023173), hBOOL(hAPP(hAPP(c_member(_1022944), _1023175), _1022952)), c_Nitpick_Ofold__graph_H(_1022944, _1022946, _1022948, _1022950, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1022944, tc_HOL_Obool)), _1022952), hAPP(hAPP(c_Set_Oinsert(_1022944), _1023175), c_Orderings_Obot__class_Obot(tc_fun(_1022944, tc_HOL_Obool)))), _1023173)]]], (13112 ^ _782435) ^ [_1023465, _1023467, _1023469, _1023471, _1023473, _1023475, _1023477, _1023479] : [c_Fun_Oinj__on(_1023465, _1023467, _1023469, _1023471), 13118 ^ _782435 : [(13119 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1023473), 13117 ^ [_1023465, _1023467, _1023469, _1023471, _1023473, _1023475, _1023477, _1023479]), _1023475)))], (13121 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023465, tc_HOL_Obool)), hAPP(_1023477, 13117 ^ [_1023465, _1023467, _1023469, _1023471, _1023473, _1023475, _1023477, _1023479])), _1023471))]], hBOOL(hAPP(hAPP(c_member(_1023473), _1023479), _1023475)), -(hAPP(c_Set_Oimage(_1023465, _1023467, _1023469), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023473, tc_fun(_1023465, tc_HOL_Obool)), _1023475), _1023477)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1023473, tc_fun(_1023467, tc_HOL_Obool)), _1023475), hAPP(hAPP(c_COMBB(tc_fun(_1023465, tc_HOL_Obool), tc_fun(_1023467, tc_HOL_Obool), _1023473), c_Set_Oimage(_1023465, _1023467, _1023469)), _1023477)))], (13129 ^ _782435) ^ [_1023954, _1023956, _1023958, _1023960, _1023962, _1023964] : [c_Fun_Oinj__on(_1023954, _1023956, _1023958, _1023960), hBOOL(hAPP(hAPP(c_member(_1023956), _1023962), hAPP(c_Set_Oimage(_1023954, _1023956, _1023958), _1023960))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1023954, tc_HOL_Obool)), _1023960), _1023964)), -(hBOOL(hAPP(hAPP(c_member(_1023954), hAPP(c_Fun_Othe__inv__into(_1023954, _1023956, _1023960, _1023958), _1023962)), _1023964)))], (13143 ^ _782435) ^ [_1024241, _1024243, _1024245, _1024247] : [c_Fun_Oinj__on(_1024241, _1024243, _1024245, c_Orderings_Otop__class_Otop(tc_fun(_1024241, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1024241, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1024241, _1024243, _1024245), hAPP(hAPP(c_Set_Oinsert(_1024243), _1024247), c_Orderings_Obot__class_Obot(tc_fun(_1024243, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1024241), c_HOL_OThe(_1024241, hAPP(hAPP(c_COMBC(_1024241, _1024243, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1024243, tc_fun(_1024243, tc_HOL_Obool), _1024241), c_fequal), _1024245)), _1024247))), c_Orderings_Obot__class_Obot(tc_fun(_1024241, tc_HOL_Obool))))))], (13149 ^ _782435) ^ [_1024473, _1024475, _1024477, _1024479] : [-(_1024473 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1024475, tc_HOL_Obool), tc_HOL_Obool))), 13155 ^ _782435 : [(13156 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1024475, tc_HOL_Obool)), 13154 ^ [_1024473, _1024475, _1024477, _1024479]), _1024473)))], (13158 ^ _782435) ^ [] : [c_Fun_Oinj__on(_1024475, _1024477, _1024479, 13154 ^ [_1024473, _1024475, _1024477, _1024479])]], -(c_Fun_Oinj__on(_1024475, _1024477, _1024479, c_Complete__Lattice_OInf__class_OInf(tc_fun(_1024475, tc_HOL_Obool), _1024473)))], (13162 ^ _782435) ^ [_1024734, _1024736, _1024738, _1024740, _1024742, _1024744] : [hAPP(_1024734, _1024736) = _1024738, hBOOL(hAPP(hAPP(c_member(_1024740), _1024738), _1024742)), -(hBOOL(hAPP(hAPP(c_member(_1024744), _1024736), hAPP(c_Set_Ovimage(_1024744, _1024740, _1024734), _1024742))))], (13172 ^ _782435) ^ [_1024927, _1024929] : [-(hAPP(c_Set_Ovimage(_1024927, _1024927, c_COMBI(_1024927)), _1024929) = _1024929)], (13174 ^ _782435) ^ [_1024985, _1024987, _1024989, _1024991, _1024993] : [hBOOL(hAPP(hAPP(c_Set_Ovimage(_1024985, _1024987, _1024989), _1024991), _1024993)), -(hBOOL(hAPP(_1024991, hAPP(_1024989, _1024993))))], (13180 ^ _782435) ^ [_1025092, _1025094, _1025096, _1025098, _1025100] : [hBOOL(hAPP(_1025098, hAPP(_1025096, _1025100))), -(hBOOL(hAPP(hAPP(c_Set_Ovimage(_1025092, _1025094, _1025096), _1025098), _1025100)))], (13186 ^ _782435) ^ [_1025229, _1025231, _1025233, _1025235, _1025237] : [hBOOL(hAPP(hAPP(c_member(_1025229), _1025231), hAPP(c_Set_Ovimage(_1025229, _1025233, _1025235), _1025237))), -(hBOOL(hAPP(hAPP(c_member(_1025233), hAPP(_1025235, _1025231)), _1025237)))], (13192 ^ _782435) ^ [_1025356, _1025358, _1025360, _1025362, _1025364] : [hBOOL(hAPP(hAPP(c_member(_1025360), hAPP(_1025362, _1025358)), _1025364)), -(hBOOL(hAPP(hAPP(c_member(_1025356), _1025358), hAPP(c_Set_Ovimage(_1025356, _1025360, _1025362), _1025364))))], (13198 ^ _782435) ^ [_1025489, _1025491, _1025493, _1025495, _1025497] : [hBOOL(hAPP(hAPP(c_member(_1025489), _1025491), hAPP(c_Set_Ovimage(_1025489, _1025493, _1025495), _1025497))), -(hBOOL(hAPP(hAPP(c_member(_1025493), hAPP(_1025495, _1025491)), _1025497)))], (13204 ^ _782435) ^ [_1025620, _1025622, _1025624, _1025626, _1025628] : [hBOOL(hAPP(hAPP(c_member(_1025620), hAPP(_1025622, _1025624)), _1025626)), -(hBOOL(hAPP(hAPP(c_member(_1025628), _1025624), hAPP(c_Set_Ovimage(_1025628, _1025620, _1025622), _1025626))))], (13210 ^ _782435) ^ [_1025751, _1025753, _1025755] : [-(hAPP(c_Set_Ovimage(_1025751, _1025753, _1025755), c_Orderings_Obot__class_Obot(tc_fun(_1025753, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1025751, tc_HOL_Obool)))], (13212 ^ _782435) ^ [_1025795, _1025797, _1025799, _1025801, _1025803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025795, tc_HOL_Obool)), _1025797), _1025799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1025801, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1025801, _1025795, _1025803), _1025797)), hAPP(c_Set_Ovimage(_1025801, _1025795, _1025803), _1025799))))], (13218 ^ _782435) ^ [_1025946, _1025948, _1025950] : [-(hAPP(c_Set_Ovimage(_1025946, _1025948, _1025950), c_Orderings_Otop__class_Otop(tc_fun(_1025948, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1025946, tc_HOL_Obool)))], (13220 ^ _782435) ^ [_1025990, _1025992, _1025994, _1025996, _1025998] : [-(hAPP(c_Set_Ovimage(_1025990, _1025992, _1025994), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025992, tc_HOL_Obool)), _1025996), _1025998)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1025990, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1025990, _1025992, _1025994), _1025996)), hAPP(c_Set_Ovimage(_1025990, _1025992, _1025994), _1025998)))], (13222 ^ _782435) ^ [_1026064, _1026066, _1026068, _1026070, _1026072] : [-(hAPP(c_Set_Ovimage(_1026064, _1026066, _1026068), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026066, tc_HOL_Obool)), _1026070), _1026072)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1026064, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026064, _1026066, _1026068), _1026070)), hAPP(c_Set_Ovimage(_1026064, _1026066, _1026068), _1026072)))], (13224 ^ _782435) ^ [_1026138, _1026140, _1026142, _1026144, _1026146] : [-(hAPP(c_Set_Ovimage(_1026138, _1026140, _1026142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026140, tc_HOL_Obool)), _1026144), _1026146)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1026138, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026138, _1026140, _1026142), _1026144)), hAPP(c_Set_Ovimage(_1026138, _1026140, _1026142), _1026146)))], (13226 ^ _782435) ^ [_1026212, _1026214, _1026216, _1026218] : [-(hAPP(c_Set_Ovimage(_1026212, _1026214, _1026216), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026214, tc_HOL_Obool)), _1026218)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1026212, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1026212, _1026214, _1026216), _1026218)))], (13228 ^ _782435) ^ [_1026271, _1026273, _1026275, _1026277, _1026279, _1026281] : [-(hAPP(c_Set_Ovimage(_1026271, _1026273, _1026275), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026277, tc_fun(_1026273, tc_HOL_Obool)), _1026279), _1026281)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1026277, tc_fun(_1026271, tc_HOL_Obool)), _1026279), hAPP(hAPP(c_COMBB(tc_fun(_1026273, tc_HOL_Obool), tc_fun(_1026271, tc_HOL_Obool), _1026277), c_Set_Ovimage(_1026271, _1026273, _1026275)), _1026281)))], (13230 ^ _782435) ^ [_1026355, _1026357, _1026359, _1026361, _1026363, _1026365] : [-(hAPP(c_Set_Ovimage(_1026355, _1026357, _1026359), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026361, tc_fun(_1026357, tc_HOL_Obool)), _1026363), _1026365)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1026361, tc_fun(_1026355, tc_HOL_Obool)), _1026363), hAPP(hAPP(c_COMBB(tc_fun(_1026357, tc_HOL_Obool), tc_fun(_1026355, tc_HOL_Obool), _1026361), c_Set_Ovimage(_1026355, _1026357, _1026359)), _1026365)))], (13232 ^ _782435) ^ [_1026439, _1026441, _1026443, _1026445] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1026439, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1026441, _1026439, _1026443), hAPP(c_Set_Ovimage(_1026441, _1026439, _1026443), _1026445))), _1026445)))], (13234 ^ _782435) ^ [_1026492, _1026494, _1026496, _1026498] : [hAPP(c_Set_Oimage(_1026492, _1026494, _1026496), c_Orderings_Otop__class_Otop(tc_fun(_1026492, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1026494, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1026492, _1026494, _1026496), hAPP(c_Set_Ovimage(_1026492, _1026494, _1026496), _1026498)) = _1026498)], (13240 ^ _782435) ^ [_1026635, _1026637, _1026639, _1026641] : [-(hAPP(c_Set_Ovimage(_1026635, _1026637, _1026639), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1026637, tc_HOL_Obool), _1026641)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1026637, tc_HOL_Obool), tc_fun(_1026635, tc_HOL_Obool)), _1026641), c_Set_Ovimage(_1026635, _1026637, _1026639)))], (13242 ^ _782435) ^ [_1026720, _1026722, _1026724, _1026726, _1026728] : [hBOOL(hAPP(hAPP(c_member(_1026720), _1026722), hAPP(c_Set_Ovimage(_1026720, _1026724, _1026726), hAPP(hAPP(c_Set_Oinsert(_1026724), _1026728), c_Orderings_Obot__class_Obot(tc_fun(_1026724, tc_HOL_Obool)))))), -(hAPP(_1026726, _1026722) = _1026728)], (13248 ^ _782435) ^ [_1026859, _1026861, _1026863, _1026865, _1026867] : [hAPP(_1026865, _1026861) = _1026867, -(hBOOL(hAPP(hAPP(c_member(_1026859), _1026861), hAPP(c_Set_Ovimage(_1026859, _1026863, _1026865), hAPP(hAPP(c_Set_Oinsert(_1026863), _1026867), c_Orderings_Obot__class_Obot(tc_fun(_1026863, tc_HOL_Obool)))))))], (13254 ^ _782435) ^ [_1027004, _1027006, _1027008, _1027010, _1027012] : [-(hAPP(c_Set_Ovimage(_1027004, _1027006, _1027008), hAPP(hAPP(c_Set_Oinsert(_1027006), _1027010), _1027012)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1027004, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1027004, _1027006, _1027008), hAPP(hAPP(c_Set_Oinsert(_1027006), _1027010), c_Orderings_Obot__class_Obot(tc_fun(_1027006, tc_HOL_Obool))))), hAPP(c_Set_Ovimage(_1027004, _1027006, _1027008), _1027012)))], (13256 ^ _782435) ^ [_1027088, _1027090, _1027092, _1027094, _1027096] : [hAPP(c_Set_Oimage(_1027088, _1027090, _1027092), c_Orderings_Otop__class_Otop(tc_fun(_1027088, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1027090, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027088, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1027088, _1027090, _1027092), _1027094)), _1027096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1027090, tc_HOL_Obool)), _1027094), hAPP(c_Set_Oimage(_1027088, _1027090, _1027092), _1027096))))], (13266 ^ _782435) ^ [_1027331, _1027333, _1027335, _1027337] : [-(hAPP(c_Set_Oimage(_1027331, _1027333, _1027335), hAPP(c_Set_Ovimage(_1027331, _1027333, _1027335), _1027337)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1027333, tc_HOL_Obool)), _1027337), hAPP(c_Set_Oimage(_1027331, _1027333, _1027335), c_Orderings_Otop__class_Otop(tc_fun(_1027331, tc_HOL_Obool)))))], (13268 ^ _782435) ^ [_1027397, _1027399, _1027401, _1027403] : [c_Fun_Oinj__on(_1027397, _1027399, _1027401, c_Orderings_Otop__class_Otop(tc_fun(_1027397, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1027397, _1027399, _1027401), hAPP(c_Set_Oimage(_1027397, _1027399, _1027401), _1027403)) = _1027403)], (13274 ^ _782435) ^ [_1027535, _1027537, _1027539, _1027541] : [hBOOL(hAPP(hAPP(c_member(_1027535), _1027537), _1027539)), -(hAPP(c_Set_Ovimage(_1027541, _1027535, hAPP(c_COMBK(_1027535, _1027541), _1027537)), _1027539) = c_Orderings_Otop__class_Otop(tc_fun(_1027541, tc_HOL_Obool)))], (13280 ^ _782435) ^ [_1027660, _1027662, _1027664, _1027666] : [-(hBOOL(hAPP(hAPP(c_member(_1027660), _1027662), _1027664))), -(hAPP(c_Set_Ovimage(_1027666, _1027660, hAPP(c_COMBK(_1027660, _1027666), _1027662)), _1027664) = c_Orderings_Obot__class_Obot(tc_fun(_1027666, tc_HOL_Obool)))], (13286 ^ _782435) ^ [_1027727, _1027729, _1027731, _1027733] : [-(hAPP(c_Set_Ovimage(_1027727, _1027729, _1027731), _1027733) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1027729, tc_fun(_1027727, tc_HOL_Obool)), _1027733), hAPP(hAPP(c_COMBB(tc_fun(_1027729, tc_HOL_Obool), tc_fun(_1027727, tc_HOL_Obool), _1027729), c_Set_Ovimage(_1027727, _1027729, _1027731)), hAPP(hAPP(c_COMBC(_1027729, tc_fun(_1027729, tc_HOL_Obool), tc_fun(_1027729, tc_HOL_Obool)), c_Set_Oinsert(_1027729)), c_Orderings_Obot__class_Obot(tc_fun(_1027729, tc_HOL_Obool))))))], (13288 ^ _782435) ^ [_1027818, _1027820, _1027822, _1027824, _1027826] : [c_Fun_Oinj__on(_1027818, _1027820, _1027822, _1027824), hBOOL(hAPP(hAPP(c_member(_1027818), _1027826), _1027824)), -(hAPP(c_Fun_Othe__inv__into(_1027818, _1027820, _1027824, _1027822), hAPP(_1027822, _1027826)) = _1027826)], (13298 ^ _782435) ^ [_1027999, _1028001, _1028003, _1028005, _1028007, _1028009] : [c_Fun_Oinj__on(_1027999, _1028001, _1028003, _1028005), hAPP(_1028003, _1028007) = _1028009, hBOOL(hAPP(hAPP(c_member(_1027999), _1028007), _1028005)), -(hAPP(c_Fun_Othe__inv__into(_1027999, _1028001, _1028005, _1028003), _1028009) = _1028007)], (13312 ^ _782435) ^ [_1028244, _1028246, _1028248, _1028250] : [c_Fun_Oinj__on(_1028244, _1028246, _1028248, c_Orderings_Otop__class_Otop(tc_fun(_1028244, tc_HOL_Obool))), -(hAPP(c_Fun_Othe__inv__into(_1028244, _1028246, c_Orderings_Otop__class_Otop(tc_fun(_1028244, tc_HOL_Obool)), _1028248), hAPP(_1028248, _1028250)) = _1028250)], (13318 ^ _782435) ^ [_1028371, _1028373, _1028375, _1028377] : [c_Fun_Oinj__on(_1028371, _1028373, _1028375, _1028377), -(hAPP(c_Set_Oimage(_1028373, _1028371, c_Fun_Othe__inv__into(_1028371, _1028373, _1028377, _1028375)), hAPP(c_Set_Oimage(_1028371, _1028373, _1028375), _1028377)) = _1028377)], (13324 ^ _782435) ^ [_1028494, _1028496, _1028498, _1028500] : [c_Fun_Oinj__on(_1028494, _1028496, _1028498, _1028500), -(c_Fun_Oinj__on(_1028496, _1028494, c_Fun_Othe__inv__into(_1028494, _1028496, _1028500, _1028498), hAPP(c_Set_Oimage(_1028494, _1028496, _1028498), _1028500)))], (13330 ^ _782435) ^ [_1028607, _1028609, _1028611, _1028613, _1028615] : [c_Fun_Oinj__on(_1028607, _1028609, _1028611, c_Orderings_Otop__class_Otop(tc_fun(_1028607, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028609, tc_HOL_Obool)), _1028613), hAPP(c_Set_Oimage(_1028607, _1028609, _1028611), _1028615))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1028607, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1028607, _1028609, _1028611), _1028613)), _1028615)))], (13340 ^ _782435) ^ [_1028830, _1028832, _1028834, _1028836, _1028838] : [-(hAPP(c_Fun_Othe__inv__into(_1028830, _1028832, _1028834, _1028836), _1028838) = c_HOL_OThe(_1028830, hAPP(hAPP(c_COMBS(_1028830, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1028830), c_fconj), hAPP(hAPP(c_COMBC(_1028830, tc_fun(_1028830, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028830)), _1028834))), hAPP(hAPP(c_COMBC(_1028830, _1028832, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1028832, tc_fun(_1028832, tc_HOL_Obool), _1028830), c_fequal), _1028836)), _1028838))))], (13342 ^ _782435) ^ [_1028951, _1028953, _1028955, _1028957, _1028959, _1028961] : [hBOOL(hAPP(hAPP(c_member(_1028951), _1028953), _1028955)), 13345 ^ _782435 : [(13346 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1028951), _1028957), _1028955)), -(hAPP(c_Set_Ovimage(_1028959, _1028951, hAPP(hAPP(c_COMBC(_1028959, _1028951, _1028951), hAPP(hAPP(c_COMBC(_1028959, _1028951, tc_fun(_1028951, _1028951)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1028951, tc_fun(_1028951, _1028951)), _1028959), c_If(_1028951)), hAPP(hAPP(c_COMBC(_1028959, tc_fun(_1028959, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028959)), _1028961))), _1028953)), _1028957)), _1028955) = c_Orderings_Otop__class_Otop(tc_fun(_1028959, tc_HOL_Obool)))], (13352 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1028951), _1028957), _1028955))), -(hAPP(c_Set_Ovimage(_1028959, _1028951, hAPP(hAPP(c_COMBC(_1028959, _1028951, _1028951), hAPP(hAPP(c_COMBC(_1028959, _1028951, tc_fun(_1028951, _1028951)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1028951, tc_fun(_1028951, _1028951)), _1028959), c_If(_1028951)), hAPP(hAPP(c_COMBC(_1028959, tc_fun(_1028959, tc_HOL_Obool), tc_HOL_Obool), c_member(_1028959)), _1028961))), _1028953)), _1028957)), _1028955) = _1028961)]]], (13358 ^ _782435) ^ [_1029442, _1029444, _1029446, _1029448, _1029450, _1029452] : [-(hBOOL(hAPP(hAPP(c_member(_1029442), _1029444), _1029446))), 13361 ^ _782435 : [(13362 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1029442), _1029448), _1029446)), -(hAPP(c_Set_Ovimage(_1029450, _1029442, hAPP(hAPP(c_COMBC(_1029450, _1029442, _1029442), hAPP(hAPP(c_COMBC(_1029450, _1029442, tc_fun(_1029442, _1029442)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1029442, tc_fun(_1029442, _1029442)), _1029450), c_If(_1029442)), hAPP(hAPP(c_COMBC(_1029450, tc_fun(_1029450, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029450)), _1029452))), _1029444)), _1029448)), _1029446) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1029450, tc_HOL_Obool)), _1029452))], (13368 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1029442), _1029448), _1029446))), -(hAPP(c_Set_Ovimage(_1029450, _1029442, hAPP(hAPP(c_COMBC(_1029450, _1029442, _1029442), hAPP(hAPP(c_COMBC(_1029450, _1029442, tc_fun(_1029442, _1029442)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1029442, tc_fun(_1029442, _1029442)), _1029450), c_If(_1029442)), hAPP(hAPP(c_COMBC(_1029450, tc_fun(_1029450, tc_HOL_Obool), tc_HOL_Obool), c_member(_1029450)), _1029452))), _1029444)), _1029448)), _1029446) = c_Orderings_Obot__class_Obot(tc_fun(_1029450, tc_HOL_Obool)))]]], (13374 ^ _782435) ^ [_1029947, _1029949, _1029951, _1029953, _1029955] : [c_Fun_Oinj__on(_1029947, _1029949, _1029951, _1029953), hBOOL(hAPP(hAPP(c_member(_1029949), _1029955), hAPP(c_Set_Oimage(_1029947, _1029949, _1029951), _1029953))), -(hAPP(_1029951, hAPP(c_Fun_Othe__inv__into(_1029947, _1029949, _1029953, _1029951), _1029955)) = _1029955)], (13384 ^ _782435) ^ [_1030142, _1030144, _1030146, _1030148] : [class_Orderings_Oorder(_1030142), class_Enum_Oenum(_1030144), 13391 ^ _782435 : [(13392 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1030144, _1030142)), _1030146), _1030148)), 13395 ^ _782435 : [(13396 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1030144, _1030142)), _1030146), _1030148)))], (13398 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1030144), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1030144), c_fNot), hAPP(hAPP(c_COMBS(_1030144, _1030142, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1030142, tc_fun(_1030142, tc_HOL_Obool), _1030144), c_fequal), _1030146)), _1030148)))))]]], (13400 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1030144, _1030142)), _1030146), _1030148))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1030144, _1030142)), _1030146), _1030148)), hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1030144), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1030144), c_fNot), hAPP(hAPP(c_COMBS(_1030144, _1030142, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1030142, tc_fun(_1030142, tc_HOL_Obool), _1030144), c_fequal), _1030146)), _1030148))))]]], (13410 ^ _782435) ^ [_1030661, _1030663, _1030665, _1030667, _1030669, _1030671] : [-(_1030661 = c_Orderings_Obot__class_Obot(tc_fun(_1030663, tc_HOL_Obool))), 13416 ^ _782435 : [(13417 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1030663), 13415 ^ [_1030661, _1030663, _1030665, _1030667, _1030669, _1030671]), _1030661)))], (13419 ^ _782435) ^ [] : [c_Fun_Oinj__on(_1030665, _1030667, _1030669, hAPP(_1030671, 13415 ^ [_1030661, _1030663, _1030665, _1030667, _1030669, _1030671]))]], -(c_Fun_Oinj__on(_1030665, _1030667, _1030669, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1030663, tc_fun(_1030665, tc_HOL_Obool)), _1030661), _1030671)))], (13423 ^ _782435) ^ [_1030953] : [-(c_Finite__Set_Ofun__left__comm__idem(_1030953, tc_fun(_1030953, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1030953, tc_HOL_Obool), tc_fun(tc_fun(_1030953, tc_HOL_Obool), tc_fun(_1030953, tc_HOL_Obool)), _1030953), hAPP(c_COMBC(tc_fun(_1030953, tc_HOL_Obool), tc_fun(_1030953, tc_HOL_Obool), tc_fun(_1030953, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1030953, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1030953, tc_fun(_1030953, tc_HOL_Obool), tc_fun(_1030953, tc_HOL_Obool)), c_Set_Oinsert(_1030953)), c_Orderings_Obot__class_Obot(tc_fun(_1030953, tc_HOL_Obool))))))], (13425 ^ _782435) ^ [_1031046, _1031048] : [-(c_HOL_OThe(_1031046, hAPP(hAPP(c_COMBC(_1031046, _1031046, tc_HOL_Obool), c_fequal), _1031048)) = _1031048)], (13427 ^ _782435) ^ [_1031084, _1031086] : [-(c_HOL_OThe(_1031084, hAPP(c_fequal, _1031086)) = _1031086)], (13429 ^ _782435) ^ [_1031115, _1031117, _1031119, _1031121, _1031123, _1031125, _1031127] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1031115, _1031117, _1031119, _1031121, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1031115, tc_HOL_Obool)), _1031123), hAPP(hAPP(c_Set_Oinsert(_1031115), _1031125), c_Orderings_Obot__class_Obot(tc_fun(_1031115, tc_HOL_Obool))))), _1031127)), hBOOL(hAPP(hAPP(c_member(_1031115), _1031125), _1031123)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1031115, _1031117, _1031119, _1031121, _1031123), hAPP(hAPP(_1031119, _1031125), _1031127))))], (13439 ^ _782435) ^ [_1031370, _1031372, _1031374, _1031376] : [hBOOL(hAPP(hAPP(c_member(_1031370), _1031372), hAPP(c_Set_Oimage(_1031374, _1031370, _1031376), c_Orderings_Otop__class_Otop(tc_fun(_1031374, tc_HOL_Obool))))), -(_1031372 = hAPP(_1031376, 13442 ^ [_1031370, _1031372, _1031374, _1031376]))], (13446 ^ _782435) ^ [_1031536, _1031538, _1031540, _1031542] : [c_Partial__Function_Omk__less(_1031536, _1031538, _1031540, _1031542), 13449 ^ _782435 : [(13450 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1031538, _1031540), _1031542)))], (13452 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1031538, _1031542), _1031540))]]], (13454 ^ _782435) ^ [_1031671, _1031673, _1031675, _1031677] : [-(c_Partial__Function_Omk__less(_1031671, _1031673, _1031675, _1031677)), hBOOL(hAPP(hAPP(_1031673, _1031675), _1031677)), -(hBOOL(hAPP(hAPP(_1031673, _1031677), _1031675)))], (13464 ^ _782435) ^ [_1031837, _1031839] : [class_Enum_Oenum(_1031837), 13467 ^ _782435 : [(13468 ^ _782435) ^ [] : [13469 ^ _782435 : [(13470 ^ _782435) ^ [_1031939] : [hBOOL(hAPP(_1031839, _1031939))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1031837), _1031839)))], (13474 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1031837), _1031839)), -(hBOOL(hAPP(_1031839, 13477 ^ [_1031837, _1031839])))]]], (13481 ^ _782435) ^ [_1032080, _1032082] : [class_Enum_Oenum(_1032080), 13484 ^ _782435 : [(13485 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1032080), _1032082)), -(hBOOL(hAPP(_1032082, 13488 ^ [_1032080, _1032082])))], (13492 ^ _782435) ^ [] : [13493 ^ _782435 : [(13494 ^ _782435) ^ [_1032260] : [hBOOL(hAPP(_1032082, _1032260))]], -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1032080), _1032082)))]]], (13498 ^ _782435) ^ [_1032323, _1032325, _1032327, _1032329, _1032331] : [c_Finite__Set_Ofun__left__comm__idem(_1032323, _1032325, _1032327), -(hAPP(hAPP(_1032327, _1032329), hAPP(hAPP(_1032327, _1032329), _1032331)) = hAPP(hAPP(_1032327, _1032329), _1032331))], (13504 ^ _782435) ^ [_1032444, _1032446, _1032448, _1032450, _1032452] : [c_Finite__Set_Ofun__left__comm__idem(_1032444, _1032446, _1032448), -(c_Finite__Set_Ofun__left__comm__idem(_1032450, _1032446, hAPP(hAPP(c_COMBB(_1032444, tc_fun(_1032446, _1032446), _1032450), _1032448), _1032452)))], (13510 ^ _782435) ^ [_1032557, _1032559, _1032561, _1032563] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032557, _1032559, _1032561, _1032563, c_Orderings_Obot__class_Obot(tc_fun(_1032557, tc_HOL_Obool))), _1032563)))], (13512 ^ _782435) ^ [_1032599, _1032601, _1032603, _1032605] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032599, _1032601, _1032603, _1032605, c_Orderings_Obot__class_Obot(tc_fun(_1032599, tc_HOL_Obool))), _1032605)))], (13514 ^ _782435) ^ [_1032641, _1032643, _1032645, _1032647, _1032649] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032641, _1032643, _1032645, _1032647, c_Orderings_Obot__class_Obot(tc_fun(_1032641, tc_HOL_Obool))), _1032649)), -(_1032649 = _1032647)], (13520 ^ _782435) ^ [_1032750] : [-(c_Finite__Set_Ofun__left__comm__idem(_1032750, tc_fun(_1032750, tc_HOL_Obool), c_Set_Oinsert(_1032750)))], (13522 ^ _782435) ^ [_1032779] : [class_Lattices_Osemilattice__sup(_1032779), -(c_Finite__Set_Ofun__left__comm__idem(_1032779, _1032779, c_Lattices_Osemilattice__sup__class_Osup(_1032779)))], (13528 ^ _782435) ^ [_1032858] : [class_Lattices_Osemilattice__inf(_1032858), -(c_Finite__Set_Ofun__left__comm__idem(_1032858, _1032858, c_Lattices_Osemilattice__inf__class_Oinf(_1032858)))], (13534 ^ _782435) ^ [_1032936, _1032938, _1032940, _1032942, _1032944, _1032946, _1032948] : [-(hBOOL(hAPP(hAPP(c_member(_1032936), _1032938), _1032940))), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032936, _1032942, _1032944, _1032946, _1032940), _1032948)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1032936, _1032942, _1032944, _1032946, hAPP(hAPP(c_Set_Oinsert(_1032936), _1032938), _1032940)), hAPP(hAPP(_1032944, _1032938), _1032948))))], (13544 ^ _782435) ^ [_1033150, _1033152, _1033154, _1033156, _1033158] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033150, _1033150, _1033152, _1033154, _1033156), _1033158)), -(hBOOL(hAPP(hAPP(c_member(_1033150), _1033154), _1033156))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1033150, _1033152, hAPP(hAPP(c_Set_Oinsert(_1033150), _1033154), _1033156)), _1033158)))], (13554 ^ _782435) ^ [_1033306, _1033308, _1033310, _1033312, _1033314] : [class_Groups_Oab__semigroup__mult(_1033306), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033306, _1033306, c_Groups_Otimes__class_Otimes(_1033306), _1033308, _1033310), _1033312)), hBOOL(hAPP(hAPP(c_member(_1033306), _1033314), _1033310)), -(hBOOL(hAPP(hAPP(c_member(_1033306), _1033308), _1033310))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1033306, _1033306, c_Groups_Otimes__class_Otimes(_1033306), _1033314, hAPP(hAPP(c_Set_Oinsert(_1033306), _1033308), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1033306, tc_HOL_Obool)), _1033310), hAPP(hAPP(c_Set_Oinsert(_1033306), _1033314), c_Orderings_Obot__class_Obot(tc_fun(_1033306, tc_HOL_Obool)))))), _1033312)))], (13572 ^ _782435) ^ [_1033650, _1033652, _1033654, _1033656, _1033658] : [c_Fun_Obij__betw(_1033650, _1033652, _1033654, c_Orderings_Otop__class_Otop(tc_fun(_1033650, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1033652, tc_HOL_Obool))), 13575 ^ _782435 : [(13576 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033650, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1033650, _1033652, _1033654), _1033656)), _1033658)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033652, tc_HOL_Obool)), _1033656), hAPP(c_Set_Oimage(_1033650, _1033652, _1033654), _1033658))))], (13582 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033652, tc_HOL_Obool)), _1033656), hAPP(c_Set_Oimage(_1033650, _1033652, _1033654), _1033658))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1033650, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1033650, _1033652, _1033654), _1033656)), _1033658)))]]], (13588 ^ _782435) ^ [_1034003, _1034005, _1034007] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1034003, tc_HOL_Obool)), _1034005), _1034007)), -(hBOOL(hAPP(hAPP(c_member(_1034003), 13591 ^ [_1034003, _1034005, _1034007]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1034003, tc_HOL_Obool)), _1034007), _1034005))))], (13595 ^ _782435) ^ [_1034152, _1034154, _1034156, _1034158, _1034160, _1034162, _1034164] : [c_Fun_Oinj__on(_1034152, _1034154, _1034156, hAPP(c_Set_Oimage(_1034158, _1034152, _1034160), _1034162)), c_Fun_Oinj__on(_1034158, _1034152, _1034160, _1034162), hBOOL(hAPP(hAPP(c_member(_1034154), _1034164), hAPP(c_Set_Oimage(_1034152, _1034154, _1034156), hAPP(c_Set_Oimage(_1034158, _1034152, _1034160), _1034162)))), -(hAPP(c_Fun_Othe__inv__into(_1034158, _1034154, _1034162, hAPP(c_Fun_Ocomp(_1034152, _1034154, _1034158, _1034156), _1034160)), _1034164) = hAPP(hAPP(c_Fun_Ocomp(_1034152, _1034158, _1034154, c_Fun_Othe__inv__into(_1034158, _1034152, _1034162, _1034160)), c_Fun_Othe__inv__into(_1034152, _1034154, hAPP(c_Set_Oimage(_1034158, _1034152, _1034160), _1034162), _1034156)), _1034164))], (13609 ^ _782435) ^ [_1034536, _1034538, _1034540, _1034542, _1034544, _1034546] : [hBOOL(hAPP(hAPP(c_member(_1034536), _1034538), _1034540)), -(hAPP(c_Fun_Ooverride__on(_1034536, _1034542, _1034544, _1034546, _1034540), _1034538) = hAPP(_1034546, _1034538))], (13615 ^ _782435) ^ [_1034653, _1034655, _1034657, _1034659, _1034661, _1034663] : [-(hBOOL(hAPP(hAPP(c_member(_1034653), _1034655), _1034657))), -(hAPP(c_Fun_Ooverride__on(_1034653, _1034659, _1034661, _1034663, _1034657), _1034655) = hAPP(_1034661, _1034655))], (13621 ^ _782435) ^ [_1034718, _1034720, _1034722, _1034724, _1034726, _1034728] : [13623 ^ _782435 : [(13624 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1034718), 13622 ^ [_1034718, _1034720, _1034722, _1034724, _1034726, _1034728]), _1034720)))], (13626 ^ _782435) ^ [] : [hAPP(_1034722, 13622 ^ [_1034718, _1034720, _1034722, _1034724, _1034726, _1034728]) = hAPP(_1034724, 13622 ^ [_1034718, _1034720, _1034722, _1034724, _1034726, _1034728])]], -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034718, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1034718, _1034726, _1034722), _1034728)), _1034720) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1034718, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1034718, _1034726, _1034724), _1034728)), _1034720))], (13630 ^ _782435) ^ [_1035009, _1035011, _1035013, _1035015] : [c_Finite__Set_Ofolding__one(_1035009, _1035011, _1035013), -(hAPP(_1035013, hAPP(hAPP(c_Set_Oinsert(_1035009), _1035015), c_Orderings_Obot__class_Obot(tc_fun(_1035009, tc_HOL_Obool)))) = _1035015)], (13636 ^ _782435) ^ [_1035124, _1035126, _1035128, _1035130, _1035132, _1035134] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035124, _1035126, _1035128, hAPP(c_COMBK(_1035126, _1035124), _1035130)), _1035132), _1035134) = _1035130)], (13638 ^ _782435) ^ [_1035174, _1035176, _1035178, _1035180, _1035182, _1035184, _1035186] : [hAPP(c_Fun_Ocomp(_1035174, _1035176, _1035178, _1035180), _1035182) = _1035184, -(hAPP(_1035180, hAPP(_1035182, _1035186)) = hAPP(_1035184, _1035186))], (13644 ^ _782435) ^ [_1035295, _1035297] : [class_Lattices_Oab__semigroup__idem__mult(_1035295), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035295), _1035297), _1035297) = _1035297)], (13650 ^ _782435) ^ [_1035386, _1035388] : [class_Lattices_Oab__semigroup__idem__mult(_1035386), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035386), _1035388), _1035388) = _1035388)], (13656 ^ _782435) ^ [_1035477, _1035479, _1035481] : [class_Lattices_Oab__semigroup__idem__mult(_1035477), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035477), _1035479), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035477), _1035479), _1035481)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035477), _1035479), _1035481))], (13662 ^ _782435) ^ [_1035602, _1035604, _1035606, _1035608] : [class_Groups_Oab__semigroup__mult(_1035602), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035602), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035602), _1035604), _1035606)), _1035608) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035602), _1035604), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1035602), _1035606), _1035608)))], (13668 ^ _782435) ^ [_1035745, _1035747, _1035749, _1035751, _1035753, _1035755] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035745, _1035747, _1035749, _1035751), _1035753), _1035755) = hAPP(_1035751, hAPP(_1035753, _1035755)))], (13670 ^ _782435) ^ [_1035795, _1035797, _1035799, _1035801, _1035803, _1035805, _1035807] : [-(hAPP(c_Fun_Ocomp(_1035795, _1035797, _1035799, _1035801), hAPP(c_Fun_Ocomp(_1035803, _1035795, _1035799, _1035805), _1035807)) = hAPP(c_Fun_Ocomp(_1035803, _1035797, _1035799, hAPP(c_Fun_Ocomp(_1035795, _1035797, _1035803, _1035801), _1035805)), _1035807))], (13672 ^ _782435) ^ [_1035862, _1035864, _1035866, _1035868, _1035870, _1035872] : [-(hAPP(hAPP(c_Fun_Ocomp(_1035862, _1035864, _1035866, _1035868), _1035870), _1035872) = hAPP(_1035868, hAPP(_1035870, _1035872)))], (13674 ^ _782435) ^ [_1035912, _1035914, _1035916, _1035918, _1035920, _1035922, _1035924, _1035926, _1035928] : [hAPP(c_Fun_Ocomp(_1035912, _1035914, _1035916, _1035918), _1035920) = hAPP(c_Fun_Ocomp(_1035922, _1035914, _1035916, _1035924), _1035926), -(hAPP(_1035918, hAPP(_1035920, _1035928)) = hAPP(_1035924, hAPP(_1035926, _1035928)))], (13680 ^ _782435) ^ [_1036059, _1036061, _1036063, _1036065, _1036067, _1036069, _1036071, _1036073] : [hAPP(c_Fun_Ocomp(_1036059, _1036061, _1036063, _1036065), _1036067) = hAPP(c_Fun_Ocomp(_1036069, _1036061, _1036063, _1036071), _1036073), 13683 ^ _782435 : [(13684 ^ _782435) ^ [_1036174] : [-(hAPP(_1036065, hAPP(_1036067, _1036174)) = hAPP(_1036071, hAPP(_1036073, _1036174)))]]], (13686 ^ _782435) ^ [_1036213, _1036215, _1036217, _1036219, _1036221, _1036223, _1036225, _1036227] : [c_Fun_Obij__betw(_1036213, _1036215, _1036217, _1036219, _1036221), 13689 ^ _782435 : [(13690 ^ _782435) ^ [] : [c_Fun_Obij__betw(_1036215, _1036223, _1036225, _1036221, _1036227), -(c_Fun_Obij__betw(_1036213, _1036223, hAPP(c_Fun_Ocomp(_1036215, _1036223, _1036213, _1036225), _1036217), _1036219, _1036227))], (13696 ^ _782435) ^ [] : [c_Fun_Obij__betw(_1036213, _1036223, hAPP(c_Fun_Ocomp(_1036215, _1036223, _1036213, _1036225), _1036217), _1036219, _1036227), -(c_Fun_Obij__betw(_1036215, _1036223, _1036225, _1036221, _1036227))]]], (13702 ^ _782435) ^ [_1036504, _1036506, _1036508, _1036510, _1036512, _1036514, _1036516, _1036518] : [c_Fun_Obij__betw(_1036504, _1036506, _1036508, _1036510, _1036512), c_Fun_Obij__betw(_1036506, _1036514, _1036516, _1036512, _1036518), -(c_Fun_Obij__betw(_1036504, _1036514, hAPP(c_Fun_Ocomp(_1036506, _1036514, _1036504, _1036516), _1036508), _1036510, _1036518))], (13712 ^ _782435) ^ [_1036691, _1036693, _1036695, _1036697, _1036699] : [c_Fun_Obij__betw(_1036691, _1036693, _1036695, c_Orderings_Otop__class_Otop(tc_fun(_1036691, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036693, tc_HOL_Obool))), c_Fun_Obij__betw(_1036693, _1036697, _1036699, c_Orderings_Otop__class_Otop(tc_fun(_1036693, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036697, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1036691, _1036697, hAPP(c_Fun_Ocomp(_1036693, _1036697, _1036691, _1036699), _1036695), c_Orderings_Otop__class_Otop(tc_fun(_1036691, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1036697, tc_HOL_Obool))))], (13722 ^ _782435) ^ [_1036926, _1036928, _1036930, _1036932, _1036934, _1036936, _1036938, _1036940] : [c_Fun_Obij__betw(_1036926, _1036928, _1036930, _1036932, _1036934), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1036926, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1036936, _1036926, _1036938), _1036940)), _1036932)), 13729 ^ _782435 : [(13730 ^ _782435) ^ [] : [c_Fun_Obij__betw(_1036936, _1036926, _1036938, _1036940, _1036932), -(c_Fun_Obij__betw(_1036936, _1036928, hAPP(c_Fun_Ocomp(_1036926, _1036928, _1036936, _1036930), _1036938), _1036940, _1036934))], (13736 ^ _782435) ^ [] : [c_Fun_Obij__betw(_1036936, _1036928, hAPP(c_Fun_Ocomp(_1036926, _1036928, _1036936, _1036930), _1036938), _1036940, _1036934), -(c_Fun_Obij__betw(_1036936, _1036926, _1036938, _1036940, _1036932))]]], (13742 ^ _782435) ^ [_1037315, _1037317, _1037319, _1037321, _1037323, _1037325] : [-(hAPP(c_Set_Oimage(_1037315, _1037317, hAPP(c_Fun_Ocomp(_1037319, _1037317, _1037315, _1037321), _1037323)), _1037325) = hAPP(c_Set_Oimage(_1037319, _1037317, _1037321), hAPP(c_Set_Oimage(_1037315, _1037319, _1037323), _1037325)))], (13744 ^ _782435) ^ [_1037377, _1037379, _1037381, _1037383, _1037385, _1037387] : [c_Fun_Oinj__on(_1037377, _1037379, hAPP(c_Fun_Ocomp(_1037381, _1037379, _1037377, _1037383), _1037385), _1037387), -(c_Fun_Oinj__on(_1037377, _1037381, _1037385, _1037387))], (13750 ^ _782435) ^ [_1037486, _1037488, _1037490, _1037492] : [c_Fun_Obij__betw(_1037486, _1037488, _1037490, _1037492, c_Orderings_Obot__class_Obot(tc_fun(_1037488, tc_HOL_Obool))), -(_1037492 = c_Orderings_Obot__class_Obot(tc_fun(_1037486, tc_HOL_Obool)))], (13756 ^ _782435) ^ [_1037593, _1037595, _1037597, _1037599] : [c_Fun_Obij__betw(_1037593, _1037595, _1037597, c_Orderings_Obot__class_Obot(tc_fun(_1037593, tc_HOL_Obool)), _1037599), -(_1037599 = c_Orderings_Obot__class_Obot(tc_fun(_1037595, tc_HOL_Obool)))], (13762 ^ _782435) ^ [_1037700, _1037702, _1037704, _1037706, _1037708, _1037710, _1037712] : [-(hAPP(c_Fun_Ocomp(_1037700, _1037702, _1037704, _1037706), c_Fun_Ofun__upd(_1037704, _1037700, _1037708, _1037710, _1037712)) = c_Fun_Ofun__upd(_1037704, _1037702, hAPP(c_Fun_Ocomp(_1037700, _1037702, _1037704, _1037706), _1037708), _1037710, hAPP(_1037706, _1037712)))], (13764 ^ _782435) ^ [_1037766, _1037768, _1037770, _1037772, _1037774, _1037776] : [-(hAPP(c_Set_Ovimage(_1037766, _1037768, hAPP(c_Fun_Ocomp(_1037770, _1037768, _1037766, _1037772), _1037774)), _1037776) = hAPP(c_Set_Ovimage(_1037766, _1037770, _1037774), hAPP(c_Set_Ovimage(_1037770, _1037768, _1037772), _1037776)))], (13766 ^ _782435) ^ [_1037828, _1037830, _1037832, _1037834, _1037836] : [c_Fun_Obij__betw(_1037828, _1037830, _1037832, _1037834, _1037836), -(c_Fun_Oinj__on(_1037828, _1037830, _1037832, _1037834))], (13772 ^ _782435) ^ [_1037921, _1037923, _1037925, _1037927] : [c_Finite__Set_Ofun__left__comm__idem(_1037921, _1037923, _1037925), -(hAPP(c_Fun_Ocomp(_1037923, _1037923, _1037923, hAPP(_1037925, _1037927)), hAPP(_1037925, _1037927)) = hAPP(_1037925, _1037927))], (13778 ^ _782435) ^ [_1038038, _1038040, _1038042, _1038044, _1038046] : [c_Fun_Obij__betw(_1038038, _1038040, _1038042, _1038044, _1038046), -(c_Fun_Obij__betw(_1038040, _1038038, c_Fun_Othe__inv__into(_1038038, _1038040, _1038044, _1038042), _1038046, _1038044))], (13784 ^ _782435) ^ [_1038143] : [class_Lattices_Oab__semigroup__idem__mult(_1038143), -(c_Finite__Set_Ofun__left__comm__idem(_1038143, _1038143, c_Groups_Otimes__class_Otimes(_1038143)))], (13790 ^ _782435) ^ [_1038222, _1038224, _1038226, _1038228, _1038230] : [hAPP(c_Set_Oimage(_1038222, _1038224, _1038226), c_Orderings_Otop__class_Otop(tc_fun(_1038222, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038224, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1038224, _1038228, _1038230), c_Orderings_Otop__class_Otop(tc_fun(_1038224, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038228, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1038222, _1038228, hAPP(c_Fun_Ocomp(_1038224, _1038228, _1038222, _1038230), _1038226)), c_Orderings_Otop__class_Otop(tc_fun(_1038222, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1038228, tc_HOL_Obool)))], (13800 ^ _782435) ^ [_1038481, _1038483, _1038485, _1038487, _1038489, _1038491] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038481, tc_fun(_1038483, tc_HOL_Obool)), _1038485), hAPP(c_Fun_Ocomp(_1038487, tc_fun(_1038483, tc_HOL_Obool), _1038481, _1038489), _1038491)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1038487, tc_fun(_1038483, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1038481, _1038487, _1038491), _1038485)), _1038489))], (13802 ^ _782435) ^ [_1038556, _1038558, _1038560, _1038562, _1038564] : [c_Fun_Oinj__on(_1038556, _1038558, _1038560, c_Orderings_Otop__class_Otop(tc_fun(_1038556, tc_HOL_Obool))), c_Fun_Oinj__on(_1038562, _1038556, _1038564, c_Orderings_Otop__class_Otop(tc_fun(_1038562, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1038562, _1038558, hAPP(c_Fun_Ocomp(_1038556, _1038558, _1038562, _1038560), _1038564), c_Orderings_Otop__class_Otop(tc_fun(_1038562, tc_HOL_Obool))))], (13812 ^ _782435) ^ [_1038755, _1038757, _1038759, _1038761, _1038763, _1038765] : [c_Fun_Oinj__on(_1038755, _1038757, hAPP(c_Fun_Ocomp(_1038759, _1038757, _1038755, _1038761), _1038763), _1038765), -(c_Fun_Oinj__on(_1038759, _1038757, _1038761, hAPP(c_Set_Oimage(_1038755, _1038759, _1038763), _1038765)))], (13818 ^ _782435) ^ [_1038878, _1038880, _1038882, _1038884, _1038886, _1038888] : [c_Fun_Oinj__on(_1038878, _1038880, _1038882, _1038884), c_Fun_Oinj__on(_1038880, _1038886, _1038888, hAPP(c_Set_Oimage(_1038878, _1038880, _1038882), _1038884)), -(c_Fun_Oinj__on(_1038878, _1038886, hAPP(c_Fun_Ocomp(_1038880, _1038886, _1038878, _1038888), _1038882), _1038884))], (13828 ^ _782435) ^ [_1039065, _1039067, _1039069, _1039071, _1039073, _1039075] : [c_Fun_Oinj__on(_1039065, _1039067, _1039069, _1039071), 13831 ^ _782435 : [(13832 ^ _782435) ^ [] : [c_Fun_Oinj__on(_1039067, _1039073, _1039075, hAPP(c_Set_Oimage(_1039065, _1039067, _1039069), _1039071)), -(c_Fun_Oinj__on(_1039065, _1039073, hAPP(c_Fun_Ocomp(_1039067, _1039073, _1039065, _1039075), _1039069), _1039071))], (13838 ^ _782435) ^ [] : [c_Fun_Oinj__on(_1039065, _1039073, hAPP(c_Fun_Ocomp(_1039067, _1039073, _1039065, _1039075), _1039069), _1039071), -(c_Fun_Oinj__on(_1039067, _1039073, _1039075, hAPP(c_Set_Oimage(_1039065, _1039067, _1039069), _1039071)))]]], (13844 ^ _782435) ^ [_1039357, _1039359, _1039361, _1039363, _1039365, _1039367, _1039369] : [c_Fun_Obij__betw(_1039357, _1039359, _1039361, _1039363, _1039365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1039357, tc_HOL_Obool)), _1039367), _1039363)), hAPP(c_Set_Oimage(_1039357, _1039359, _1039361), _1039367) = _1039369, -(c_Fun_Obij__betw(_1039357, _1039359, _1039361, _1039367, _1039369))], (13858 ^ _782435) ^ [_1039614, _1039616, _1039618, _1039620] : [c_Fun_Obij__betw(_1039614, _1039616, _1039618, _1039620, c_Orderings_Otop__class_Otop(tc_fun(_1039616, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1039614, _1039616, _1039618), c_Orderings_Otop__class_Otop(tc_fun(_1039614, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1039616, tc_HOL_Obool)))], (13864 ^ _782435) ^ [_1039745, _1039747, _1039749] : [c_Fun_Obij__betw(_1039745, _1039747, _1039749, c_Orderings_Otop__class_Otop(tc_fun(_1039745, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039747, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1039745, _1039747, _1039749), c_Orderings_Otop__class_Otop(tc_fun(_1039745, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1039747, tc_HOL_Obool)))], (13870 ^ _782435) ^ [_1039884, _1039886, _1039888] : [c_Fun_Obij__betw(_1039884, _1039886, _1039888, c_Orderings_Otop__class_Otop(tc_fun(_1039884, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1039886, tc_HOL_Obool))), -(c_Fun_Oinj__on(_1039884, _1039886, _1039888, c_Orderings_Otop__class_Otop(tc_fun(_1039884, tc_HOL_Obool))))], (13876 ^ _782435) ^ [_1040003, _1040005, _1040007, _1040009] : [c_Fun_Oinj__on(_1040003, _1040005, _1040007, _1040009), -(c_Fun_Obij__betw(_1040003, _1040005, _1040007, _1040009, hAPP(c_Set_Oimage(_1040003, _1040005, _1040007), _1040009)))], (13882 ^ _782435) ^ [_1040132, _1040134, _1040136, _1040138, _1040140] : [c_Fun_Obij__betw(_1040132, _1040134, _1040136, _1040138, _1040140), 13885 ^ _782435 : [(13886 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1040132, _1040134, _1040136, _1040138))], (13888 ^ _782435) ^ [] : [-(hAPP(c_Set_Oimage(_1040132, _1040134, _1040136), _1040138) = _1040140)]]], (13890 ^ _782435) ^ [_1040261, _1040263, _1040265, _1040267, _1040269] : [-(c_Fun_Obij__betw(_1040261, _1040263, _1040265, _1040267, _1040269)), c_Fun_Oinj__on(_1040261, _1040263, _1040265, _1040267), hAPP(c_Set_Oimage(_1040261, _1040263, _1040265), _1040267) = _1040269], (13900 ^ _782435) ^ [_1040428, _1040430, _1040432, _1040434] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1040428, _1040430, _1040432), _1040434)), _1040432 = c_Orderings_Obot__class_Obot(tc_fun(_1040428, tc_HOL_Obool))], (13906 ^ _782435) ^ [_1040547, _1040549, _1040551] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1040547, _1040549, c_Orderings_Obot__class_Obot(tc_fun(_1040547, tc_HOL_Obool))), _1040551))], (13908 ^ _782435) ^ [_1040585, _1040587, _1040589, _1040591, _1040593, _1040595, _1040597] : [c_Fun_Obij__betw(_1040585, _1040587, _1040589, _1040591, _1040593), c_Fun_Obij__betw(_1040585, _1040587, _1040589, _1040595, _1040597), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040587, tc_HOL_Obool)), _1040593), _1040597) = c_Orderings_Obot__class_Obot(tc_fun(_1040587, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1040585, _1040587, _1040589, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040585, tc_HOL_Obool)), _1040591), _1040595), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040587, tc_HOL_Obool)), _1040593), _1040597)))], (13922 ^ _782435) ^ [_1040890, _1040892, _1040894, _1040896, _1040898, _1040900, _1040902] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040890, tc_HOL_Obool)), _1040892), _1040894) = c_Orderings_Obot__class_Obot(tc_fun(_1040890, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1040896, tc_HOL_Obool)), _1040898), _1040900) = c_Orderings_Obot__class_Obot(tc_fun(_1040896, tc_HOL_Obool)), c_Fun_Obij__betw(_1040890, _1040896, _1040902, _1040892, _1040898), c_Fun_Obij__betw(_1040890, _1040896, _1040902, _1040894, _1040900), -(c_Fun_Obij__betw(_1040890, _1040896, _1040902, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040890, tc_HOL_Obool)), _1040892), _1040894), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1040896, tc_HOL_Obool)), _1040898), _1040900)))], (13940 ^ _782435) ^ [_1041307, _1041309, _1041311] : [c_Fun_Obij__betw(_1041307, _1041309, _1041311, c_Orderings_Otop__class_Otop(tc_fun(_1041307, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041309, tc_HOL_Obool))), 13943 ^ _782435 : [(13944 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1041307, _1041309, _1041311, c_Orderings_Otop__class_Otop(tc_fun(_1041307, tc_HOL_Obool))))], (13946 ^ _782435) ^ [] : [-(hAPP(c_Set_Oimage(_1041307, _1041309, _1041311), c_Orderings_Otop__class_Otop(tc_fun(_1041307, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041309, tc_HOL_Obool)))]]], (13948 ^ _782435) ^ [_1041482, _1041484, _1041486] : [-(c_Fun_Obij__betw(_1041482, _1041484, _1041486, c_Orderings_Otop__class_Otop(tc_fun(_1041482, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041484, tc_HOL_Obool)))), c_Fun_Oinj__on(_1041482, _1041484, _1041486, c_Orderings_Otop__class_Otop(tc_fun(_1041482, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1041482, _1041484, _1041486), c_Orderings_Otop__class_Otop(tc_fun(_1041482, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041484, tc_HOL_Obool))], (13958 ^ _782435) ^ [_1041691, _1041693, _1041695] : [c_Fun_Oinj__on(_1041691, _1041693, _1041695, c_Orderings_Otop__class_Otop(tc_fun(_1041691, tc_HOL_Obool))), hAPP(c_Set_Oimage(_1041691, _1041693, _1041695), c_Orderings_Otop__class_Otop(tc_fun(_1041691, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1041693, tc_HOL_Obool)), -(c_Fun_Obij__betw(_1041691, _1041693, _1041695, c_Orderings_Otop__class_Otop(tc_fun(_1041691, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1041693, tc_HOL_Obool))))], (13968 ^ _782435) ^ [_1041898, _1041900, _1041902, _1041904, _1041906, _1041908] : [hBOOL(hAPP(hAPP(c_member(_1041898), _1041900), _1041902)), -(hAPP(c_Fun_Ooverride__on(_1041898, _1041904, _1041906, _1041908, _1041902), _1041900) = hAPP(_1041908, _1041900))], (13974 ^ _782435) ^ [_1042017, _1042019, _1042021, _1042023, _1042025, _1042027] : [-(hBOOL(hAPP(hAPP(c_member(_1042017), _1042019), _1042021))), -(hAPP(c_Fun_Ooverride__on(_1042017, _1042023, _1042025, _1042027, _1042021), _1042019) = hAPP(_1042025, _1042019))], (13980 ^ _782435) ^ [_1042080, _1042082, _1042084, _1042086] : [c_Fun_Obij__betw(_1042080, _1042082, _1042084, c_Orderings_Otop__class_Otop(tc_fun(_1042080, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1042082, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1042080, _1042082, _1042084), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042080, tc_HOL_Obool)), _1042086)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1042082, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1042080, _1042082, _1042084), _1042086)))], (13986 ^ _782435) ^ [_1042247, _1042249, _1042251, _1042253] : [-(c_Fun_Ooverride__on(_1042247, _1042249, _1042251, _1042253, c_Orderings_Obot__class_Obot(tc_fun(_1042247, tc_HOL_Obool))) = _1042251)], (13988 ^ _782435) ^ [_1042287, _1042289, _1042291, _1042293, _1042295] : [class_Groups_Oab__semigroup__mult(_1042287), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042287, _1042287, c_Groups_Otimes__class_Otimes(_1042287), _1042289, _1042291), _1042293)), -(hBOOL(hAPP(hAPP(c_member(_1042287), _1042289), _1042291))), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1042287, _1042287, c_Groups_Otimes__class_Otimes(_1042287), _1042295, hAPP(hAPP(c_Set_Oinsert(_1042287), _1042289), _1042291)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042287), _1042295), _1042293))))], (14002 ^ _782435) ^ [_1042527, _1042529, _1042531, _1042533, _1042535, _1042537] : [c_Fun_Obij__betw(_1042527, _1042529, _1042531, c_Orderings_Otop__class_Otop(tc_fun(_1042527, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1042529, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1042527, _1042529, _1042531), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042533, tc_fun(_1042527, tc_HOL_Obool)), _1042535), _1042537)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1042533, tc_fun(_1042529, tc_HOL_Obool)), _1042535), hAPP(hAPP(c_COMBB(tc_fun(_1042527, tc_HOL_Obool), tc_fun(_1042529, tc_HOL_Obool), _1042533), c_Set_Oimage(_1042527, _1042529, _1042531)), _1042537)))], (14008 ^ _782435) ^ [_1042761, _1042763, _1042765, _1042767] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1042761, _1042763, hAPP(hAPP(c_Set_Oinsert(_1042761), _1042765), c_Orderings_Obot__class_Obot(tc_fun(_1042761, tc_HOL_Obool)))), _1042767)), -(_1042765 = _1042767)], (14014 ^ _782435) ^ [_1042876, _1042878, _1042880, _1042882] : [_1042880 = _1042882, -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1042876, _1042878, hAPP(hAPP(c_Set_Oinsert(_1042876), _1042880), c_Orderings_Obot__class_Obot(tc_fun(_1042876, tc_HOL_Obool)))), _1042882)))], (14020 ^ _782435) ^ [_1042997, _1042999, _1043001] : [class_Rings_Oring(_1042997), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1042997), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042997), _1042999), _1043001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1042997), _1042999), hAPP(c_Groups_Ouminus__class_Ouminus(_1042997), _1043001)))], (14026 ^ _782435) ^ [_1043126, _1043128, _1043130] : [class_Rings_Oring(_1043126), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1043126), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043126), _1043128), _1043130)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043126), hAPP(c_Groups_Ouminus__class_Ouminus(_1043126), _1043128)), _1043130))], (14032 ^ _782435) ^ [_1043255, _1043257, _1043259] : [class_Rings_Oring(_1043255), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043255), hAPP(c_Groups_Ouminus__class_Ouminus(_1043255), _1043257)), _1043259) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043255), _1043257), hAPP(c_Groups_Ouminus__class_Ouminus(_1043255), _1043259)))], (14038 ^ _782435) ^ [_1043384, _1043386, _1043388] : [class_Rings_Oring(_1043384), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043384), hAPP(c_Groups_Ouminus__class_Ouminus(_1043384), _1043386)), hAPP(c_Groups_Ouminus__class_Ouminus(_1043384), _1043388)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043384), _1043386), _1043388))], (14044 ^ _782435) ^ [_1043513, _1043515, _1043517] : [class_Rings_Oidom(_1043513), 14047 ^ _782435 : [(14058 ^ _782435) ^ [] : [14059 ^ _782435 : [(14060 ^ _782435) ^ [] : [_1043515 = _1043517], (14062 ^ _782435) ^ [] : [_1043515 = hAPP(c_Groups_Ouminus__class_Ouminus(_1043513), _1043517)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043513), _1043515), _1043515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043513), _1043517), _1043517))], (14048 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043513), _1043515), _1043515) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1043513), _1043517), _1043517), -(_1043515 = _1043517), -(_1043515 = hAPP(c_Groups_Ouminus__class_Ouminus(_1043513), _1043517))]]], (14066 ^ _782435) ^ [_1043832, _1043834, _1043836, _1043838, _1043840] : [c_Finite__Set_Ofolding__one(_1043832, _1043834, _1043836), hBOOL(hAPP(c_Finite__Set_Ofinite(_1043832), _1043838)), hBOOL(hAPP(hAPP(c_member(_1043832), _1043840), _1043838)), 14077 ^ _782435 : [(14078 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043832, tc_HOL_Obool)), _1043838), hAPP(hAPP(c_Set_Oinsert(_1043832), _1043840), c_Orderings_Obot__class_Obot(tc_fun(_1043832, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1043832, tc_HOL_Obool)), -(hAPP(_1043836, _1043838) = _1043840)], (14084 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043832, tc_HOL_Obool)), _1043838), hAPP(hAPP(c_Set_Oinsert(_1043832), _1043840), c_Orderings_Obot__class_Obot(tc_fun(_1043832, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1043832, tc_HOL_Obool))), -(hAPP(_1043836, _1043838) = hAPP(hAPP(_1043834, _1043840), hAPP(_1043836, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1043832, tc_HOL_Obool)), _1043838), hAPP(hAPP(c_Set_Oinsert(_1043832), _1043840), c_Orderings_Obot__class_Obot(tc_fun(_1043832, tc_HOL_Obool)))))))]]], (14090 ^ _782435) ^ [_1044378, _1044380, _1044382, _1044384, _1044386] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1044378, _1044380, hAPP(hAPP(c_Set_Oinsert(_1044378), _1044382), _1044384)), _1044386)), 14095 ^ _782435 : [(14096 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1044378), _1044382), _1044384) = hAPP(hAPP(c_Set_Oinsert(_1044378), 14093 ^ [_1044378, _1044380, _1044382, _1044384, _1044386]), 14094 ^ [_1044378, _1044380, _1044382, _1044384, _1044386]))], (14098 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1044378, _1044378, _1044380, 14093 ^ [_1044378, _1044380, _1044382, _1044384, _1044386], 14094 ^ [_1044378, _1044380, _1044382, _1044384, _1044386]), _1044386)))], (14100 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1044378), 14093 ^ [_1044378, _1044380, _1044382, _1044384, _1044386]), 14094 ^ [_1044378, _1044380, _1044382, _1044384, _1044386]))]]], (14102 ^ _782435) ^ [_1044769, _1044771, _1044773, _1044775, _1044777] : [-(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1044769, _1044771, hAPP(hAPP(c_Set_Oinsert(_1044769), _1044773), _1044775)), _1044777))), 14103 ^ _782435 : [(14104 ^ _782435) ^ [_1044873, _1044875] : [hAPP(hAPP(c_Set_Oinsert(_1044769), _1044773), _1044775) = hAPP(hAPP(c_Set_Oinsert(_1044769), _1044875), _1044873), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1044769, _1044769, _1044771, _1044875, _1044873), _1044777)), -(hBOOL(hAPP(hAPP(c_member(_1044769), _1044875), _1044873)))]]], (14116 ^ _782435) ^ [_1045130, _1045132, _1045134, _1045136, _1045138] : [hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1045130, _1045132, hAPP(hAPP(c_Set_Oinsert(_1045130), _1045134), _1045136)), _1045138)), 14121 ^ _782435 : [(14122 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Set_Oinsert(_1045130), _1045134), _1045136) = hAPP(hAPP(c_Set_Oinsert(_1045130), 14119 ^ [_1045130, _1045132, _1045134, _1045136, _1045138]), 14120 ^ [_1045130, _1045132, _1045134, _1045136, _1045138]))], (14124 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1045130, _1045130, _1045132, 14119 ^ [_1045130, _1045132, _1045134, _1045136, _1045138], 14120 ^ [_1045130, _1045132, _1045134, _1045136, _1045138]), _1045138)))], (14126 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1045130), 14119 ^ [_1045130, _1045132, _1045134, _1045136, _1045138]), 14120 ^ [_1045130, _1045132, _1045134, _1045136, _1045138]))]]], (14128 ^ _782435) ^ [_1045523] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045523), c_Orderings_Obot__class_Obot(tc_fun(_1045523, tc_HOL_Obool)))))], (14130 ^ _782435) ^ [_1045555, _1045557, _1045559] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045555), _1045557)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045555), hAPP(hAPP(c_Set_Oinsert(_1045555), _1045559), _1045557))))], (14136 ^ _782435) ^ [_1045666, _1045668, _1045670, _1045672] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045666), _1045668)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045670), hAPP(c_Set_Oimage(_1045666, _1045670, _1045672), _1045668))))], (14142 ^ _782435) ^ [_1045777, _1045779, _1045781] : [14143 ^ _782435 : [(14144 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045777), _1045779))], (14146 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045777), _1045781))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045777), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1045777, tc_HOL_Obool)), _1045779), _1045781))))], (14150 ^ _782435) ^ [_1045940, _1045942, _1045944] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1045940), _1045942)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1045940), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1045940, tc_HOL_Obool)), _1045942), _1045944))))], (14156 ^ _782435) ^ [_1046057, _1046059] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046057), c_Complete__Lattice_OInf__class_OInf(tc_fun(_1046057, tc_HOL_Obool), _1046059)))), 14157 ^ _782435 : [(14158 ^ _782435) ^ [_1046121] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1046057, tc_HOL_Obool)), _1046121), _1046059)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046057), _1046121))]]], (14166 ^ _782435) ^ [_1046265, _1046267, _1046269, _1046271] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046269), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1046265, tc_fun(_1046269, tc_HOL_Obool)), _1046267), _1046271)))), 14167 ^ _782435 : [(14168 ^ _782435) ^ [_1046339] : [hBOOL(hAPP(hAPP(c_member(_1046265), _1046339), _1046267)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1046269), hAPP(_1046271, _1046339)))]]], (14176 ^ _782435) ^ [_1046508, _1046510] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046508, tc_HOL_Obool)), hAPP(c_Set_OPow(_1046508), _1046510))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046508), _1046510)))], (14182 ^ _782435) ^ [_1046613, _1046615] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046613), _1046615)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046613, tc_HOL_Obool)), hAPP(c_Set_OPow(_1046613), _1046615))))], (14188 ^ _782435) ^ [_1046724, _1046726] : [class_Finite__Set_Ofinite(_1046724), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046724), _1046726)))], (14194 ^ _782435) ^ [_1046807, _1046809] : [class_Finite__Set_Ofinite(_1046807), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1046807), _1046809)))], (14200 ^ _782435) ^ [_1046890, _1046892] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1046890), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1046890, tc_HOL_Obool), _1046892))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1046890, tc_HOL_Obool)), _1046892)))], (14206 ^ _782435) ^ [_1047001, _1047003] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047001), c_Orderings_Otop__class_Otop(tc_fun(_1047001, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047003), c_Orderings_Otop__class_Otop(tc_fun(_1047003, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1047001, _1047003)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1047001, _1047003), tc_HOL_Obool)))))], (14216 ^ _782435) ^ [_1047211, _1047213] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1047211, _1047213)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1047211, _1047213), tc_HOL_Obool)))), 14219 ^ _782435 : [(14220 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047211), c_Orderings_Otop__class_Otop(tc_fun(_1047211, tc_HOL_Obool)))))], (14222 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047213), c_Orderings_Otop__class_Otop(tc_fun(_1047213, tc_HOL_Obool)))))]]], (14224 ^ _782435) ^ [_1047376, _1047378] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(_1047376, _1047378)), c_Orderings_Otop__class_Otop(tc_fun(tc_sum(_1047376, _1047378), tc_HOL_Obool))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047376), c_Orderings_Otop__class_Otop(tc_fun(_1047376, tc_HOL_Obool)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1047378), c_Orderings_Otop__class_Otop(tc_fun(_1047378, tc_HOL_Obool))))], (14234 ^ _782435) ^ [_1047585] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1047585)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1047585), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047585), c_Orderings_Otop__class_Otop(tc_fun(_1047585, tc_HOL_Obool)))))], (14240 ^ _782435) ^ [_1047700] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047700), c_Orderings_Otop__class_Otop(tc_fun(_1047700, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(_1047700)), c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(_1047700), tc_HOL_Obool)))))], (14246 ^ _782435) ^ [_1047821] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047821), c_Orderings_Obot__class_Obot(tc_fun(_1047821, tc_HOL_Obool)))))], (14248 ^ _782435) ^ [_1047871, _1047873, _1047875] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047871), hAPP(hAPP(c_Set_Oinsert(_1047871), _1047873), _1047875))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047871), _1047875)))], (14254 ^ _782435) ^ [_1047978, _1047980, _1047982] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1047978), _1047982)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1047978), hAPP(hAPP(c_Set_Oinsert(_1047978), _1047980), _1047982))))], (14260 ^ _782435) ^ [_1048091, _1048093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1048091, _1048093)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1048091, _1048093), tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048093), c_Orderings_Otop__class_Otop(tc_fun(_1048093, tc_HOL_Obool)))))], (14266 ^ _782435) ^ [_1048216, _1048218, _1048220] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048216, tc_HOL_Obool)), _1048218), _1048220)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048216), _1048220)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048216), _1048218)))], (14276 ^ _782435) ^ [_1048385, _1048387, _1048389] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048385), _1048387)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1048385, tc_HOL_Obool)), _1048389), _1048387)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048385), _1048389)))], (14286 ^ _782435) ^ [_1048554] : [class_Finite__Set_Ofinite(_1048554), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048554), c_Orderings_Otop__class_Otop(tc_fun(_1048554, tc_HOL_Obool)))))], (14292 ^ _782435) ^ [_1048663, _1048665, _1048667] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048663), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048663, tc_HOL_Obool)), _1048665), _1048667))), 14295 ^ _782435 : [(14296 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048663), _1048665)))], (14298 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048663), _1048667)))]]], (14300 ^ _782435) ^ [_1048810, _1048812, _1048814] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048810), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048810, tc_HOL_Obool)), _1048812), _1048814)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048810), _1048812)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048810), _1048814))], (14310 ^ _782435) ^ [_1048991, _1048993, _1048995] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1048991), _1048993)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1048991), _1048995)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1048991), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1048991, tc_HOL_Obool)), _1048993), _1048995))))], (14320 ^ _782435) ^ [_1049170, _1049172, _1049174] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049170), _1049172)), 14323 ^ _782435 : [(14324 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049170), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049170, tc_HOL_Obool)), _1049174), _1049172))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049170), _1049174)))], (14330 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049170), _1049174)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049170), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1049170, tc_HOL_Obool)), _1049174), _1049172))))]]], (14336 ^ _782435) ^ [_1049448, _1049450, _1049452, _1049454] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049448), _1049450)), 14339 ^ _782435 : [(14350 ^ _782435) ^ [] : [14352 ^ _782435 : [(14353 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1049448), 14351 ^ [_1049448, _1049450, _1049452, _1049454]), _1049450)))], (14355 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049452), hAPP(_1049454, 14351 ^ [_1049448, _1049450, _1049452, _1049454])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049452), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049448, tc_fun(_1049452, tc_HOL_Obool)), _1049450), _1049454))))], (14340 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049452), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1049448, tc_fun(_1049452, tc_HOL_Obool)), _1049450), _1049454))), 14343 ^ _782435 : [(14344 ^ _782435) ^ [_1049632] : [hBOOL(hAPP(hAPP(c_member(_1049448), _1049632), _1049450)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049452), hAPP(_1049454, _1049632))))]]]]], (14359 ^ _782435) ^ [_1049923, _1049925, _1049927, _1049929, _1049931] : [c_Fun_Obij__betw(_1049923, _1049925, _1049927, _1049929, _1049931), 14362 ^ _782435 : [(14363 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049923), _1049929)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049925), _1049931)))], (14369 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1049925), _1049931)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1049923), _1049929)))]]], (14375 ^ _782435) ^ [_1050178, _1050180, _1050182, _1050184, _1050186, _1050188] : [hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1050178, _1050180, _1050182, _1050184, _1050186), _1050188)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050178), _1050186)))], (14381 ^ _782435) ^ [_1050287, _1050289, _1050291, _1050293, _1050295] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050287), _1050289)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1050291, tc_HOL_Obool)), _1050293), hAPP(c_Set_Oimage(_1050287, _1050291, _1050295), _1050289))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050291), _1050293)))], (14391 ^ _782435) ^ [_1050499, _1050501, _1050503, _1050505] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050499), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050499, tc_HOL_Obool)), _1050501), hAPP(hAPP(c_Set_Oinsert(_1050499), _1050503), _1050505)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050499), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050499, tc_HOL_Obool)), _1050501), _1050505))))], (14397 ^ _782435) ^ [_1050652, _1050654, _1050656, _1050658] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050652, tc_HOL_Obool)), _1050654), _1050658))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050652), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1050652, tc_HOL_Obool)), _1050654), hAPP(hAPP(c_Set_Oinsert(_1050652), _1050656), _1050658)))))], (14403 ^ _782435) ^ [_1050811, _1050813, _1050815, _1050817] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050811), hAPP(c_Set_Oimage(_1050813, _1050811, _1050815), _1050817))), c_Fun_Oinj__on(_1050813, _1050811, _1050815, _1050817), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050813), _1050817)))], (14413 ^ _782435) ^ [_1050982, _1050984] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050982), _1050984)), 14416 ^ _782435 : [(14417 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050982), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1050982, tc_HOL_Obool)), _1050984))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050982), c_Orderings_Otop__class_Otop(tc_fun(_1050982, tc_HOL_Obool)))))], (14423 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1050982), c_Orderings_Otop__class_Otop(tc_fun(_1050982, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1050982), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1050982, tc_HOL_Obool)), _1050984))))]]], (14429 ^ _782435) ^ [_1051260, _1051262, _1051264, _1051266, _1051268] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051260), hAPP(c_Set_Oimage(_1051262, _1051260, _1051264), c_Orderings_Otop__class_Otop(tc_fun(_1051262, tc_HOL_Obool))))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1051266), hAPP(c_Set_Oimage(_1051262, _1051266, hAPP(hAPP(c_COMBB(_1051260, _1051266, _1051262), _1051268), _1051264)), c_Orderings_Otop__class_Otop(tc_fun(_1051262, tc_HOL_Obool))))))], (14435 ^ _782435) ^ [_1051427, _1051429, _1051431] : [class_Rings_Olinordered__idom(_1051427), -(_1051429 = _1051431), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051427), _1051429), _1051431))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1051427), _1051431), _1051429)))], (14449 ^ _782435) ^ [_1051562, _1051564, _1051566] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051562), _1051564)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051562, tc_HOL_Obool)), _1051564), hAPP(c_Set_Oimage(_1051562, _1051562, _1051566), _1051564))), -(c_Fun_Oinj__on(_1051562, _1051562, _1051566, _1051564))], (14459 ^ _782435) ^ [_1051741, _1051743, _1051745] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051741), _1051743)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1051741, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1051741, _1051741, _1051745), _1051743)), _1051743)), c_Fun_Oinj__on(_1051741, _1051741, _1051745, _1051743), -(hAPP(c_Set_Oimage(_1051741, _1051741, _1051745), _1051743) = _1051743)], (14473 ^ _782435) ^ [_1051988, _1051990] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1051988), c_Orderings_Otop__class_Otop(tc_fun(_1051988, tc_HOL_Obool)))), hAPP(c_Set_Oimage(_1051988, _1051988, _1051990), c_Orderings_Otop__class_Otop(tc_fun(_1051988, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1051988, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1051988, _1051988, _1051990, c_Orderings_Otop__class_Otop(tc_fun(_1051988, tc_HOL_Obool))))], (14483 ^ _782435) ^ [_1052183, _1052185] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052183), c_Orderings_Otop__class_Otop(tc_fun(_1052183, tc_HOL_Obool)))), c_Fun_Oinj__on(_1052183, _1052183, _1052185, c_Orderings_Otop__class_Otop(tc_fun(_1052183, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1052183, _1052183, _1052185), c_Orderings_Otop__class_Otop(tc_fun(_1052183, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052183, tc_HOL_Obool)))], (14493 ^ _782435) ^ [_1052378, _1052380, _1052382, _1052384] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052378), hAPP(c_Set_Ovimage(_1052378, _1052380, _1052382), _1052384))), hAPP(c_Set_Oimage(_1052378, _1052380, _1052382), c_Orderings_Otop__class_Otop(tc_fun(_1052378, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1052380, tc_HOL_Obool)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052380), _1052384)))], (14503 ^ _782435) ^ [_1052579, _1052581, _1052583, _1052585] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052579), _1052581)), c_Fun_Oinj__on(_1052583, _1052579, _1052585, c_Orderings_Otop__class_Otop(tc_fun(_1052583, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052583), hAPP(c_Set_Ovimage(_1052583, _1052579, _1052585), _1052581))))], (14513 ^ _782435) ^ [_1052760, _1052762, _1052764, _1052766] : [c_Fun_Obij__betw(_1052760, _1052762, _1052764, c_Orderings_Otop__class_Otop(tc_fun(_1052760, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1052762, tc_HOL_Obool))), 14516 ^ _782435 : [(14517 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052760), hAPP(c_Set_Ovimage(_1052760, _1052762, _1052764), _1052766))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052762), _1052766)))], (14523 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1052762), _1052766)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1052760), hAPP(c_Set_Ovimage(_1052760, _1052762, _1052764), _1052766))))]]], (14529 ^ _782435) ^ [_1053050, _1053052, _1053054, _1053056, _1053058] : [c_Finite__Set_Ofolding__one(_1053050, _1053052, _1053054), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053050), _1053056)), -(hBOOL(hAPP(hAPP(c_member(_1053050), _1053058), _1053056))), -(_1053056 = c_Orderings_Obot__class_Obot(tc_fun(_1053050, tc_HOL_Obool))), -(hAPP(_1053054, hAPP(hAPP(c_Set_Oinsert(_1053050), _1053058), _1053056)) = hAPP(hAPP(_1053052, _1053058), hAPP(_1053054, _1053056)))], (14547 ^ _782435) ^ [_1053295, _1053297, _1053299, _1053301, _1053303] : [c_Finite__Set_Ofolding__one(_1053295, _1053297, _1053299), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053295), _1053301)), 14554 ^ _782435 : [(14555 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053295, tc_HOL_Obool)), _1053301), hAPP(hAPP(c_Set_Oinsert(_1053295), _1053303), c_Orderings_Obot__class_Obot(tc_fun(_1053295, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1053295, tc_HOL_Obool)), -(hAPP(_1053299, hAPP(hAPP(c_Set_Oinsert(_1053295), _1053303), _1053301)) = _1053303)], (14561 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053295, tc_HOL_Obool)), _1053301), hAPP(hAPP(c_Set_Oinsert(_1053295), _1053303), c_Orderings_Obot__class_Obot(tc_fun(_1053295, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1053295, tc_HOL_Obool))), -(hAPP(_1053299, hAPP(hAPP(c_Set_Oinsert(_1053295), _1053303), _1053301)) = hAPP(hAPP(_1053297, _1053303), hAPP(_1053299, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1053295, tc_HOL_Obool)), _1053301), hAPP(hAPP(c_Set_Oinsert(_1053295), _1053303), c_Orderings_Obot__class_Obot(tc_fun(_1053295, tc_HOL_Obool)))))))]]], (14567 ^ _782435) ^ [_1053777, _1053779, _1053781, _1053783, _1053785] : [c_Finite__Set_Ofolding__one(_1053777, _1053779, _1053781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053777), _1053783)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1053777), _1053785)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053777, tc_HOL_Obool)), _1053783), _1053785) = c_Orderings_Obot__class_Obot(tc_fun(_1053777, tc_HOL_Obool))), -(hAPP(hAPP(_1053779, hAPP(_1053781, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1053777, tc_HOL_Obool)), _1053783), _1053785))), hAPP(_1053781, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1053777, tc_HOL_Obool)), _1053783), _1053785))) = hAPP(hAPP(_1053779, hAPP(_1053781, _1053783)), hAPP(_1053781, _1053785)))], (14585 ^ _782435) ^ [_1054133, _1054135, _1054137, _1054139, _1054141] : [c_Finite__Set_Ofolding__one(_1054133, _1054135, _1054137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054133), _1054139)), -(_1054139 = c_Orderings_Obot__class_Obot(tc_fun(_1054133, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054133), _1054141)), -(_1054141 = c_Orderings_Obot__class_Obot(tc_fun(_1054133, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1054133, tc_HOL_Obool)), _1054139), _1054141) = c_Orderings_Obot__class_Obot(tc_fun(_1054133, tc_HOL_Obool)), -(hAPP(_1054137, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1054133, tc_HOL_Obool)), _1054139), _1054141)) = hAPP(hAPP(_1054135, hAPP(_1054137, _1054139)), hAPP(_1054137, _1054141)))], (14611 ^ _782435) ^ [_1054634, _1054636, _1054638, _1054640, _1054642, _1054644] : [c_Finite__Set_Ofolding(_1054634, _1054636, _1054638, _1054640), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054634), _1054642)), hBOOL(hAPP(hAPP(c_member(_1054634), _1054644), _1054642)), -(hAPP(_1054640, _1054642) = hAPP(c_Fun_Ocomp(_1054636, _1054636, _1054636, hAPP(_1054640, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054634, tc_HOL_Obool)), _1054642), hAPP(hAPP(c_Set_Oinsert(_1054634), _1054644), c_Orderings_Obot__class_Obot(tc_fun(_1054634, tc_HOL_Obool)))))), hAPP(_1054638, _1054644)))], (14625 ^ _782435) ^ [_1054947, _1054949, _1054951, _1054953, _1054955, _1054957, _1054959, _1054961] : [c_Finite__Set_Ofolding__image__simple(_1054947, _1054949, _1054951, _1054953, _1054955, _1054957), hBOOL(hAPP(c_Finite__Set_Ofinite(_1054949), _1054959)), hBOOL(hAPP(hAPP(c_member(_1054949), _1054961), _1054959)), -(hAPP(_1054957, _1054959) = hAPP(hAPP(_1054951, hAPP(_1054955, _1054961)), hAPP(_1054957, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1054949, tc_HOL_Obool)), _1054959), hAPP(hAPP(c_Set_Oinsert(_1054949), _1054961), c_Orderings_Obot__class_Obot(tc_fun(_1054949, tc_HOL_Obool)))))))], (14639 ^ _782435) ^ [_1055272, _1055274, _1055276, _1055278, _1055280, _1055282, _1055284, _1055286] : [c_Finite__Set_Ofolding__image(_1055272, _1055274, _1055276, _1055278, _1055280), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055274), _1055282)), c_Fun_Oinj__on(_1055274, _1055274, _1055284, _1055282), -(hAPP(hAPP(_1055280, _1055286), hAPP(c_Set_Oimage(_1055274, _1055274, _1055284), _1055282)) = hAPP(hAPP(_1055280, hAPP(c_Fun_Ocomp(_1055274, _1055272, _1055274, _1055286), _1055284)), _1055282))], (14653 ^ _782435) ^ [_1055561, _1055563, _1055565, _1055567, _1055569, _1055571] : [c_Finite__Set_Ofolding(_1055561, _1055563, _1055565, _1055567), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055561), _1055569)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055561), _1055571)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1055561, tc_HOL_Obool)), _1055569), _1055571) = c_Orderings_Obot__class_Obot(tc_fun(_1055561, tc_HOL_Obool)), -(hAPP(_1055567, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1055561, tc_HOL_Obool)), _1055569), _1055571)) = hAPP(c_Fun_Ocomp(_1055563, _1055563, _1055563, hAPP(_1055567, _1055569)), hAPP(_1055567, _1055571)))], (14671 ^ _782435) ^ [_1055934, _1055936, _1055938, _1055940, _1055942, _1055944] : [c_Finite__Set_Ofolding(_1055934, _1055936, _1055938, _1055940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1055934), _1055942)), -(hAPP(_1055940, hAPP(hAPP(c_Set_Oinsert(_1055934), _1055944), _1055942)) = hAPP(c_Fun_Ocomp(_1055936, _1055936, _1055936, hAPP(_1055940, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1055934, tc_HOL_Obool)), _1055942), hAPP(hAPP(c_Set_Oinsert(_1055934), _1055944), c_Orderings_Obot__class_Obot(tc_fun(_1055934, tc_HOL_Obool)))))), hAPP(_1055938, _1055944)))], (14681 ^ _782435) ^ [_1056189, _1056191, _1056193, _1056195, _1056197, _1056199, _1056201, _1056203] : [c_Finite__Set_Ofolding__image__simple(_1056189, _1056191, _1056193, _1056195, _1056197, _1056199), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056191), _1056201)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056191), _1056203)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1056191, tc_HOL_Obool)), _1056201), _1056203) = c_Orderings_Obot__class_Obot(tc_fun(_1056191, tc_HOL_Obool)), -(hAPP(_1056199, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1056191, tc_HOL_Obool)), _1056201), _1056203)) = hAPP(hAPP(_1056193, hAPP(_1056199, _1056201)), hAPP(_1056199, _1056203)))], (14699 ^ _782435) ^ [_1056578, _1056580, _1056582, _1056584, _1056586, _1056588, _1056590, _1056592] : [c_Finite__Set_Ofolding__image__simple(_1056578, _1056580, _1056582, _1056584, _1056586, _1056588), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056580), _1056590)), -(hAPP(_1056588, hAPP(hAPP(c_Set_Oinsert(_1056580), _1056592), _1056590)) = hAPP(hAPP(_1056582, hAPP(_1056586, _1056592)), hAPP(_1056588, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056580, tc_HOL_Obool)), _1056590), hAPP(hAPP(c_Set_Oinsert(_1056580), _1056592), c_Orderings_Obot__class_Obot(tc_fun(_1056580, tc_HOL_Obool)))))))], (14709 ^ _782435) ^ [_1056841, _1056843, _1056845] : [class_Lattices_Olattice(_1056841), hBOOL(hAPP(c_Finite__Set_Ofinite(_1056841), _1056843)), hBOOL(hAPP(hAPP(c_member(_1056841), _1056845), _1056843)), 14720 ^ _782435 : [(14721 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056841, tc_HOL_Obool)), _1056843), hAPP(hAPP(c_Set_Oinsert(_1056841), _1056845), c_Orderings_Obot__class_Obot(tc_fun(_1056841, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1056841, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1056841, _1056843) = _1056845)], (14727 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056841, tc_HOL_Obool)), _1056843), hAPP(hAPP(c_Set_Oinsert(_1056841), _1056845), c_Orderings_Obot__class_Obot(tc_fun(_1056841, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1056841, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1056841, _1056843) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1056841), _1056845), c_Big__Operators_Olattice__class_OInf__fin(_1056841, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1056841, tc_HOL_Obool)), _1056843), hAPP(hAPP(c_Set_Oinsert(_1056841), _1056845), c_Orderings_Obot__class_Obot(tc_fun(_1056841, tc_HOL_Obool)))))))]]], (14733 ^ _782435) ^ [_1057347, _1057349, _1057351, _1057353, _1057355, _1057357, _1057359, _1057361, _1057363, _1057365, _1057367] : [c_Finite__Set_Ofolding(_1057347, _1057349, _1057351, _1057353), -(hAPP(c_Fun_Ocomp(_1057355, _1057357, _1057359, _1057361), hAPP(c_Fun_Ocomp(_1057363, _1057355, _1057359, _1057365), _1057367)) = hAPP(c_Fun_Ocomp(_1057363, _1057357, _1057359, hAPP(c_Fun_Ocomp(_1057355, _1057357, _1057363, _1057361), _1057365)), _1057367))], (14739 ^ _782435) ^ [_1057510, _1057512, _1057514, _1057516, _1057518, _1057520] : [c_Finite__Set_Ofolding(_1057510, _1057512, _1057514, _1057516), -(hAPP(c_Fun_Ocomp(_1057512, _1057512, _1057512, hAPP(_1057514, _1057518)), hAPP(_1057514, _1057520)) = hAPP(c_Fun_Ocomp(_1057512, _1057512, _1057512, hAPP(_1057514, _1057520)), hAPP(_1057514, _1057518)))], (14745 ^ _782435) ^ [_1057655, _1057657, _1057659, _1057661, _1057663, _1057665, _1057667, _1057669] : [c_Finite__Set_Ofolding(_1057655, _1057657, _1057659, _1057661), -(hAPP(c_Fun_Ocomp(_1057657, _1057657, _1057663, hAPP(_1057659, _1057665)), hAPP(c_Fun_Ocomp(_1057657, _1057657, _1057663, hAPP(_1057659, _1057667)), _1057669)) = hAPP(c_Fun_Ocomp(_1057657, _1057657, _1057663, hAPP(_1057659, _1057667)), hAPP(c_Fun_Ocomp(_1057657, _1057657, _1057663, hAPP(_1057659, _1057665)), _1057669)))], (14751 ^ _782435) ^ [_1057836, _1057838, _1057840, _1057842, _1057844, _1057846] : [c_Finite__Set_Ofolding__image__simple(_1057836, _1057838, _1057840, _1057842, _1057844, _1057846), -(hAPP(_1057846, c_Orderings_Obot__class_Obot(tc_fun(_1057838, tc_HOL_Obool))) = _1057842)], (14757 ^ _782435) ^ [_1057945, _1057947] : [class_Lattices_Olattice(_1057945), -(c_Big__Operators_Olattice__class_OInf__fin(_1057945, hAPP(hAPP(c_Set_Oinsert(_1057945), _1057947), c_Orderings_Obot__class_Obot(tc_fun(_1057945, tc_HOL_Obool)))) = _1057947)], (14763 ^ _782435) ^ [_1058052, _1058054, _1058056, _1058058, _1058060, _1058062, _1058064, _1058066] : [c_Finite__Set_Ofolding__image(_1058052, _1058054, _1058056, _1058058, _1058060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058054), _1058062)), -(hAPP(hAPP(_1058060, hAPP(hAPP(c_COMBS(_1058054, _1058052, _1058052), hAPP(hAPP(c_COMBB(_1058052, tc_fun(_1058052, _1058052), _1058054), _1058056), _1058064)), _1058066)), _1058062) = hAPP(hAPP(_1058056, hAPP(hAPP(_1058060, _1058064), _1058062)), hAPP(hAPP(_1058060, _1058066), _1058062)))], (14773 ^ _782435) ^ [_1058313, _1058315, _1058317, _1058319, _1058321, _1058323, _1058325, _1058327] : [c_Finite__Set_Ofolding(_1058313, _1058315, _1058317, _1058319), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058313), _1058321)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058313), _1058323)), -(hAPP(c_Fun_Ocomp(_1058315, _1058315, _1058325, hAPP(_1058319, _1058323)), hAPP(c_Fun_Ocomp(_1058315, _1058315, _1058325, hAPP(_1058319, _1058321)), _1058327)) = hAPP(c_Fun_Ocomp(_1058315, _1058315, _1058325, hAPP(_1058319, _1058321)), hAPP(c_Fun_Ocomp(_1058315, _1058315, _1058325, hAPP(_1058319, _1058323)), _1058327)))], (14787 ^ _782435) ^ [_1058638, _1058640, _1058642, _1058644, _1058646, _1058648] : [c_Finite__Set_Ofolding(_1058638, _1058640, _1058642, _1058644), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058638), _1058646)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058638), _1058648)), -(hAPP(c_Fun_Ocomp(_1058640, _1058640, _1058640, hAPP(_1058644, _1058648)), hAPP(_1058644, _1058646)) = hAPP(c_Fun_Ocomp(_1058640, _1058640, _1058640, hAPP(_1058644, _1058646)), hAPP(_1058644, _1058648)))], (14801 ^ _782435) ^ [_1058919, _1058921, _1058923, _1058925, _1058927, _1058929, _1058931, _1058933] : [c_Finite__Set_Ofolding(_1058919, _1058921, _1058923, _1058925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1058919), _1058927)), -(hAPP(c_Fun_Ocomp(_1058921, _1058921, _1058929, hAPP(_1058923, _1058931)), hAPP(c_Fun_Ocomp(_1058921, _1058921, _1058929, hAPP(_1058925, _1058927)), _1058933)) = hAPP(c_Fun_Ocomp(_1058921, _1058921, _1058929, hAPP(_1058925, _1058927)), hAPP(c_Fun_Ocomp(_1058921, _1058921, _1058929, hAPP(_1058923, _1058931)), _1058933)))], (14811 ^ _782435) ^ [_1059172, _1059174, _1059176, _1059178, _1059180, _1059182] : [c_Finite__Set_Ofolding(_1059172, _1059174, _1059176, _1059178), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059172), _1059180)), -(hAPP(c_Fun_Ocomp(_1059174, _1059174, _1059174, hAPP(_1059176, _1059182)), hAPP(_1059178, _1059180)) = hAPP(c_Fun_Ocomp(_1059174, _1059174, _1059174, hAPP(_1059178, _1059180)), hAPP(_1059176, _1059182)))], (14821 ^ _782435) ^ [_1059385, _1059387, _1059389] : [class_Lattices_Olattice(_1059385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059385), _1059387)), hBOOL(hAPP(hAPP(c_member(_1059385), _1059389), _1059387)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1059385), _1059389), c_Big__Operators_Olattice__class_OInf__fin(_1059385, _1059387)) = _1059389)], (14835 ^ _782435) ^ [_1059614, _1059616, _1059618] : [class_Lattices_Olattice(_1059614), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059614), _1059616)), hBOOL(hAPP(hAPP(c_member(_1059614), _1059618), _1059616)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1059614), _1059618), c_Big__Operators_Olattice__class_OInf__fin(_1059614, _1059616)) = c_Big__Operators_Olattice__class_OInf__fin(_1059614, _1059616))], (14849 ^ _782435) ^ [_1059849, _1059851] : [class_Complete__Lattice_Ocomplete__lattice(_1059849), hBOOL(hAPP(c_Finite__Set_Ofinite(_1059849), _1059851)), -(_1059851 = c_Orderings_Obot__class_Obot(tc_fun(_1059849, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1059849, _1059851) = c_Complete__Lattice_OInf__class_OInf(_1059849, _1059851))], (14863 ^ _782435) ^ [_1060021, _1060023, _1060025] : [class_Lattices_Olattice(_1060021), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060021), _1060023)), -(_1060023 = c_Orderings_Obot__class_Obot(tc_fun(_1060021, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060021, hAPP(hAPP(c_Set_Oinsert(_1060021), _1060025), _1060023)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060021), _1060025), c_Big__Operators_Olattice__class_OInf__fin(_1060021, _1060023)))], (14877 ^ _782435) ^ [_1060229, _1060231, _1060233] : [class_Lattices_Olattice(_1060229), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060229), _1060231)), -(_1060233 = c_Orderings_Obot__class_Obot(tc_fun(_1060229, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1060229, tc_HOL_Obool)), _1060233), _1060231)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060229), c_Big__Operators_Olattice__class_OInf__fin(_1060229, _1060233)), c_Big__Operators_Olattice__class_OInf__fin(_1060229, _1060231)) = c_Big__Operators_Olattice__class_OInf__fin(_1060229, _1060231))], (14895 ^ _782435) ^ [_1060543, _1060545, _1060547] : [class_Lattices_Olattice(_1060543), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060543), _1060545)), -(_1060545 = c_Orderings_Obot__class_Obot(tc_fun(_1060543, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060543), _1060547)), -(_1060547 = c_Orderings_Obot__class_Obot(tc_fun(_1060543, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1060543, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1060543, tc_HOL_Obool)), _1060545), _1060547)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1060543), c_Big__Operators_Olattice__class_OInf__fin(_1060543, _1060545)), c_Big__Operators_Olattice__class_OInf__fin(_1060543, _1060547)))], (14917 ^ _782435) ^ [_1060892, _1060894, _1060896, _1060898, _1060900, _1060902, _1060904, _1060906] : [c_Finite__Set_Ofolding__image__simple(_1060892, _1060894, _1060896, _1060898, _1060900, _1060902), hBOOL(hAPP(c_Finite__Set_Ofinite(_1060894), _1060904)), -(hBOOL(hAPP(hAPP(c_member(_1060894), _1060906), _1060904))), -(hAPP(_1060902, hAPP(hAPP(c_Set_Oinsert(_1060894), _1060906), _1060904)) = hAPP(hAPP(_1060896, hAPP(_1060900, _1060906)), hAPP(_1060902, _1060904)))], (14931 ^ _782435) ^ [_1061136, _1061138, _1061140, _1061142, _1061144, _1061146, _1061148, _1061150] : [c_Finite__Set_Ofolding__image__simple(_1061136, _1061138, _1061140, _1061142, _1061144, _1061146), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061138), _1061148)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061138), _1061150)), -(hAPP(hAPP(_1061140, hAPP(_1061146, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1061138, tc_HOL_Obool)), _1061148), _1061150))), hAPP(_1061146, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1061138, tc_HOL_Obool)), _1061148), _1061150))) = hAPP(hAPP(_1061140, hAPP(_1061146, _1061148)), hAPP(_1061146, _1061150)))], (14945 ^ _782435) ^ [_1061469, _1061471, _1061473] : [class_Lattices_Olattice(_1061469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061469), _1061471)), -(hBOOL(hAPP(hAPP(c_member(_1061469), _1061473), _1061471))), -(_1061471 = c_Orderings_Obot__class_Obot(tc_fun(_1061469, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061469, hAPP(hAPP(c_Set_Oinsert(_1061469), _1061473), _1061471)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061469), _1061473), c_Big__Operators_Olattice__class_OInf__fin(_1061469, _1061471)))], (14963 ^ _782435) ^ [_1061706, _1061708, _1061710] : [class_Lattices_Olattice(_1061706), hBOOL(hAPP(c_Finite__Set_Ofinite(_1061706), _1061708)), 14970 ^ _782435 : [(14971 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061706, tc_HOL_Obool)), _1061708), hAPP(hAPP(c_Set_Oinsert(_1061706), _1061710), c_Orderings_Obot__class_Obot(tc_fun(_1061706, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1061706, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1061706, hAPP(hAPP(c_Set_Oinsert(_1061706), _1061710), _1061708)) = _1061710)], (14977 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061706, tc_HOL_Obool)), _1061708), hAPP(hAPP(c_Set_Oinsert(_1061706), _1061710), c_Orderings_Obot__class_Obot(tc_fun(_1061706, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1061706, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OInf__fin(_1061706, hAPP(hAPP(c_Set_Oinsert(_1061706), _1061710), _1061708)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1061706), _1061710), c_Big__Operators_Olattice__class_OInf__fin(_1061706, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1061706, tc_HOL_Obool)), _1061708), hAPP(hAPP(c_Set_Oinsert(_1061706), _1061710), c_Orderings_Obot__class_Obot(tc_fun(_1061706, tc_HOL_Obool)))))))]]], (14983 ^ _782435) ^ [_1062176, _1062178, _1062180] : [class_Lattices_Olattice(_1062176), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062176), _1062178)), -(_1062178 = c_Orderings_Obot__class_Obot(tc_fun(_1062176, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062176), _1062180)), -(_1062180 = c_Orderings_Obot__class_Obot(tc_fun(_1062176, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062176, tc_HOL_Obool)), _1062178), _1062180) = c_Orderings_Obot__class_Obot(tc_fun(_1062176, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OInf__fin(_1062176, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062176, tc_HOL_Obool)), _1062178), _1062180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062176), c_Big__Operators_Olattice__class_OInf__fin(_1062176, _1062178)), c_Big__Operators_Olattice__class_OInf__fin(_1062176, _1062180)))], (15009 ^ _782435) ^ [_1062653, _1062655, _1062657] : [class_Lattices_Olattice(_1062653), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062653), _1062655)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1062653), _1062657)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062653, tc_HOL_Obool)), _1062655), _1062657) = c_Orderings_Obot__class_Obot(tc_fun(_1062653, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062653), c_Big__Operators_Olattice__class_OInf__fin(_1062653, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1062653, tc_HOL_Obool)), _1062655), _1062657))), c_Big__Operators_Olattice__class_OInf__fin(_1062653, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1062653, tc_HOL_Obool)), _1062655), _1062657))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1062653), c_Big__Operators_Olattice__class_OInf__fin(_1062653, _1062655)), c_Big__Operators_Olattice__class_OInf__fin(_1062653, _1062657)))], (15027 ^ _782435) ^ [_1063001, _1063003, _1063005, _1063007, _1063009, _1063011] : [c_Finite__Set_Ofolding(_1063001, _1063003, _1063005, _1063007), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063001), _1063009)), -(hBOOL(hAPP(hAPP(c_member(_1063001), _1063011), _1063009))), -(hAPP(_1063007, hAPP(hAPP(c_Set_Oinsert(_1063001), _1063011), _1063009)) = hAPP(c_Fun_Ocomp(_1063003, _1063003, _1063003, hAPP(_1063007, _1063009)), hAPP(_1063005, _1063011)))], (15041 ^ _782435) ^ [_1063237, _1063239, _1063241, _1063243, _1063245, _1063247] : [c_Finite__Set_Ofolding(_1063237, _1063239, _1063241, _1063243), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063237), _1063245)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063237), _1063247)), -(hAPP(c_Fun_Ocomp(_1063239, _1063239, _1063239, hAPP(_1063243, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1063237, tc_HOL_Obool)), _1063245), _1063247))), hAPP(_1063243, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1063237, tc_HOL_Obool)), _1063245), _1063247))) = hAPP(c_Fun_Ocomp(_1063239, _1063239, _1063239, hAPP(_1063243, _1063245)), hAPP(_1063243, _1063247)))], (15055 ^ _782435) ^ [_1063562, _1063564] : [class_Lattices_Olattice(_1063562), hBOOL(hAPP(c_Finite__Set_Ofinite(_1063562), _1063564)), -(_1063564 = c_Orderings_Obot__class_Obot(tc_fun(_1063562, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1063562), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1063562), 15068 ^ [_1063562, _1063564]), 15069 ^ [_1063562, _1063564])), hAPP(hAPP(c_Set_Oinsert(_1063562), 15068 ^ [_1063562, _1063564]), hAPP(hAPP(c_Set_Oinsert(_1063562), 15069 ^ [_1063562, _1063564]), c_Orderings_Obot__class_Obot(tc_fun(_1063562, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1063562), c_Big__Operators_Olattice__class_OInf__fin(_1063562, _1063564)), _1063564)))], (15075 ^ _782435) ^ [_1064006, _1064008] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1064006, tc_HOL_Obool)), _1064008)), 15081 ^ _782435 : [(15082 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1064006, tc_HOL_Obool)), 15080 ^ [_1064006, _1064008]), _1064008)))], (15084 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1064006), 15080 ^ [_1064006, _1064008]))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1064006), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1064006, tc_HOL_Obool), _1064008))))], (15088 ^ _782435) ^ [_1064265, _1064267, _1064269] : [class_Lattices_Olattice(_1064265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064265), _1064267)), hBOOL(hAPP(hAPP(c_member(_1064265), _1064269), _1064267)), 15099 ^ _782435 : [(15100 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064265, tc_HOL_Obool)), _1064267), hAPP(hAPP(c_Set_Oinsert(_1064265), _1064269), c_Orderings_Obot__class_Obot(tc_fun(_1064265, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1064265, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1064265, _1064267) = _1064269)], (15106 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064265, tc_HOL_Obool)), _1064267), hAPP(hAPP(c_Set_Oinsert(_1064265), _1064269), c_Orderings_Obot__class_Obot(tc_fun(_1064265, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1064265, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1064265, _1064267) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1064265), _1064269), c_Big__Operators_Olattice__class_OSup__fin(_1064265, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1064265, tc_HOL_Obool)), _1064267), hAPP(hAPP(c_Set_Oinsert(_1064265), _1064269), c_Orderings_Obot__class_Obot(tc_fun(_1064265, tc_HOL_Obool)))))))]]], (15112 ^ _782435) ^ [_1064771, _1064773, _1064775, _1064777, _1064779, _1064781] : [c_Finite__Set_Ofolding__idem(_1064771, _1064773, _1064775, _1064777), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064771), _1064779)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1064771), _1064781)), -(hAPP(_1064777, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1064771, tc_HOL_Obool)), _1064779), _1064781)) = hAPP(c_Fun_Ocomp(_1064773, _1064773, _1064773, hAPP(_1064777, _1064779)), hAPP(_1064777, _1064781)))], (15126 ^ _782435) ^ [_1065052, _1065054, _1065056, _1065058, _1065060, _1065062] : [c_Finite__Set_Ofolding__idem(_1065052, _1065054, _1065056, _1065058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065052), _1065060)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1065052, tc_HOL_Obool)), _1065062), _1065060)), -(hAPP(c_Fun_Ocomp(_1065054, _1065054, _1065054, hAPP(_1065058, _1065060)), hAPP(_1065058, _1065062)) = hAPP(_1065058, _1065060))], (15140 ^ _782435) ^ [_1065323, _1065325, _1065327, _1065329, _1065331, _1065333] : [c_Finite__Set_Ofolding__idem(_1065323, _1065325, _1065327, _1065329), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065323), _1065331)), -(hAPP(_1065329, hAPP(hAPP(c_Set_Oinsert(_1065323), _1065333), _1065331)) = hAPP(c_Fun_Ocomp(_1065325, _1065325, _1065325, hAPP(_1065329, _1065331)), hAPP(_1065327, _1065333)))], (15150 ^ _782435) ^ [_1065530, _1065532, _1065534, _1065536] : [c_Finite__Set_Ofolding__one(_1065530, _1065532, _1065534), hBOOL(hAPP(c_Finite__Set_Ofinite(_1065530), _1065536)), -(_1065536 = c_Orderings_Obot__class_Obot(tc_fun(_1065530, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1065530), hAPP(hAPP(_1065532, 15163 ^ [_1065530, _1065532, _1065534, _1065536]), 15164 ^ [_1065530, _1065532, _1065534, _1065536])), hAPP(hAPP(c_Set_Oinsert(_1065530), 15163 ^ [_1065530, _1065532, _1065534, _1065536]), hAPP(hAPP(c_Set_Oinsert(_1065530), 15164 ^ [_1065530, _1065532, _1065534, _1065536]), c_Orderings_Obot__class_Obot(tc_fun(_1065530, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1065530), hAPP(_1065534, _1065536)), _1065536)))], (15170 ^ _782435) ^ [_1066016, _1066018, _1066020, _1066022, _1066024, _1066026] : [c_Finite__Set_Ofolding__idem(_1066016, _1066018, _1066020, _1066022), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066016), _1066024)), hBOOL(hAPP(hAPP(c_member(_1066016), _1066026), _1066024)), -(hAPP(c_Fun_Ocomp(_1066018, _1066018, _1066018, hAPP(_1066022, _1066024)), hAPP(_1066020, _1066026)) = hAPP(_1066022, _1066024))], (15184 ^ _782435) ^ [_1066281, _1066283] : [class_Lattices_Olattice(_1066281), -(c_Big__Operators_Olattice__class_OSup__fin(_1066281, hAPP(hAPP(c_Set_Oinsert(_1066281), _1066283), c_Orderings_Obot__class_Obot(tc_fun(_1066281, tc_HOL_Obool)))) = _1066283)], (15190 ^ _782435) ^ [_1066388, _1066390, _1066392, _1066394, _1066396, _1066398, _1066400] : [c_Finite__Set_Ofolding__idem(_1066388, _1066390, _1066392, _1066394), -(hAPP(c_Fun_Ocomp(_1066390, _1066390, _1066396, hAPP(_1066392, _1066398)), hAPP(c_Fun_Ocomp(_1066390, _1066390, _1066396, hAPP(_1066392, _1066398)), _1066400)) = hAPP(c_Fun_Ocomp(_1066390, _1066390, _1066396, hAPP(_1066392, _1066398)), _1066400))], (15196 ^ _782435) ^ [_1066545, _1066547, _1066549, _1066551, _1066553] : [c_Finite__Set_Ofolding__idem(_1066545, _1066547, _1066549, _1066551), -(hAPP(c_Fun_Ocomp(_1066547, _1066547, _1066547, hAPP(_1066549, _1066553)), hAPP(_1066549, _1066553)) = hAPP(_1066549, _1066553))], (15202 ^ _782435) ^ [_1066666, _1066668, _1066670] : [class_Lattices_Olattice(_1066666), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066666), _1066668)), hBOOL(hAPP(hAPP(c_member(_1066666), _1066670), _1066668)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1066666), _1066670), c_Big__Operators_Olattice__class_OSup__fin(_1066666, _1066668)) = c_Big__Operators_Olattice__class_OSup__fin(_1066666, _1066668))], (15216 ^ _782435) ^ [_1066901, _1066903, _1066905] : [class_Lattices_Olattice(_1066901), hBOOL(hAPP(c_Finite__Set_Ofinite(_1066901), _1066903)), hBOOL(hAPP(hAPP(c_member(_1066901), _1066905), _1066903)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1066901), _1066905), c_Big__Operators_Olattice__class_OSup__fin(_1066901, _1066903)) = _1066905)], (15230 ^ _782435) ^ [_1067130, _1067132] : [class_Complete__Lattice_Ocomplete__lattice(_1067130), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067130), _1067132)), -(_1067132 = c_Orderings_Obot__class_Obot(tc_fun(_1067130, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067130, _1067132) = c_Complete__Lattice_OSup__class_OSup(_1067130, _1067132))], (15244 ^ _782435) ^ [_1067302, _1067304, _1067306] : [class_Lattices_Olattice(_1067302), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067302), _1067304)), -(_1067304 = c_Orderings_Obot__class_Obot(tc_fun(_1067302, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067302, hAPP(hAPP(c_Set_Oinsert(_1067302), _1067306), _1067304)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067302), _1067306), c_Big__Operators_Olattice__class_OSup__fin(_1067302, _1067304)))], (15258 ^ _782435) ^ [_1067510, _1067512, _1067514] : [class_Lattices_Olattice(_1067510), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067510), _1067512)), -(_1067514 = c_Orderings_Obot__class_Obot(tc_fun(_1067510, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1067510, tc_HOL_Obool)), _1067514), _1067512)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067510), c_Big__Operators_Olattice__class_OSup__fin(_1067510, _1067514)), c_Big__Operators_Olattice__class_OSup__fin(_1067510, _1067512)) = c_Big__Operators_Olattice__class_OSup__fin(_1067510, _1067512))], (15276 ^ _782435) ^ [_1067824, _1067826, _1067828] : [class_Lattices_Olattice(_1067824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067824), _1067826)), -(_1067826 = c_Orderings_Obot__class_Obot(tc_fun(_1067824, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1067824), _1067828)), -(_1067828 = c_Orderings_Obot__class_Obot(tc_fun(_1067824, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1067824, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1067824, tc_HOL_Obool)), _1067826), _1067828)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1067824), c_Big__Operators_Olattice__class_OSup__fin(_1067824, _1067826)), c_Big__Operators_Olattice__class_OSup__fin(_1067824, _1067828)))], (15298 ^ _782435) ^ [_1068173, _1068175] : [class_Lattices_Olattice(_1068173), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068173), _1068175)), -(_1068175 = c_Orderings_Obot__class_Obot(tc_fun(_1068173, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1068173), c_Big__Operators_Olattice__class_OInf__fin(_1068173, _1068175)), c_Big__Operators_Olattice__class_OSup__fin(_1068173, _1068175))))], (15312 ^ _782435) ^ [_1068359, _1068361, _1068363] : [class_Lattices_Olattice(_1068359), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068359), _1068361)), -(hBOOL(hAPP(hAPP(c_member(_1068359), _1068363), _1068361))), -(_1068361 = c_Orderings_Obot__class_Obot(tc_fun(_1068359, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1068359, hAPP(hAPP(c_Set_Oinsert(_1068359), _1068363), _1068361)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068359), _1068363), c_Big__Operators_Olattice__class_OSup__fin(_1068359, _1068361)))], (15330 ^ _782435) ^ [_1068596, _1068598, _1068600] : [class_Lattices_Olattice(_1068596), hBOOL(hAPP(c_Finite__Set_Ofinite(_1068596), _1068598)), 15337 ^ _782435 : [(15338 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068596, tc_HOL_Obool)), _1068598), hAPP(hAPP(c_Set_Oinsert(_1068596), _1068600), c_Orderings_Obot__class_Obot(tc_fun(_1068596, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068596, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1068596, hAPP(hAPP(c_Set_Oinsert(_1068596), _1068600), _1068598)) = _1068600)], (15344 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068596, tc_HOL_Obool)), _1068598), hAPP(hAPP(c_Set_Oinsert(_1068596), _1068600), c_Orderings_Obot__class_Obot(tc_fun(_1068596, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1068596, tc_HOL_Obool))), -(c_Big__Operators_Olattice__class_OSup__fin(_1068596, hAPP(hAPP(c_Set_Oinsert(_1068596), _1068600), _1068598)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1068596), _1068600), c_Big__Operators_Olattice__class_OSup__fin(_1068596, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1068596, tc_HOL_Obool)), _1068598), hAPP(hAPP(c_Set_Oinsert(_1068596), _1068600), c_Orderings_Obot__class_Obot(tc_fun(_1068596, tc_HOL_Obool)))))))]]], (15350 ^ _782435) ^ [_1069066, _1069068, _1069070] : [class_Lattices_Olattice(_1069066), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069066), _1069068)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069066), _1069070)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069066, tc_HOL_Obool)), _1069068), _1069070) = c_Orderings_Obot__class_Obot(tc_fun(_1069066, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069066), c_Big__Operators_Olattice__class_OSup__fin(_1069066, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069066, tc_HOL_Obool)), _1069068), _1069070))), c_Big__Operators_Olattice__class_OSup__fin(_1069066, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069066, tc_HOL_Obool)), _1069068), _1069070))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069066), c_Big__Operators_Olattice__class_OSup__fin(_1069066, _1069068)), c_Big__Operators_Olattice__class_OSup__fin(_1069066, _1069070)))], (15368 ^ _782435) ^ [_1069414, _1069416, _1069418] : [class_Lattices_Olattice(_1069414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069414), _1069416)), -(_1069416 = c_Orderings_Obot__class_Obot(tc_fun(_1069414, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069414), _1069418)), -(_1069418 = c_Orderings_Obot__class_Obot(tc_fun(_1069414, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1069414, tc_HOL_Obool)), _1069416), _1069418) = c_Orderings_Obot__class_Obot(tc_fun(_1069414, tc_HOL_Obool)), -(c_Big__Operators_Olattice__class_OSup__fin(_1069414, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1069414, tc_HOL_Obool)), _1069416), _1069418)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069414), c_Big__Operators_Olattice__class_OSup__fin(_1069414, _1069416)), c_Big__Operators_Olattice__class_OSup__fin(_1069414, _1069418)))], (15394 ^ _782435) ^ [_1069891, _1069893] : [class_Lattices_Olattice(_1069891), hBOOL(hAPP(c_Finite__Set_Ofinite(_1069891), _1069893)), -(_1069893 = c_Orderings_Obot__class_Obot(tc_fun(_1069891, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1069891), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1069891), 15407 ^ [_1069891, _1069893]), 15408 ^ [_1069891, _1069893])), hAPP(hAPP(c_Set_Oinsert(_1069891), 15407 ^ [_1069891, _1069893]), hAPP(hAPP(c_Set_Oinsert(_1069891), 15408 ^ [_1069891, _1069893]), c_Orderings_Obot__class_Obot(tc_fun(_1069891, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1069891), c_Big__Operators_Olattice__class_OSup__fin(_1069891, _1069893)), _1069893)))], (15414 ^ _782435) ^ [_1070335, _1070337, _1070339] : [class_Lattices_Olattice(_1070335), hAPP(_1070337, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070335), 15419 ^ [_1070335, _1070337, _1070339]), 15420 ^ [_1070335, _1070337, _1070339])) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1070335), hAPP(_1070337, 15419 ^ [_1070335, _1070337, _1070339])), hAPP(_1070337, 15420 ^ [_1070335, _1070337, _1070339])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070335), _1070339)), -(_1070339 = c_Orderings_Obot__class_Obot(tc_fun(_1070335, tc_HOL_Obool))), -(hAPP(_1070337, c_Big__Operators_Olattice__class_OInf__fin(_1070335, _1070339)) = c_Big__Operators_Olattice__class_OInf__fin(_1070335, hAPP(c_Set_Oimage(_1070335, _1070335, _1070337), _1070339)))], (15434 ^ _782435) ^ [_1070738, _1070740, _1070742] : [class_Lattices_Olattice(_1070738), hAPP(_1070740, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070738), 15439 ^ [_1070738, _1070740, _1070742]), 15440 ^ [_1070738, _1070740, _1070742])) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1070738), hAPP(_1070740, 15439 ^ [_1070738, _1070740, _1070742])), hAPP(_1070740, 15440 ^ [_1070738, _1070740, _1070742])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1070738), _1070742)), -(_1070742 = c_Orderings_Obot__class_Obot(tc_fun(_1070738, tc_HOL_Obool))), -(hAPP(_1070740, c_Big__Operators_Olattice__class_OSup__fin(_1070738, _1070742)) = c_Big__Operators_Olattice__class_OSup__fin(_1070738, hAPP(c_Set_Oimage(_1070738, _1070738, _1070740), _1070742)))], (15454 ^ _782435) ^ [_1071141, _1071143, _1071145] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1071141), _1071143)), hBOOL(hAPP(_1071145, _1071143)), 15465 ^ _782435 : [(15466 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1071141), 15464 ^ [_1071141, _1071143, _1071145])))], (15468 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1071141), 15463 ^ [_1071141, _1071143, _1071145]), 15464 ^ [_1071141, _1071143, _1071145])))], (15470 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1071145, 15464 ^ [_1071141, _1071143, _1071145])))], (15472 ^ _782435) ^ [] : [hBOOL(hAPP(_1071145, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1071141, tc_HOL_Obool)), 15464 ^ [_1071141, _1071143, _1071145]), hAPP(hAPP(c_Set_Oinsert(_1071141), 15463 ^ [_1071141, _1071143, _1071145]), c_Orderings_Obot__class_Obot(tc_fun(_1071141, tc_HOL_Obool))))))]], -(hBOOL(hAPP(_1071145, c_Orderings_Obot__class_Obot(tc_fun(_1071141, tc_HOL_Obool)))))], (15476 ^ _782435) ^ [_1071666, _1071668, _1071670, _1071672, _1071674] : [c_Finite__Set_Ofolding__one__idem(_1071666, _1071668, _1071670), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071666), _1071672)), -(_1071672 = c_Orderings_Obot__class_Obot(tc_fun(_1071666, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1071666), _1071674)), -(_1071674 = c_Orderings_Obot__class_Obot(tc_fun(_1071666, tc_HOL_Obool))), -(hAPP(_1071670, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1071666, tc_HOL_Obool)), _1071672), _1071674)) = hAPP(hAPP(_1071668, hAPP(_1071670, _1071672)), hAPP(_1071670, _1071674)))], (15498 ^ _782435) ^ [_1072031, _1072033, _1072035, _1072037] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1072031), _1072033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072031, tc_HOL_Obool)), _1072033), _1072035)), hBOOL(hAPP(_1072037, c_Orderings_Obot__class_Obot(tc_fun(_1072031, tc_HOL_Obool)))), 15513 ^ _782435 : [(15514 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1072031), 15512 ^ [_1072031, _1072033, _1072035, _1072037])))], (15516 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1072031), 15511 ^ [_1072031, _1072033, _1072035, _1072037]), _1072035)))], (15518 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1072031), 15511 ^ [_1072031, _1072033, _1072035, _1072037]), 15512 ^ [_1072031, _1072033, _1072035, _1072037]))], (15520 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1072037, 15512 ^ [_1072031, _1072033, _1072035, _1072037])))], (15522 ^ _782435) ^ [] : [hBOOL(hAPP(_1072037, hAPP(hAPP(c_Set_Oinsert(_1072031), 15511 ^ [_1072031, _1072033, _1072035, _1072037]), 15512 ^ [_1072031, _1072033, _1072035, _1072037])))]], -(hBOOL(hAPP(_1072037, _1072033)))], (15526 ^ _782435) ^ [_1072696, _1072698, _1072700, _1072702, _1072704] : [c_Finite__Set_Ofolding__one__idem(_1072696, _1072698, _1072700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1072696), _1072702)), -(_1072704 = c_Orderings_Obot__class_Obot(tc_fun(_1072696, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1072696, tc_HOL_Obool)), _1072704), _1072702)), -(hAPP(hAPP(_1072698, hAPP(_1072700, _1072704)), hAPP(_1072700, _1072702)) = hAPP(_1072700, _1072702))], (15544 ^ _782435) ^ [_1073026, _1073028, _1073030, _1073032, _1073034] : [c_Finite__Set_Ofolding__one__idem(_1073026, _1073028, _1073030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073026), _1073032)), -(_1073032 = c_Orderings_Obot__class_Obot(tc_fun(_1073026, tc_HOL_Obool))), -(hAPP(_1073030, hAPP(hAPP(c_Set_Oinsert(_1073026), _1073034), _1073032)) = hAPP(hAPP(_1073028, _1073034), hAPP(_1073030, _1073032)))], (15558 ^ _782435) ^ [_1073242, _1073244, _1073246, _1073248] : [c_Finite__Set_Ofolding__one__idem(_1073242, _1073244, _1073246), -(hAPP(hAPP(_1073244, _1073248), _1073248) = _1073248)], (15564 ^ _782435) ^ [_1073337, _1073339, _1073341, _1073343, _1073345] : [c_Finite__Set_Ofolding__one__idem(_1073337, _1073339, _1073341), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073337), _1073343)), hBOOL(hAPP(hAPP(c_member(_1073337), _1073345), _1073343)), -(hAPP(hAPP(_1073339, _1073345), hAPP(_1073341, _1073343)) = hAPP(_1073341, _1073343))], (15578 ^ _782435) ^ [_1073584, _1073586, _1073588, _1073590] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1073584), _1073586)), -(hAPP(c_Set_Oimage(_1073584, _1073588, _1073590), _1073586) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(_1073588, tc_HOL_Obool), _1073584, c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073588, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1073584, tc_fun(_1073588, tc_HOL_Obool), tc_fun(_1073588, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(_1073588, tc_fun(tc_fun(_1073588, tc_HOL_Obool), tc_fun(_1073588, tc_HOL_Obool)), _1073584), c_Set_Oinsert(_1073588)), _1073590)), c_Orderings_Obot__class_Obot(tc_fun(_1073588, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(_1073588, tc_HOL_Obool))), _1073586))], (15584 ^ _782435) ^ [_1073823, _1073825, _1073827] : [class_Groups_Oab__semigroup__mult(_1073823), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073823), _1073825)), -(_1073825 = c_Orderings_Obot__class_Obot(tc_fun(_1073823, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1073823), _1073827)), -(_1073827 = c_Orderings_Obot__class_Obot(tc_fun(_1073823, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1073823, tc_HOL_Obool)), _1073825), _1073827) = c_Orderings_Obot__class_Obot(tc_fun(_1073823, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ofold1(_1073823, c_Groups_Otimes__class_Otimes(_1073823)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1073823, tc_HOL_Obool)), _1073825), _1073827)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1073823), hAPP(c_Finite__Set_Ofold1(_1073823, c_Groups_Otimes__class_Otimes(_1073823)), _1073825)), hAPP(c_Finite__Set_Ofold1(_1073823, c_Groups_Otimes__class_Otimes(_1073823)), _1073827)))], (15610 ^ _782435) ^ [_1074330, _1074332, _1074334, _1074336, _1074338] : [c_Finite__Set_Ofolding__one__idem(_1074330, _1074332, _1074334), hAPP(_1074336, hAPP(hAPP(_1074332, 15615 ^ [_1074330, _1074332, _1074334, _1074336, _1074338]), 15616 ^ [_1074330, _1074332, _1074334, _1074336, _1074338])) = hAPP(hAPP(_1074332, hAPP(_1074336, 15615 ^ [_1074330, _1074332, _1074334, _1074336, _1074338])), hAPP(_1074336, 15616 ^ [_1074330, _1074332, _1074334, _1074336, _1074338])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074330), _1074338)), -(_1074338 = c_Orderings_Obot__class_Obot(tc_fun(_1074330, tc_HOL_Obool))), -(hAPP(_1074336, hAPP(_1074334, _1074338)) = hAPP(_1074334, hAPP(c_Set_Oimage(_1074330, _1074330, _1074336), _1074338)))], (15630 ^ _782435) ^ [_1074765, _1074767, _1074769, _1074771, _1074773, _1074775, _1074777, _1074779] : [c_Finite__Set_Ofolding__image__simple(_1074765, _1074767, _1074769, _1074771, _1074773, _1074775), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074767), _1074777)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1074767), _1074779)), 15644 ^ _782435 : [(15645 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1074767), 15643 ^ [_1074765, _1074767, _1074769, _1074771, _1074773, _1074775, _1074777, _1074779]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1074767, tc_HOL_Obool)), _1074777), _1074779))))], (15647 ^ _782435) ^ [] : [hAPP(_1074773, 15643 ^ [_1074765, _1074767, _1074769, _1074771, _1074773, _1074775, _1074777, _1074779]) = _1074771]], -(hAPP(_1074775, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1074767, tc_HOL_Obool)), _1074777), _1074779)) = hAPP(hAPP(_1074769, hAPP(_1074775, _1074777)), hAPP(_1074775, _1074779)))], (15651 ^ _782435) ^ [_1075266, _1075268, _1075270] : [class_Groups_Oab__semigroup__mult(_1075266), -(_1075268 = c_Orderings_Obot__class_Obot(tc_fun(_1075266, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075266), _1075268)), -(hBOOL(hAPP(hAPP(c_member(_1075266), _1075270), _1075268))), -(hAPP(c_Finite__Set_Ofold1(_1075266, c_Groups_Otimes__class_Otimes(_1075266)), hAPP(hAPP(c_Set_Oinsert(_1075266), _1075270), _1075268)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1075266), _1075270), hAPP(c_Finite__Set_Ofold1(_1075266, c_Groups_Otimes__class_Otimes(_1075266)), _1075268)))], (15669 ^ _782435) ^ [_1075565, _1075567, _1075569, _1075571, _1075573, _1075575, _1075577] : [class_Groups_Oab__semigroup__mult(_1075565), hBOOL(hAPP(c_Finite__Set_Ofinite(_1075567), _1075569)), c_Fun_Oinj__on(_1075567, _1075571, _1075573, _1075569), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075565, _1075571, c_Groups_Otimes__class_Otimes(_1075565)), _1075575), _1075577), hAPP(c_Set_Oimage(_1075567, _1075571, _1075573), _1075569)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1075565, _1075567, c_Groups_Otimes__class_Otimes(_1075565)), hAPP(c_Fun_Ocomp(_1075571, _1075565, _1075567, _1075575), _1075573)), _1075577), _1075569))], (15683 ^ _782435) ^ [_1075876, _1075878, _1075880, _1075882] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075876), _1075878)), 15689 ^ _782435 : [(15690 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1075876), 15688 ^ [_1075876, _1075878, _1075880, _1075882]), _1075878)))], (15692 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1075880), hAPP(_1075882, 15688 ^ [_1075876, _1075878, _1075880, _1075882])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1075880), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1075876, tc_fun(_1075880, tc_HOL_Obool)), _1075878), _1075882))))], (15696 ^ _782435) ^ [_1076163, _1076165, _1076167, _1076169, _1076171] : [-(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076163, _1076165, _1076167), _1076169), _1076171), c_Orderings_Obot__class_Obot(tc_fun(_1076165, tc_HOL_Obool))) = _1076171)], (15698 ^ _782435) ^ [_1076212, _1076214, _1076216, _1076218] : [_1076212 = c_Finite__Set_Ofold1(_1076214, _1076216), -(hAPP(_1076212, hAPP(hAPP(c_Set_Oinsert(_1076214), _1076218), c_Orderings_Obot__class_Obot(tc_fun(_1076214, tc_HOL_Obool)))) = _1076218)], (15704 ^ _782435) ^ [_1076331, _1076333, _1076335] : [-(hAPP(c_Finite__Set_Ofold1(_1076331, _1076333), hAPP(hAPP(c_Set_Oinsert(_1076331), _1076335), c_Orderings_Obot__class_Obot(tc_fun(_1076331, tc_HOL_Obool)))) = _1076335)], (15706 ^ _782435) ^ [_1076377, _1076379, _1076381, _1076383, _1076385, _1076387, _1076389] : [c_Finite__Set_Ofolding__image__simple(_1076377, _1076379, _1076381, _1076383, _1076385, _1076387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076379), _1076389)), -(hAPP(_1076387, _1076389) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076377, _1076379, _1076381), _1076385), _1076383), _1076389))], (15716 ^ _782435) ^ [_1076574, _1076576, _1076578, _1076580, _1076582, _1076584, _1076586] : [c_Finite__Set_Ofolding__image(_1076574, _1076576, _1076578, _1076580, _1076582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076576), _1076584)), -(hAPP(hAPP(_1076582, _1076586), _1076584) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1076574, _1076576, _1076578), _1076586), _1076580), _1076584))], (15726 ^ _782435) ^ [_1076775, _1076777, _1076779, _1076781] : [c_Finite__Set_Ofolding__one(_1076775, _1076777, _1076779), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076775), _1076781)), -(hAPP(_1076779, _1076781) = hAPP(c_Finite__Set_Ofold1(_1076775, _1076777), _1076781))], (15736 ^ _782435) ^ [_1076940, _1076942, _1076944] : [-(hAPP(c_Finite__Set_Ofold1(_1076940, _1076942), _1076944) = c_HOL_OThe(_1076940, c_Finite__Set_Ofold1Set(_1076940, _1076942, _1076944)))], (15738 ^ _782435) ^ [_1076980, _1076982] : [class_Lattices_Olattice(_1076980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1076980), _1076982)), -(c_Big__Operators_Olattice__class_OSup__fin(_1076980, _1076982) = hAPP(c_Finite__Set_Ofold1(_1076980, c_Lattices_Osemilattice__sup__class_Osup(_1076980)), _1076982))], (15748 ^ _782435) ^ [_1077137, _1077139] : [class_Lattices_Olattice(_1077137), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077137), _1077139)), -(c_Big__Operators_Olattice__class_OInf__fin(_1077137, _1077139) = hAPP(c_Finite__Set_Ofold1(_1077137, c_Lattices_Osemilattice__inf__class_Oinf(_1077137)), _1077139))], (15758 ^ _782435) ^ [_1077294, _1077296, _1077298, _1077300, _1077302, _1077304] : [class_Groups_Oab__semigroup__mult(_1077294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077296), _1077298)), -(hBOOL(hAPP(hAPP(c_member(_1077296), _1077300), _1077298))), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1077294, _1077296, c_Groups_Otimes__class_Otimes(_1077294)), _1077302), _1077304), hAPP(hAPP(c_Set_Oinsert(_1077296), _1077300), _1077298)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1077294), hAPP(_1077302, _1077300)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1077294, _1077296, c_Groups_Otimes__class_Otimes(_1077294)), _1077302), _1077304), _1077298)))], (15772 ^ _782435) ^ [_1077572, _1077574, _1077576] : [class_Lattices_Osemilattice__inf(_1077572), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077572), _1077574)), hBOOL(hAPP(hAPP(c_member(_1077572), _1077576), _1077574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077572), hAPP(c_Finite__Set_Ofold1(_1077572, c_Lattices_Osemilattice__inf__class_Oinf(_1077572)), _1077574)), _1077576)))], (15786 ^ _782435) ^ [_1077809, _1077811, _1077813] : [class_Lattices_Osemilattice__inf(_1077809), hBOOL(hAPP(c_Finite__Set_Ofinite(_1077809), _1077811)), -(_1077811 = c_Orderings_Obot__class_Obot(tc_fun(_1077809, tc_HOL_Obool))), 15797 ^ _782435 : [(15808 ^ _782435) ^ [] : [15810 ^ _782435 : [(15811 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1077809), 15809 ^ [_1077809, _1077811, _1077813]), _1077811)))], (15813 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077809), _1077813), 15809 ^ [_1077809, _1077811, _1077813]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077809), _1077813), hAPP(c_Finite__Set_Ofold1(_1077809, c_Lattices_Osemilattice__inf__class_Oinf(_1077809)), _1077811))))], (15798 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077809), _1077813), hAPP(c_Finite__Set_Ofold1(_1077809, c_Lattices_Osemilattice__inf__class_Oinf(_1077809)), _1077811))), 15801 ^ _782435 : [(15802 ^ _782435) ^ [_1078102] : [hBOOL(hAPP(hAPP(c_member(_1077809), _1078102), _1077811)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1077809), _1077813), _1078102)))]]]]], (15817 ^ _782435) ^ [_1078387, _1078389, _1078391] : [class_Lattices_Oab__semigroup__idem__mult(_1078387), -(_1078389 = c_Orderings_Obot__class_Obot(tc_fun(_1078387, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078387), _1078389)), -(hAPP(c_Finite__Set_Ofold1(_1078387, c_Groups_Otimes__class_Otimes(_1078387)), hAPP(hAPP(c_Set_Oinsert(_1078387), _1078391), _1078389)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078387), _1078391), hAPP(c_Finite__Set_Ofold1(_1078387, c_Groups_Otimes__class_Otimes(_1078387)), _1078389)))], (15831 ^ _782435) ^ [_1078657, _1078659, _1078661] : [class_Lattices_Oab__semigroup__idem__mult(_1078657), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078657), _1078659)), -(_1078659 = c_Orderings_Obot__class_Obot(tc_fun(_1078657, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1078657), _1078661)), -(_1078661 = c_Orderings_Obot__class_Obot(tc_fun(_1078657, tc_HOL_Obool))), -(hAPP(c_Finite__Set_Ofold1(_1078657, c_Groups_Otimes__class_Otimes(_1078657)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1078657, tc_HOL_Obool)), _1078659), _1078661)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1078657), hAPP(c_Finite__Set_Ofold1(_1078657, c_Groups_Otimes__class_Otimes(_1078657)), _1078659)), hAPP(c_Finite__Set_Ofold1(_1078657, c_Groups_Otimes__class_Otimes(_1078657)), _1078661)))], (15853 ^ _782435) ^ [_1079036, _1079038, _1079040, _1079042] : [c_Big__Operators_Osemilattice__big(_1079036, _1079038, _1079040), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079036), _1079042)), -(hAPP(_1079040, _1079042) = hAPP(c_Finite__Set_Ofold1(_1079036, _1079038), _1079042))], (15863 ^ _782435) ^ [_1079201, _1079203, _1079205, _1079207, _1079209, _1079211, _1079213] : [c_Big__Operators_Ocomm__monoid__big(_1079201, _1079203, _1079205, _1079207, _1079209), 15866 ^ _782435 : [(15867 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1079203), _1079211)), -(hAPP(hAPP(_1079209, _1079213), _1079211) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1079201, _1079203, _1079205), _1079213), _1079207), _1079211))], (15873 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1079203), _1079211))), -(hAPP(hAPP(_1079209, _1079213), _1079211) = _1079207)]]], (15879 ^ _782435) ^ [_1079469, _1079471] : [class_Groups_Oab__semigroup__mult(_1079469), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079469), _1079471)), -(_1079471 = c_Orderings_Obot__class_Obot(tc_fun(_1079469, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1079469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079469), 15892 ^ [_1079469, _1079471]), 15893 ^ [_1079469, _1079471])), hAPP(hAPP(c_Set_Oinsert(_1079469), 15892 ^ [_1079469, _1079471]), hAPP(hAPP(c_Set_Oinsert(_1079469), 15893 ^ [_1079469, _1079471]), c_Orderings_Obot__class_Obot(tc_fun(_1079469, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1079469), hAPP(c_Finite__Set_Ofold1(_1079469, c_Groups_Otimes__class_Otimes(_1079469)), _1079471)), _1079471)))], (15899 ^ _782435) ^ [_1079923, _1079925, _1079927] : [class_Lattices_Oab__semigroup__idem__mult(_1079923), hAPP(_1079925, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079923), 15904 ^ [_1079923, _1079925, _1079927]), 15905 ^ [_1079923, _1079925, _1079927])) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1079923), hAPP(_1079925, 15904 ^ [_1079923, _1079925, _1079927])), hAPP(_1079925, 15905 ^ [_1079923, _1079925, _1079927])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1079923), _1079927)), -(_1079927 = c_Orderings_Obot__class_Obot(tc_fun(_1079923, tc_HOL_Obool))), -(hAPP(_1079925, hAPP(c_Finite__Set_Ofold1(_1079923, c_Groups_Otimes__class_Otimes(_1079923)), _1079927)) = hAPP(c_Finite__Set_Ofold1(_1079923, c_Groups_Otimes__class_Otimes(_1079923)), hAPP(c_Set_Oimage(_1079923, _1079923, _1079925), _1079927)))], (15919 ^ _782435) ^ [_1080346, _1080348, _1080350, _1080352, _1080354] : [class_Groups_Ocomm__monoid__mult(_1080346), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080348), _1080350)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080348), _1080352)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1080348, tc_HOL_Obool)), _1080350), _1080352) = c_Orderings_Obot__class_Obot(tc_fun(_1080348, tc_HOL_Obool)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080346, _1080348, c_Groups_Otimes__class_Otimes(_1080346)), _1080354), c_Groups_Oone__class_Oone(_1080346)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1080348, tc_HOL_Obool)), _1080350), _1080352)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1080346), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080346, _1080348, c_Groups_Otimes__class_Otimes(_1080346)), _1080354), c_Groups_Oone__class_Oone(_1080346)), _1080350)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1080346, _1080348, c_Groups_Otimes__class_Otimes(_1080346)), _1080354), c_Groups_Oone__class_Oone(_1080346)), _1080352)))], (15937 ^ _782435) ^ [_1080789, _1080791, _1080793, _1080795, _1080797] : [class_Groups_Oab__group__add(_1080789), hBOOL(hAPP(c_Finite__Set_Ofinite(_1080791), _1080793)), 15944 ^ _782435 : [(15945 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1080791), _1080795), _1080793)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080791, _1080789), _1080797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080791, tc_HOL_Obool)), _1080793), hAPP(hAPP(c_Set_Oinsert(_1080791), _1080795), c_Orderings_Obot__class_Obot(tc_fun(_1080791, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1080789), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080791, _1080789), _1080797), _1080793)), hAPP(_1080797, _1080795)))], (15951 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1080791), _1080795), _1080793))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080791, _1080789), _1080797), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1080791, tc_HOL_Obool)), _1080793), hAPP(hAPP(c_Set_Oinsert(_1080791), _1080795), c_Orderings_Obot__class_Obot(tc_fun(_1080791, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1080791, _1080789), _1080797), _1080793))]]], (15957 ^ _782435) ^ [_1081259, _1081261, _1081263, _1081265, _1081267] : [class_Rings_Oring(_1081259), hBOOL(hAPP(c_Finite__Set_Ofinite(_1081261), _1081263)), hBOOL(hAPP(hAPP(c_member(_1081261), _1081265), _1081263)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081261, _1081259), _1081267), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1081261, tc_HOL_Obool)), _1081263), hAPP(hAPP(c_Set_Oinsert(_1081261), _1081265), c_Orderings_Obot__class_Obot(tc_fun(_1081261, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1081259), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081261, _1081259), _1081267), _1081263)), hAPP(_1081267, _1081265)))], (15971 ^ _782435) ^ [_1081584, _1081586] : [class_Groups_Oone(_1081584), 15974 ^ _782435 : [(15975 ^ _782435) ^ [] : [c_Groups_Oone__class_Oone(_1081584) = _1081586, -(_1081586 = c_Groups_Oone__class_Oone(_1081584))], (15981 ^ _782435) ^ [] : [_1081586 = c_Groups_Oone__class_Oone(_1081584), -(c_Groups_Oone__class_Oone(_1081584) = _1081586)]]], (15987 ^ _782435) ^ [_1081801, _1081803, _1081805, _1081807, _1081809, _1081811] : [class_Groups_Ocomm__monoid__add(_1081801), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081803, _1081801), hAPP(hAPP(c_COMBC(_1081803, tc_fun(_1081805, tc_HOL_Obool), _1081801), hAPP(hAPP(c_COMBB(tc_fun(_1081805, _1081801), tc_fun(tc_fun(_1081805, tc_HOL_Obool), _1081801), _1081803), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081805, _1081801)), _1081807)), _1081809)), _1081811) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081805, _1081801), hAPP(hAPP(c_COMBC(_1081805, tc_fun(_1081803, tc_HOL_Obool), _1081801), hAPP(hAPP(c_COMBB(tc_fun(_1081803, _1081801), tc_fun(tc_fun(_1081803, tc_HOL_Obool), _1081801), _1081805), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1081803, _1081801)), hAPP(c_COMBC(_1081803, _1081805, _1081801), _1081807))), _1081811)), _1081809))], (15993 ^ _782435) ^ [_1082074, _1082076, _1082078, _1082080, _1082082] : [class_Groups_Oab__group__add(_1082074), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082076), _1082078)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1082078), _1082080)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1082074), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082074), _1082082), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082076), _1082080))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082074), _1082082), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082076), _1082078))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1082074), _1082082), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1082078), _1082080)))], (16007 ^ _782435) ^ [_1082397, _1082399] : [class_Groups_Omonoid__mult(_1082397), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082397), c_Groups_Oone__class_Oone(_1082397)), _1082399) = _1082399)], (16013 ^ _782435) ^ [_1082492, _1082494] : [class_Groups_Ocomm__monoid__mult(_1082492), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082492), c_Groups_Oone__class_Oone(_1082492)), _1082494) = _1082494)], (16019 ^ _782435) ^ [_1082587, _1082589] : [class_Groups_Omonoid__mult(_1082587), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082587), _1082589), c_Groups_Oone__class_Oone(_1082587)) = _1082589)], (16025 ^ _782435) ^ [_1082682, _1082684] : [class_Groups_Ocomm__monoid__mult(_1082682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082682), _1082684), c_Groups_Oone__class_Oone(_1082682)) = _1082684)], (16031 ^ _782435) ^ [_1082777, _1082779, _1082781, _1082783, _1082785] : [class_Rings_Osemiring__0(_1082777), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082777), _1082779), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082781, _1082777), _1082783), _1082785)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082781, _1082777), hAPP(hAPP(c_COMBB(_1082777, _1082777, _1082781), hAPP(c_Groups_Otimes__class_Otimes(_1082777), _1082779)), _1082783)), _1082785))], (16037 ^ _782435) ^ [_1082940, _1082942, _1082944, _1082946, _1082948] : [class_Rings_Osemiring__0(_1082940), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1082940), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082942, _1082940), _1082944), _1082946)), _1082948) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1082942, _1082940), hAPP(hAPP(c_COMBC(_1082942, _1082940, _1082940), hAPP(hAPP(c_COMBB(_1082940, tc_fun(_1082940, _1082940), _1082942), c_Groups_Otimes__class_Otimes(_1082940)), _1082944)), _1082948)), _1082946))], (16043 ^ _782435) ^ [_1083123, _1083125, _1083127, _1083129, _1083131, _1083133, _1083135] : [class_Rings_Osemiring__0(_1083123), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083123), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083125, _1083123), _1083127), _1083129)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083131, _1083123), _1083133), _1083135)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083125, _1083123), hAPP(hAPP(c_COMBC(_1083125, tc_fun(_1083131, tc_HOL_Obool), _1083123), hAPP(hAPP(c_COMBB(tc_fun(_1083131, _1083123), tc_fun(tc_fun(_1083131, tc_HOL_Obool), _1083123), _1083125), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083131, _1083123)), hAPP(hAPP(c_COMBC(_1083125, tc_fun(_1083131, _1083123), tc_fun(_1083131, _1083123)), hAPP(hAPP(c_COMBB(tc_fun(_1083123, _1083123), tc_fun(tc_fun(_1083131, _1083123), tc_fun(_1083131, _1083123)), _1083125), c_COMBB(_1083123, _1083123, _1083131)), hAPP(hAPP(c_COMBB(_1083123, tc_fun(_1083123, _1083123), _1083125), c_Groups_Otimes__class_Otimes(_1083123)), _1083127))), _1083133))), _1083135)), _1083129))], (16049 ^ _782435) ^ [_1083462, _1083464, _1083466, _1083468, _1083470] : [class_Groups_Oab__group__add(_1083462), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083464, _1083462), hAPP(hAPP(c_COMBS(_1083464, _1083462, _1083462), hAPP(hAPP(c_COMBB(_1083462, tc_fun(_1083462, _1083462), _1083464), c_Groups_Ominus__class_Ominus(_1083462)), _1083466)), _1083468)), _1083470) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1083462), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083464, _1083462), _1083466), _1083470)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083464, _1083462), _1083468), _1083470)))], (16055 ^ _782435) ^ [_1083663, _1083665, _1083667, _1083669] : [class_Groups_Oab__group__add(_1083663), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083665, _1083663), hAPP(hAPP(c_COMBB(_1083663, _1083663, _1083665), c_Groups_Ouminus__class_Ouminus(_1083663)), _1083667)), _1083669) = hAPP(c_Groups_Ouminus__class_Ouminus(_1083663), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1083665, _1083663), _1083667), _1083669)))], (16061 ^ _782435) ^ [_1083812, _1083814, _1083816] : [class_Rings_Olinordered__semidom(_1083812), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083812), c_Groups_Oone__class_Oone(_1083812)), _1083814)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083812), c_Groups_Oone__class_Oone(_1083812)), _1083816)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1083812), c_Groups_Oone__class_Oone(_1083812)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1083812), _1083814), _1083816))))], (16075 ^ _782435) ^ [_1084067, _1084069] : [class_Rings_Oring__1__no__zero__divisors(_1084067), 16078 ^ _782435 : [(16089 ^ _782435) ^ [] : [16090 ^ _782435 : [(16091 ^ _782435) ^ [] : [_1084069 = c_Groups_Oone__class_Oone(_1084067)], (16093 ^ _782435) ^ [] : [_1084069 = hAPP(c_Groups_Ouminus__class_Ouminus(_1084067), c_Groups_Oone__class_Oone(_1084067))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084067), _1084069), _1084069) = c_Groups_Oone__class_Oone(_1084067))], (16079 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084067), _1084069), _1084069) = c_Groups_Oone__class_Oone(_1084067), -(_1084069 = c_Groups_Oone__class_Oone(_1084067)), -(_1084069 = hAPP(c_Groups_Ouminus__class_Ouminus(_1084067), c_Groups_Oone__class_Oone(_1084067)))]]], (16097 ^ _782435) ^ [_1084374, _1084376, _1084378, _1084380] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1084374), _1084376)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1084374, tc_HOL_Obool)), _1084376), _1084378)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084374, tc_Nat_Onat), _1084380), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1084374, tc_HOL_Obool)), _1084378), _1084376)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084374, tc_Nat_Onat), _1084380), _1084378)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084374, tc_Nat_Onat), _1084380), _1084376)))], (16107 ^ _782435) ^ [_1084627, _1084629, _1084631, _1084633, _1084635, _1084637] : [class_Groups_Ocomm__monoid__add(_1084627), c_Fun_Oinj__on(_1084629, _1084631, _1084633, _1084635), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084631, _1084627), _1084637), hAPP(c_Set_Oimage(_1084629, _1084631, _1084633), _1084635)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1084629, _1084627), hAPP(c_Fun_Ocomp(_1084631, _1084627, _1084629, _1084637), _1084633)), _1084635))], (16117 ^ _782435) ^ [_1084840, _1084842, _1084844, _1084846, _1084848] : [class_Groups_Ocomm__monoid__mult(_1084840), hBOOL(hAPP(c_Finite__Set_Ofinite(_1084842), _1084844)), -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084840, _1084842, c_Groups_Otimes__class_Otimes(_1084840)), hAPP(hAPP(c_COMBS(_1084842, _1084840, _1084840), hAPP(hAPP(c_COMBB(_1084840, tc_fun(_1084840, _1084840), _1084842), c_Groups_Otimes__class_Otimes(_1084840)), _1084846)), _1084848)), c_Groups_Oone__class_Oone(_1084840)), _1084844) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1084840), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084840, _1084842, c_Groups_Otimes__class_Otimes(_1084840)), _1084846), c_Groups_Oone__class_Oone(_1084840)), _1084844)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1084840, _1084842, c_Groups_Otimes__class_Otimes(_1084840)), _1084848), c_Groups_Oone__class_Oone(_1084840)), _1084844)))], (16127 ^ _782435) ^ [_1085170, _1085172, _1085174, _1085176] : [hBOOL(hAPP(hAPP(c_member(_1085170), _1085172), _1085174)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085170, tc_Nat_Onat), _1085176), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085170, tc_HOL_Obool)), _1085174), hAPP(hAPP(c_Set_Oinsert(_1085170), _1085172), c_Orderings_Obot__class_Obot(tc_fun(_1085170, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085170, tc_Nat_Onat), _1085176), _1085174)), hAPP(_1085176, _1085172)))], (16133 ^ _782435) ^ [_1085361, _1085363, _1085365, _1085367] : [-(hBOOL(hAPP(hAPP(c_member(_1085361), _1085363), _1085365))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085361, tc_Nat_Onat), _1085367), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085361, tc_HOL_Obool)), _1085365), hAPP(hAPP(c_Set_Oinsert(_1085361), _1085363), c_Orderings_Obot__class_Obot(tc_fun(_1085361, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085361, tc_Nat_Onat), _1085367), _1085365))], (16139 ^ _782435) ^ [_1085452, _1085454, _1085456, _1085458, _1085460] : [class_Groups_Oab__group__add(_1085452), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085454), _1085456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1085454, tc_HOL_Obool)), _1085458), _1085456)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085454, _1085452), _1085460), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1085454, tc_HOL_Obool)), _1085456), _1085458)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1085452), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085454, _1085452), _1085460), _1085456)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085454, _1085452), _1085460), _1085458)))], (16153 ^ _782435) ^ [_1085769, _1085771, _1085773, _1085775, _1085777] : [class_Groups_Ocomm__monoid__add(_1085769), hBOOL(hAPP(c_Finite__Set_Ofinite(_1085771), _1085773)), c_Fun_Oinj__on(_1085771, _1085771, _1085775, _1085773), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085771, _1085769), _1085777), hAPP(c_Set_Oimage(_1085771, _1085771, _1085775), _1085773)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1085771, _1085769), hAPP(c_Fun_Ocomp(_1085771, _1085769, _1085771, _1085777), _1085775)), _1085773))], (16167 ^ _782435) ^ [_1086044, _1086046, _1086048, _1086050, _1086052, _1086054, _1086056] : [c_Big__Operators_Ocomm__monoid__big(_1086044, _1086046, _1086048, _1086050, _1086052), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1086046), _1086054))), -(hAPP(hAPP(_1086052, _1086056), _1086054) = _1086050)], (16177 ^ _782435) ^ [_1086172, _1086174, _1086176, _1086178, _1086180] : [class_Groups_Ocomm__monoid__mult(_1086172), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086174), _1086176)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086174), _1086178)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086172), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086172, _1086174, c_Groups_Otimes__class_Otimes(_1086172)), _1086180), c_Groups_Oone__class_Oone(_1086172)), _1086176)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086172, _1086174, c_Groups_Otimes__class_Otimes(_1086172)), _1086180), c_Groups_Oone__class_Oone(_1086172)), _1086178)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086172), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086172, _1086174, c_Groups_Otimes__class_Otimes(_1086172)), _1086180), c_Groups_Oone__class_Oone(_1086172)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086174, tc_HOL_Obool)), _1086176), _1086178))), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086172, _1086174, c_Groups_Otimes__class_Otimes(_1086172)), _1086180), c_Groups_Oone__class_Oone(_1086172)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086174, tc_HOL_Obool)), _1086176), _1086178))))], (16191 ^ _782435) ^ [_1086597, _1086599] : [class_Rings_Ocomm__ring__1(_1086597), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1086597), _1086599) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086597), hAPP(c_Groups_Ouminus__class_Ouminus(_1086597), c_Groups_Oone__class_Oone(_1086597))), _1086599))], (16197 ^ _782435) ^ [_1086712, _1086714, _1086716, _1086718, _1086720] : [class_Groups_Ocomm__monoid__mult(_1086712), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086714), _1086716)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1086714), _1086718)), 16211 ^ _782435 : [(16212 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1086714), 16210 ^ [_1086712, _1086714, _1086716, _1086718, _1086720]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1086714, tc_HOL_Obool)), _1086716), _1086718))))], (16214 ^ _782435) ^ [] : [hAPP(_1086720, 16210 ^ [_1086712, _1086714, _1086716, _1086718, _1086720]) = c_Groups_Oone__class_Oone(_1086712)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086712, _1086714, c_Groups_Otimes__class_Otimes(_1086712)), _1086720), c_Groups_Oone__class_Oone(_1086712)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1086714, tc_HOL_Obool)), _1086716), _1086718)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1086712), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086712, _1086714, c_Groups_Otimes__class_Otimes(_1086712)), _1086720), c_Groups_Oone__class_Oone(_1086712)), _1086716)), hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1086712, _1086714, c_Groups_Otimes__class_Otimes(_1086712)), _1086720), c_Groups_Oone__class_Oone(_1086712)), _1086718)))], (16218 ^ _782435) ^ [_1087255, _1087257] : [class_Rings_Ocomm__semiring__1(_1087255), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087255), c_Groups_Oone__class_Oone(_1087255)), _1087257) = _1087257)], (16224 ^ _782435) ^ [_1087350, _1087352] : [class_Rings_Ocomm__semiring__1(_1087350), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1087350), _1087352), c_Groups_Oone__class_Oone(_1087350)) = _1087352)], (16230 ^ _782435) ^ [_1087445, _1087447, _1087449, _1087451, _1087453] : [class_Groups_Ocomm__monoid__add(_1087445), class_Groups_Oordered__cancel__ab__semigroup__add(_1087445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087447), _1087449)), -(_1087449 = c_Orderings_Obot__class_Obot(tc_fun(_1087447, tc_HOL_Obool))), 16248 ^ _782435 : [(16249 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1087447), 16247 ^ [_1087445, _1087447, _1087449, _1087451, _1087453]), _1087449)))], (16251 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087445), hAPP(_1087451, 16247 ^ [_1087445, _1087447, _1087449, _1087451, _1087453])), hAPP(_1087453, 16247 ^ [_1087445, _1087447, _1087449, _1087451, _1087453])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1087445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087447, _1087445), _1087451), _1087449)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087447, _1087445), _1087453), _1087449))))], (16255 ^ _782435) ^ [_1087976, _1087978, _1087980, _1087982, _1087984] : [class_Groups_Ocomm__monoid__add(_1087976), hBOOL(hAPP(c_Finite__Set_Ofinite(_1087978), _1087980)), hBOOL(hAPP(hAPP(c_member(_1087978), _1087982), _1087980)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087978, _1087976), _1087984), _1087980) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1087976), hAPP(_1087984, _1087982)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1087978, _1087976), _1087984), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1087978, tc_HOL_Obool)), _1087980), hAPP(hAPP(c_Set_Oinsert(_1087978), _1087982), c_Orderings_Obot__class_Obot(tc_fun(_1087978, tc_HOL_Obool)))))))], (16269 ^ _782435) ^ [_1088301, _1088303, _1088305, _1088307, _1088309] : [class_Groups_Ocomm__monoid__add(_1088301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1088303), _1088305)), hBOOL(hAPP(hAPP(c_member(_1088303), _1088307), _1088305)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088303, _1088301), _1088309), _1088305) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088301), hAPP(_1088309, _1088307)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1088303, _1088301), _1088309), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1088303, tc_HOL_Obool)), _1088305), hAPP(hAPP(c_Set_Oinsert(_1088303), _1088307), c_Orderings_Obot__class_Obot(tc_fun(_1088303, tc_HOL_Obool)))))))], (16283 ^ _782435) ^ [_1088626, _1088628] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088626), _1088628))))], (16285 ^ _782435) ^ [_1088659, _1088661, _1088663, _1088665, _1088667] : [class_Groups_Ocomm__monoid__add(_1088659), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088661), _1088663)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088663), _1088665)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088659), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088659), _1088667), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088661), _1088663))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088659), _1088667), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088663), _1088665))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088659), _1088667), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1088661), _1088665)))], (16299 ^ _782435) ^ [_1088982, _1088984, _1088986, _1088988, _1088990] : [class_Groups_Ocomm__monoid__add(_1088982), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1088984), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1088986), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088982), _1088988), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1088984, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1088986), _1088990))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1088982), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088982), _1088988), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1088984, _1088986))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1088982), _1088988), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1088986), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1088986), _1088990)))))], (16309 ^ _782435) ^ [_1089273, _1089275, _1089277, _1089279, _1089281] : [class_Groups_Ocomm__monoid__add(_1089273), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089273), _1089275), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089277), _1089279)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089281), _1089279))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089273), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1089273, tc_Nat_Onat), _1089275), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1089279))), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1089277), _1089281)))], (16315 ^ _782435) ^ [_1089464, _1089466, _1089468, _1089470, _1089472] : [class_Groups_Ocomm__monoid__add(_1089464), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089464), _1089466), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089468), _1089470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1089472), _1089470))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089464), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1089464, tc_Nat_Onat), _1089466), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1089470))), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089468, _1089472)))], (16321 ^ _782435) ^ [_1089647, _1089649, _1089651, _1089653] : [class_Groups_Ocomm__monoid__add(_1089647), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089649), _1089651)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089647), _1089653), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1089649, _1089651)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1089647), hAPP(_1089653, _1089649)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1089647), _1089653), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1089649, _1089651))))], (16342 ^ _782435) ^ [_1090065] : [16344 ^ _782435 : [(16345 ^ _782435) ^ [_1090141] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 16343 ^ [_1090065, _1090141]), _1090065)))], (16347 ^ _782435) ^ [_1090175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 16343 ^ [_1090065, _1090175]), _1090175))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1090065)))], (16331 ^ _782435) ^ [_1089878] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1089878)), 16335 ^ _782435 : [(16336 ^ _782435) ^ [_1089958] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1089958), _1089878)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1089958), 16334 ^ [_1089878])))]]], (16351 ^ _782435) ^ [_1090244, _1090246, _1090248, _1090250, _1090252] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1090244), 16354 ^ _782435 : [(16365 ^ _782435) ^ [] : [16366 ^ _782435 : [(16367 ^ _782435) ^ [] : [_1090246 = _1090250], (16369 ^ _782435) ^ [] : [_1090248 = _1090252]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090246), _1090248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090250), _1090252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090246), _1090252)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090250), _1090248)))], (16355 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090246), _1090248)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090250), _1090252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090244), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090246), _1090252)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090244), _1090250), _1090248)), -(_1090246 = _1090250), -(_1090248 = _1090252)]]], (16373 ^ _782435) ^ [_1090656, _1090658, _1090660, _1090662] : [class_Rings_Ocomm__semiring__1(_1090656), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090656), _1090658), _1090660)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090656), _1090662), _1090660)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090656), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090656), _1090658), _1090662)), _1090660))], (16379 ^ _782435) ^ [_1090815, _1090817, _1090819, _1090821] : [class_Rings_Ocomm__semiring__1(_1090815), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090815), _1090817), _1090819)), _1090821) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090815), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090815), _1090817), _1090821)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090815), _1090819), _1090821)))], (16385 ^ _782435) ^ [_1090974, _1090976, _1090978, _1090980, _1090982] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1090974), 16388 ^ _782435 : [(16399 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090976), _1090980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090978), _1090982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090976), _1090982)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090978), _1090980))), 16402 ^ _782435 : [(16403 ^ _782435) ^ [] : [_1090976 = _1090978], (16405 ^ _782435) ^ [] : [_1090980 = _1090982]]], (16389 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090976), _1090980)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090978), _1090982)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1090974), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090976), _1090982)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1090974), _1090978), _1090980)), -(_1090976 = _1090978), -(_1090980 = _1090982)]]], (16407 ^ _782435) ^ [_1091392, _1091394, _1091396, _1091398] : [class_Rings_Ocomm__semiring__1(_1091392), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091392), _1091394), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091392), _1091396), _1091398)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091392), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091392), _1091394), _1091396)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1091392), _1091394), _1091398)))], (16413 ^ _782435) ^ [_1091551, _1091553, _1091555] : [-(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)), _1091551)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091553), _1091555)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091553), _1091551)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091555), _1091551)))], (16415 ^ _782435) ^ [_1091612, _1091614, _1091616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1091612), _1091614)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091612), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091614), _1091616)) = 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, _1091612), _1091614)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1091614), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1091614), _1091616))))], (16421 ^ _782435) ^ [_1091773, _1091775, _1091777, _1091779] : [class_Groups_Ocancel__semigroup__add(_1091773), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091773), _1091775), _1091777) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091773), _1091779), _1091777), -(_1091775 = _1091779)], (16431 ^ _782435) ^ [_1091940, _1091942, _1091944, _1091946] : [class_Groups_Ocancel__ab__semigroup__add(_1091940), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091940), _1091942), _1091944) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1091940), _1091942), _1091946), -(_1091944 = _1091946)], (16441 ^ _782435) ^ [_1092107, _1092109, _1092111, _1092113] : [class_Groups_Ocancel__semigroup__add(_1092107), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092107), _1092109), _1092111) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092107), _1092109), _1092113), -(_1092111 = _1092113)], (16451 ^ _782435) ^ [_1092274, _1092276, _1092278, _1092280] : [class_Groups_Ocancel__semigroup__add(_1092274), 16454 ^ _782435 : [(16455 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092274), _1092276), _1092278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092274), _1092280), _1092278), -(_1092276 = _1092280)], (16461 ^ _782435) ^ [] : [_1092276 = _1092280, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092274), _1092276), _1092278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092274), _1092280), _1092278))]]], (16467 ^ _782435) ^ [_1092539, _1092541, _1092543, _1092545] : [class_Groups_Ocancel__semigroup__add(_1092539), 16470 ^ _782435 : [(16471 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092539), _1092541), _1092543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092539), _1092541), _1092545), -(_1092543 = _1092545)], (16477 ^ _782435) ^ [] : [_1092543 = _1092545, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092539), _1092541), _1092543) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092539), _1092541), _1092545))]]], (16483 ^ _782435) ^ [_1092804, _1092806, _1092808, _1092810] : [class_Groups_Oab__semigroup__add(_1092804), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092804), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092804), _1092806), _1092808)), _1092810) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092804), _1092806), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092804), _1092808), _1092810)))], (16489 ^ _782435) ^ [_1092947, _1092949, _1092951] : [class_Rings_Ocomm__semiring__1(_1092947), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092947), _1092949), _1092951) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1092947), _1092951), _1092949))], (16495 ^ _782435) ^ [_1093056, _1093058, _1093060, _1093062] : [class_Rings_Ocomm__semiring__1(_1093056), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093056), _1093058), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093056), _1093060), _1093062)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093056), _1093060), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093056), _1093058), _1093062)))], (16501 ^ _782435) ^ [_1093199, _1093201, _1093203, _1093205] : [class_Rings_Ocomm__semiring__1(_1093199), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093199), _1093201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093199), _1093203), _1093205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093199), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093199), _1093201), _1093203)), _1093205))], (16507 ^ _782435) ^ [_1093342, _1093344, _1093346, _1093348] : [class_Rings_Ocomm__semiring__1(_1093342), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093342), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093342), _1093344), _1093346)), _1093348) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093342), _1093344), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093342), _1093346), _1093348)))], (16513 ^ _782435) ^ [_1093485, _1093487, _1093489, _1093491] : [class_Rings_Ocomm__semiring__1(_1093485), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093485), _1093487), _1093489)), _1093491) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093485), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093485), _1093487), _1093491)), _1093489))], (16519 ^ _782435) ^ [_1093628, _1093630, _1093632, _1093634, _1093636] : [class_Rings_Ocomm__semiring__1(_1093628), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093628), _1093630), _1093632)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093628), _1093634), _1093636)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093628), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093628), _1093630), _1093634)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093628), _1093632), _1093636)))], (16525 ^ _782435) ^ [_1093805, _1093807, _1093809, _1093811] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1093805), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093805), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093805), _1093807), _1093809)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1093805), _1093807), _1093811))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1093805), _1093809), _1093811)))], (16535 ^ _782435) ^ [_1094000, _1094002, _1094004, _1094006] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1094000), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094000), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094000), _1094002), _1094004)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094000), _1094006), _1094004))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094000), _1094002), _1094006)))], (16545 ^ _782435) ^ [_1094195, _1094197, _1094199, _1094201, _1094203] : [class_Groups_Oordered__ab__semigroup__add(_1094195), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094195), _1094197), _1094199)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094195), _1094201), _1094203)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094195), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094195), _1094197), _1094201)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094195), _1094199), _1094203))))], (16559 ^ _782435) ^ [_1094466, _1094468, _1094470, _1094472] : [class_Groups_Oordered__ab__semigroup__add(_1094466), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094466), _1094468), _1094470)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094466), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094466), _1094472), _1094468)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094466), _1094472), _1094470))))], (16569 ^ _782435) ^ [_1094661, _1094663, _1094665, _1094667] : [class_Groups_Oordered__ab__semigroup__add(_1094661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094661), _1094663), _1094665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094661), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094661), _1094663), _1094667)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094661), _1094665), _1094667))))], (16579 ^ _782435) ^ [_1094856, _1094858, _1094860, _1094862] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1094856), 16582 ^ _782435 : [(16583 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094856), _1094858), _1094860)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094856), _1094858), _1094862))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094856), _1094860), _1094862)))], (16589 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094856), _1094860), _1094862)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1094856), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094856), _1094858), _1094860)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1094856), _1094858), _1094862))))]]], (16595 ^ _782435) ^ [_1095163, _1095165, _1095167, _1095169] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095163), 16598 ^ _782435 : [(16599 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095163), _1095165), _1095167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095163), _1095169), _1095167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095163), _1095165), _1095169)))], (16605 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095163), _1095165), _1095169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1095163), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095163), _1095165), _1095167)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095163), _1095169), _1095167))))]]], (16611 ^ _782435) ^ [_1095470, _1095472, _1095474, _1095476] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095470), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095470), _1095472), _1095474)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095470), _1095472), _1095476))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095470), _1095474), _1095476)))], (16621 ^ _782435) ^ [_1095665, _1095667, _1095669, _1095671] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1095665), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095665), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095665), _1095667), _1095669)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095665), _1095671), _1095669))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095665), _1095667), _1095671)))], (16631 ^ _782435) ^ [_1095860, _1095862, _1095864, _1095866, _1095868] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1095860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095860), _1095862), _1095864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095860), _1095866), _1095868)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1095860), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095860), _1095862), _1095866)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1095860), _1095864), _1095868))))], (16645 ^ _782435) ^ [_1096131, _1096133, _1096135, _1096137] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1096131), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096131), _1096133), _1096135)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096131), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096131), _1096137), _1096133)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096131), _1096137), _1096135))))], (16655 ^ _782435) ^ [_1096326, _1096328, _1096330, _1096332] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1096326), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096326), _1096328), _1096330)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096326), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096326), _1096328), _1096332)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096326), _1096330), _1096332))))], (16665 ^ _782435) ^ [_1096521, _1096523, _1096525, _1096527] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1096521), 16668 ^ _782435 : [(16669 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096521), _1096523), _1096525)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096521), _1096523), _1096527))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096521), _1096525), _1096527)))], (16675 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096521), _1096525), _1096527)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096521), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096521), _1096523), _1096525)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096521), _1096523), _1096527))))]]], (16681 ^ _782435) ^ [_1096828, _1096830, _1096832, _1096834] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1096828), 16684 ^ _782435 : [(16685 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096828), _1096830), _1096832)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096828), _1096834), _1096832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096828), _1096830), _1096834)))], (16691 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096828), _1096830), _1096834)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1096828), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096828), _1096830), _1096832)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1096828), _1096834), _1096832))))]]], (16697 ^ _782435) ^ [_1097135, _1097137, _1097139, _1097141, _1097143] : [class_Rings_Osemiring(_1097135), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097135), _1097137), _1097139)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097135), _1097141), _1097139)), _1097143)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097135), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097135), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097135), _1097137), _1097141)), _1097139)), _1097143))], (16703 ^ _782435) ^ [_1097328, _1097330, _1097332, _1097334] : [class_Rings_Ocomm__semiring(_1097328), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097328), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097328), _1097330), _1097332)), _1097334) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097328), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097328), _1097330), _1097334)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1097328), _1097332), _1097334)))], (16709 ^ _782435) ^ [_1097487, _1097489, _1097491] : [class_Groups_Ogroup__add(_1097487), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097487), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097487), _1097489), _1097491)), _1097491) = _1097489)], (16715 ^ _782435) ^ [_1097596, _1097598, _1097600] : [class_Groups_Ogroup__add(_1097596), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097596), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1097596), _1097598), _1097600)), _1097600) = _1097598)], (16721 ^ _782435) ^ [_1097705, _1097707, _1097709] : [class_Groups_Oab__group__add(_1097705), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097705), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097705), _1097707), _1097709)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097705), hAPP(c_Groups_Ouminus__class_Ouminus(_1097705), _1097707)), hAPP(c_Groups_Ouminus__class_Ouminus(_1097705), _1097709)))], (16727 ^ _782435) ^ [_1097844, _1097846, _1097848] : [class_Groups_Ogroup__add(_1097844), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1097844), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097844), _1097846), _1097848)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097844), hAPP(c_Groups_Ouminus__class_Ouminus(_1097844), _1097848)), hAPP(c_Groups_Ouminus__class_Ouminus(_1097844), _1097846)))], (16733 ^ _782435) ^ [_1097983, _1097985, _1097987] : [class_Groups_Ogroup__add(_1097983), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097983), _1097985), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1097983), hAPP(c_Groups_Ouminus__class_Ouminus(_1097983), _1097985)), _1097987)) = _1097987)], (16739 ^ _782435) ^ [_1098102, _1098104, _1098106] : [class_Groups_Ogroup__add(_1098102), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098102), hAPP(c_Groups_Ouminus__class_Ouminus(_1098102), _1098104)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098102), _1098104), _1098106)) = _1098106)], (16745 ^ _782435) ^ [_1098221, _1098223, _1098225] : [class_Rings_Ocomm__semiring__1(_1098221), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098221), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098221), _1098223), _1098225)), _1098225) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098221), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098221), _1098223), c_Groups_Oone__class_Oone(_1098221))), _1098225))], (16751 ^ _782435) ^ [_1098366, _1098368, _1098370] : [class_Rings_Ocomm__semiring__1(_1098366), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098366), _1098368), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098366), _1098370), _1098368)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098366), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098366), _1098370), c_Groups_Oone__class_Oone(_1098366))), _1098368))], (16757 ^ _782435) ^ [_1098511, _1098513] : [class_Rings_Ocomm__semiring__1(_1098511), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098511), _1098513), _1098513) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1098511), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098511), c_Groups_Oone__class_Oone(_1098511)), c_Groups_Oone__class_Oone(_1098511))), _1098513))], (16763 ^ _782435) ^ [_1098642, _1098644, _1098646] : [class_Rings_Ocomm__ring__1(_1098642), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1098642), _1098644), _1098646) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098642), _1098644), hAPP(c_Groups_Ouminus__class_Ouminus(_1098642), _1098646)))], (16769 ^ _782435) ^ [_1098761, _1098763, _1098765, _1098767, _1098769] : [class_Groups_Ocomm__monoid__add(_1098761), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098763, _1098761), hAPP(hAPP(c_COMBS(_1098763, _1098761, _1098761), hAPP(hAPP(c_COMBB(_1098761, tc_fun(_1098761, _1098761), _1098763), c_Groups_Oplus__class_Oplus(_1098761)), _1098765)), _1098767)), _1098769) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098761), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098763, _1098761), _1098765), _1098769)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1098763, _1098761), _1098767), _1098769)))], (16775 ^ _782435) ^ [_1098962, _1098964, _1098966, _1098968, _1098970] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1098962), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1098962), _1098964), _1098966)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098962), _1098968), _1098970)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1098962), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098962), _1098964), _1098968)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1098962), _1098966), _1098970))))], (16789 ^ _782435) ^ [_1099233, _1099235, _1099237, _1099239, _1099241] : [class_Groups_Oordered__cancel__ab__semigroup__add(_1099233), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099233), _1099235), _1099237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1099233), _1099239), _1099241)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099233), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099233), _1099235), _1099239)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099233), _1099237), _1099241))))], (16803 ^ _782435) ^ [_1099504, _1099506] : [class_Rings_Olinordered__semidom(_1099504), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1099504), _1099506), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099504), _1099506), c_Groups_Oone__class_Oone(_1099504)))))], (16809 ^ _782435) ^ [_1099613, _1099615, _1099617, _1099619, _1099621, _1099623] : [class_Rings_Oring(_1099613), 16812 ^ _782435 : [(16813 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099613), _1099615), _1099617)), _1099619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099613), _1099621), _1099617)), _1099623), -(_1099619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099613), _1099621), _1099615)), _1099617)), _1099623))], (16819 ^ _782435) ^ [] : [_1099619 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099613), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1099613), _1099621), _1099615)), _1099617)), _1099623), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099613), _1099615), _1099617)), _1099619) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1099613), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1099613), _1099621), _1099617)), _1099623))]]], (16825 ^ _782435) ^ [_1100010, _1100012, _1100014, _1100016, _1100018, _1100020] : [class_Rings_Oring(_1100010), 16828 ^ _782435 : [(16829 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100010), _1100012), _1100014)), _1100016) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100010), _1100018), _1100014)), _1100020), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100010), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100010), _1100012), _1100018)), _1100014)), _1100016) = _1100020)], (16835 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100010), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100010), _1100012), _1100018)), _1100014)), _1100016) = _1100020, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100010), _1100012), _1100014)), _1100016) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100010), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1100010), _1100018), _1100014)), _1100020))]]], (16841 ^ _782435) ^ [_1100407, _1100409, _1100411] : [class_Groups_Ogroup__add(_1100407), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100407), _1100409), _1100411) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100407), _1100409), hAPP(c_Groups_Ouminus__class_Ouminus(_1100407), _1100411)))], (16847 ^ _782435) ^ [_1100526, _1100528, _1100530] : [class_Groups_Oab__group__add(_1100526), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100526), _1100528), _1100530) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100526), _1100528), hAPP(c_Groups_Ouminus__class_Ouminus(_1100526), _1100530)))], (16853 ^ _782435) ^ [_1100645, _1100647, _1100649] : [class_Groups_Ogroup__add(_1100645), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1100645), _1100647), hAPP(c_Groups_Ouminus__class_Ouminus(_1100645), _1100649)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100645), _1100647), _1100649))], (16859 ^ _782435) ^ [_1100764, _1100766, _1100768, _1100770, _1100772] : [class_Groups_Ocomm__monoid__add(_1100764), hBOOL(hAPP(c_Finite__Set_Ofinite(_1100766), _1100768)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100766, _1100764), hAPP(hAPP(c_COMBS(_1100766, _1100764, _1100764), hAPP(hAPP(c_COMBB(_1100764, tc_fun(_1100764, _1100764), _1100766), c_Groups_Oplus__class_Oplus(_1100764)), _1100770)), _1100772)), _1100768) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1100764), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100766, _1100764), _1100770), _1100768)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1100766, _1100764), _1100772), _1100768)))], (16869 ^ _782435) ^ [_1101031, _1101033, _1101035, _1101037, _1101039, _1101041] : [class_Rings_Oordered__ring(_1101031), 16872 ^ _782435 : [(16873 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101031), _1101033), _1101035)), _1101037)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101031), _1101039), _1101035)), _1101041))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101031), _1101033), _1101039)), _1101035)), _1101037)), _1101041)))], (16879 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101031), _1101033), _1101039)), _1101035)), _1101037)), _1101041)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101031), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101031), _1101033), _1101035)), _1101037)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101031), _1101039), _1101035)), _1101041))))]]], (16885 ^ _782435) ^ [_1101470, _1101472, _1101474, _1101476, _1101478, _1101480] : [class_Rings_Oordered__ring(_1101470), 16888 ^ _782435 : [(16889 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101470), _1101472), _1101474)), _1101476)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101470), _1101478), _1101474)), _1101480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101470), _1101476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101470), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101470), _1101478), _1101472)), _1101474)), _1101480))))], (16895 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101470), _1101476), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101470), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101470), _1101478), _1101472)), _1101474)), _1101480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1101470), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101470), _1101472), _1101474)), _1101476)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101470), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101470), _1101478), _1101474)), _1101480))))]]], (16901 ^ _782435) ^ [_1101909, _1101911, _1101913, _1101915, _1101917, _1101919] : [class_Rings_Oordered__ring(_1101909), 16904 ^ _782435 : [(16905 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101909), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101909), _1101911), _1101913)), _1101915)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101909), _1101917), _1101913)), _1101919))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101909), _1101915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101909), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1101909), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1101909), _1101917), _1101911)), _1101913)), _1101919))))], (16911 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1101909), _1101915), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1101909), 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hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106569), _1106573)), _1106577))))]]], (17107 ^ _782435) ^ [_1106960, _1106962, _1106964, _1106966, _1106968] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1106960), _1106962)), 17110 ^ _782435 : [(17111 ^ _782435) ^ [] : [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), _1106962), _1106964)), _1106966)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1106960), _1106964)), _1106968))), -(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), _1106962), _1106960)), _1106964)), _1106966)), _1106968)))], (17117 ^ 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_1107357)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107351), _1107355)), _1107359)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1107353), _1107351)), _1107355)), _1107357)), _1107359))], (17129 ^ _782435) ^ [_1107552, _1107554, _1107556, _1107558, _1107560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107552), _1107554)), 17132 ^ _782435 : [(17133 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107554), _1107556)), _1107558) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107552), _1107556)), _1107560), -(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), _1107554), _1107552)), _1107556)), _1107558) = _1107560)], (17139 ^ _782435) ^ [] : [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), _1107554), _1107552)), _1107556)), _1107558) = _1107560, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107554), _1107556)), _1107558) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107552), _1107556)), _1107560))]]], (17145 ^ _782435) ^ [_1107913, _1107915, _1107917, _1107919, _1107921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107913), _1107915)), 17148 ^ _782435 : [(17149 ^ _782435) ^ [] : [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), _1107913), _1107917)), _1107919)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107915), _1107917)), _1107921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107919), 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), _1107915), _1107913)), _1107917)), _1107921))))], (17155 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1107919), 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), _1107915), _1107913)), _1107917)), _1107921))), -(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), _1107913), _1107917)), _1107919)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1107915), _1107917)), _1107921))))]]], (17161 ^ _782435) ^ [_1108304, _1108306, _1108308, _1108310, _1108312] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1108304), _1108306)), -(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), _1108304), _1108308)), _1108310)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108306), _1108308)), _1108312)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1108310), 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), _1108306), _1108304)), _1108308)), _1108312)))], (17167 ^ _782435) ^ [_1108505, _1108507] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1108505, _1108507))))], (17169 ^ _782435) ^ [_1108536] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1108536))))], (17171 ^ _782435) ^ [_1108564] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1108564))))], (17173 ^ _782435) ^ [_1108592, _1108594] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108592, _1108594))))], (17175 ^ _782435) ^ [_1108623, _1108625] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1108623, _1108625))))], (17177 ^ _782435) ^ [_1108654, _1108656, _1108658, _1108660] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108654), _1108656)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1108658), _1108656)), _1108660)) = 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), _1108654), _1108658)), _1108656)), _1108660))], (17179 ^ _782435) ^ [_1108725, _1108727, _1108729, _1108731] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1108725, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1108727)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1108725, tc_HOL_Obool), tc_Nat_Onat), _1108729), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1108731))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1108725, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108731, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108727), _1108731))), _1108729))], (17181 ^ _782435) ^ [_1108807, _1108809, _1108811] : [-(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)), _1108807)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1108809, _1108811)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108809), _1108807), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1108811), _1108807)))], (17194 ^ _782435) ^ [_1109063] : [17196 ^ _782435 : [(17197 ^ _782435) ^ [_1109139] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 17195 ^ [_1109063, _1109139]), _1109063)))], (17199 ^ _782435) ^ [_1109173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 17195 ^ [_1109063, _1109173]), _1109173))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1109063)))], (17183 ^ _782435) ^ [_1108876] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1108876)), 17187 ^ _782435 : [(17188 ^ _782435) ^ [_1108956] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1108956), _1108876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1108956), 17186 ^ [_1108876])))]]], (17203 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (17205 ^ _782435) ^ [_1109266, _1109268, _1109270, _1109272, _1109274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109266), _1109268)), 17208 ^ _782435 : [(17209 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109266), _1109270)), _1109272) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109268), _1109270)), _1109274), -(_1109272 = 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), _1109268), _1109266)), _1109270)), _1109274))], (17215 ^ _782435) ^ [] : [_1109272 = 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), _1109268), _1109266)), _1109270)), _1109274), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109266), _1109270)), _1109272) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1109268), _1109270)), _1109274))]]], (17221 ^ _782435) ^ [_1109627, _1109629, _1109631] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109627), _1109629)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109629), _1109631)), _1109627) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109629), _1109627)), _1109631))], (17227 ^ _782435) ^ [_1109764, _1109766, _1109768] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109764), _1109766)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109766), _1109764)), _1109768) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109766), _1109768)), _1109764))], (17233 ^ _782435) ^ [_1109901, _1109903, _1109905] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1109901), _1109903)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109905), _1109903)), _1109901) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1109905), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1109903), _1109901)))], (17239 ^ _782435) ^ [_1110038, _1110040, _1110042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110038), _1110040)), 17242 ^ _782435 : [(17243 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110040), _1110038) = _1110042, -(_1110040 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110042), _1110038))], (17249 ^ _782435) ^ [] : [_1110040 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110042), _1110038), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110040), _1110038) = _1110042)]]], (17255 ^ _782435) ^ [_1110297, _1110299] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110297), _1110299)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110299), _1110297)), _1110297) = _1110299)], (17261 ^ _782435) ^ [_1110408, _1110410, _1110412] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110408), _1110410)), 17264 ^ _782435 : [(17265 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110410), _1110408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110412), _1110408)), _1110410)))], (17271 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110412), _1110408)), _1110410)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110412), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110410), _1110408))))]]], (17277 ^ _782435) ^ [_1110697, _1110699, _1110701] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1110697), _1110699)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110701), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1110699), _1110697)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1110701), _1110699)), _1110697))], (17283 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1110915] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110915), _1110915))], (17303 ^ _782435) ^ [_1111001, _1111003] : [17304 ^ _782435 : [(17305 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111001), _1111003))], (17307 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111003), _1111001))]], _1111001 = _1111003], (17293 ^ _782435) ^ [_1110952, _1110954] : [-(_1110952 = _1110954), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110952), _1110954))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1110954), _1110952)))], (17311 ^ _782435) ^ [_1111135, _1111137] : [-(_1111135 = _1111137), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111135), _1111137))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111137), _1111135)))], (17321 ^ _782435) ^ [_1111197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111197), _1111197))], (17323 ^ _782435) ^ [_1111225, _1111227] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111225), _1111227)), _1111227 = _1111225], (17329 ^ _782435) ^ [_1111313, _1111315] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111313), _1111315)), _1111313 = _1111315], (17335 ^ _782435) ^ [_1111401, _1111403, _1111405] : [17336 ^ _782435 : [(17337 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111401), _1111403)))], (17339 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1111405, _1111403), _1111401))]], 17342 ^ _782435 : [(17343 ^ _782435) ^ [] : [-(_1111401 = _1111403)], (17345 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1111405, _1111403), _1111401))]], 17348 ^ _782435 : [(17349 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1111403), _1111401)))], (17351 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1111405, _1111403), _1111401))]], -(hBOOL(hAPP(hAPP(_1111405, _1111403), _1111401)))], (17355 ^ _782435) ^ [_1111765, _1111767, _1111769] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111765), _1111767) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111769), _1111767), -(_1111765 = _1111769)], (17361 ^ _782435) ^ [_1111864, _1111866, _1111868] : [_1111864 = _1111868, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111864), _1111866) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111868), _1111866))], (17367 ^ _782435) ^ [_1111987, _1111989, _1111991] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111987), _1111989) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1111987), _1111991), -(_1111989 = _1111991)], (17373 ^ _782435) ^ [_1112086, _1112088, _1112090] : [_1112088 = _1112090, -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112086), _1112088) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112086), _1112090))], (17379 ^ _782435) ^ [_1112191, _1112193, _1112195] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112191), _1112193)), _1112195) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112191), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112193), _1112195)))], (17381 ^ _782435) ^ [_1112242, _1112244, _1112246] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112242), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112244), _1112246)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112244), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112242), _1112246)))], (17383 ^ _782435) ^ [_1112293, _1112295] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112293), _1112295) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112295), _1112293))], (17385 ^ _782435) ^ [_1112330] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112330), _1112330)))], (17387 ^ _782435) ^ [_1112354, _1112356] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112354), _1112356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112356), _1112354)))], (17393 ^ _782435) ^ [_1112400, _1112402] : [_1112400 = _1112402, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112400), _1112402)))], (17399 ^ _782435) ^ [_1112487, _1112489, _1112491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112487), _1112489)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112489), _1112491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112487), _1112491)))], (17409 ^ _782435) ^ [_1112650, _1112652] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112650), _1112652)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1112652), _1112650)), -(_1112650 = _1112652)], (17419 ^ _782435) ^ [_1112799, _1112801, _1112803] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112799), _1112801)), _1112803) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1112799), _1112803)), _1112801))], (17421 ^ _782435) ^ [_1112850, _1112852, _1112854] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112850), _1112852)), _1112854) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112852), _1112854)))], (17423 ^ _782435) ^ [_1112901, _1112903] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112901), _1112903) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1112903), _1112901))], (17425 ^ _782435) ^ [_1112938, _1112940] : [-(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)), _1112938), _1112940))], (17427 ^ _782435) ^ [_1112968, _1112970, _1112972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1112968), _1112970)), _1112972)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1112968), _1112972)))], (17433 ^ _782435) ^ [_1113079, _1113081, _1113083, _1113085] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113079), _1113081)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113083), _1113081) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113079), _1113085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113083), _1113085)))], (17443 ^ _782435) ^ [_1113260, _1113262, _1113264, _1113266] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113260), _1113262)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113264), _1113266)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113260), _1113264)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113262), _1113266))))], (17453 ^ _782435) ^ [_1113451, _1113453, _1113455] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113451), _1113453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113451), _1113455)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113453), _1113455))))], (17459 ^ _782435) ^ [_1113574, _1113576, _1113578] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113574), _1113576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113574), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113578), _1113576))))], (17465 ^ _782435) ^ [_1113685, _1113687, _1113689] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113685), _1113687)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113687), _1113689))))], (17471 ^ _782435) ^ [_1113814, _1113816, _1113818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113814), _1113816)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113814), _1113818))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113816), _1113818)))], (17477 ^ _782435) ^ [_1113933, _1113935, _1113937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1113935), _1113937)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113933), _1113935)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1113933), _1113937))))], (17483 ^ _782435) ^ [_1114070, _1114072] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114070), _1114072)), _1114072))], (17485 ^ _782435) ^ [_1114118, _1114120] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1114118), _1114120)), _1114118))], (17487 ^ _782435) ^ [_1114169, _1114171] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114169), _1114171)), 17490 ^ _782435 : [(17491 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114169), _1114171)))], (17493 ^ _782435) ^ [] : [_1114169 = _1114171]]], (17495 ^ _782435) ^ [_1114296, _1114298] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114296), _1114298))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114296), _1114298)), -(_1114296 = _1114298)], (17515 ^ _782435) ^ [_1114571, _1114573] : [17516 ^ _782435 : [(17517 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114571), _1114573))], (17519 ^ _782435) ^ [] : [_1114571 = _1114573]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114571), _1114573)))], (17505 ^ _782435) ^ [_1114465, _1114467] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114465), _1114467)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114465), _1114467))), -(_1114465 = _1114467)], (17523 ^ _782435) ^ [_1114708, _1114710] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114708), _1114710)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114708), _1114710)))], (17529 ^ _782435) ^ [_1114805, _1114807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114805), _1114807)), -(_1114805 = _1114807), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114805), _1114807)))], (17539 ^ _782435) ^ [_1114917, _1114919] : [17540 ^ _782435 : [(17541 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1114917), _1114919))], (17543 ^ _782435) ^ [] : [_1114917 = _1114919]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1114917), _1114919)))], (17547 ^ _782435) ^ [_1115052, _1115054] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115052), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115054), _1115052))))], (17549 ^ _782435) ^ [_1115088, _1115090] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115088), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115088), _1115090))))], (17551 ^ _782435) ^ [_1115139, _1115141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115139), _1115141)), -(_1115141 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115139), 17554 ^ [_1115139, _1115141]))], (17558 ^ _782435) ^ [_1115246, _1115248] : [17559 ^ _782435 : [(17560 ^ _782435) ^ [_1115296] : [_1115248 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115246), _1115296)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115246), _1115248)))], (17564 ^ _782435) ^ [_1115378, _1115380, _1115382] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115378), _1115380)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115378), _1115382))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115380), _1115382)))], (17570 ^ _782435) ^ [_1115497, _1115499, _1115501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115499), _1115501)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115497), _1115499)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115497), _1115501))))], (17576 ^ _782435) ^ [_1115622, _1115624, _1115626] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115622), _1115624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115624), _1115626))))], (17582 ^ _782435) ^ [_1115733, _1115735, _1115737] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115733), _1115735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115733), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115737), _1115735))))], (17588 ^ _782435) ^ [_1115844, _1115846, _1115848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115844), _1115846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115844), _1115848)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115846), _1115848))))], (17594 ^ _782435) ^ [_1115967, _1115969, _1115971, _1115973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115967), _1115969)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1115971), _1115973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115967), _1115971)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1115969), _1115973))))], (17604 ^ _782435) ^ [_1116158, _1116160, _1116162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116158), _1116160)), _1116162)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116160), _1116162)))], (17610 ^ _782435) ^ [_1116269, _1116271, _1116273] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116269), _1116271)), _1116273)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116269), _1116273)))], (17616 ^ _782435) ^ [_1116380, _1116382, _1116384] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116380), _1116382)), _1116384)), 17619 ^ _782435 : [(17620 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116380), _1116384)))], (17622 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1116382), _1116384)))]]], (17624 ^ _782435) ^ [_1116531, _1116533, _1116535] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116531), _1116533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116531), _1116535)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116535), _1116533)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116535), _1116531))))], (17634 ^ _782435) ^ [_1116718, _1116720, _1116722] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1116718), _1116720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116718), _1116722)), _1116720)))], (17640 ^ _782435) ^ [_1116829, _1116831] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116829), _1116831)), _1116831) = _1116829)], (17642 ^ _782435) ^ [_1116866, _1116868] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116866), _1116868)), _1116866) = _1116868)], (17644 ^ _782435) ^ [_1116903, _1116905, _1116907] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116903), _1116905)), _1116907) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116905), _1116907)))], (17646 ^ _782435) ^ [_1116954, _1116956, _1116958] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116954), _1116956)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1116954), _1116958)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1116956), _1116958))], (17648 ^ _782435) ^ [_1117005, _1117007, _1117009] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117005), _1117007)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117009), _1117007)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117005), _1117009))], (17650 ^ _782435) ^ [_1117056, _1117058, _1117060] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117056), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117058), _1117060)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117056), _1117058)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117056), _1117060)))], (17652 ^ _782435) ^ [_1117113, _1117115, _1117117] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1117113), _1117115)), _1117117) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117113), _1117117)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1117115), _1117117)))], (17654 ^ _782435) ^ [_1117170, _1117172] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117170), _1117172)), _1117170)))], (17656 ^ _782435) ^ [_1117206, _1117208, _1117210] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117206), _1117208)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117210), _1117208)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117210), _1117206))))], (17662 ^ _782435) ^ [_1117329, _1117331, _1117333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117329), _1117331)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117329), _1117333)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117331), _1117333))))], (17668 ^ _782435) ^ [_1117452, _1117454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117452), _1117454)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117454), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117454), _1117452)) = _1117452)], (17674 ^ _782435) ^ [_1117563, _1117565, _1117567] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117563), _1117565)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117563), _1117567)), 17681 ^ _782435 : [(17682 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117565), _1117563) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117567), _1117563), -(_1117565 = _1117567)], (17688 ^ _782435) ^ [] : [_1117565 = _1117567, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117565), _1117563) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117567), _1117563))]]], (17694 ^ _782435) ^ [_1117886, _1117888, _1117890] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117886), _1117888)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1117886), _1117890)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117888), _1117886)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117890), _1117886)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1117888), _1117890))], (17704 ^ _782435) ^ [_1118087, _1118089, _1118091] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118087), _1118089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118087), _1118091)), 17711 ^ _782435 : [(17712 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118089), _1118087)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118091), _1118087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118089), _1118091)))], (17718 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118089), _1118091)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118089), _1118087)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118091), _1118087))))]]], (17724 ^ _782435) ^ [_1118440, _1118442, _1118444, _1118446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118440), _1118442)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118444), _1118446)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118440), _1118444)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118442), _1118446))))], (17734 ^ _782435) ^ [_1118631, _1118633, _1118635] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118631), _1118633)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118635), _1118631)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118635), _1118633))))], (17740 ^ _782435) ^ [_1118754, _1118756, _1118758] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118754), _1118756)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118754), _1118758)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118756), _1118758))))], (17746 ^ _782435) ^ [_1118877] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118877), _1118877)))))], (17748 ^ _782435) ^ [_1118917] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1118917), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118917), _1118917))))], (17750 ^ _782435) ^ [_1118951, _1118953, _1118955] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1118951), _1118953)), _1118955) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118951), _1118955)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1118953), _1118955)))], (17752 ^ _782435) ^ [_1119008, _1119010, _1119012] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119008), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119010), _1119012)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119008), _1119010)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119008), _1119012)))], (17754 ^ _782435) ^ [_1119065] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1119065) = _1119065)], (17756 ^ _782435) ^ [_1119106, _1119108] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119106), _1119108), 17759 ^ _782435 : [(17760 ^ _782435) ^ [] : [-(_1119106 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17762 ^ _782435) ^ [] : [-(_1119108 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17764 ^ _782435) ^ [_1119217, _1119219] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119217), _1119219)), _1119217 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1119219 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (17774 ^ _782435) ^ [_1119360] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119360), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1119360)], (17776 ^ _782435) ^ [_1119404, _1119406] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119404), _1119406) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 17779 ^ _782435 : [(17780 ^ _782435) ^ [] : [-(_1119404 = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (17782 ^ _782435) ^ [] : [-(_1119406 = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]], (17784 ^ _782435) ^ [_1119515, _1119517] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1119515), _1119517) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1119515 = c_Groups_Oone__class_Oone(tc_Nat_Onat), _1119517 = c_Groups_Oone__class_Oone(tc_Nat_Onat)], (17794 ^ _782435) ^ [_1119654, _1119656] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119654), _1119656))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119656), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119654), _1119656)) = _1119654)], (17800 ^ _782435) ^ [_1119725, _1119727, _1119729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119725), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119727), _1119729))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119725), _1119729)), _1119727)))], (17806 ^ _782435) ^ [_1119844, _1119846, _1119848] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1119844), _1119848)), _1119846)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119844), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119846), _1119848))))], (17812 ^ _782435) ^ [_1119969, _1119971, _1119973] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119969), _1119971)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1119969), _1119973)), 17819 ^ _782435 : [(17820 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119971), _1119969)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119973), _1119969))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119971), _1119973)))], (17826 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1119971), _1119973)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119971), _1119969)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1119973), _1119969))))]]], (17832 ^ _782435) ^ [_1120322, _1120324, _1120326] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1120322), _1120324)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120326), _1120322)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120322), _1120326)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120324), _1120326))))], (17842 ^ _782435) ^ [_1120509, _1120511, _1120513] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120509), _1120511)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120513), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120511), _1120509)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120513), _1120509)), _1120511))], (17848 ^ _782435) ^ [_1120664, _1120666, _1120668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120664), _1120666)), _1120668)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120664), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120668), _1120666))))], (17854 ^ _782435) ^ [_1120783, _1120785, _1120787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120787), _1120785))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1120783), _1120785)), _1120787)))], (17860 ^ _782435) ^ [_1120908, _1120910, _1120912] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120908), _1120910)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1120912), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1120910), _1120912)), _1120908))))], (17866 ^ _782435) ^ [_1121031, _1121033] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121031), _1121033)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121031), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121033), _1121031)) = _1121033)], (17872 ^ _782435) ^ [_1121142, _1121144, _1121146, _1121148] : [class_Rings_Ocomm__semiring__1(_1121142), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121142), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121142), c_Groups_Oone__class_Oone(_1121142)), c_Groups_Oone__class_Oone(_1121142))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121142), hAPP(hAPP(c_COMBB(_1121142, _1121142, tc_Nat_Onat), hAPP(c_Groups_Oplus__class_Oplus(_1121142), _1121144)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1121142, _1121142), hAPP(hAPP(c_COMBB(_1121142, tc_fun(_1121142, _1121142), tc_Nat_Onat), c_Groups_Otimes__class_Otimes(_1121142)), c_Nat_Osemiring__1__class_Oof__nat(_1121142))), _1121146))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1121148))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121142), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121142), _1121148)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121142), _1121144), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1121142), _1121144), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1121142), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1121142), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1121148), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1121146)))))], (17878 ^ _782435) ^ [_1121465, _1121467, _1121469, _1121471] : [class_Groups_Oab__group__add(_1121465), 17881 ^ _782435 : [(17882 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121467), _1121469)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121465), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1121465, _1121465), hAPP(hAPP(c_COMBB(_1121465, tc_fun(_1121465, _1121465), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1121465)), _1121471)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1121465, tc_Nat_Onat), _1121471), 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, _1121467, _1121469)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1121465), hAPP(_1121471, _1121467)), hAPP(_1121471, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121469), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (17888 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121467), _1121469))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1121465), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1121465, _1121465), hAPP(hAPP(c_COMBB(_1121465, tc_fun(_1121465, _1121465), tc_Nat_Onat), c_Groups_Ominus__class_Ominus(_1121465)), _1121471)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1121465, tc_Nat_Onat), _1121471), 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, _1121467, _1121469)) = c_Groups_Ozero__class_Ozero(_1121465))]]], (17894 ^ _782435) ^ [_1121903, _1121905, _1121907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121903), _1121905)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1121903), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1121905), _1121907))))], (17900 ^ _782435) ^ [_1122014, _1122016, _1122018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122014), _1122016)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122018), _1122016))))], (17906 ^ _782435) ^ [_1122125, _1122127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122125), _1122127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1122125), _1122127)))], (17912 ^ _782435) ^ [_1122222, _1122224, _1122226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122222), _1122224)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122222), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122226), _1122224))))], (17918 ^ _782435) ^ [_1122333, _1122335, _1122337] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122333), _1122335)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122333), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1122335), _1122337))))], (17924 ^ _782435) ^ [_1122453] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1122453), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (17926 ^ _782435) ^ [_1122481] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122481)))], (17928 ^ _782435) ^ [_1122506, _1122508] : [class_Rings_Olinordered__semidom(_1122506), 17931 ^ _782435 : [(17932 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122506), c_Groups_Ozero__class_Ozero(_1122506)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122506), _1122508))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122508)))], (17938 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1122508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122506), c_Groups_Ozero__class_Ozero(_1122506)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122506), _1122508))))]]], (17944 ^ _782435) ^ [_1122759, _1122761] : [class_Rings_Olinordered__semidom(_1122759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1122759), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122759), _1122761)), c_Groups_Ozero__class_Ozero(_1122759)))], (17950 ^ _782435) ^ [_1122863] : [class_Rings_Osemiring__1(_1122863), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122863), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1122863))], (17956 ^ _782435) ^ [_1122950, _1122952, _1122954] : [class_Nat_Osemiring__char__0(_1122950), 17959 ^ _782435 : [(17960 ^ _782435) ^ [] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122950), _1122952) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122950), _1122954), -(_1122952 = _1122954)], (17966 ^ _782435) ^ [] : [_1122952 = _1122954, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122950), _1122952) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1122950), _1122954))]]], (17972 ^ _782435) ^ [_1123191, _1123193] : [class_Rings_Olinordered__semidom(_1123191), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123191), c_Groups_Ozero__class_Ozero(_1123191)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1123191), _1123193))))], (17978 ^ _782435) ^ [_1123294, _1123296] : [class_Rings_Olinordered__semidom(_1123294), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1123294), c_Groups_Ozero__class_Ozero(_1123294)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1123294), _1123296))))], (17984 ^ _782435) ^ [_1123397, _1123399] : [class_Groups_Ozero(_1123397), 17987 ^ _782435 : [(17988 ^ _782435) ^ [] : [c_Groups_Ozero__class_Ozero(_1123397) = _1123399, -(_1123399 = c_Groups_Ozero__class_Ozero(_1123397))], (17994 ^ _782435) ^ [] : [_1123399 = c_Groups_Ozero__class_Ozero(_1123397), -(c_Groups_Ozero__class_Ozero(_1123397) = _1123399)]]], (18000 ^ _782435) ^ [_1123614, _1123616, _1123618] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1123614), 18003 ^ _782435 : [(18004 ^ _782435) ^ [] : [_1123616 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123614), _1123616), _1123618), -(_1123618 = c_Groups_Ozero__class_Ozero(_1123614))], (18010 ^ _782435) ^ [] : [_1123618 = c_Groups_Ozero__class_Ozero(_1123614), -(_1123616 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123614), _1123616), _1123618))]]], (18016 ^ _782435) ^ [_1123855, _1123857] : [class_Rings_Ocomm__semiring__1(_1123855), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123855), _1123857), c_Groups_Ozero__class_Ozero(_1123855)) = _1123857)], (18022 ^ _782435) ^ [_1123950, _1123952] : [class_Rings_Ocomm__semiring__1(_1123950), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1123950), c_Groups_Ozero__class_Ozero(_1123950)), _1123952) = _1123952)], (18028 ^ _782435) ^ [_1124045, _1124047] : [class_Groups_Omonoid__add(_1124045), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124045), c_Groups_Ozero__class_Ozero(_1124045)), _1124047) = _1124047)], (18034 ^ _782435) ^ [_1124140, _1124142] : [class_Groups_Ocomm__monoid__add(_1124140), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124140), c_Groups_Ozero__class_Ozero(_1124140)), _1124142) = _1124142)], (18040 ^ _782435) ^ [_1124235, _1124237] : [class_Groups_Olinordered__ab__group__add(_1124235), 18043 ^ _782435 : [(18044 ^ _782435) ^ [] : [c_Groups_Ozero__class_Ozero(_1124235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124235), _1124237), _1124237), -(_1124237 = c_Groups_Ozero__class_Ozero(_1124235))], (18050 ^ _782435) ^ [] : [_1124237 = c_Groups_Ozero__class_Ozero(_1124235), -(c_Groups_Ozero__class_Ozero(_1124235) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124235), _1124237), _1124237))]]], (18056 ^ _782435) ^ [_1124476, _1124478] : [class_Groups_Omonoid__add(_1124476), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124476), _1124478), c_Groups_Ozero__class_Ozero(_1124476)) = _1124478)], (18062 ^ _782435) ^ [_1124571, _1124573] : [class_Groups_Ocomm__monoid__add(_1124571), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1124571), _1124573), c_Groups_Ozero__class_Ozero(_1124571)) = _1124573)], (18068 ^ _782435) ^ [_1124666, _1124668] : [class_Rings_Omult__zero(_1124666), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124666), c_Groups_Ozero__class_Ozero(_1124666)), _1124668) = c_Groups_Ozero__class_Ozero(_1124666))], (18074 ^ _782435) ^ [_1124765, _1124767] : [class_Rings_Omult__zero(_1124765), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124765), _1124767), c_Groups_Ozero__class_Ozero(_1124765)) = c_Groups_Ozero__class_Ozero(_1124765))], (18080 ^ _782435) ^ [_1124864, _1124866, _1124868] : [class_Rings_Oring__no__zero__divisors(_1124864), 18083 ^ _782435 : [(18094 ^ _782435) ^ [] : [18095 ^ _782435 : [(18096 ^ _782435) ^ [] : [_1124866 = c_Groups_Ozero__class_Ozero(_1124864)], (18098 ^ _782435) ^ [] : [_1124868 = c_Groups_Ozero__class_Ozero(_1124864)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124864), _1124866), _1124868) = c_Groups_Ozero__class_Ozero(_1124864))], (18084 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1124864), _1124866), _1124868) = c_Groups_Ozero__class_Ozero(_1124864), -(_1124866 = c_Groups_Ozero__class_Ozero(_1124864)), -(_1124868 = c_Groups_Ozero__class_Ozero(_1124864))]]], (18102 ^ _782435) ^ [_1125162, _1125164, _1125166] : [class_Rings_Ono__zero__divisors(_1125162), -(_1125164 = c_Groups_Ozero__class_Ozero(_1125162)), -(_1125166 = c_Groups_Ozero__class_Ozero(_1125162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125162), _1125164), _1125166) = c_Groups_Ozero__class_Ozero(_1125162)], (18116 ^ _782435) ^ [_1125382, _1125384, _1125386] : [class_Rings_Ono__zero__divisors(_1125382), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125382), _1125384), _1125386) = c_Groups_Ozero__class_Ozero(_1125382), -(_1125384 = c_Groups_Ozero__class_Ozero(_1125382)), -(_1125386 = c_Groups_Ozero__class_Ozero(_1125382))], (18130 ^ _782435) ^ [_1125554, _1125556] : [class_Rings_Ocomm__semiring__1(_1125554), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125554), c_Groups_Ozero__class_Ozero(_1125554)), _1125556) = c_Groups_Ozero__class_Ozero(_1125554))], (18136 ^ _782435) ^ [_1125653, _1125655] : [class_Rings_Ocomm__semiring__1(_1125653), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1125653), _1125655), c_Groups_Ozero__class_Ozero(_1125653)) = c_Groups_Ozero__class_Ozero(_1125653))], (18142 ^ _782435) ^ [_1125752, _1125754] : [class_Groups_Ogroup__add(_1125752), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125752), _1125754), c_Groups_Ozero__class_Ozero(_1125752)) = _1125754)], (18148 ^ _782435) ^ [_1125847, _1125849] : [class_Groups_Ogroup__add(_1125847), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125847), _1125849), _1125849) = c_Groups_Ozero__class_Ozero(_1125847))], (18154 ^ _782435) ^ [_1125942, _1125944, _1125946] : [class_Groups_Oab__group__add(_1125942), 18157 ^ _782435 : [(18158 ^ _782435) ^ [] : [_1125944 = _1125946, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125942), _1125944), _1125946) = c_Groups_Ozero__class_Ozero(_1125942))], (18164 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1125942), _1125944), _1125946) = c_Groups_Ozero__class_Ozero(_1125942), -(_1125944 = _1125946)]]], (18170 ^ _782435) ^ [_1126183, _1126185, _1126187] : [class_Groups_Ogroup__add(_1126183), 18173 ^ _782435 : [(18174 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126183), _1126185), _1126187) = c_Groups_Ozero__class_Ozero(_1126183), -(_1126185 = _1126187)], (18180 ^ _782435) ^ [] : [_1126185 = _1126187, -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1126183), _1126185), _1126187) = c_Groups_Ozero__class_Ozero(_1126183))]]], (18186 ^ _782435) ^ [_1126424] : [class_Rings_Ozero__neq__one(_1126424), c_Groups_Oone__class_Oone(_1126424) = c_Groups_Ozero__class_Ozero(_1126424)], (18192 ^ _782435) ^ [_1126506] : [class_Rings_Ozero__neq__one(_1126506), c_Groups_Ozero__class_Ozero(_1126506) = c_Groups_Oone__class_Oone(_1126506)], (18198 ^ _782435) ^ [_1126588, _1126590] : [class_Groups_Olinordered__ab__group__add(_1126588), 18201 ^ _782435 : [(18202 ^ _782435) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1126588), _1126590) = _1126590, -(_1126590 = c_Groups_Ozero__class_Ozero(_1126588))], (18208 ^ _782435) ^ [] : [_1126590 = c_Groups_Ozero__class_Ozero(_1126588), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126588), _1126590) = _1126590)]]], (18214 ^ _782435) ^ [_1126814, _1126816] : [class_Groups_Ogroup__add(_1126814), 18217 ^ _782435 : [(18218 ^ _782435) ^ [] : [hAPP(c_Groups_Ouminus__class_Ouminus(_1126814), _1126816) = c_Groups_Ozero__class_Ozero(_1126814), -(_1126816 = c_Groups_Ozero__class_Ozero(_1126814))], (18224 ^ _782435) ^ [] : [_1126816 = c_Groups_Ozero__class_Ozero(_1126814), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1126814), _1126816) = c_Groups_Ozero__class_Ozero(_1126814))]]], (18230 ^ _782435) ^ [_1127046, _1127048] : [class_Groups_Olinordered__ab__group__add(_1127046), 18233 ^ _782435 : [(18234 ^ _782435) ^ [] : [_1127048 = hAPP(c_Groups_Ouminus__class_Ouminus(_1127046), _1127048), -(_1127048 = c_Groups_Ozero__class_Ozero(_1127046))], (18240 ^ _782435) ^ [] : [_1127048 = c_Groups_Ozero__class_Ozero(_1127046), -(_1127048 = hAPP(c_Groups_Ouminus__class_Ouminus(_1127046), _1127048))]]], (18246 ^ _782435) ^ [_1127272, _1127274] : [class_Groups_Ogroup__add(_1127272), 18249 ^ _782435 : [(18250 ^ _782435) ^ [] : [c_Groups_Ozero__class_Ozero(_1127272) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127272), _1127274), -(c_Groups_Ozero__class_Ozero(_1127272) = _1127274)], (18256 ^ _782435) ^ [] : [c_Groups_Ozero__class_Ozero(_1127272) = _1127274, -(c_Groups_Ozero__class_Ozero(_1127272) = hAPP(c_Groups_Ouminus__class_Ouminus(_1127272), _1127274))]]], (18262 ^ _782435) ^ [_1127504] : [class_Groups_Ogroup__add(_1127504), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1127504), c_Groups_Ozero__class_Ozero(_1127504)) = c_Groups_Ozero__class_Ozero(_1127504))], (18268 ^ _782435) ^ [_1127604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127604), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18270 ^ _782435) ^ [_1127638] : [-(_1127638 = 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)), _1127638)))], (18276 ^ _782435) ^ [_1127670] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1127670)), _1127670 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18282 ^ _782435) ^ [_1127761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127761), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (18284 ^ _782435) ^ [_1127789, _1127791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1127789), _1127791)), _1127791 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18290 ^ _782435) ^ [_1127873] : [-(_1127873 = 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)), _1127873)))], (18296 ^ _782435) ^ [_1127909, _1127911] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1127909), _1127911) = _1127909, -(_1127911 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18302 ^ _782435) ^ [_1128013, _1128015] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128013), _1128015) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 18305 ^ _782435 : [(18306 ^ _782435) ^ [] : [-(_1128013 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18308 ^ _782435) ^ [] : [-(_1128015 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (18310 ^ _782435) ^ [_1128124, _1128126] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128124), _1128126) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128124 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1128126 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18320 ^ _782435) ^ [_1128267] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1128267), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1128267)], (18322 ^ _782435) ^ [_1128296] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128296) = _1128296)], (18324 ^ _782435) ^ [_1128322] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128322)))], (18326 ^ _782435) ^ [_1128359] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128359), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(_1128359 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18332 ^ _782435) ^ [_1128440] : [_1128440 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1128440), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (18338 ^ _782435) ^ [_1128527] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1128527) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18340 ^ _782435) ^ [_1128553] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128553), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1128553)], (18342 ^ _782435) ^ [_1128582] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128582), _1128582) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18344 ^ _782435) ^ [_1128611, _1128613] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128611), _1128613) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1128613), _1128611) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1128611 = _1128613)], (18364 ^ _782435) ^ [_1128894, _1128896, _1128898] : [18365 ^ _782435 : [(18366 ^ _782435) ^ [] : [_1128894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18368 ^ _782435) ^ [] : [_1128896 = _1128898]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128894), _1128896) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128894), _1128898))], (18354 ^ _782435) ^ [_1128782, _1128784, _1128786] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128782), _1128784) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1128782), _1128786), -(_1128782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1128784 = _1128786)], (18382 ^ _782435) ^ [_1129167, _1129169, _1129171] : [18383 ^ _782435 : [(18384 ^ _782435) ^ [] : [_1129167 = _1129171], (18386 ^ _782435) ^ [] : [_1129169 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129167), _1129169) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129171), _1129169))], (18372 ^ _782435) ^ [_1129055, _1129057, _1129059] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129055), _1129057) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129059), _1129057), -(_1129055 = _1129059), -(_1129057 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18400 ^ _782435) ^ [_1129440, _1129442, _1129444] : [18401 ^ _782435 : [(18402 ^ _782435) ^ [] : [_1129442 = _1129444], (18404 ^ _782435) ^ [] : [_1129440 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129440), _1129442) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129440), _1129444))], (18390 ^ _782435) ^ [_1129328, _1129330, _1129332] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129328), _1129330) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129328), _1129332), -(_1129330 = _1129332), -(_1129328 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18418 ^ _782435) ^ [_1129696, _1129698] : [18419 ^ _782435 : [(18420 ^ _782435) ^ [] : [_1129696 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (18422 ^ _782435) ^ [] : [_1129698 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129696), _1129698) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18408 ^ _782435) ^ [_1129598, _1129600] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129598), _1129600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1129598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1129600 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18426 ^ _782435) ^ [_1129825] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1129825), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18428 ^ _782435) ^ [_1129854] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1129854) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (18430 ^ _782435) ^ [_1129880] : [class_Nat_Osemiring__char__0(_1129880), -(c_Fun_Oinj__on(tc_Nat_Onat, _1129880, c_Nat_Osemiring__1__class_Oof__nat(_1129880), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (18436 ^ _782435) ^ [_1129961] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1129961), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (18438 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1130044, _1130046, _1130048] : [class_Groups_Ocomm__monoid__add(_1130044), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1130046, _1130044), hAPP(c_COMBK(_1130044, _1130046), c_Groups_Ozero__class_Ozero(_1130044))), _1130048) = c_Groups_Ozero__class_Ozero(_1130044))], (18450 ^ _782435) ^ [_1130159, _1130161, _1130163] : [class_Rings_Olinordered__semidom(_1130159), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130159), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130159), _1130161)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130159), _1130163))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130161), _1130163)))], (18460 ^ _782435) ^ [_1130334, _1130336, _1130338] : [class_Rings_Olinordered__semidom(_1130334), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130336), _1130338)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130334), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130334), _1130336)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130334), _1130338))))], (18470 ^ _782435) ^ [_1130509, _1130511, _1130513] : [class_Rings_Olinordered__semidom(_1130509), 18473 ^ _782435 : [(18474 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130509), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130509), _1130511)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130509), _1130513))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130511), _1130513)))], (18480 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1130511), _1130513)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1130509), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130509), _1130511)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130509), _1130513))))]]], (18486 ^ _782435) ^ [_1130786, _1130788, _1130790] : [class_Rings_Olinordered__semidom(_1130786), 18489 ^ _782435 : [(18490 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130786), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130786), _1130788)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130786), _1130790))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130788), _1130790)))], (18496 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1130788), _1130790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1130786), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130786), _1130788)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1130786), _1130790))))]]], (18502 ^ _782435) ^ [_1131063, _1131065, _1131067] : [class_Rings_Osemiring__1(_1131063), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1131065), _1131067)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131063), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131063), _1131065)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1131063), _1131067)))], (18508 ^ _782435) ^ [_1131198, _1131200] : [class_Groups_Olinordered__ab__group__add(_1131198), 18511 ^ _782435 : [(18512 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131198), c_Groups_Ozero__class_Ozero(_1131198)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131198), _1131200), _1131200))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131198), c_Groups_Ozero__class_Ozero(_1131198)), _1131200)))], (18518 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131198), c_Groups_Ozero__class_Ozero(_1131198)), _1131200)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131198), c_Groups_Ozero__class_Ozero(_1131198)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131198), _1131200), _1131200))))]]], (18524 ^ _782435) ^ [_1131481, _1131483] : [class_Groups_Olinordered__ab__group__add(_1131481), 18527 ^ _782435 : [(18528 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131481), _1131483), _1131483)), c_Groups_Ozero__class_Ozero(_1131481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131481), _1131483), c_Groups_Ozero__class_Ozero(_1131481))))], (18534 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131481), _1131483), c_Groups_Ozero__class_Ozero(_1131481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131481), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131481), _1131483), _1131483)), c_Groups_Ozero__class_Ozero(_1131481))))]]], (18540 ^ _782435) ^ [_1131764, _1131766, _1131768] : [class_Groups_Oordered__comm__monoid__add(_1131764), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131764), c_Groups_Ozero__class_Ozero(_1131764)), _1131766)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131764), c_Groups_Ozero__class_Ozero(_1131764)), _1131768)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1131764), c_Groups_Ozero__class_Ozero(_1131764)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1131764), _1131766), _1131768))))], (18554 ^ _782435) ^ [_1132019, _1132021, _1132023] : [class_Groups_Oordered__comm__monoid__add(_1132019), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132019), c_Groups_Ozero__class_Ozero(_1132019)), _1132021)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132019), c_Groups_Ozero__class_Ozero(_1132019)), _1132023)), 18565 ^ _782435 : [(18566 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132019), _1132021), _1132023) = c_Groups_Ozero__class_Ozero(_1132019), 18569 ^ _782435 : [(18570 ^ _782435) ^ [] : [-(_1132021 = c_Groups_Ozero__class_Ozero(_1132019))], (18572 ^ _782435) ^ [] : [-(_1132023 = c_Groups_Ozero__class_Ozero(_1132019))]]], (18574 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132019), _1132021), _1132023) = c_Groups_Ozero__class_Ozero(_1132019)), _1132021 = c_Groups_Ozero__class_Ozero(_1132019), _1132023 = c_Groups_Ozero__class_Ozero(_1132019)]]], (18584 ^ _782435) ^ [_1132490, _1132492, _1132494, _1132496] : [class_Groups_Oordered__comm__monoid__add(_1132490), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132490), c_Groups_Ozero__class_Ozero(_1132490)), _1132492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132490), _1132494), _1132496)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132490), _1132494), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132490), _1132492), _1132496))))], (18598 ^ _782435) ^ [_1132743, _1132745, _1132747, _1132749] : [class_Groups_Oordered__comm__monoid__add(_1132743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132743), c_Groups_Ozero__class_Ozero(_1132743)), _1132745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132743), _1132747), _1132749)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132743), _1132747), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132743), _1132749), _1132745))))], (18612 ^ _782435) ^ [_1132996, _1132998, _1133000] : [class_Groups_Oordered__comm__monoid__add(_1132996), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132996), _1132998), c_Groups_Ozero__class_Ozero(_1132996))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132996), _1133000), c_Groups_Ozero__class_Ozero(_1132996))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1132996), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1132996), _1132998), _1133000)), c_Groups_Ozero__class_Ozero(_1132996))))], (18626 ^ _782435) ^ [_1133251, _1133253, _1133255] : [class_Rings_Oordered__cancel__semiring(_1133251), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133251), _1133253), _1133255)), c_Groups_Ozero__class_Ozero(_1133251)))), 18631 ^ _782435 : [(18632 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133251), c_Groups_Ozero__class_Ozero(_1133251)), _1133253)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133251), _1133255), c_Groups_Ozero__class_Ozero(_1133251)))], (18638 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133251), _1133253), c_Groups_Ozero__class_Ozero(_1133251))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133251), c_Groups_Ozero__class_Ozero(_1133251)), _1133255))]]], (18646 ^ _782435) ^ [_1133627, _1133629, _1133631] : [class_Rings_Oordered__ring(_1133627), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133627), c_Groups_Ozero__class_Ozero(_1133627)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1133627), _1133629), _1133631)))), 18651 ^ _782435 : [(18652 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133627), c_Groups_Ozero__class_Ozero(_1133627)), _1133629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133627), c_Groups_Ozero__class_Ozero(_1133627)), _1133631))], (18658 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133627), _1133629), c_Groups_Ozero__class_Ozero(_1133627))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1133627), _1133631), c_Groups_Ozero__class_Ozero(_1133627)))]]], (18666 ^ _782435) ^ [_1134003, _1134005, _1134007, _1134009, _1134011] : [class_Rings_Oordered__semiring(_1134003), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134003), _1134005), _1134007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134003), _1134009), _1134011)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134003), c_Groups_Ozero__class_Ozero(_1134003)), _1134007)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134003), c_Groups_Ozero__class_Ozero(_1134003)), _1134009)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134003), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134003), _1134005), _1134009)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134003), _1134007), _1134011))))], (18688 ^ _782435) ^ [_1134426, _1134428, _1134430, _1134432, _1134434] : [class_Rings_Oordered__semiring(_1134426), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134426), _1134428), _1134430)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134426), _1134432), _1134434)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134426), c_Groups_Ozero__class_Ozero(_1134426)), _1134428)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134426), c_Groups_Ozero__class_Ozero(_1134426)), _1134432)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134426), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134426), _1134428), _1134432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134426), _1134430), _1134434))))], (18710 ^ _782435) ^ [_1134849, _1134851, _1134853, _1134855] : [class_Rings_Oordered__ring(_1134849), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134849), _1134851), _1134853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134849), _1134855), c_Groups_Ozero__class_Ozero(_1134849))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1134849), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134849), _1134855), _1134853)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1134849), _1134855), _1134851))))], (18724 ^ _782435) ^ [_1135118, _1135120, _1135122, _1135124] : [class_Rings_Oordered__ring(_1135118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135118), _1135120), _1135122)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135118), _1135124), c_Groups_Ozero__class_Ozero(_1135118))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135118), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135118), _1135122), _1135124)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135118), _1135120), _1135124))))], (18738 ^ _782435) ^ [_1135387, _1135389, _1135391, _1135393] : [class_Rings_Oordered__comm__semiring(_1135387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135387), _1135389), _1135391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135387), c_Groups_Ozero__class_Ozero(_1135387)), _1135393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135387), _1135393), _1135389)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135387), _1135393), _1135391))))], (18752 ^ _782435) ^ [_1135656, _1135658, _1135660, _1135662] : [class_Rings_Oordered__semiring(_1135656), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135656), _1135658), _1135660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135656), c_Groups_Ozero__class_Ozero(_1135656)), _1135662)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135656), _1135662), _1135658)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135656), _1135662), _1135660))))], (18766 ^ _782435) ^ [_1135925, _1135927, _1135929, _1135931] : [class_Rings_Oordered__semiring(_1135925), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135925), _1135927), _1135929)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135925), c_Groups_Ozero__class_Ozero(_1135925)), _1135931)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1135925), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135925), _1135927), _1135931)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1135925), _1135929), _1135931))))], (18780 ^ _782435) ^ [_1136194, _1136196, _1136198] : [class_Rings_Oordered__ring(_1136194), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136194), _1136196), c_Groups_Ozero__class_Ozero(_1136194))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136194), _1136198), c_Groups_Ozero__class_Ozero(_1136194))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136194), c_Groups_Ozero__class_Ozero(_1136194)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136194), _1136196), _1136198))))], (18794 ^ _782435) ^ [_1136449, _1136451, _1136453] : [class_Rings_Oordered__cancel__semiring(_1136449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136449), _1136451), c_Groups_Ozero__class_Ozero(_1136449))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136449), c_Groups_Ozero__class_Ozero(_1136449)), _1136453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136449), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136449), _1136451), _1136453)), c_Groups_Ozero__class_Ozero(_1136449))))], (18808 ^ _782435) ^ [_1136704, _1136706, _1136708] : [class_Rings_Oordered__cancel__semiring(_1136704), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136704), c_Groups_Ozero__class_Ozero(_1136704)), _1136706)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136704), _1136708), c_Groups_Ozero__class_Ozero(_1136704))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136704), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136704), _1136708), _1136706)), c_Groups_Ozero__class_Ozero(_1136704))))], (18822 ^ _782435) ^ [_1136959, _1136961, _1136963] : [class_Rings_Oordered__cancel__semiring(_1136959), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136959), c_Groups_Ozero__class_Ozero(_1136959)), _1136961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136959), _1136963), c_Groups_Ozero__class_Ozero(_1136959))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1136959), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1136959), _1136961), _1136963)), c_Groups_Ozero__class_Ozero(_1136959))))], (18836 ^ _782435) ^ [_1137214, _1137216, _1137218] : [class_Rings_Oordered__cancel__semiring(_1137214), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137214), c_Groups_Ozero__class_Ozero(_1137214)), _1137216)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137214), c_Groups_Ozero__class_Ozero(_1137214)), _1137218)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137214), c_Groups_Ozero__class_Ozero(_1137214)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137214), _1137216), _1137218))))], (18850 ^ _782435) ^ [_1137469, _1137471, _1137473] : [class_Rings_Olinordered__ring__strict(_1137469), 18853 ^ _782435 : [(18854 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137469), _1137471), _1137473)), c_Groups_Ozero__class_Ozero(_1137469))), 18859 ^ _782435 : [(18860 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), c_Groups_Ozero__class_Ozero(_1137469)), _1137471)))], (18862 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), _1137473), c_Groups_Ozero__class_Ozero(_1137469))))]], 18863 ^ _782435 : [(18864 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), _1137471), c_Groups_Ozero__class_Ozero(_1137469))))], (18866 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), c_Groups_Ozero__class_Ozero(_1137469)), _1137473)))]]], (18868 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1137469), _1137471), _1137473)), c_Groups_Ozero__class_Ozero(_1137469)))), 18869 ^ _782435 : [(18870 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), c_Groups_Ozero__class_Ozero(_1137469)), _1137471)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), _1137473), c_Groups_Ozero__class_Ozero(_1137469)))], (18876 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), _1137471), c_Groups_Ozero__class_Ozero(_1137469))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1137469), c_Groups_Ozero__class_Ozero(_1137469)), _1137473))]]]]], (18884 ^ _782435) ^ [_1138059, _1138061, _1138063] : [class_Rings_Olinordered__ring__strict(_1138059), 18887 ^ _782435 : [(18888 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), c_Groups_Ozero__class_Ozero(_1138059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138059), _1138061), _1138063))), 18893 ^ _782435 : [(18894 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), c_Groups_Ozero__class_Ozero(_1138059)), _1138061)))], (18896 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), c_Groups_Ozero__class_Ozero(_1138059)), _1138063)))]], 18897 ^ _782435 : [(18898 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), _1138061), c_Groups_Ozero__class_Ozero(_1138059))))], (18900 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), _1138063), c_Groups_Ozero__class_Ozero(_1138059))))]]], (18902 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), c_Groups_Ozero__class_Ozero(_1138059)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138059), _1138061), _1138063)))), 18903 ^ _782435 : [(18904 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), c_Groups_Ozero__class_Ozero(_1138059)), _1138061)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), c_Groups_Ozero__class_Ozero(_1138059)), _1138063))], (18910 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), _1138061), c_Groups_Ozero__class_Ozero(_1138059))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138059), _1138063), c_Groups_Ozero__class_Ozero(_1138059)))]]]]], (18918 ^ _782435) ^ [_1138649, _1138651] : [class_Rings_Olinordered__ring(_1138649), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1138649), c_Groups_Ozero__class_Ozero(_1138649)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1138649), _1138651), _1138651))))], (18924 ^ _782435) ^ [_1138758, _1138760, _1138762, _1138764] : [class_Rings_Olinordered__semidom(_1138758), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138758), c_Groups_Ozero__class_Ozero(_1138758)), _1138760)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138758), _1138762), _1138764)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1138758), _1138762), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1138758), _1138760), _1138764))))], (18938 ^ _782435) ^ [_1139011, _1139013] : [class_Groups_Olinordered__ab__group__add(_1139011), 18941 ^ _782435 : [(18942 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139011), c_Groups_Ozero__class_Ozero(_1139011)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139011), _1139013), _1139013))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139011), c_Groups_Ozero__class_Ozero(_1139011)), _1139013)))], (18948 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139011), c_Groups_Ozero__class_Ozero(_1139011)), _1139013)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139011), c_Groups_Ozero__class_Ozero(_1139011)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139011), _1139013), _1139013))))]]], (18954 ^ _782435) ^ [_1139294, _1139296] : [class_Groups_Olinordered__ab__group__add(_1139294), 18957 ^ _782435 : [(18958 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139294), _1139296), _1139296)), c_Groups_Ozero__class_Ozero(_1139294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139294), _1139296), c_Groups_Ozero__class_Ozero(_1139294))))], (18964 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139294), _1139296), c_Groups_Ozero__class_Ozero(_1139294))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139294), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139294), _1139296), _1139296)), c_Groups_Ozero__class_Ozero(_1139294))))]]], (18970 ^ _782435) ^ [_1139577, _1139579, _1139581] : [class_Groups_Oordered__comm__monoid__add(_1139577), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), c_Groups_Ozero__class_Ozero(_1139577)), _1139579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), c_Groups_Ozero__class_Ozero(_1139577)), _1139581)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139577), c_Groups_Ozero__class_Ozero(_1139577)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139577), _1139579), _1139581))))], (18984 ^ _782435) ^ [_1139832, _1139834, _1139836] : [class_Groups_Oordered__comm__monoid__add(_1139832), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139832), _1139834), c_Groups_Ozero__class_Ozero(_1139832))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139832), _1139836), c_Groups_Ozero__class_Ozero(_1139832))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1139832), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1139832), _1139834), _1139836)), c_Groups_Ozero__class_Ozero(_1139832))))], (18998 ^ _782435) ^ [_1140087, _1140089, _1140091, _1140093] : [class_Rings_Olinordered__ring__strict(_1140087), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140087), _1140089), _1140091)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140087), _1140093), c_Groups_Ozero__class_Ozero(_1140087))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140087), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140087), _1140093), _1140091)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140087), _1140093), _1140089))))], (19012 ^ _782435) ^ [_1140356, _1140358, _1140360, _1140362] : [class_Rings_Olinordered__ring__strict(_1140356), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140356), _1140358), _1140360)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140356), _1140362), c_Groups_Ozero__class_Ozero(_1140356))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140356), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140356), _1140360), _1140362)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140356), _1140358), _1140362))))], (19026 ^ _782435) ^ [_1140625, _1140627, _1140629, _1140631] : [class_Rings_Olinordered__comm__semiring__strict(_1140625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140625), _1140627), _1140629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140625), c_Groups_Ozero__class_Ozero(_1140625)), _1140631)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140625), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140625), _1140631), _1140627)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140625), _1140631), _1140629))))], (19040 ^ _782435) ^ [_1140894, _1140896, _1140898, _1140900] : [class_Rings_Olinordered__semiring__strict(_1140894), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140894), _1140896), _1140898)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140894), c_Groups_Ozero__class_Ozero(_1140894)), _1140900)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1140894), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140894), _1140900), _1140896)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1140894), _1140900), _1140898))))], (19054 ^ _782435) ^ [_1141163, _1141165, _1141167, _1141169] : [class_Rings_Olinordered__semiring__strict(_1141163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141163), _1141165), _1141167)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141163), c_Groups_Ozero__class_Ozero(_1141163)), _1141169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141163), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141163), _1141165), _1141169)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141163), _1141167), _1141169))))], (19068 ^ _782435) ^ [_1141432, _1141434, _1141436] : [class_Rings_Olinordered__ring__strict(_1141432), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141432), _1141434), c_Groups_Ozero__class_Ozero(_1141432))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141432), _1141436), c_Groups_Ozero__class_Ozero(_1141432))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141432), c_Groups_Ozero__class_Ozero(_1141432)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141432), _1141434), _1141436))))], (19082 ^ _782435) ^ [_1141687, _1141689, _1141691] : [class_Rings_Olinordered__semiring__strict(_1141687), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141687), _1141689), c_Groups_Ozero__class_Ozero(_1141687))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141687), c_Groups_Ozero__class_Ozero(_1141687)), _1141691)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141687), _1141689), _1141691)), c_Groups_Ozero__class_Ozero(_1141687))))], (19096 ^ _782435) ^ [_1141942, _1141944, _1141946, _1141948] : [class_Rings_Olinordered__ring__strict(_1141942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141942), _1141944), c_Groups_Ozero__class_Ozero(_1141942))), 19103 ^ _782435 : [(19104 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141942), _1141944), _1141946)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141942), _1141944), _1141948))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141942), _1141948), _1141946)))], (19110 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141942), _1141948), _1141946)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1141942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141942), _1141944), _1141946)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1141942), _1141944), _1141948))))]]], (19116 ^ _782435) ^ [_1142323, _1142325, _1142327] : [class_Rings_Olinordered__semiring__strict(_1142323), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142323), c_Groups_Ozero__class_Ozero(_1142323)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142323), _1142325), _1142327))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142323), c_Groups_Ozero__class_Ozero(_1142323)), _1142327)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142323), c_Groups_Ozero__class_Ozero(_1142323)), _1142325)))], (19130 ^ _782435) ^ [_1142578, _1142580, _1142582] : [class_Rings_Olinordered__semiring__strict(_1142578), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142578), c_Groups_Ozero__class_Ozero(_1142578)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142578), _1142580), _1142582))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142578), c_Groups_Ozero__class_Ozero(_1142578)), _1142580)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142578), c_Groups_Ozero__class_Ozero(_1142578)), _1142582)))], (19144 ^ _782435) ^ [_1142833, _1142835, _1142837] : [class_Rings_Olinordered__semiring__strict(_1142833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142833), c_Groups_Ozero__class_Ozero(_1142833)), _1142835)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142833), _1142837), c_Groups_Ozero__class_Ozero(_1142833))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1142833), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1142833), _1142837), _1142835)), c_Groups_Ozero__class_Ozero(_1142833))))], (19158 ^ _782435) ^ [_1143088, _1143090, _1143092] : [class_Rings_Olinordered__semiring__strict(_1143088), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143088), c_Groups_Ozero__class_Ozero(_1143088)), _1143090)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143088), _1143092), c_Groups_Ozero__class_Ozero(_1143088))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143088), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143088), _1143090), _1143092)), c_Groups_Ozero__class_Ozero(_1143088))))], (19172 ^ _782435) ^ [_1143343, _1143345, _1143347] : [class_Rings_Olinordered__semiring__strict(_1143343), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143343), c_Groups_Ozero__class_Ozero(_1143343)), _1143345)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143343), c_Groups_Ozero__class_Ozero(_1143343)), _1143347)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143343), c_Groups_Ozero__class_Ozero(_1143343)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143343), _1143345), _1143347))))], (19186 ^ _782435) ^ [_1143598, _1143600, _1143602, _1143604] : [class_Rings_Olinordered__ring__strict(_1143598), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143598), c_Groups_Ozero__class_Ozero(_1143598)), _1143600)), 19193 ^ _782435 : [(19194 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143598), _1143600), _1143602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143598), _1143600), _1143604))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143598), _1143602), _1143604)))], (19200 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143598), _1143602), _1143604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143598), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143598), _1143600), _1143602)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143598), _1143600), _1143604))))]]], (19206 ^ _782435) ^ [_1143979, _1143981, _1143983, _1143985] : [class_Rings_Olinordered__ring__strict(_1143979), 19209 ^ _782435 : [(19210 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143979), _1143981), _1143983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143979), _1143981), _1143985))), 19215 ^ _782435 : [(19216 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), c_Groups_Ozero__class_Ozero(_1143979)), _1143981)))], (19218 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), _1143983), _1143985)))]], 19219 ^ _782435 : [(19220 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), _1143981), c_Groups_Ozero__class_Ozero(_1143979))))], (19222 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), _1143985), _1143983)))]]], (19224 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143979), _1143981), _1143983)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1143979), _1143981), _1143985)))), 19225 ^ _782435 : [(19226 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), c_Groups_Ozero__class_Ozero(_1143979)), _1143981)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), _1143983), _1143985))], (19232 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), _1143981), c_Groups_Ozero__class_Ozero(_1143979))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1143979), _1143985), _1143983))]]]]], (19240 ^ _782435) ^ [_1144585, _1144587, _1144589, _1144591] : [class_Rings_Olinordered__ring__strict(_1144585), 19243 ^ _782435 : [(19244 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144585), _1144587), _1144589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144585), _1144591), _1144589))), 19249 ^ _782435 : [(19250 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), c_Groups_Ozero__class_Ozero(_1144585)), _1144589)))], (19252 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144587), _1144591)))]], 19253 ^ _782435 : [(19254 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144589), c_Groups_Ozero__class_Ozero(_1144585))))], (19256 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144591), _1144587)))]]], (19258 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144585), _1144587), _1144589)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1144585), _1144591), _1144589)))), 19259 ^ _782435 : [(19260 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), c_Groups_Ozero__class_Ozero(_1144585)), _1144589)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144587), _1144591))], (19266 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144589), c_Groups_Ozero__class_Ozero(_1144585))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1144585), _1144591), _1144587))]]]]], (19274 ^ _782435) ^ [_1145191, _1145193] : [class_Rings_Olinordered__ring(_1145191), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145191), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145191), _1145193), _1145193)), c_Groups_Ozero__class_Ozero(_1145191)))], (19280 ^ _782435) ^ [_1145301, _1145303, _1145305] : [class_Rings_Osemiring__1(_1145301), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145301), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1145303), _1145305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1145301), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145301), _1145303)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1145301), _1145305)))], (19286 ^ _782435) ^ [_1145436, _1145438, _1145440] : [class_Groups_Oordered__ab__group__add(_1145436), 19289 ^ _782435 : [(19290 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145436), _1145438), _1145440)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145436), _1145438), _1145440)), c_Groups_Ozero__class_Ozero(_1145436))))], (19296 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145436), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145436), _1145438), _1145440)), c_Groups_Ozero__class_Ozero(_1145436))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1145436), _1145438), _1145440)))]]], (19302 ^ _782435) ^ [_1145719, _1145721, _1145723] : [class_Groups_Oordered__ab__group__add(_1145719), 19305 ^ _782435 : [(19306 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145719), _1145721), _1145723)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145719), _1145721), _1145723)), c_Groups_Ozero__class_Ozero(_1145719))))], (19312 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145719), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1145719), _1145721), _1145723)), c_Groups_Ozero__class_Ozero(_1145719))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1145719), _1145721), _1145723)))]]], (19318 ^ _782435) ^ [_1146002, _1146004, _1146006, _1146008, _1146010, _1146012] : [class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(_1146002), -(_1146004 = c_Groups_Ozero__class_Ozero(_1146002)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146002), _1146006), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146002), _1146004), _1146010)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1146002), _1146008), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1146002), _1146004), _1146012)), _1146006 = _1146008, -(_1146010 = _1146012)], (19336 ^ _782435) ^ [_1146340] : [class_Rings_Olinordered__semidom(_1146340), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146340), c_Groups_Oone__class_Oone(_1146340)), c_Groups_Ozero__class_Ozero(_1146340)))], (19342 ^ _782435) ^ [_1146436] : [class_Rings_Olinordered__semidom(_1146436), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146436), c_Groups_Ozero__class_Ozero(_1146436)), c_Groups_Oone__class_Oone(_1146436))))], (19348 ^ _782435) ^ [_1146531] : [class_Rings_Olinordered__semidom(_1146531), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146531), c_Groups_Oone__class_Oone(_1146531)), c_Groups_Ozero__class_Ozero(_1146531)))], (19354 ^ _782435) ^ [_1146627] : [class_Rings_Olinordered__semidom(_1146627), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1146627), c_Groups_Ozero__class_Ozero(_1146627)), c_Groups_Oone__class_Oone(_1146627))))], (19360 ^ _782435) ^ [_1146722, _1146724] : [class_Groups_Olinordered__ab__group__add(_1146722), 19363 ^ _782435 : [(19364 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146722), hAPP(c_Groups_Ouminus__class_Ouminus(_1146722), _1146724)), _1146724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146722), c_Groups_Ozero__class_Ozero(_1146722)), _1146724)))], (19370 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146722), c_Groups_Ozero__class_Ozero(_1146722)), _1146724)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146722), hAPP(c_Groups_Ouminus__class_Ouminus(_1146722), _1146724)), _1146724)))]]], (19376 ^ _782435) ^ [_1146990, _1146992] : [class_Groups_Oordered__ab__group__add(_1146990), 19379 ^ _782435 : [(19380 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146990), hAPP(c_Groups_Ouminus__class_Ouminus(_1146990), _1146992)), c_Groups_Ozero__class_Ozero(_1146990))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146990), c_Groups_Ozero__class_Ozero(_1146990)), _1146992)))], (19386 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146990), c_Groups_Ozero__class_Ozero(_1146990)), _1146992)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1146990), hAPP(c_Groups_Ouminus__class_Ouminus(_1146990), _1146992)), c_Groups_Ozero__class_Ozero(_1146990))))]]], (19392 ^ _782435) ^ [_1147264, _1147266] : [class_Groups_Olinordered__ab__group__add(_1147264), 19395 ^ _782435 : [(19396 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147264), _1147266), hAPP(c_Groups_Ouminus__class_Ouminus(_1147264), _1147266))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147264), _1147266), c_Groups_Ozero__class_Ozero(_1147264))))], (19402 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147264), _1147266), c_Groups_Ozero__class_Ozero(_1147264))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147264), _1147266), hAPP(c_Groups_Ouminus__class_Ouminus(_1147264), _1147266))))]]], (19408 ^ _782435) ^ [_1147532, _1147534] : [class_Groups_Oordered__ab__group__add(_1147532), 19411 ^ _782435 : [(19412 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147532), c_Groups_Ozero__class_Ozero(_1147532)), hAPP(c_Groups_Ouminus__class_Ouminus(_1147532), _1147534))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147532), _1147534), c_Groups_Ozero__class_Ozero(_1147532))))], (19418 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147532), _1147534), c_Groups_Ozero__class_Ozero(_1147532))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1147532), c_Groups_Ozero__class_Ozero(_1147532)), hAPP(c_Groups_Ouminus__class_Ouminus(_1147532), _1147534))))]]], (19424 ^ _782435) ^ [_1147806, _1147808] : [class_Groups_Olinordered__ab__group__add(_1147806), 19427 ^ _782435 : [(19428 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147806), hAPP(c_Groups_Ouminus__class_Ouminus(_1147806), _1147808)), _1147808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147806), c_Groups_Ozero__class_Ozero(_1147806)), _1147808)))], (19434 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147806), c_Groups_Ozero__class_Ozero(_1147806)), _1147808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1147806), hAPP(c_Groups_Ouminus__class_Ouminus(_1147806), _1147808)), _1147808)))]]], (19440 ^ _782435) ^ [_1148074, _1148076] : [class_Groups_Oordered__ab__group__add(_1148074), 19443 ^ _782435 : [(19444 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148074), hAPP(c_Groups_Ouminus__class_Ouminus(_1148074), _1148076)), c_Groups_Ozero__class_Ozero(_1148074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148074), c_Groups_Ozero__class_Ozero(_1148074)), _1148076)))], (19450 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148074), c_Groups_Ozero__class_Ozero(_1148074)), _1148076)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148074), hAPP(c_Groups_Ouminus__class_Ouminus(_1148074), _1148076)), c_Groups_Ozero__class_Ozero(_1148074))))]]], (19456 ^ _782435) ^ [_1148348, _1148350] : [class_Groups_Oordered__ab__group__add(_1148348), 19459 ^ _782435 : [(19460 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148348), c_Groups_Ozero__class_Ozero(_1148348)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148348), _1148350))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148348), _1148350), c_Groups_Ozero__class_Ozero(_1148348))))], (19466 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148348), _1148350), c_Groups_Ozero__class_Ozero(_1148348))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148348), c_Groups_Ozero__class_Ozero(_1148348)), hAPP(c_Groups_Ouminus__class_Ouminus(_1148348), _1148350))))]]], (19472 ^ _782435) ^ [_1148622, _1148624] : [class_Rings_Olinordered__idom(_1148622), 19475 ^ _782435 : [(19476 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148622), _1148624), hAPP(c_Groups_Ouminus__class_Ouminus(_1148622), _1148624))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148622), _1148624), c_Groups_Ozero__class_Ozero(_1148622))))], (19482 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148622), _1148624), c_Groups_Ozero__class_Ozero(_1148622))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1148622), _1148624), hAPP(c_Groups_Ouminus__class_Ouminus(_1148622), _1148624))))]]], (19488 ^ _782435) ^ [_1148890, _1148892, _1148894] : [class_Groups_Ogroup__add(_1148890), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1148890), _1148892), _1148894) = c_Groups_Ozero__class_Ozero(_1148890), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1148890), _1148892) = _1148894)], (19498 ^ _782435) ^ [_1149051, _1149053] : [class_Groups_Oab__group__add(_1149051), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149051), hAPP(c_Groups_Ouminus__class_Ouminus(_1149051), _1149053)), _1149053) = c_Groups_Ozero__class_Ozero(_1149051))], (19504 ^ _782435) ^ [_1149156, _1149158] : [class_Groups_Ogroup__add(_1149156), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149156), hAPP(c_Groups_Ouminus__class_Ouminus(_1149156), _1149158)), _1149158) = c_Groups_Ozero__class_Ozero(_1149156))], (19510 ^ _782435) ^ [_1149261, _1149263, _1149265] : [class_Groups_Ogroup__add(_1149261), 19513 ^ _782435 : [(19514 ^ _782435) ^ [] : [_1149263 = hAPP(c_Groups_Ouminus__class_Ouminus(_1149261), _1149265), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149261), _1149263), _1149265) = c_Groups_Ozero__class_Ozero(_1149261))], (19520 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149261), _1149263), _1149265) = c_Groups_Ozero__class_Ozero(_1149261), -(_1149263 = hAPP(c_Groups_Ouminus__class_Ouminus(_1149261), _1149265))]]], (19526 ^ _782435) ^ [_1149517, _1149519] : [class_Groups_Ogroup__add(_1149517), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1149517), _1149519), hAPP(c_Groups_Ouminus__class_Ouminus(_1149517), _1149519)) = c_Groups_Ozero__class_Ozero(_1149517))], (19532 ^ _782435) ^ [_1149622] : [class_Rings_Osemiring__1(_1149622), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1149622), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1149622))], (19538 ^ _782435) ^ [_1149709, _1149711] : [class_Groups_Ogroup__add(_1149709), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1149709), c_Groups_Ozero__class_Ozero(_1149709)), _1149711) = hAPP(c_Groups_Ouminus__class_Ouminus(_1149709), _1149711))], (19544 ^ _782435) ^ [_1149814, _1149816, _1149818] : [class_Groups_Ocomm__monoid__add(_1149814), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149816, _1149814), _1149818), c_Orderings_Obot__class_Obot(tc_fun(_1149816, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1149814))], (19550 ^ _782435) ^ [_1149923, _1149925, _1149927] : [class_Groups_Ocomm__monoid__add(_1149923), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1149925, _1149923), _1149927), c_Orderings_Obot__class_Obot(tc_fun(_1149925, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(_1149923))], (19556 ^ _782435) ^ [_1150032, _1150034, _1150036, _1150038] : [class_Groups_Ocomm__monoid__add(_1150032), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150034), _1150036))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150034, _1150032), _1150038), _1150036) = c_Groups_Ozero__class_Ozero(_1150032))], (19566 ^ _782435) ^ [_1150156, _1150158, _1150160, _1150162] : [class_Groups_Ocomm__monoid__add(_1150156), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1150158), _1150160))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1150158, _1150156), _1150162), _1150160) = c_Groups_Ozero__class_Ozero(_1150156))], (19586 ^ _782435) ^ [_1150405, _1150407] : [19587 ^ _782435 : [(19588 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150405))], (19590 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150407))]], -(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), _1150405), _1150407))))], (19576 ^ _782435) ^ [_1150295, _1150297] : [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), _1150295), _1150297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150295))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150297)))], (19594 ^ _782435) ^ [_1150546, _1150548] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150546)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150548)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1150548), _1150546)), _1150548)))], (19604 ^ _782435) ^ [_1150720, _1150722] : [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), _1150720), _1150722))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150722), _1150720)))], (19610 ^ _782435) ^ [_1150819, _1150821] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1150821), _1150819)), -(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), _1150819), _1150821))))], (19616 ^ _782435) ^ [_1150924, _1150926, _1150928] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1150924)), 19619 ^ _782435 : [(19620 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150924), _1150926) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150924), _1150928), -(_1150926 = _1150928)], (19626 ^ _782435) ^ [] : [_1150926 = _1150928, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150924), _1150926) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1150924), _1150928))]]], (19632 ^ _782435) ^ [_1151177, _1151179, _1151181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151177)), 19635 ^ _782435 : [(19636 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151177), _1151179)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151177), _1151181))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151179), _1151181)))], (19642 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151179), _1151181)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151177), _1151179)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151177), _1151181))))]]], (19648 ^ _782435) ^ [_1151475, _1151477] : [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), _1151475), _1151477))), 19651 ^ _782435 : [(19652 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151475)))], (19654 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151477)))]]], (19656 ^ _782435) ^ [_1151598, _1151600] : [-(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), _1151598), _1151600)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151600))], (19666 ^ _782435) ^ [_1151771, _1151773, _1151775] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151771), _1151773)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151771), _1151775))), 19669 ^ _782435 : [(19670 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151771)))], (19672 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151773), _1151775)))]]], (19674 ^ _782435) ^ [_1151920, _1151922, _1151924] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151920), _1151922)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1151920), _1151924)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1151920)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1151922), _1151924))], (19684 ^ _782435) ^ [_1152121, _1152123, _1152125] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152121), _1152123)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152125), _1152123))), 19687 ^ _782435 : [(19688 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152123)))], (19690 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152121), _1152125)))]]], (19692 ^ _782435) ^ [_1152270, _1152272, _1152274] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152270), _1152272)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152274), _1152272)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152272)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152270), _1152274))], (19702 ^ _782435) ^ [_1152453, _1152455, _1152457] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152453), _1152455)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152457)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152453), _1152457)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152455), _1152457))))], (19712 ^ _782435) ^ [_1152634, _1152636, _1152638] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1152634), _1152636)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1152638)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152638), _1152634)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1152638), _1152636))))], (19722 ^ _782435) ^ [_1152815, _1152817] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152815), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1152815), _1152817)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19724 ^ _782435) ^ [_1152852, _1152854] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152852), _1152854)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152852), _1152854) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19730 ^ _782435) ^ [_1152966, _1152968] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1152966), _1152968) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1152966), _1152968)))], (19736 ^ _782435) ^ [_1153061, _1153063] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1153061), _1153063)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1153061), _1153063) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19742 ^ _782435) ^ [_1153162, _1153164] : [_1153162 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1153162), _1153164), -(_1153164 = c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(_1153162 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19752 ^ _782435) ^ [_1153264, _1153266, _1153268] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1153264), _1153266)), 19755 ^ _782435 : [(19766 ^ _782435) ^ [] : [19768 ^ _782435 : [(19769 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1153264), 19767 ^ [_1153264, _1153266, _1153268]), _1153266)))], (19771 ^ _782435) ^ [] : [hAPP(_1153268, 19767 ^ [_1153264, _1153266, _1153268]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153264, tc_Nat_Onat), _1153268), _1153266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (19756 ^ _782435) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1153264, tc_Nat_Onat), _1153268), _1153266) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 19759 ^ _782435 : [(19760 ^ _782435) ^ [_1153426] : [hBOOL(hAPP(hAPP(c_member(_1153264), _1153426), _1153266)), -(hAPP(_1153268, _1153426) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]]]], (19775 ^ _782435) ^ [_1153684] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1153684) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1153684))], (19777 ^ _782435) ^ [_1153713] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1153713) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1153713))], (19779 ^ _782435) ^ [_1153743, _1153745, _1153747] : [class_Groups_Oordered__comm__monoid__add(_1153743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153743), c_Groups_Ozero__class_Ozero(_1153743)), _1153745)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153743), c_Groups_Ozero__class_Ozero(_1153743)), _1153747)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153743), c_Groups_Ozero__class_Ozero(_1153743)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153743), _1153745), _1153747))))], (19793 ^ _782435) ^ [_1153998, _1154000, _1154002] : [class_Groups_Oordered__comm__monoid__add(_1153998), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1153998), c_Groups_Ozero__class_Ozero(_1153998)), _1154000)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153998), c_Groups_Ozero__class_Ozero(_1153998)), _1154002)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1153998), c_Groups_Ozero__class_Ozero(_1153998)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1153998), _1154000), _1154002))))], (19807 ^ _782435) ^ [_1154253, _1154255, _1154257, _1154259] : [class_Groups_Oordered__comm__monoid__add(_1154253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154253), c_Groups_Ozero__class_Ozero(_1154253)), _1154255)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154253), _1154257), _1154259)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154253), _1154257), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154253), _1154255), _1154259))))], (19821 ^ _782435) ^ [_1154506, _1154508, _1154510, _1154512] : [class_Groups_Oordered__comm__monoid__add(_1154506), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154506), c_Groups_Ozero__class_Ozero(_1154506)), _1154508)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154506), _1154510), _1154512)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154506), _1154510), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154506), _1154508), _1154512))))], (19835 ^ _782435) ^ [_1154759, _1154761, _1154763] : [class_Groups_Oordered__comm__monoid__add(_1154759), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154759), _1154761), c_Groups_Ozero__class_Ozero(_1154759))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1154759), _1154763), c_Groups_Ozero__class_Ozero(_1154759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1154759), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1154759), _1154761), _1154763)), c_Groups_Ozero__class_Ozero(_1154759))))], (19849 ^ _782435) ^ [_1155014, _1155016, _1155018] : [class_Groups_Oordered__comm__monoid__add(_1155014), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155014), _1155016), c_Groups_Ozero__class_Ozero(_1155014))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155014), _1155018), c_Groups_Ozero__class_Ozero(_1155014))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155014), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1155014), _1155016), _1155018)), c_Groups_Ozero__class_Ozero(_1155014))))], (19863 ^ _782435) ^ [_1155269, _1155271, _1155273, _1155275] : [class_Rings_Olinordered__ring__strict(_1155269), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155269), c_Groups_Ozero__class_Ozero(_1155269)), _1155271)), 19870 ^ _782435 : [(19871 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155269), _1155271), _1155273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155269), _1155271), _1155275))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155269), _1155273), _1155275)))], (19877 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155269), _1155273), _1155275)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155269), _1155271), _1155273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155269), _1155271), _1155275))))]]], (19883 ^ _782435) ^ [_1155650, _1155652, _1155654, _1155656] : [class_Rings_Olinordered__ring__strict(_1155650), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1155650), _1155652), c_Groups_Ozero__class_Ozero(_1155650))), 19890 ^ _782435 : [(19891 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155650), _1155652), _1155654)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155650), _1155652), _1155656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155650), _1155656), _1155654)))], (19897 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155650), _1155656), _1155654)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1155650), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155650), _1155652), _1155654)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1155650), _1155652), _1155656))))]]], (19903 ^ _782435) ^ [_1156031, _1156033, _1156035, _1156037, _1156039] : [class_Rings_Olinordered__semiring__strict(_1156031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156031), _1156033), _1156035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156031), _1156037), _1156039)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156031), c_Groups_Ozero__class_Ozero(_1156031)), _1156035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156031), c_Groups_Ozero__class_Ozero(_1156031)), _1156037)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156031), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156031), _1156033), _1156037)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156031), _1156035), _1156039))))], (19925 ^ _782435) ^ [_1156454, _1156456, _1156458, _1156460, _1156462] : [class_Rings_Olinordered__semiring__strict(_1156454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156454), _1156456), _1156458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156454), _1156460), _1156462)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156454), c_Groups_Ozero__class_Ozero(_1156454)), _1156456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156454), c_Groups_Ozero__class_Ozero(_1156454)), _1156460)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156454), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156454), _1156456), _1156460)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156454), _1156458), _1156462))))], (19947 ^ _782435) ^ [_1156877, _1156879, _1156881, _1156883, _1156885] : [class_Rings_Olinordered__semiring__strict(_1156877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156877), _1156879), _1156881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156877), _1156883), _1156885)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1156877), c_Groups_Ozero__class_Ozero(_1156877)), _1156879)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156877), c_Groups_Ozero__class_Ozero(_1156877)), _1156883)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1156877), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156877), _1156879), _1156883)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1156877), _1156881), _1156885))))], (19969 ^ _782435) ^ [_1157300, _1157302, _1157304, _1157306, _1157308] : [class_Rings_Olinordered__semiring__strict(_1157300), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157300), _1157302), _1157304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157300), _1157306), _1157308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157300), c_Groups_Ozero__class_Ozero(_1157300)), _1157302)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157300), c_Groups_Ozero__class_Ozero(_1157300)), _1157306)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157300), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157300), _1157302), _1157306)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157300), _1157304), _1157308))))], (19991 ^ _782435) ^ [_1157723, _1157725, _1157727, _1157729] : [class_Rings_Olinordered__semiring(_1157723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157723), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157723), _1157725), _1157727)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157723), _1157729), _1157727))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157723), c_Groups_Ozero__class_Ozero(_1157723)), _1157727)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157723), _1157725), _1157729)))], (20005 ^ _782435) ^ [_1157992, _1157994, _1157996, _1157998] : [class_Rings_Olinordered__semiring__strict(_1157992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157992), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157992), _1157994), _1157996)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1157992), _1157998), _1157996))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1157992), c_Groups_Ozero__class_Ozero(_1157992)), _1157996)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1157992), _1157994), _1157998)))], (20019 ^ _782435) ^ [_1158261, _1158263, _1158265, _1158267] : [class_Rings_Olinordered__semiring(_1158261), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158261), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158261), _1158263), _1158265)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158261), _1158263), _1158267))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158261), c_Groups_Ozero__class_Ozero(_1158261)), _1158263)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158261), _1158265), _1158267)))], (20033 ^ _782435) ^ [_1158530, _1158532, _1158534, _1158536] : [class_Rings_Olinordered__semiring__strict(_1158530), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158530), _1158532), _1158534)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158530), _1158532), _1158536))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158530), c_Groups_Ozero__class_Ozero(_1158530)), _1158532)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158530), _1158534), _1158536)))], (20047 ^ _782435) ^ [_1158799, _1158801, _1158803, _1158805] : [class_Rings_Olinordered__semiring__strict(_1158799), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158799), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158799), _1158801), _1158803)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1158799), _1158805), _1158803))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1158799), c_Groups_Ozero__class_Ozero(_1158799)), _1158803)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1158799), _1158801), _1158805)))], (20061 ^ _782435) ^ [_1159068, _1159070, _1159072, _1159074] : [class_Rings_Olinordered__semiring__strict(_1159068), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159068), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159068), _1159070), _1159072)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159068), _1159070), _1159074))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159068), c_Groups_Ozero__class_Ozero(_1159068)), _1159070)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159068), _1159072), _1159074)))], (20075 ^ _782435) ^ [_1159337, _1159339, _1159341] : [class_Rings_Olinordered__idom(_1159337), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159337), c_Groups_Ozero__class_Ozero(_1159337)), _1159339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159337), c_Groups_Ozero__class_Ozero(_1159337)), _1159341)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159337), _1159341), c_Groups_Oone__class_Oone(_1159337))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159337), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159337), _1159339), _1159341)), _1159339)))], (20093 ^ _782435) ^ [_1159660, _1159662, _1159664] : [class_Rings_Olinordered__idom(_1159660), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159660), c_Groups_Ozero__class_Ozero(_1159660)), _1159662)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159660), c_Groups_Ozero__class_Ozero(_1159660)), _1159664)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159660), _1159664), c_Groups_Oone__class_Oone(_1159660))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1159660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1159660), _1159664), _1159662)), _1159662)))], (20111 ^ _782435) ^ [_1159983] : [class_Rings_Olinordered__semidom(_1159983), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1159983), c_Groups_Ozero__class_Ozero(_1159983)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1159983), c_Groups_Oone__class_Oone(_1159983)), c_Groups_Oone__class_Oone(_1159983)))))], (20117 ^ _782435) ^ [_1160098, _1160100, _1160102] : [class_Rings_Oring__1(_1160098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1160100), _1160102)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160098), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160102), _1160100)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1160098), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160098), _1160102)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1160098), _1160100)))], (20143 ^ _782435) ^ [_1160599, _1160601, _1160603] : [-(hBOOL(hAPP(_1160599, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160601), _1160603)))), 20146 ^ _782435 : [(20147 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160601), _1160603)))], (20149 ^ _782435) ^ [] : [hBOOL(hAPP(_1160599, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20151 ^ _782435 : [(20152 ^ _782435) ^ [] : [-(_1160601 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160603), 20150 ^ [_1160599, _1160601, _1160603]))], (20154 ^ _782435) ^ [] : [hBOOL(hAPP(_1160599, 20150 ^ [_1160599, _1160601, _1160603]))]]], (20127 ^ _782435) ^ [_1160315, _1160317, _1160319] : [hBOOL(hAPP(_1160315, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160317), _1160319))), 20130 ^ _782435 : [(20131 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160317), _1160319)), -(hBOOL(hAPP(_1160315, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20137 ^ _782435) ^ [_1160500] : [_1160317 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160319), _1160500), -(hBOOL(hAPP(_1160315, _1160500)))]]], (20174 ^ _782435) ^ [_1161194, _1161196, _1161198] : [-(hBOOL(hAPP(_1161194, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1161196), _1161198)))), 20177 ^ _782435 : [(20178 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1161196), _1161198)))], (20180 ^ _782435) ^ [] : [hBOOL(hAPP(_1161194, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 20182 ^ _782435 : [(20183 ^ _782435) ^ [] : [-(_1161196 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1161198), 20181 ^ [_1161194, _1161196, _1161198]))], (20185 ^ _782435) ^ [] : [hBOOL(hAPP(_1161194, 20181 ^ [_1161194, _1161196, _1161198]))]]], (20158 ^ _782435) ^ [_1160902, _1160904, _1160906] : [hBOOL(hAPP(_1160902, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1160904), _1160906))), 20161 ^ _782435 : [(20162 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1160904), _1160906)), -(hBOOL(hAPP(_1160902, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20168 ^ _782435) ^ [_1161093] : [_1160904 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1160906), _1161093), -(hBOOL(hAPP(_1160902, _1161093)))]]], (20189 ^ _782435) ^ [_1161487, _1161489, _1161491] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161487)), 20192 ^ _782435 : [(20193 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161487), _1161489)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161487), _1161491))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161489), _1161491)))], (20199 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161489), _1161491)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161487), _1161489)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161487), _1161491))))]]], (20215 ^ _782435) ^ [_1161965, _1161967, _1161969] : [20216 ^ _782435 : [(20217 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161967)))], (20219 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161965), _1161969))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161965), _1161967)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161969), _1161967))))], (20205 ^ _782435) ^ [_1161788, _1161790, _1161792] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161788), _1161790)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1161792), _1161790))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1161790)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1161788), _1161792)))], (20233 ^ _782435) ^ [_1162322, _1162324, _1162326] : [20234 ^ _782435 : [(20235 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162322)))], (20237 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162324), _1162326))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162322), _1162324)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162322), _1162326))))], (20223 ^ _782435) ^ [_1162145, _1162147, _1162149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162145), _1162147)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1162145), _1162149))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1162145)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1162147), _1162149)))], (20241 ^ _782435) ^ [_1162484, _1162486, _1162488, _1162490, _1162492, _1162494, _1162496, _1162498, _1162500, _1162502, _1162504] : [hAPP(_1162484, hAPP(_1162486, _1162488)) = hAPP(_1162490, hAPP(_1162492, _1162494)), -(hAPP(hAPP(c_Fun_Ocomp(_1162496, _1162498, _1162500, _1162484), _1162486), _1162488) = hAPP(hAPP(c_Fun_Ocomp(_1162502, _1162498, _1162504, _1162490), _1162492), _1162494))], (20247 ^ _782435) ^ [_1162647, _1162649, _1162651] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1162647), _1162649)), 20250 ^ _782435 : [(20251 ^ _782435) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1162647, tc_Nat_Onat), _1162651), _1162649) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20255 ^ _782435 : [(20256 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1162647), 20254 ^ [_1162647, _1162649, _1162651]), _1162649)))], (20258 ^ _782435) ^ [] : [-(hAPP(_1162651, 20254 ^ [_1162647, _1162649, _1162651]) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (20260 ^ _782435) ^ [_1162967] : [hBOOL(hAPP(hAPP(c_member(_1162647), _1162967), _1162649)), -(20254 ^ [_1162647, _1162649, _1162651] = _1162967), -(hAPP(_1162651, _1162967) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20270 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1162647, tc_Nat_Onat), _1162651), _1162649) = c_Groups_Oone__class_Oone(tc_Nat_Onat)), 20271 ^ _782435 : [(20272 ^ _782435) ^ [_1163128] : [hBOOL(hAPP(hAPP(c_member(_1162647), _1163128), _1162649)), hAPP(_1162651, _1163128) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 20280 ^ _782435 : [(20281 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1162647), 20279 ^ [_1162647, _1162649, _1162651, _1163128]), _1162649)))], (20283 ^ _782435) ^ [] : [_1163128 = 20279 ^ [_1162647, _1162649, _1162651, _1163128]], (20285 ^ _782435) ^ [] : [hAPP(_1162651, 20279 ^ [_1162647, _1162649, _1162651, _1163128]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (20289 ^ _782435) ^ [_1163481, _1163483, _1163485, _1163487, _1163489] : [class_Groups_Ocomm__monoid__add(_1163481), hBOOL(hAPP(c_Finite__Set_Ofinite(_1163483), _1163485)), 20296 ^ _782435 : [(20297 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1163483), _1163487), _1163485)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163483, _1163481), hAPP(hAPP(c_COMBC(_1163483, _1163481, _1163481), hAPP(hAPP(c_COMBS(_1163483, _1163481, tc_fun(_1163481, _1163481)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163481, tc_fun(_1163481, _1163481)), _1163483), c_If(_1163481)), hAPP(c_fequal, _1163487))), _1163489)), c_Groups_Ozero__class_Ozero(_1163481))), _1163485) = hAPP(_1163489, _1163487))], (20303 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1163483), _1163487), _1163485))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163483, _1163481), hAPP(hAPP(c_COMBC(_1163483, _1163481, _1163481), hAPP(hAPP(c_COMBS(_1163483, _1163481, tc_fun(_1163481, _1163481)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163481, tc_fun(_1163481, _1163481)), _1163483), c_If(_1163481)), hAPP(c_fequal, _1163487))), _1163489)), c_Groups_Ozero__class_Ozero(_1163481))), _1163485) = c_Groups_Ozero__class_Ozero(_1163481))]]], (20309 ^ _782435) ^ [_1163991, _1163993, _1163995, _1163997, _1163999] : [class_Groups_Ocomm__monoid__add(_1163991), hBOOL(hAPP(c_Finite__Set_Ofinite(_1163993), _1163995)), 20316 ^ _782435 : [(20317 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1163993), _1163997), _1163995)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163993, _1163991), hAPP(hAPP(c_COMBC(_1163993, _1163991, _1163991), hAPP(hAPP(c_COMBS(_1163993, _1163991, tc_fun(_1163991, _1163991)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163991, tc_fun(_1163991, _1163991)), _1163993), c_If(_1163991)), hAPP(hAPP(c_COMBC(_1163993, _1163993, tc_HOL_Obool), c_fequal), _1163997))), _1163999)), c_Groups_Ozero__class_Ozero(_1163991))), _1163995) = hAPP(_1163999, _1163997))], (20323 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1163993), _1163997), _1163995))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1163993, _1163991), hAPP(hAPP(c_COMBC(_1163993, _1163991, _1163991), hAPP(hAPP(c_COMBS(_1163993, _1163991, tc_fun(_1163991, _1163991)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1163991, tc_fun(_1163991, _1163991)), _1163993), c_If(_1163991)), hAPP(hAPP(c_COMBC(_1163993, _1163993, tc_HOL_Obool), c_fequal), _1163997))), _1163999)), c_Groups_Ozero__class_Ozero(_1163991))), _1163995) = c_Groups_Ozero__class_Ozero(_1163991))]]], (20329 ^ _782435) ^ [_1164529, _1164531, _1164533, _1164535, _1164537, _1164539] : [class_Rings_Olinordered__semiring__1(_1164529), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164529), _1164531), _1164533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164529), _1164535), _1164533)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164529), c_Groups_Ozero__class_Ozero(_1164529)), _1164537)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164529), c_Groups_Ozero__class_Ozero(_1164529)), _1164539)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164529), _1164537), _1164539) = c_Groups_Oone__class_Oone(_1164529), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1164529), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1164529), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164529), _1164537), _1164531)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1164529), _1164539), _1164535))), _1164533)))], (20355 ^ _782435) ^ [_1165058, _1165060] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165058, 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(_1165058, tc_HOL_Obool)), tc_fun(_1165058, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_fun(_1165058, tc_HOL_Obool)), tc_fun(_1165058, tc_HOL_Obool)), tc_Nat_Onat), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165058, tc_HOL_Obool))), c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), _1165060)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1165058, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1165060))], (20357 ^ _782435) ^ [_1165154, _1165156, _1165158, _1165160] : [class_Groups_Ocomm__monoid__add(_1165154), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165156), _1165158)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165156, _1165154), _1165160), _1165158) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1165154, _1165156, c_Groups_Oplus__class_Oplus(_1165154)), _1165160), c_Groups_Ozero__class_Ozero(_1165154)), _1165158))], (20367 ^ _782435) ^ [_1165349, _1165351, _1165353, _1165355] : [class_Groups_Ocomm__monoid__add(_1165349), 20370 ^ _782435 : [(20371 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1165351), _1165353)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165351, _1165349), _1165355), _1165353) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1165349, _1165351, c_Groups_Oplus__class_Oplus(_1165349)), _1165355), c_Groups_Ozero__class_Ozero(_1165349)), _1165353))], (20377 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1165351), _1165353))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165351, _1165349), _1165355), _1165353) = c_Groups_Ozero__class_Ozero(_1165349))]]], (20383 ^ _782435) ^ [_1165621, _1165623, _1165625, _1165627, _1165629] : [class_Groups_Ocomm__monoid__add(_1165621), hBOOL(hAPP(c_Finite__Set_Ofinite(_1165623), _1165625)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165623, _1165621), _1165627), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1165623, tc_HOL_Obool)), _1165625), _1165629)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1165623, _1165621), hAPP(hAPP(c_COMBC(_1165623, _1165621, _1165621), hAPP(hAPP(c_COMBS(_1165623, _1165621, tc_fun(_1165621, _1165621)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1165621, tc_fun(_1165621, _1165621)), _1165623), c_If(_1165621)), hAPP(hAPP(c_COMBC(_1165623, tc_fun(_1165623, tc_HOL_Obool), tc_HOL_Obool), c_member(_1165623)), _1165629))), _1165627)), c_Groups_Ozero__class_Ozero(_1165621))), _1165625))], (20393 ^ _782435) ^ [_1165942, _1165944, _1165946, _1165948, _1165950, _1165952] : [class_Rings_Olinordered__semiring__1__strict(_1165942), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165942), _1165944), _1165946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165942), _1165948), _1165946)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165942), c_Groups_Ozero__class_Ozero(_1165942)), _1165950)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1165942), c_Groups_Ozero__class_Ozero(_1165942)), _1165952)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165942), _1165950), _1165952) = c_Groups_Oone__class_Oone(_1165942), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1165942), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1165942), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165942), _1165950), _1165944)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1165942), _1165952), _1165948))), _1165946)))], (20419 ^ _782435) ^ [_1166483, _1166485, _1166487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166483), _1166485)), -(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)), _1166483)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166487), _1166485)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166487), _1166483)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1166485), _1166483)))], (20425 ^ _782435) ^ [_1166635, _1166637, _1166639] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166635), _1166637))), 20428 ^ _782435 : [(20429 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166639), _1166637)), -(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)), _1166635)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166639), _1166637)) = 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 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1166639), _1166637))), -(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)), _1166635)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1166639), _1166637)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))]]], (20441 ^ _782435) ^ [_1166904, _1166906, _1166908] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1166904, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1166906)), _1166908) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1166904, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1166904, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1166906)), _1166908)), hAPP(_1166908, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (20443 ^ _782435) ^ [_1166976, _1166978] : [class_Rings_Ocomm__semiring__1(_1166976), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166976), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166976), c_Groups_Oone__class_Oone(_1166976)), c_Groups_Oone__class_Oone(_1166976))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1166976), c_Nat_Osemiring__1__class_Oof__nat(_1166976)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), _1166978))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1166976), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1166976), _1166978)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1166976), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1166976), _1166978)), c_Groups_Oone__class_Oone(_1166976))))], (20449 ^ _782435) ^ [_1167186, _1167188] : [_1167186 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167186), _1167188) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20455 ^ _782435) ^ [_1167269, _1167271] : [-(_1167269 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1167269), _1167271) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1167271), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1167269), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1167271)))], (20461 ^ _782435) ^ [_1167331, _1167333, _1167335] : [class_Rings_Olinordered__ring(_1167331), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167331), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167331), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167331), _1167333), _1167333)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167331), _1167335), _1167335))), c_Groups_Ozero__class_Ozero(_1167331)))], (20467 ^ _782435) ^ [_1167475, _1167477, _1167479] : [class_Rings_Olinordered__ring__strict(_1167475), 20470 ^ _782435 : [(20481 ^ _782435) ^ [] : [20482 ^ _782435 : [(20483 ^ _782435) ^ [] : [-(_1167477 = c_Groups_Ozero__class_Ozero(_1167475))], (20485 ^ _782435) ^ [] : [-(_1167479 = c_Groups_Ozero__class_Ozero(_1167475))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167475), c_Groups_Ozero__class_Ozero(_1167475)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167475), _1167477), _1167477)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167475), _1167479), _1167479)))))], (20471 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1167475), c_Groups_Ozero__class_Ozero(_1167475)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167475), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167475), _1167477), _1167477)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167475), _1167479), _1167479)))), _1167477 = c_Groups_Ozero__class_Ozero(_1167475), _1167479 = c_Groups_Ozero__class_Ozero(_1167475)]]], (20489 ^ _782435) ^ [_1167850, _1167852, _1167854] : [class_Rings_Olinordered__ring(_1167850), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167850), c_Groups_Ozero__class_Ozero(_1167850)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167850), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167850), _1167852), _1167852)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167850), _1167854), _1167854)))))], (20495 ^ _782435) ^ [_1167993, _1167995, _1167997] : [class_Rings_Olinordered__ring__strict(_1167993), 20498 ^ _782435 : [(20499 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167993), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167993), _1167995), _1167995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167993), _1167997), _1167997))), c_Groups_Ozero__class_Ozero(_1167993))), 20502 ^ _782435 : [(20503 ^ _782435) ^ [] : [-(_1167995 = c_Groups_Ozero__class_Ozero(_1167993))], (20505 ^ _782435) ^ [] : [-(_1167997 = c_Groups_Ozero__class_Ozero(_1167993))]]], (20507 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1167993), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1167993), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167993), _1167995), _1167995)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1167993), _1167997), _1167997))), c_Groups_Ozero__class_Ozero(_1167993)))), _1167995 = c_Groups_Ozero__class_Ozero(_1167993), _1167997 = c_Groups_Ozero__class_Ozero(_1167993)]]], (20517 ^ _782435) ^ [_1168389, _1168391, _1168393, _1168395] : [class_Rings_Osemiring__1(_1168389), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168389), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168391, tc_Nat_Onat), _1168393), _1168395)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1168391, _1168389), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1168389, _1168391), c_Nat_Osemiring__1__class_Oof__nat(_1168389)), _1168393)), _1168395))], (20523 ^ _782435) ^ [_1168538, _1168540] : [class_Rings_Osemiring__1(_1168538), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1168538), _1168540) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1168538, hAPP(hAPP(c_COMBC(_1168538, _1168538, _1168538), c_Groups_Oplus__class_Oplus(_1168538)), c_Groups_Oone__class_Oone(_1168538)), _1168540, c_Groups_Ozero__class_Ozero(_1168538)))], (20529 ^ _782435) ^ [_1168665, _1168667, _1168669] : [class_Rings_Osemiring__1(_1168665), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1168665, _1168667, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1168669) = _1168669)], (20535 ^ _782435) ^ [] : [-(c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20537 ^ _782435) ^ [_1168785, _1168787] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168785)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168787)))), 20540 ^ _782435 : [(20541 ^ _782435) ^ [] : [-(_1168785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20543 ^ _782435) ^ [] : [-(_1168787 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20545 ^ _782435) ^ [_1168912, _1168914] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168912)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1168914))))), _1168912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1168914 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20555 ^ _782435) ^ [_1169083] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169083)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(_1169083 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20561 ^ _782435) ^ [_1169170] : [_1169170 = 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), _1169170)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20567 ^ _782435) ^ [_1169275] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169275) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1169275 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20573 ^ _782435) ^ [_1169352] : [_1169352 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169352) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20579 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1169468, _1169470] : [hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169468)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169470), 20584 ^ _782435 : [(20585 ^ _782435) ^ [] : [-(_1169468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (20587 ^ _782435) ^ [] : [-(_1169470 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (20589 ^ _782435) ^ [_1169585, _1169587] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169585)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169587)), _1169585 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1169587 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (20599 ^ _782435) ^ [_1169749, _1169751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169749)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169751))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169749), _1169751)))], (20605 ^ _782435) ^ [_1169854, _1169856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1169854), _1169856)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169854)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1169856))))], (20611 ^ _782435) ^ [_1169977] : [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), _1169977))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1169977)))], (20617 ^ _782435) ^ [_1170062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170062)), -(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), _1170062))))], (20623 ^ _782435) ^ [_1170153, _1170155, _1170157] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1170153), _1170155)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1170157)), -(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), _1170157)), _1170153)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170157)), _1170155))))], (20633 ^ _782435) ^ [_1170346, _1170348] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170346)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170348)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1170346), _1170348)))], (20635 ^ _782435) ^ [_1170392, _1170394, _1170396] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170392)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170394)), _1170396)) = 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), _1170392), _1170394))), _1170396))], (20637 ^ _782435) ^ [_1170467, _1170469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170467)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170467), _1170469)))], (20643 ^ _782435) ^ [_1170572, _1170574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1170572), _1170574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170572)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170574))))], (20649 ^ _782435) ^ [_1170683, _1170685] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170683), _1170685)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170683)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170685)))], (20651 ^ _782435) ^ [_1170729, _1170731] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170729)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1170731)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1170729), _1170731)))], (20653 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1170811, _1170813, _1170815] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170811, tc_Nat_Onat), _1170813), _1170815)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1170811, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1170811), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1170813)), _1170815))], (20659 ^ _782435) ^ [_1170869, _1170871] : [class_Groups_Olinordered__ab__group__add(_1170869), 20662 ^ _782435 : [(20663 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170869), _1170871), _1170871) = c_Groups_Ozero__class_Ozero(_1170869), -(_1170871 = c_Groups_Ozero__class_Ozero(_1170869))], (20669 ^ _782435) ^ [] : [_1170871 = c_Groups_Ozero__class_Ozero(_1170869), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1170869), _1170871), _1170871) = c_Groups_Ozero__class_Ozero(_1170869))]]], (20675 ^ _782435) ^ [_1171110, _1171112] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1171110), _1171112)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1171112)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1171110)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1171112), _1171110)))], (20681 ^ _782435) ^ [_1171239, _1171241] : [class_Rings_Olinordered__idom(_1171239), 20684 ^ _782435 : [(20685 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171239), _1171241), _1171241)), c_Groups_Ozero__class_Ozero(_1171239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171239), _1171241), c_Groups_Ozero__class_Ozero(_1171239))))], (20691 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171239), _1171241), c_Groups_Ozero__class_Ozero(_1171239))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1171239), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171239), _1171241), _1171241)), c_Groups_Ozero__class_Ozero(_1171239))))]]], (20697 ^ _782435) ^ [_1171522, _1171524, _1171526] : [class_Rings_Olinordered__ring__strict(_1171522), 20700 ^ _782435 : [(20701 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171522), _1171524), _1171524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171522), _1171526), _1171526)) = c_Groups_Ozero__class_Ozero(_1171522), 20704 ^ _782435 : [(20705 ^ _782435) ^ [] : [-(_1171524 = c_Groups_Ozero__class_Ozero(_1171522))], (20707 ^ _782435) ^ [] : [-(_1171526 = c_Groups_Ozero__class_Ozero(_1171522))]]], (20709 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1171522), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171522), _1171524), _1171524)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1171522), _1171526), _1171526)) = c_Groups_Ozero__class_Ozero(_1171522)), _1171524 = c_Groups_Ozero__class_Ozero(_1171522), _1171526 = c_Groups_Ozero__class_Ozero(_1171522)]]], (20719 ^ _782435) ^ [_1171912, _1171914] : [20727 ^ _782435 : [(20728 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20726 ^ [_1171912, _1171914]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1171912))))], (20730 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1171914, 20726 ^ [_1171912, _1171914])))]], 20720 ^ _782435 : [(20721 ^ _782435) ^ [_1171981] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1171981), _1171912)), hBOOL(hAPP(_1171914, _1171981))]]], (20732 ^ _782435) ^ [_1172142, _1172144] : [20740 ^ _782435 : [(20741 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20739 ^ [_1172142, _1172144]), _1172142)))], (20743 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1172144, 20739 ^ [_1172142, _1172144])))]], 20733 ^ _782435 : [(20734 ^ _782435) ^ [_1172211] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1172211), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172142))), hBOOL(hAPP(_1172144, _1172211))]]], (20745 ^ _782435) ^ [_1172397, _1172399] : [20747 ^ _782435 : [(20748 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 20746 ^ [_1172397, _1172399]), _1172397)))], (20750 ^ _782435) ^ [] : [hBOOL(hAPP(_1172399, 20746 ^ [_1172397, _1172399]))]], 20751 ^ _782435 : [(20752 ^ _782435) ^ [_1172548] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1172548), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172397))), -(hBOOL(hAPP(_1172399, _1172548)))]]], (20758 ^ _782435) ^ [_1172651, _1172653] : [20760 ^ _782435 : [(20761 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20759 ^ [_1172651, _1172653]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1172651))))], (20763 ^ _782435) ^ [] : [hBOOL(hAPP(_1172653, 20759 ^ [_1172651, _1172653]))]], 20764 ^ _782435 : [(20765 ^ _782435) ^ [_1172806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1172806), _1172651)), -(hBOOL(hAPP(_1172653, _1172806)))]]], (20771 ^ _782435) ^ [_1172922, _1172924] : [20779 ^ _782435 : [(20780 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20778 ^ [_1172922, _1172924]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1172922))))], (20782 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1172924, 20778 ^ [_1172922, _1172924])))]], 20772 ^ _782435 : [(20773 ^ _782435) ^ [_1172990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1172990), _1172922)), hBOOL(hAPP(_1172924, _1172990))]]], (20784 ^ _782435) ^ [_1173150, _1173152] : [20792 ^ _782435 : [(20793 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20791 ^ [_1173150, _1173152]), _1173150)))], (20795 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1173152, 20791 ^ [_1173150, _1173152])))]], 20785 ^ _782435 : [(20786 ^ _782435) ^ [_1173218] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173218), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173150))), hBOOL(hAPP(_1173152, _1173218))]]], (20797 ^ _782435) ^ [_1173402, _1173404] : [20799 ^ _782435 : [(20800 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 20798 ^ [_1173402, _1173404]), _1173402)))], (20802 ^ _782435) ^ [] : [hBOOL(hAPP(_1173404, 20798 ^ [_1173402, _1173404]))]], 20803 ^ _782435 : [(20804 ^ _782435) ^ [_1173552] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1173552), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173402))), -(hBOOL(hAPP(_1173404, _1173552)))]]], (20810 ^ _782435) ^ [_1173653, _1173655] : [20812 ^ _782435 : [(20813 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 20811 ^ [_1173653, _1173655]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1173653))))], (20815 ^ _782435) ^ [] : [hBOOL(hAPP(_1173655, 20811 ^ [_1173653, _1173655]))]], 20816 ^ _782435 : [(20817 ^ _782435) ^ [_1173806] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173806), _1173653)), -(hBOOL(hAPP(_1173655, _1173806)))]]], (20839 ^ _782435) ^ [_1174214, _1174216, _1174218] : [-(hBOOL(hAPP(_1174214, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1174216), _1174218))))), 20842 ^ _782435 : [(20843 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1174218), _1174216)))], (20845 ^ _782435) ^ [] : [hBOOL(hAPP(_1174214, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174216)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174218))))]], 20846 ^ _782435 : [(20847 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1174216), _1174218)))], (20849 ^ _782435) ^ [] : [hBOOL(hAPP(_1174214, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (20823 ^ _782435) ^ [_1173925, _1173927, _1173929] : [hBOOL(hAPP(_1173925, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1173927), _1173929)))), 20826 ^ _782435 : [(20827 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1173929), _1173927)), -(hBOOL(hAPP(_1173925, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173927)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1173929)))))], (20833 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1173927), _1173929)), -(hBOOL(hAPP(_1173925, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (20853 ^ _782435) ^ [_1174489, _1174491, _1174493, _1174495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174489, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174489, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 20854 ^ [_1174489, _1174491, _1174493, _1174495])), _1174491)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174489, 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 ^ [_1174489, _1174491, _1174493, _1174495]), _1174493))), _1174495))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1174489, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174489, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1174491)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1174489, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1174495))))], (20860 ^ _782435) ^ [_1174819, _1174821] : [-(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), _1174819))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174821))))], (20862 ^ _782435) ^ [_1174858] : [-(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), _1174858))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20864 ^ _782435) ^ [_1174892] : [-(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), _1174892))))], (20866 ^ _782435) ^ [_1174935, _1174937] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174935) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1174937), -(_1174935 = _1174937)], (20872 ^ _782435) ^ [_1175020, _1175022] : [_1175020 = _1175022, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175020) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175022))], (20878 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Groups_Oone__class_Oone(tc_Int_Oint)], (20884 ^ _782435) ^ [_1175171, _1175173] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175171)), 20887 ^ _782435 : [(20888 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175171), _1175173) = c_Groups_Oone__class_Oone(tc_Int_Oint), 20891 ^ _782435 : [(20892 ^ _782435) ^ [] : [-(_1175171 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (20894 ^ _782435) ^ [] : [-(_1175173 = c_Groups_Oone__class_Oone(tc_Int_Oint))]]], (20896 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175171), _1175173) = c_Groups_Oone__class_Oone(tc_Int_Oint)), _1175171 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1175173 = c_Groups_Oone__class_Oone(tc_Int_Oint)]]], (20906 ^ _782435) ^ [_1175472, _1175474, _1175476] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175472), _1175474)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1175476)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175476), _1175472)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1175476), _1175474))))], (20916 ^ _782435) ^ [_1175665, _1175667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175665)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175667))))], (20918 ^ _782435) ^ [_1175713] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1175713)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (20920 ^ _782435) ^ [_1175759, _1175761] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175759), _1175761)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175759), _1175761)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20926 ^ _782435) ^ [_1175864, _1175866] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1175864), _1175866)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1175864), _1175866)))], (20932 ^ _782435) ^ [_1175975] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1175975), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1175975)], (20934 ^ _782435) ^ [_1176004] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176004) = _1176004)], (20936 ^ _782435) ^ [_1176045, _1176047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176045), _1176047)), -(_1176047 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176045), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 20939 ^ [_1176045, _1176047])))], (20943 ^ _782435) ^ [_1176158, _1176160] : [20944 ^ _782435 : [(20945 ^ _782435) ^ [_1176211] : [_1176160 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1176158), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1176211))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1176158), _1176160)))], (20949 ^ _782435) ^ [_1176278] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1176278)), _1176278) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (20951 ^ _782435) ^ [_1176310, _1176312] : [-(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)), _1176310)), 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), _1176312), _1176310))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1176310), _1176312))], (20953 ^ _782435) ^ [_1176360] : [-(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)), _1176360))))], (20955 ^ _782435) ^ [_1176397] : [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)), _1176397)), _1176397) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (20957 ^ _782435) ^ [_1176441] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176441)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176441)))], (20963 ^ _782435) ^ [_1176520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176520)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1176520)))], (20969 ^ _782435) ^ [_1176605] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1176605)), -(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)), _1176605))))], (20975 ^ _782435) ^ [_1176706] : [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)), _1176706)), _1176706)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176706), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20981 ^ _782435) ^ [_1176815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176815), 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)), _1176815)), _1176815)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (20987 ^ _782435) ^ [_1176939, _1176941] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1176939), _1176941)), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1176941, _1176939) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint, tc_HOL_Obool)))], (20993 ^ _782435) ^ [_1177028, _1177030] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177028), _1177030))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1177030, _1177028) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint), _1177030), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177030), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1177028)))], (20999 ^ _782435) ^ [_1177106, _1177108] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177106), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177108), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177106), _1177108)))], (21005 ^ _782435) ^ [_1177211, _1177213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177211), _1177213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177211), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1177213), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21021 ^ _782435) ^ [_1177455, _1177457] : [21022 ^ _782435 : [(21023 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177455), _1177457))], (21025 ^ _782435) ^ [] : [_1177455 = _1177457]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177455), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177457), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21011 ^ _782435) ^ [_1177337, _1177339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177337), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177339), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177337), _1177339))), -(_1177337 = _1177339)], (21029 ^ _782435) ^ [_1177604, _1177606] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177604), _1177606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177604), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177606)))], (21035 ^ _782435) ^ [_1177728, _1177730] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177728), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177730)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177728), _1177730)))], (21041 ^ _782435) ^ [_1177833, _1177835] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177833), _1177835)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177833), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1177835)))], (21047 ^ _782435) ^ [_1177959, _1177961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1177959), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1177961), c_Groups_Oone__class_Oone(tc_Int_Oint)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1177959), _1177961)))], (21053 ^ _782435) ^ [_1178064, _1178066] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178064), _1178066)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178064), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178066), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (21059 ^ _782435) ^ [_1178175, _1178177, _1178179] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178175), _1178177)), _1178179) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178175), _1178179)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178177), _1178179)))], (21061 ^ _782435) ^ [_1178232, _1178234, _1178236] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178232), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178234), _1178236)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178232), _1178234)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178232), _1178236)))], (21063 ^ _782435) ^ [_1178289, _1178291, _1178293] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178289), _1178291)), _1178293) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178289), _1178293)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178291), _1178293)))], (21065 ^ _782435) ^ [_1178346, _1178348, _1178350] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178346), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178348), _1178350)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178346), _1178348)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1178346), _1178350)))], (21067 ^ _782435) ^ [_1178403, _1178405] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178403), _1178405) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178403), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178405)))], (21069 ^ _782435) ^ [_1178443, _1178445] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178443), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178445)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1178443), _1178445))], (21071 ^ _782435) ^ [_1178483, _1178485] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178483), _1178485)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178483)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1178485)))], (21073 ^ _782435) ^ [_1178529, _1178531, _1178533] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178529), _1178531)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178533), _1178529)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178533), _1178531))))], (21079 ^ _782435) ^ [_1178652, _1178654] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178652), _1178654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178654), _1178652))], (21081 ^ _782435) ^ [_1178689, _1178691, _1178693] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178689), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178691), _1178693)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178691), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178689), _1178693)))], (21083 ^ _782435) ^ [_1178740, _1178742, _1178744] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178740), _1178742)), _1178744) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178740), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1178742), _1178744)))], (21085 ^ _782435) ^ [_1178806, _1178808] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178806), _1178808)), 21088 ^ _782435 : [(21089 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178806), _1178808)))], (21091 ^ _782435) ^ [] : [_1178806 = _1178808]]], (21093 ^ _782435) ^ [_1178933, _1178935] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1178933), _1178935))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1178933), _1178935)), -(_1178933 = _1178935)], (21103 ^ _782435) ^ [_1179087, _1179089, _1179091, _1179093] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179087), _1179089)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179091), _1179093)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179087), _1179091)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179089), _1179093))))], (21113 ^ _782435) ^ [_1179278, _1179280, _1179282] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179278), _1179280)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179278), _1179282)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1179280), _1179282))))], (21119 ^ _782435) ^ [_1179397, _1179399] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179397), _1179399))), -(_1179397 = _1179399), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1179399), _1179397)))], (21129 ^ _782435) ^ [_1179450, _1179452] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179450)), _1179452) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179450), _1179452)))], (21131 ^ _782435) ^ [_1179493, _1179495] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179493), _1179495) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179495), _1179493))], (21133 ^ _782435) ^ [_1179530, _1179532, _1179534] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179530), _1179532)), _1179534) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179530), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179532), _1179534)))], (21135 ^ _782435) ^ [_1179581] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1179581), c_Groups_Oone__class_Oone(tc_Int_Oint)) = _1179581)], (21137 ^ _782435) ^ [_1179610] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1179610) = _1179610)], (21139 ^ _782435) ^ [_1179636] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1179636)) = _1179636)], (21141 ^ _782435) ^ [_1179665, _1179667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179665), _1179667)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179667), _1179665)), -(_1179665 = _1179667)], (21151 ^ _782435) ^ [_1179814, _1179816, _1179818] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179814), _1179816)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179816), _1179818)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179814), _1179818)))], (21161 ^ _782435) ^ [_1179973, _1179975] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179973), _1179975))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1179975), _1179973)))], (21167 ^ _782435) ^ [_1180019] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180019), _1180019)))], (21169 ^ _782435) ^ [_1180047, _1180049] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180047), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1180049) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1180047, _1180049))], (21171 ^ _782435) ^ [_1180088, _1180090] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180088), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180090) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1180088, _1180090))], (21173 ^ _782435) ^ [_1180127, _1180129] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1180127), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180129), c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1180127, _1180129))], (21175 ^ _782435) ^ [_1180168, _1180170, _1180172] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180168)), _1180168 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180170), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180168), _1180172)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180170), _1180168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1180172)))], (21189 ^ _782435) ^ [_1180397, _1180399, _1180401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180397)), _1180397 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1180399), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1180397), _1180401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180399)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180401), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (21203 ^ _782435) ^ [_1180626, _1180628, _1180630] : [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), _1180626), _1180628)), _1180630))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1180630), _1180626)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180626)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180628)))], (21217 ^ _782435) ^ [_1180859, _1180861, _1180863] : [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), _1180859), _1180861)), _1180863)), 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)), _1180863)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1180859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1180861), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (21231 ^ _782435) ^ [_1181098, _1181100, _1181102, _1181104, _1181106] : [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), _1181098), _1181100)), _1181102)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181098), _1181104)), _1181106))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181102), _1181098)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181106), _1181098)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181100), _1181104)))], (21249 ^ _782435) ^ [_1181447, _1181449, _1181451, _1181453, _1181455, _1181457] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181447), _1181449)), _1181451) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1181453), _1181455)), _1181457), 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), _1181453), _1181455)), _1181457))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1181457), _1181453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181451)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1181453)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181453), _1181447)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1181449), _1181455)))], (21275 ^ _782435) ^ [_1181946, _1181948] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1181946, _1181948))))], (21277 ^ _782435) ^ [_1181977, _1181979] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1181977), _1181979))))], (21279 ^ _782435) ^ [_1182010, _1182012] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1182010, _1182012))))], (21281 ^ _782435) ^ [_1182041, _1182043] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1182041, _1182043))))], (21283 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint), c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint, tc_HOL_Obool))))], (21285 ^ _782435) ^ [_1182096, _1182098, _1182100, _1182102, _1182104, _1182106] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182096), _1182098)), _1182100) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182102), _1182104)), _1182106), 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), _1182102), _1182104)), _1182106)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182100), _1182096)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182106)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1182102)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182102), _1182096)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182104), _1182098)))], (21311 ^ _782435) ^ [_1182601, _1182603, _1182605, _1182607, _1182609] : [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), _1182601), _1182603)), _1182605)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1182601), _1182607)), _1182609))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182609), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182601), _1182609)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1182601), _1182605)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1182607), _1182603)))], (21329 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1182986] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1182986)), -(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)), _1182986))))], (21337 ^ _782435) ^ [_1183071] : [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)), _1183071))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat), _1183071)))], (21343 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1183180, _1183182] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183180)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183182)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1183180), _1183182)))], (21347 ^ _782435) ^ [_1183226, _1183228] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183226)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183228)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1183226), _1183228)))], (21349 ^ _782435) ^ [_1183287, _1183289] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183287)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183289))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183287), _1183289)))], (21355 ^ _782435) ^ [_1183392, _1183394] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1183392), _1183394)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183392)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1183394))))], (21361 ^ _782435) ^ [_1183518, _1183520] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183518), _1183520)), -(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)), _1183518)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183520))))], (21367 ^ _782435) ^ [_1183623, _1183625] : [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)), _1183623)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183623), _1183625)))], (21373 ^ _782435) ^ [_1183749, _1183751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183749), _1183751)), -(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)), _1183749)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183751))))], (21379 ^ _782435) ^ [_1183854, _1183856] : [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)), _1183854)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183856))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1183854), _1183856)))], (21385 ^ _782435) ^ [_1183980, _1183982] : [_1183980 = _1183982, -(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183980) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1183982))], (21391 ^ _782435) ^ [_1184065, _1184067] : [hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184065) = hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184067), -(_1184065 = _1184067)], (21397 ^ _782435) ^ [_1184171, _1184173] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184171), _1184173)), -(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184171)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184173))))], (21403 ^ _782435) ^ [_1184276, _1184278] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184276)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1184278))), -(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1184276), _1184278)))], (21409 ^ _782435) ^ [_1184402, _1184404] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184402) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184404), -(_1184402 = _1184404)], (21415 ^ _782435) ^ [_1184487, _1184489] : [_1184487 = _1184489, -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184487) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1184489))], (21421 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1184614, _1184616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184616)), -(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), _1184614), _1184616))))], (21435 ^ _782435) ^ [_1184767] : [-(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), _1184767))))], (21448 ^ _782435) ^ [_1184977] : [21449 ^ _782435 : [(21450 ^ _782435) ^ [_1185034] : [hBOOL(hAPP(_1184977, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185034)))]], 21452 ^ _782435 : [(21453 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21451 ^ [_1184977])))], (21455 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1184977, 21451 ^ [_1184977])))]]], (21437 ^ _782435) ^ [_1184807] : [-(hBOOL(hAPP(_1184807, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21444 ^ [_1184807])))), 21438 ^ _782435 : [(21439 ^ _782435) ^ [_1184859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1184859)), hBOOL(hAPP(_1184807, _1184859))]]], (21457 ^ _782435) ^ [_1185138] : [21459 ^ _782435 : [(21460 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 21458 ^ [_1185138])))], (21462 ^ _782435) ^ [] : [hBOOL(hAPP(_1185138, 21458 ^ [_1185138]))]], 21463 ^ _782435 : [(21464 ^ _782435) ^ [_1185265] : [-(hBOOL(hAPP(_1185138, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185265))))]]], (21466 ^ _782435) ^ [_1185295] : [hBOOL(hAPP(_1185295, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 21467 ^ [_1185295]))), 21470 ^ _782435 : [(21471 ^ _782435) ^ [_1185395] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185395)), -(hBOOL(hAPP(_1185295, _1185395)))]]], (21477 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1185504, _1185506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185504)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185506)), -(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), _1185504), _1185506))))], (21489 ^ _782435) ^ [_1185672, _1185674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185672)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185672), _1185674)))], (21495 ^ _782435) ^ [_1185777, _1185779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1185777), _1185779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185777)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1185779))))], (21501 ^ _782435) ^ [_1185888, _1185890, _1185892] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1185888)), 21504 ^ _782435 : [(21505 ^ _782435) ^ [_1186022] : [21507 ^ _782435 : [(21508 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21506 ^ [_1185888, _1185890, _1185892, _1186022]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1185888))))], (21511 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21509 ^ [_1185888, _1185890, _1185892, _1186022]), _1185890)))], (21513 ^ _782435) ^ [] : [-(_1186022 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21509 ^ [_1185888, _1185890, _1185892, _1186022]), 21506 ^ [_1185888, _1185890, _1185892, _1186022]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185892), _1186022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1185892), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186022), _1185888))))]]], (21521 ^ _782435) ^ [_1186296, _1186298, _1186300] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186296)), 21524 ^ _782435 : [(21525 ^ _782435) ^ [_1186430] : [21527 ^ _782435 : [(21528 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21526 ^ [_1186296, _1186298, _1186300, _1186430]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1186296))))], (21531 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21529 ^ [_1186296, _1186298, _1186300, _1186430]), _1186298)))], (21533 ^ _782435) ^ [] : [-(_1186430 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21529 ^ [_1186296, _1186298, _1186300, _1186430]), 21526 ^ [_1186296, _1186298, _1186300, _1186430]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186430), _1186300)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1186430), _1186296)), _1186300)))]]], (21541 ^ _782435) ^ [_1186704, _1186706, _1186708] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1186704)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186706), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1186708)), 21548 ^ _782435 : [(21549 ^ _782435) ^ [_1186912] : [21551 ^ _782435 : [(21552 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21550 ^ [_1186704, _1186706, _1186708, _1186912]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1186704))))], (21555 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21553 ^ [_1186704, _1186706, _1186708, _1186912]), _1186708)))], (21557 ^ _782435) ^ [] : [-(_1186912 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21553 ^ [_1186704, _1186706, _1186708, _1186912]), 21550 ^ [_1186704, _1186706, _1186708, _1186912]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1186912), _1186706)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1186912), _1186704)), _1186706)))]]], (21565 ^ _782435) ^ [_1187188, _1187190, _1187192] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1187188)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1187190), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1187192)), 21572 ^ _782435 : [(21573 ^ _782435) ^ [_1187396] : [21575 ^ _782435 : [(21576 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21574 ^ [_1187188, _1187190, _1187192, _1187396]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1187188))))], (21579 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21577 ^ [_1187188, _1187190, _1187192, _1187396]), _1187192)))], (21581 ^ _782435) ^ [] : [-(_1187396 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21577 ^ [_1187188, _1187190, _1187192, _1187396]), 21574 ^ [_1187188, _1187190, _1187192, _1187396]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187190), _1187396)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1187190), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1187396), _1187188))))]]], (21589 ^ _782435) ^ [_1187672, _1187674, _1187676, _1187678, _1187680] : [class_Groups_Oordered__comm__monoid__add(_1187672), hBOOL(hAPP(c_Finite__Set_Ofinite(_1187674), _1187676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1187674, tc_HOL_Obool)), _1187678), _1187676)), 21603 ^ _782435 : [(21604 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1187674), 21602 ^ [_1187672, _1187674, _1187676, _1187678, _1187680]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1187674, tc_HOL_Obool)), _1187676), _1187678))))], (21606 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187672), c_Groups_Ozero__class_Ozero(_1187672)), hAPP(_1187680, 21602 ^ [_1187672, _1187674, _1187676, _1187678, _1187680])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1187672), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187674, _1187672), _1187680), _1187678)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1187674, _1187672), _1187680), _1187676))))], (21610 ^ _782435) ^ [_1188158, _1188160] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188158)), 21619 ^ _782435 : [(21620 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1188160, 21615 ^ [_1188158, _1188160])))], (21622 ^ _782435) ^ [] : [hBOOL(hAPP(_1188160, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21615 ^ [_1188158, _1188160]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 21616 ^ [_1188158, _1188160]), _1188158))))]], 21623 ^ _782435 : [(21624 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1188160, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21615 ^ [_1188158, _1188160]), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), 21616 ^ [_1188158, _1188160]), _1188158)))))], (21626 ^ _782435) ^ [] : [hBOOL(hAPP(_1188160, 21615 ^ [_1188158, _1188160]))]], 21627 ^ _782435 : [(21628 ^ _782435) ^ [] : [21629 ^ _782435 : [(21630 ^ _782435) ^ [_1188590] : [hBOOL(hAPP(_1188160, _1188590))]], 21632 ^ _782435 : [(21633 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21631 ^ [_1188158, _1188160]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188158))))], (21635 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1188160, 21631 ^ [_1188158, _1188160])))]]], (21637 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1188160, 21644 ^ [_1188158, _1188160]))), 21638 ^ _782435 : [(21639 ^ _782435) ^ [_1188705] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1188705), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188158))), hBOOL(hAPP(_1188160, _1188705))]]]]], (21648 ^ _782435) ^ [_1188852, _1188854, _1188856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1188852)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1188854), _1188856)), 21655 ^ _782435 : [(21656 ^ _782435) ^ [_1189042] : [21658 ^ _782435 : [(21659 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21657 ^ [_1188852, _1188854, _1188856, _1189042]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1188852))))], (21662 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21660 ^ [_1188852, _1188854, _1188856, _1189042]), _1188856)))], (21664 ^ _782435) ^ [] : [-(_1189042 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21660 ^ [_1188852, _1188854, _1188856, _1189042]), 21657 ^ [_1188852, _1188854, _1188856, _1189042]))]], -(_1189042 = _1188854), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1189042), _1188852) = _1188854]]], (21672 ^ _782435) ^ [_1189302, _1189304, _1189306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189302)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1189304), _1189306)), 21679 ^ _782435 : [(21680 ^ _782435) ^ [_1189492] : [21682 ^ _782435 : [(21683 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21681 ^ [_1189302, _1189304, _1189306, _1189492]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1189302))))], (21686 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21684 ^ [_1189302, _1189304, _1189306, _1189492]), _1189306)))], (21688 ^ _782435) ^ [] : [-(_1189492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21684 ^ [_1189302, _1189304, _1189306, _1189492]), 21681 ^ [_1189302, _1189304, _1189306, _1189492]))]], -(_1189492 = _1189304), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1189492), _1189302) = _1189304]]], (21696 ^ _782435) ^ [_1189752, _1189754, _1189756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1189752)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1189754), _1189756)), 21703 ^ _782435 : [(21704 ^ _782435) ^ [_1189948] : [21706 ^ _782435 : [(21707 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21705 ^ [_1189752, _1189754, _1189756, _1189948]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1189752))))], (21710 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21708 ^ [_1189752, _1189754, _1189756, _1189948]), _1189756)))], (21712 ^ _782435) ^ [] : [-(_1189948 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21708 ^ [_1189752, _1189754, _1189756, _1189948]), 21705 ^ [_1189752, _1189754, _1189756, _1189948]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189754), _1189948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1189754), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1189948), _1189752))))]]], (21720 ^ _782435) ^ [_1190224, _1190226, _1190228] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190224)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1190226), _1190228)), 21727 ^ _782435 : [(21728 ^ _782435) ^ [_1190420] : [21730 ^ _782435 : [(21731 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21729 ^ [_1190224, _1190226, _1190228, _1190420]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1190224))))], (21734 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21732 ^ [_1190224, _1190226, _1190228, _1190420]), _1190228)))], (21736 ^ _782435) ^ [] : [-(_1190420 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21732 ^ [_1190224, _1190226, _1190228, _1190420]), 21729 ^ [_1190224, _1190226, _1190228, _1190420]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1190420), _1190226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190420), _1190224)), _1190226)))]]], (21744 ^ _782435) ^ [_1190696, _1190698, _1190700] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1190696)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190698), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1190700)), 21754 ^ _782435 : [(21755 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21753 ^ [_1190696, _1190698, _1190700]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1190696))))], (21758 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21756 ^ [_1190696, _1190698, _1190700]), _1190700)))], (21760 ^ _782435) ^ [] : [-(_1190698 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21756 ^ [_1190696, _1190698, _1190700]), 21753 ^ [_1190696, _1190698, _1190700]))]], -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1190698), _1190696) = _1190698)], (21764 ^ _782435) ^ [_1191035, _1191037, _1191039] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191035)), hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191037), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1191039)), 21774 ^ _782435 : [(21775 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21773 ^ [_1191035, _1191037, _1191039]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191035))))], (21778 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21776 ^ [_1191035, _1191037, _1191039]), _1191039)))], (21780 ^ _782435) ^ [] : [-(_1191037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21776 ^ [_1191035, _1191037, _1191039]), 21773 ^ [_1191035, _1191037, _1191039]))]], -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191037), _1191035) = _1191037)], (21784 ^ _782435) ^ [_1191374, _1191376, _1191378] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191374)), 21787 ^ _782435 : [(21788 ^ _782435) ^ [_1191508] : [21790 ^ _782435 : [(21791 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21789 ^ [_1191374, _1191376, _1191378, _1191508]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191374))))], (21794 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21792 ^ [_1191374, _1191376, _1191378, _1191508]), _1191376)))], (21796 ^ _782435) ^ [] : [-(_1191508 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), 21792 ^ [_1191374, _1191376, _1191378, _1191508]), 21789 ^ [_1191374, _1191376, _1191378, _1191508]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191378), _1191508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191378), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1191508), _1191374))))]]], (21804 ^ _782435) ^ [_1191782, _1191784, _1191786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1191782)), 21807 ^ _782435 : [(21808 ^ _782435) ^ [_1191916] : [21810 ^ _782435 : [(21811 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21809 ^ [_1191782, _1191784, _1191786, _1191916]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, c_Groups_Oone__class_Oone(tc_Int_Oint), _1191782))))], (21814 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 21812 ^ [_1191782, _1191784, _1191786, _1191916]), _1191784)))], (21816 ^ _782435) ^ [] : [-(_1191916 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 21812 ^ [_1191782, _1191784, _1191786, _1191916]), 21809 ^ [_1191782, _1191784, _1191786, _1191916]))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1191916), _1191786)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1191916), _1191782)), _1191786)))]]], (21824 ^ _782435) ^ [_1192190, _1192192, _1192194, _1192196, _1192198] : [class_Groups_Ocomm__monoid__add(_1192190), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192192), _1192194)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192192), _1192196)), 21838 ^ _782435 : [(21839 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192192), 21837 ^ [_1192190, _1192192, _1192194, _1192196, _1192198]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1192192, tc_HOL_Obool)), _1192194), _1192196))))], (21841 ^ _782435) ^ [] : [hAPP(_1192198, 21837 ^ [_1192190, _1192192, _1192194, _1192196, _1192198]) = c_Groups_Ozero__class_Ozero(_1192190)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192192, _1192190), _1192198), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1192192, tc_HOL_Obool)), _1192194), _1192196)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192190), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192192, _1192190), _1192198), _1192194)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192192, _1192190), _1192198), _1192196)))], (21845 ^ _782435) ^ [_1192685, _1192687, _1192689, _1192691, _1192693] : [class_Groups_Ocomm__monoid__add(_1192685), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192687), _1192689)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1192687), _1192691)), 21859 ^ _782435 : [(21860 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1192687), 21858 ^ [_1192685, _1192687, _1192689, _1192691, _1192693]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1192687, tc_HOL_Obool)), _1192689), _1192691))))], (21862 ^ _782435) ^ [] : [hAPP(_1192693, 21858 ^ [_1192685, _1192687, _1192689, _1192691, _1192693]) = c_Groups_Ozero__class_Ozero(_1192685)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192687, _1192685), _1192693), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1192687, tc_HOL_Obool)), _1192689), _1192691)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1192685), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192687, _1192685), _1192693), _1192689)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1192687, _1192685), _1192693), _1192691)))], (21866 ^ _782435) ^ [_1193180, _1193182, _1193184, _1193186, _1193188] : [class_Groups_Ocomm__monoid__add(_1193180), class_Groups_Oordered__ab__semigroup__add(_1193180), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193182), _1193184)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1193182, tc_HOL_Obool)), _1193186), _1193184)), 21884 ^ _782435 : [(21885 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193182), 21883 ^ [_1193180, _1193182, _1193184, _1193186, _1193188]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1193182, tc_HOL_Obool)), _1193184), _1193186))))], (21887 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193180), c_Groups_Ozero__class_Ozero(_1193180)), hAPP(_1193188, 21883 ^ [_1193180, _1193182, _1193184, _1193186, _1193188])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1193180), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193182, _1193180), _1193188), _1193186)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193182, _1193180), _1193188), _1193184))))], (21891 ^ _782435) ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734] : [class_Groups_Ocomm__monoid__add(_1193724), hBOOL(hAPP(c_Finite__Set_Ofinite(_1193726), _1193728)), 21901 ^ _782435 : [(21902 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193726), 21900 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734]), _1193728)))], (21905 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1193726), 21903 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734]), _1193728)))], (21907 ^ _782435) ^ [] : [21900 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734] = 21903 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734]], (21909 ^ _782435) ^ [] : [-(hAPP(_1193730, 21900 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734]) = hAPP(_1193730, 21903 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734]))], (21911 ^ _782435) ^ [] : [hAPP(_1193732, hAPP(_1193730, 21900 ^ [_1193724, _1193726, _1193728, _1193730, _1193732, _1193734])) = c_Groups_Ozero__class_Ozero(_1193724)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193734, _1193724), _1193732), hAPP(c_Set_Oimage(_1193726, _1193734, _1193730), _1193728)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1193726, _1193724), hAPP(c_Fun_Ocomp(_1193734, _1193724, _1193726, _1193732), _1193730)), _1193728))], (21915 ^ _782435) ^ [_1194461, _1194463, _1194465, _1194467] : [hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194461, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21916 ^ [_1194461, _1194463, _1194465, _1194467])), _1194463) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194461, 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 ^ [_1194461, _1194463, _1194465, _1194467]), _1194465))), _1194467), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194461, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194463) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194461, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194467))], (21922 ^ _782435) ^ [_1194741, _1194743, _1194745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194741, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194741, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 21923 ^ [_1194741, _1194743, _1194745])), _1194743)), _1194745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1194741, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(_1194741, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), _1194743)), _1194745)))], (21929 ^ _782435) ^ [_1194976, _1194978] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1194976), _1194978)), -(c_Nat__Transfer_Otsub(_1194978, _1194976) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1194978), _1194976))], (21935 ^ _782435) ^ [_1195075, _1195077] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1195075), _1195077))), -(c_Nat__Transfer_Otsub(_1195077, _1195075) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (21941 ^ _782435) ^ [_1195121, _1195123] : [class_Rings_Olinordered__idom(_1195121), hBOOL(hAPP(hAPP(c_member(_1195121), _1195123), c_Int_Oring__1__class_OInts(_1195121))), 21948 ^ _782435 : [(21949 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195121), c_Groups_Oone__class_Oone(_1195121)), _1195123)), _1195123)), c_Groups_Ozero__class_Ozero(_1195121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195121), _1195123), c_Groups_Ozero__class_Ozero(_1195121))))], (21955 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195121), _1195123), c_Groups_Ozero__class_Ozero(_1195121))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1195121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195121), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1195121), c_Groups_Oone__class_Oone(_1195121)), _1195123)), _1195123)), c_Groups_Ozero__class_Ozero(_1195121))))]]], (21961 ^ _782435) ^ [_1195504, _1195506, _1195508] : [-(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), _1195504)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_Nat_Onat), c_Groups_Otimes__class_Otimes(tc_Nat_Onat)), _1195506))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1195508))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1195508), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195504), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1195504), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1195508), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1195506)))))], (21963 ^ _782435) ^ [_1195585, _1195587, _1195589] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1195585), _1195587)), hBOOL(hAPP(hAPP(c_member(_1195585), _1195589), _1195587)), -(hAPP(c_Finite__Set_Ocard(_1195585), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1195585, tc_HOL_Obool)), _1195587), hAPP(hAPP(c_Set_Oinsert(_1195585), _1195589), c_Orderings_Obot__class_Obot(tc_fun(_1195585, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1195585), _1195587)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (21973 ^ _782435) ^ [_1195820] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195820), hAPP(c_Nat_OSuc, _1195820))))], (21975 ^ _782435) ^ [_1195851, _1195853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1195851), _1195853)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1195851)), hAPP(c_Nat_OSuc, _1195853))))], (21981 ^ _782435) ^ [_1195960] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Nat_OSuc, _1195960))))], (21983 ^ _782435) ^ [_1195988, _1195990] : [-(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, _1195988)))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1195990))))], (21985 ^ _782435) ^ [_1196030] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1196030)) = hAPP(c_Nat_OSuc, _1196030))], (21987 ^ _782435) ^ [_1196071] : [_1196071 = hAPP(c_Nat_OSuc, _1196071)], (21989 ^ _782435) ^ [_1196106] : [hAPP(c_Nat_OSuc, _1196106) = _1196106], (21991 ^ _782435) ^ [_1196147, _1196149] : [hAPP(c_Nat_OSuc, _1196147) = hAPP(c_Nat_OSuc, _1196149), -(_1196147 = _1196149)], (21997 ^ _782435) ^ [_1196232, _1196234] : [_1196232 = _1196234, -(hAPP(c_Nat_OSuc, _1196232) = hAPP(c_Nat_OSuc, _1196234))], (22003 ^ _782435) ^ [_1196323, _1196325] : [hAPP(c_Nat_OSuc, _1196323) = hAPP(c_Nat_OSuc, _1196325), -(_1196323 = _1196325)], (22009 ^ _782435) ^ [] : [-(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc))], (22011 ^ _782435) ^ [_1196430] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1196430) = 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)), _1196430)))], (22013 ^ _782435) ^ [_1196462, _1196464] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1196462, _1196464)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1196464)), _1196462))], (22015 ^ _782435) ^ [_1196503, _1196505] : [class_Orderings_Oorder(_1196503), 22018 ^ _782435 : [(22019 ^ _782435) ^ [] : [c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1196503, _1196505), 22022 ^ _782435 : [(22023 ^ _782435) ^ [_1196637] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196503), hAPP(_1196505, _1196637)), hAPP(_1196505, hAPP(c_Nat_OSuc, _1196637)))))]]], (22025 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1196503), hAPP(_1196505, 22026 ^ [_1196503, _1196505])), hAPP(_1196505, hAPP(c_Nat_OSuc, 22026 ^ [_1196503, _1196505])))), -(c_Orderings_Oorder__class_Omono(tc_Nat_Onat, _1196503, _1196505))]]], (22032 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1196837] : [hAPP(c_Nat_OSuc, _1196837) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22036 ^ _782435) ^ [_1196872] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1196872)], (22038 ^ _782435) ^ [_1196907] : [hAPP(c_Nat_OSuc, _1196907) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22040 ^ _782435) ^ [_1196942] : [hAPP(c_Nat_OSuc, _1196942) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22042 ^ _782435) ^ [_1196977] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1196977)], (22044 ^ _782435) ^ [_1197012] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Nat_OSuc, _1197012)], (22046 ^ _782435) ^ [_1197047, _1197049] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197047), _1197049))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197049), hAPP(c_Nat_OSuc, _1197047))))], (22052 ^ _782435) ^ [_1197092, _1197094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197094), hAPP(c_Nat_OSuc, _1197092))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197092), _1197094))], (22068 ^ _782435) ^ [_1197325, _1197327] : [22069 ^ _782435 : [(22070 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197325), _1197327))], (22072 ^ _782435) ^ [] : [_1197325 = _1197327]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197325), hAPP(c_Nat_OSuc, _1197327))))], (22058 ^ _782435) ^ [_1197213, _1197215] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197213), hAPP(c_Nat_OSuc, _1197215))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197213), _1197215))), -(_1197213 = _1197215)], (22076 ^ _782435) ^ [_1197483, _1197485] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197483)), hAPP(c_Nat_OSuc, _1197485))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197483), _1197485)))], (22082 ^ _782435) ^ [_1197588, _1197590] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197588), _1197590)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1197588)), hAPP(c_Nat_OSuc, _1197590))))], (22088 ^ _782435) ^ [_1197698, _1197700] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197698), _1197700))), 22091 ^ _782435 : [(22092 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197698), hAPP(c_Nat_OSuc, _1197700))), -(_1197698 = _1197700)], (22098 ^ _782435) ^ [] : [_1197698 = _1197700, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197698), hAPP(c_Nat_OSuc, _1197700))))]]], (22104 ^ _782435) ^ [_1197931, _1197933] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197931), _1197933))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1197931), hAPP(c_Nat_OSuc, _1197933))), -(_1197933 = _1197931)], (22114 ^ _782435) ^ [_1198079, _1198081] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198079), _1198081)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198079), hAPP(c_Nat_OSuc, _1198081))))], (22120 ^ _782435) ^ [_1198182, _1198184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198182), _1198184)), -(hAPP(c_Nat_OSuc, _1198182) = _1198184), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198182)), _1198184)))], (22130 ^ _782435) ^ [_1198306, _1198308, _1198310] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198306), _1198308)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198308), _1198310)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198306)), _1198310)))], (22140 ^ _782435) ^ [_1198475, _1198477] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198475), hAPP(c_Nat_OSuc, _1198477))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198475), _1198477))), -(_1198475 = _1198477)], (22150 ^ _782435) ^ [_1198593, _1198595] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198593)), _1198595)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198593), _1198595)))], (22156 ^ _782435) ^ [_1198696, _1198698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198696)), hAPP(c_Nat_OSuc, _1198698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1198696), _1198698)))], (22162 ^ _782435) ^ [_1198805, _1198807] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198805)), _1198807) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198805), hAPP(c_Nat_OSuc, _1198807)))], (22164 ^ _782435) ^ [_1198848, _1198850] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198848)), _1198850) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198848), _1198850)))], (22166 ^ _782435) ^ [_1198891, _1198893] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198891), hAPP(c_Nat_OSuc, _1198893)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1198891), _1198893)))], (22168 ^ _782435) ^ [_1198943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198943)), _1198943))], (22170 ^ _782435) ^ [_1198983, _1198985] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1198983), _1198985))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1198985)), _1198983)))], (22176 ^ _782435) ^ [_1199028, _1199030] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199030)), _1199028)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199028), _1199030))], (22192 ^ _782435) ^ [_1199267, _1199269] : [22193 ^ _782435 : [(22194 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199267), _1199269))], (22196 ^ _782435) ^ [] : [_1199267 = hAPP(c_Nat_OSuc, _1199269)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199267), hAPP(c_Nat_OSuc, _1199269))))], (22182 ^ _782435) ^ [_1199149, _1199151] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199149), hAPP(c_Nat_OSuc, _1199151))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199149), _1199151))), -(_1199149 = hAPP(c_Nat_OSuc, _1199151))], (22200 ^ _782435) ^ [_1199431, _1199433] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199431)), hAPP(c_Nat_OSuc, _1199433))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199431), _1199433)))], (22206 ^ _782435) ^ [_1199536, _1199538] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199536), _1199538)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199536)), hAPP(c_Nat_OSuc, _1199538))))], (22212 ^ _782435) ^ [_1199647, _1199649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199647), _1199649)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199647), hAPP(c_Nat_OSuc, _1199649))))], (22218 ^ _782435) ^ [_1199750, _1199752] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199750), hAPP(c_Nat_OSuc, _1199752))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199750), _1199752))), -(_1199750 = hAPP(c_Nat_OSuc, _1199752))], (22228 ^ _782435) ^ [_1199874, _1199876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1199874)), _1199876)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1199874), _1199876)))], (22234 ^ _782435) ^ [_1199977, _1199979, _1199981, _1199983, _1199985] : [c_Fun_Obij__betw(_1199977, _1199979, _1199981, _1199983, _1199985), -(hAPP(c_Finite__Set_Ocard(_1199977), _1199983) = hAPP(c_Finite__Set_Ocard(_1199979), _1199985))], (22240 ^ _782435) ^ [_1200086, _1200088] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200086)), hAPP(c_Nat_OSuc, _1200088)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200086), _1200088))], (22242 ^ _782435) ^ [_1200129, _1200131, _1200133] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200129)), _1200131)), hAPP(c_Nat_OSuc, _1200133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200129), _1200131)), _1200133))], (22244 ^ _782435) ^ [_1200204, _1200206, _1200208] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200204)), _1200206) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200204)), _1200208), -(_1200206 = _1200208)], (22250 ^ _782435) ^ [_1200315, _1200317, _1200319] : [_1200317 = _1200319, -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200315)), _1200317) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1200315)), _1200319))], (22256 ^ _782435) ^ [_1200432, _1200434] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1200432, _1200434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1200434), hAPP(c_Nat_OSuc, _1200432)))], (22258 ^ _782435) ^ [_1200473] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1200473)) = _1200473)], (22260 ^ _782435) ^ [_1200502, _1200504, _1200506] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200502), _1200504)), 22263 ^ _782435 : [(22264 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1200502), _1200506), _1200504)), -(hAPP(c_Finite__Set_Ocard(_1200502), hAPP(hAPP(c_Set_Oinsert(_1200502), _1200506), _1200504)) = hAPP(c_Finite__Set_Ocard(_1200502), _1200504))], (22270 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1200502), _1200506), _1200504))), -(hAPP(c_Finite__Set_Ocard(_1200502), hAPP(hAPP(c_Set_Oinsert(_1200502), _1200506), _1200504)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1200502), _1200504)))]]], (22276 ^ _782435) ^ [_1200796, _1200798, _1200800] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1200796), _1200798)), -(hBOOL(hAPP(hAPP(c_member(_1200796), _1200800), _1200798))), -(hAPP(c_Finite__Set_Ocard(_1200796), hAPP(hAPP(c_Set_Oinsert(_1200796), _1200800), _1200798)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1200796), _1200798)))], (22286 ^ _782435) ^ [_1200954, _1200956] : [hBOOL(hAPP(_1200954, _1200956)), -(hBOOL(hAPP(_1200954, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1200954) = 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), _1200954), c_Nat_OSuc))))], (22296 ^ _782435) ^ [_1201084, _1201086, _1201088, _1201090] : [class_Rings_Osemiring__1(_1201084), -(c_Nat_Osemiring__1__class_Oof__nat__aux(_1201084, _1201086, hAPP(c_Nat_OSuc, _1201088), _1201090) = c_Nat_Osemiring__1__class_Oof__nat__aux(_1201084, _1201086, _1201088, hAPP(_1201086, _1201090)))], (22302 ^ _782435) ^ [_1201195, _1201197, _1201199] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201195), _1201197)), -(hAPP(c_Finite__Set_Ocard(_1201195), hAPP(hAPP(c_Set_Oinsert(_1201195), _1201199), _1201197)) = hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1201195), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1201195, tc_HOL_Obool)), _1201197), hAPP(hAPP(c_Set_Oinsert(_1201195), _1201199), c_Orderings_Obot__class_Obot(tc_fun(_1201195, tc_HOL_Obool)))))))], (22308 ^ _782435) ^ [_1201372] : [-(hAPP(c_Finite__Set_Ocard(_1201372), c_Orderings_Obot__class_Obot(tc_fun(_1201372, tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22310 ^ _782435) ^ [_1201401, _1201403] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1201401), _1201403))), -(hAPP(c_Finite__Set_Ocard(_1201401), _1201403) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22316 ^ _782435) ^ [_1201446] : [-(c_Fun_Oinj__on(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc, _1201446))], (22318 ^ _782435) ^ [_1201471, _1201473] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201471), c_Orderings_Otop__class_Otop(tc_fun(_1201471, tc_HOL_Obool)))), hAPP(c_Finite__Set_Ocard(_1201471), _1201473) = hAPP(c_Finite__Set_Ocard(_1201471), c_Orderings_Otop__class_Otop(tc_fun(_1201471, tc_HOL_Obool))), -(_1201473 = c_Orderings_Otop__class_Otop(tc_fun(_1201471, tc_HOL_Obool)))], (22328 ^ _782435) ^ [_1201658, _1201660, _1201662, _1201664] : [c_Fun_Oinj__on(_1201658, _1201660, _1201662, _1201664), -(hAPP(c_Finite__Set_Ocard(_1201660), hAPP(c_Set_Oimage(_1201658, _1201660, _1201662), _1201664)) = hAPP(c_Finite__Set_Ocard(_1201658), _1201664))], (22334 ^ _782435) ^ [_1201777, _1201779, _1201781, _1201783] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1201777), _1201779)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1201781), _1201783)), 22341 ^ _782435 : [(22342 ^ _782435) ^ [] : [22343 ^ _782435 : [(22344 ^ _782435) ^ [_1201966] : [c_Fun_Obij__betw(_1201777, _1201781, _1201966, _1201779, _1201783)]], -(hAPP(c_Finite__Set_Ocard(_1201777), _1201779) = hAPP(c_Finite__Set_Ocard(_1201781), _1201783))], (22348 ^ _782435) ^ [] : [hAPP(c_Finite__Set_Ocard(_1201777), _1201779) = hAPP(c_Finite__Set_Ocard(_1201781), _1201783), -(c_Fun_Obij__betw(_1201777, _1201781, 22351 ^ [_1201777, _1201779, _1201781, _1201783], _1201779, _1201783))]]], (22355 ^ _782435) ^ [_1202146, _1202148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202146), hAPP(c_Nat_OSuc, _1202148))), -(_1202146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22363 ^ _782435 : [(22364 ^ _782435) ^ [] : [-(_1202146 = hAPP(c_Nat_OSuc, 22362 ^ [_1202146, _1202148]))], (22366 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 22362 ^ [_1202146, _1202148]), _1202148)))]]], (22368 ^ _782435) ^ [_1202326, _1202328] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202326), hAPP(c_Nat_OSuc, _1202328)))), 22369 ^ _782435 : [(22370 ^ _782435) ^ [] : [_1202326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22372 ^ _782435) ^ [_1202414] : [_1202326 = hAPP(c_Nat_OSuc, _1202414), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202414), _1202328))]]], (22380 ^ _782435) ^ [_1202560] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202560), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(_1202560 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22386 ^ _782435) ^ [_1202641] : [_1202641 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1202641), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (22392 ^ _782435) ^ [_1202740] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202740)), -(_1202740 = hAPP(c_Nat_OSuc, 22395 ^ [_1202740]))], (22399 ^ _782435) ^ [_1202831] : [22400 ^ _782435 : [(22401 ^ _782435) ^ [_1202873] : [_1202831 = hAPP(c_Nat_OSuc, _1202873)]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1202831)))], (22405 ^ _782435) ^ [_1202946, _1202948] : [hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1202946), _1202948), 22410 ^ _782435 : [(22411 ^ _782435) ^ [] : [-(_1202946 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22413 ^ _782435) ^ [] : [-(_1202948 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22414 ^ _782435 : [(22415 ^ _782435) ^ [] : [-(_1202946 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22417 ^ _782435) ^ [] : [-(_1202948 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (22419 ^ _782435) ^ [_1203130, _1203132] : [-(hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203130), _1203132)), 22420 ^ _782435 : [(22421 ^ _782435) ^ [] : [_1203130 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203132 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22427 ^ _782435) ^ [] : [_1203130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1203132 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22435 ^ _782435) ^ [_1203371, _1203373] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203371), _1203373) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22440 ^ _782435 : [(22441 ^ _782435) ^ [] : [-(_1203371 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22443 ^ _782435) ^ [] : [-(_1203373 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], 22444 ^ _782435 : [(22445 ^ _782435) ^ [] : [-(_1203371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22447 ^ _782435) ^ [] : [-(_1203373 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (22449 ^ _782435) ^ [_1203555, _1203557] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203555), _1203557) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 22450 ^ _782435 : [(22451 ^ _782435) ^ [] : [_1203555 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1203557 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (22457 ^ _782435) ^ [] : [_1203555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1203557 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22465 ^ _782435) ^ [_1203781, _1203783] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203781), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203781), _1203783)))))], (22467 ^ _782435) ^ [_1203820, _1203822] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203820), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203822), _1203820)))))], (22469 ^ _782435) ^ [_1203874, _1203876] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203874), _1203876)), -(_1203876 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203874), 22472 ^ [_1203874, _1203876])))], (22476 ^ _782435) ^ [_1203987, _1203989] : [22477 ^ _782435 : [(22478 ^ _782435) ^ [_1204040] : [_1203989 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1203987), _1204040))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1203987), _1203989)))], (22482 ^ _782435) ^ [_1204122, _1204124] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204122), _1204124)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204122)), _1204124)))], (22488 ^ _782435) ^ [_1204221, _1204223] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204221)), _1204223)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204221), _1204223)))], (22494 ^ _782435) ^ [_1204341, _1204343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204341), hAPP(c_Nat_OSuc, _1204343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204341), _1204343)))], (22500 ^ _782435) ^ [_1204440, _1204442] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204440), _1204442)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204440), hAPP(c_Nat_OSuc, _1204442))))], (22506 ^ _782435) ^ [_1204560, _1204562] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204560)), _1204562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204560), _1204562)))], (22512 ^ _782435) ^ [_1204659, _1204661] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204659), _1204661)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204659)), _1204661)))], (22518 ^ _782435) ^ [_1204764, _1204766] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204764), _1204766)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204764), hAPP(c_Nat_OSuc, _1204766))))], (22524 ^ _782435) ^ [_1204867, _1204869] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204867), _1204869)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1204867)), _1204869)))], (22530 ^ _782435) ^ [_1204970, _1204972] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1204970), _1204972)), 22533 ^ _782435 : [(22534 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204972), hAPP(c_Nat_OSuc, _1204970))), -(_1204972 = _1204970)], (22540 ^ _782435) ^ [] : [_1204972 = _1204970, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1204972), hAPP(c_Nat_OSuc, _1204970))))]]], (22546 ^ _782435) ^ [_1205211, _1205213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205211)), _1205213)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205211), _1205213)))], (22552 ^ _782435) ^ [_1205329, _1205331] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205329), _1205331) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22555 ^ _782435 : [(22556 ^ _782435) ^ [] : [-(_1205329 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22558 ^ _782435) ^ [] : [-(_1205331 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (22560 ^ _782435) ^ [_1205440, _1205442] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205440), _1205442) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1205440 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1205442 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22570 ^ _782435) ^ [_1205583, _1205585] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1205583), _1205585)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205585), _1205583))], (22572 ^ _782435) ^ [_1205623, _1205625] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1205623), _1205625)), hAPP(c_Nat_OSuc, _1205623))))], (22574 ^ _782435) ^ [_1205680, _1205682, _1205684] : [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, _1205680)), _1205682)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205680)), _1205684))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205682), _1205684)))], (22580 ^ _782435) ^ [_1205811, _1205813, _1205815] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1205813), _1205815)), -(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, _1205811)), _1205813)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205811)), _1205815))))], (22586 ^ _782435) ^ [_1205948, _1205950] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1205948)), _1205950) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1205950), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205948), _1205950)))], (22588 ^ _782435) ^ [_1205994, _1205996] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205994), hAPP(c_Nat_OSuc, _1205996)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1205994), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1205994), _1205996)))], (22590 ^ _782435) ^ [_1206040, _1206042] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206040), _1206042)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206042)), _1206040) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206042), _1206040)))], (22596 ^ _782435) ^ [_1206181, _1206183, _1206185] : [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, _1206181)), _1206183)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206181)), _1206185))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206183), _1206185)))], (22602 ^ _782435) ^ [_1206312, _1206314, _1206316] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1206314), _1206316)), -(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, _1206312)), _1206314)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206312)), _1206316))))], (22608 ^ _782435) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22610 ^ _782435) ^ [_1206467] : [-(hAPP(c_Nat_OSuc, _1206467) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1206467), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (22612 ^ _782435) ^ [_1206499] : [-(hAPP(c_Nat_OSuc, _1206499) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1206499))], (22614 ^ _782435) ^ [_1206528] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206528)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1206528)], (22616 ^ _782435) ^ [_1206560, _1206562] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206560), hAPP(c_Nat_OSuc, _1206562)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1206560), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1206562))], (22618 ^ _782435) ^ [_1206606, _1206608] : [hAPP(_1206606, 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), _1206606), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1206608)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, tc_Nat_Onat), _1206606), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1206608)))], (22624 ^ _782435) ^ [_1206729, _1206731, _1206733] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1206729), _1206731)), hBOOL(hAPP(hAPP(c_member(_1206729), _1206733), _1206731)), -(hAPP(c_Nat_OSuc, hAPP(c_Finite__Set_Ocard(_1206729), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1206729, tc_HOL_Obool)), _1206731), hAPP(hAPP(c_Set_Oinsert(_1206729), _1206733), c_Orderings_Obot__class_Obot(tc_fun(_1206729, tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(_1206729), _1206731))], (22634 ^ _782435) ^ [_1206958, _1206960] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1206958), hAPP(c_Nat_OSuc, _1206960)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1206958, _1206960))], (22636 ^ _782435) ^ [_1206996] : [-(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1206996) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1206996)))], (22638 ^ _782435) ^ [_1207028, _1207030] : [-(hAPP(c_Finite__Set_Ocard(_1207028), _1207030) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1207028, tc_Nat_Onat), hAPP(c_COMBK(tc_Nat_Onat, _1207028), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1207030))], (22640 ^ _782435) ^ [_1207073, _1207075] : [-(hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1207073, _1207075)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1207075), _1207073))], (22642 ^ _782435) ^ [_1207111] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207111)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1207111))], (22644 ^ _782435) ^ [_1207143] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207143)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1207143), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1207143)))], (22646 ^ _782435) ^ [_1207181, _1207183] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207181), _1207183)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207181)), hAPP(c_Nat_OSuc, _1207183)))], (22648 ^ _782435) ^ [_1207227] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207227)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1207227)), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1207227)))], (22650 ^ _782435) ^ [_1207268, _1207270] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1207268, _1207270)), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1207268, _1207270), tc_HOL_Obool)))), -(hAPP(c_Finite__Set_Ocard(_1207270), c_Orderings_Otop__class_Otop(tc_fun(_1207270, tc_HOL_Obool))) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1207268), c_Orderings_Otop__class_Otop(tc_fun(_1207268, tc_HOL_Obool)))))], (22660 ^ _782435) ^ [_1207428, _1207430, _1207432, _1207434] : [class_Groups_Ocomm__monoid__add(_1207428), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207428), _1207430), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207432)), hAPP(c_Nat_OSuc, _1207434))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207428), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207428, tc_Nat_Onat), _1207430), c_Nat_OSuc)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1207432), _1207434)))], (22666 ^ _782435) ^ [_1207599, _1207601] : [-(hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Nat_Onat, c_Nat_OSuc), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1207599, _1207601)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207599), hAPP(c_Nat_OSuc, _1207601)))], (22668 ^ _782435) ^ [_1207641, _1207643, _1207645, _1207647] : [class_Groups_Ocomm__monoid__add(_1207641), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207641), _1207643), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1207645), hAPP(c_Nat_OSuc, _1207647))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1207641), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1207641, tc_Nat_Onat), _1207643), c_Nat_OSuc)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1207645, _1207647)))], (22684 ^ _782435) ^ [_1207974, _1207976] : [22685 ^ _782435 : [(22686 ^ _782435) ^ [] : [_1207976 = c_Orderings_Obot__class_Obot(tc_fun(_1207974, tc_HOL_Obool))], (22688 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1207974), _1207976)))]], -(hAPP(c_Finite__Set_Ocard(_1207974), _1207976) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (22674 ^ _782435) ^ [_1207819, _1207821] : [hAPP(c_Finite__Set_Ocard(_1207819), _1207821) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1207821 = c_Orderings_Obot__class_Obot(tc_fun(_1207819, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1207819), _1207821))], (22692 ^ _782435) ^ [_1208118, _1208120] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208118), _1208120) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1208118, _1208120))], (22694 ^ _782435) ^ [_1208154, _1208156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1208154), _1208156))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1208154), _1208156)))], (22700 ^ _782435) ^ [_1208253, _1208255, _1208257] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208253), _1208255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208253), _1208255)), hAPP(c_Finite__Set_Ocard(_1208253), hAPP(hAPP(c_Set_Oinsert(_1208253), _1208257), _1208255)))))], (22706 ^ _782435) ^ [_1208386, _1208388, _1208390] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208386), _1208388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208386, tc_HOL_Obool)), _1208390), _1208388)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208386), _1208390)), hAPP(c_Finite__Set_Ocard(_1208386), _1208388))))], (22716 ^ _782435) ^ [_1208577, _1208579, _1208581] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208577), _1208579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1208577, tc_HOL_Obool)), _1208581), _1208579)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208577), _1208579)), hAPP(c_Finite__Set_Ocard(_1208577), _1208581))), -(_1208581 = _1208579)], (22730 ^ _782435) ^ [_1208822, _1208824, _1208826, _1208828] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1208822), _1208824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1208826), hAPP(c_Set_Oimage(_1208822, _1208826, _1208828), _1208824))), hAPP(c_Finite__Set_Ocard(_1208822), _1208824))))], (22736 ^ _782435) ^ [_1208955, _1208957] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1208955)), _1208957) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1208955, _1208957))], (22738 ^ _782435) ^ [_1208993] : [class_Rings_Oring__1(_1208993), -(hBOOL(hAPP(hAPP(c_member(_1208993), c_Groups_Ozero__class_Ozero(_1208993)), c_Int_Oring__1__class_OInts(_1208993))))], (22744 ^ _782435) ^ [_1209088, _1209090, _1209092, _1209094] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209088), _1209090)), hAPP(c_Finite__Set_Ocard(_1209092), hAPP(c_Set_Oimage(_1209088, _1209092, _1209094), _1209090)) = hAPP(c_Finite__Set_Ocard(_1209088), _1209090), -(c_Fun_Oinj__on(_1209088, _1209092, _1209094, _1209090))], (22754 ^ _782435) ^ [_1209271, _1209273, _1209275, _1209277] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1209271), _1209273)), 22757 ^ _782435 : [(22758 ^ _782435) ^ [] : [c_Fun_Oinj__on(_1209271, _1209275, _1209277, _1209273), -(hAPP(c_Finite__Set_Ocard(_1209275), hAPP(c_Set_Oimage(_1209271, _1209275, _1209277), _1209273)) = hAPP(c_Finite__Set_Ocard(_1209271), _1209273))], (22764 ^ _782435) ^ [] : [hAPP(c_Finite__Set_Ocard(_1209275), hAPP(c_Set_Oimage(_1209271, _1209275, _1209277), _1209273)) = hAPP(c_Finite__Set_Ocard(_1209271), _1209273), -(c_Fun_Oinj__on(_1209271, _1209275, _1209277, _1209273))]]], (22770 ^ _782435) ^ [_1209555, _1209557, _1209559, _1209561] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1209555), hAPP(c_Set_Oimage(_1209557, _1209555, _1209559), _1209561))), hAPP(c_Finite__Set_Ocard(_1209557), _1209561))), c_Fun_Oinj__on(_1209557, _1209555, _1209559, _1209561)], (22776 ^ _782435) ^ [_1209685, _1209687, _1209689] : [class_Rings_Oring__1(_1209685), hBOOL(hAPP(hAPP(c_member(_1209685), _1209687), c_Int_Oring__1__class_OInts(_1209685))), hBOOL(hAPP(hAPP(c_member(_1209685), _1209689), c_Int_Oring__1__class_OInts(_1209685))), -(hBOOL(hAPP(hAPP(c_member(_1209685), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1209685), _1209687), _1209689)), c_Int_Oring__1__class_OInts(_1209685))))], (22790 ^ _782435) ^ [_1209940, _1209942, _1209944] : [class_Rings_Oring__1(_1209940), hBOOL(hAPP(hAPP(c_member(_1209940), _1209942), c_Int_Oring__1__class_OInts(_1209940))), hBOOL(hAPP(hAPP(c_member(_1209940), _1209944), c_Int_Oring__1__class_OInts(_1209940))), -(hBOOL(hAPP(hAPP(c_member(_1209940), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1209940), _1209942), _1209944)), c_Int_Oring__1__class_OInts(_1209940))))], (22804 ^ _782435) ^ [_1210195, _1210197, _1210199] : [class_Rings_Oring__1(_1210195), hBOOL(hAPP(hAPP(c_member(_1210195), _1210197), c_Int_Oring__1__class_OInts(_1210195))), hBOOL(hAPP(hAPP(c_member(_1210195), _1210199), c_Int_Oring__1__class_OInts(_1210195))), -(hBOOL(hAPP(hAPP(c_member(_1210195), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1210195), _1210197), _1210199)), c_Int_Oring__1__class_OInts(_1210195))))], (22818 ^ _782435) ^ [_1210450] : [class_Rings_Oring__1(_1210450), -(hBOOL(hAPP(hAPP(c_member(_1210450), c_Groups_Oone__class_Oone(_1210450)), c_Int_Oring__1__class_OInts(_1210450))))], (22824 ^ _782435) ^ [_1210545, _1210547] : [class_Rings_Oring__1(_1210545), hBOOL(hAPP(hAPP(c_member(_1210545), _1210547), c_Int_Oring__1__class_OInts(_1210545))), -(hBOOL(hAPP(hAPP(c_member(_1210545), hAPP(c_Groups_Ouminus__class_Ouminus(_1210545), _1210547)), c_Int_Oring__1__class_OInts(_1210545))))], (22834 ^ _782435) ^ [_1210718, _1210720] : [class_Rings_Oring__1(_1210718), -(hBOOL(hAPP(hAPP(c_member(_1210718), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1210718), _1210720)), c_Int_Oring__1__class_OInts(_1210718))))], (22840 ^ _782435) ^ [_1210821, _1210823, _1210825] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1210821), _1210823)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1210821, tc_HOL_Obool)), _1210825), _1210823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1210821), _1210825)), hAPP(c_Finite__Set_Ocard(_1210821), _1210823))))], (22850 ^ _782435) ^ [_1211012, _1211014] : [class_Rings_Osemiring__1(_1211012), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211012), hAPP(c_Nat_OSuc, _1211014)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1211012), c_Groups_Oone__class_Oone(_1211012)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1211012), _1211014)))], (22856 ^ _782435) ^ [_1211133] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211133)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211133), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = _1211133)], (22862 ^ _782435) ^ [_1211230, _1211232] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1211230)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1211230), hAPP(c_Nat_OSuc, _1211232))), _1211230)))], (22868 ^ _782435) ^ [_1211339, _1211341] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211339)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211341)), -(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), _1211341), _1211339))))], (22878 ^ _782435) ^ [_1211492, _1211494] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211492)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211494)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211492), _1211494))))], (22888 ^ _782435) ^ [_1211651, _1211653] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211651)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211653)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1211651), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1211653), _1211651))))], (22898 ^ _782435) ^ [_1211825, _1211827] : [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), _1211825), _1211827))), 22901 ^ _782435 : [(22902 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211825)))], (22904 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211827)))]]], (22906 ^ _782435) ^ [_1211948, _1211950] : [-(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), _1211948), _1211950)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211948)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1211950))], (22916 ^ _782435) ^ [_1212103, _1212105, _1212107] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212103), _1212105)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212105), _1212103))), _1212107) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1212105)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212103), _1212107)))], (22922 ^ _782435) ^ [_1212252, _1212254, _1212256] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1212252), _1212254)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212256), hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1212254), _1212252))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1212256), _1212252)), hAPP(c_Nat_OSuc, _1212254)))], (22928 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1212434, _1212436] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212434), _1212436)), -(_1212436 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212434), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, 22933 ^ [_1212434, _1212436]))))], (22937 ^ _782435) ^ [_1212553, _1212555] : [22938 ^ _782435 : [(22939 ^ _782435) ^ [_1212609] : [_1212555 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1212553), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1212609)))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1212553), _1212555)))], (22943 ^ _782435) ^ [_1212679] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Nat_OSuc, _1212679)) = 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), _1212679)))], (22945 ^ _782435) ^ [_1212714, _1212716, _1212718] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1212714), _1212716)), 22948 ^ _782435 : [(22949 ^ _782435) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212714, tc_Nat_Onat), _1212718), _1212716) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22953 ^ _782435 : [(22954 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212714), 22952 ^ [_1212714, _1212716, _1212718]), _1212716)))], (22956 ^ _782435) ^ [] : [-(hAPP(_1212718, 22952 ^ [_1212714, _1212716, _1212718]) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (22958 ^ _782435) ^ [_1213034] : [hBOOL(hAPP(hAPP(c_member(_1212714), _1213034), _1212716)), -(22952 ^ [_1212714, _1212716, _1212718] = _1213034), -(hAPP(_1212718, _1213034) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (22968 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1212714, tc_Nat_Onat), _1212718), _1212716) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), 22969 ^ _782435 : [(22970 ^ _782435) ^ [_1213195] : [hBOOL(hAPP(hAPP(c_member(_1212714), _1213195), _1212716)), hAPP(_1212718, _1213195) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 22978 ^ _782435 : [(22979 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1212714), 22977 ^ [_1212714, _1212716, _1212718, _1213195]), _1212716)))], (22981 ^ _782435) ^ [] : [_1213195 = 22977 ^ [_1212714, _1212716, _1212718, _1213195]], (22983 ^ _782435) ^ [] : [hAPP(_1212718, 22977 ^ [_1212714, _1212716, _1212718, _1213195]) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]]]]]], (22987 ^ _782435) ^ [_1213548, _1213550, _1213552, _1213554] : [class_Rings_Osemiring__1(_1213548), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1213550, _1213548), hAPP(c_COMBK(_1213548, _1213550), _1213552)), _1213554) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1213548), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1213548), hAPP(c_Finite__Set_Ocard(_1213550), _1213554))), _1213552))], (22993 ^ _782435) ^ [_1213693] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213693)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1213693))], (22995 ^ _782435) ^ [_1213725, _1213727] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1213725), hAPP(c_Nat_OSuc, _1213727))), -(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1213725, hAPP(c_Nat_OSuc, _1213727)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1213727)), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1213725, _1213727)))], (23001 ^ _782435) ^ [_1213858, _1213860] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1213858), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1213860), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213860), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1213858))))), -(_1213858 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1213860), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1213860), hAPP(c_Finite__Set_Ocard(tc_Nat_Onat), _1213858))))], (23007 ^ _782435) ^ [_1214005] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1214005), hAPP(c_Nat_OSuc, _1214005)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1214005), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (23009 ^ _782435) ^ [_1214058, _1214060] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1214058), _1214060))), 23012 ^ _782435 : [(23013 ^ _782435) ^ [] : [_1214060 = c_Orderings_Obot__class_Obot(tc_fun(_1214058, tc_HOL_Obool))], (23015 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1214058), _1214060)))]]], (23017 ^ _782435) ^ [_1214199, _1214201] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1214199), _1214201)))), -(_1214201 = c_Orderings_Obot__class_Obot(tc_fun(_1214199, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214199), _1214201))], (23027 ^ _782435) ^ [_1214365] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214365), c_Orderings_Otop__class_Otop(tc_fun(_1214365, 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(_1214365), c_Orderings_Otop__class_Otop(tc_fun(_1214365, tc_HOL_Obool))))))], (23033 ^ _782435) ^ [_1214482, _1214484, _1214486] : [class_Groups_Ocomm__monoid__add(_1214482), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214482), _1214484), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1214486))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1214482), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1214482), _1214484), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1214486))), hAPP(_1214484, _1214486)))], (23039 ^ _782435) ^ [_1214635, _1214637, _1214639] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214635), _1214637)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214635), _1214639)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214635), _1214637)), hAPP(c_Finite__Set_Ocard(_1214635), _1214639)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214635), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214635, tc_HOL_Obool)), _1214637), _1214639))), hAPP(c_Finite__Set_Ocard(_1214635), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1214635, tc_HOL_Obool)), _1214637), _1214639))))], (23049 ^ _782435) ^ [_1214892, _1214894, _1214896] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1214892), _1214894)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1214892), _1214896)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214892), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1214892, tc_HOL_Obool)), _1214894), _1214896))), hAPP(c_Finite__Set_Ocard(_1214892), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1214892, tc_HOL_Obool)), _1214894), _1214896))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1214892), _1214894)), hAPP(c_Finite__Set_Ocard(_1214892), _1214896)))], (23059 ^ _782435) ^ [_1215149, _1215151, _1215153, _1215155, _1215157, _1215159] : [c_Fun_Oinj__on(_1215149, _1215151, _1215153, _1215155), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215151, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215149, _1215151, _1215153), _1215155)), _1215157)), c_Fun_Oinj__on(_1215151, _1215149, _1215159, _1215157), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215149, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1215151, _1215149, _1215159), _1215157)), _1215155)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1215149), _1215155)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1215151), _1215157)), -(hAPP(c_Finite__Set_Ocard(_1215149), _1215155) = hAPP(c_Finite__Set_Ocard(_1215151), _1215157))], (23085 ^ _782435) ^ [_1215646, _1215648, _1215650] : [class_Groups_Ocomm__monoid__add(_1215646), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215646), _1215648), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1215650))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1215646), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1215646), _1215648), hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1215650))), hAPP(_1215648, hAPP(c_Nat_OSuc, _1215650))))], (23091 ^ _782435) ^ [_1215805, _1215807, _1215809] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1215805), _1215807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1215805, tc_HOL_Obool)), _1215807), _1215809)), -(hAPP(c_Finite__Set_Ocard(_1215805), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1215805, tc_HOL_Obool)), _1215809), _1215807)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1215805), _1215809)), hAPP(c_Finite__Set_Ocard(_1215805), _1215807)))], (23101 ^ _782435) ^ [_1216030, _1216032, _1216034] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216030), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216030, tc_HOL_Obool)), _1216032), _1216034))), -(hAPP(c_Finite__Set_Ocard(_1216030), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216030, tc_HOL_Obool)), _1216032), _1216034)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1216030), _1216032)), hAPP(c_Finite__Set_Ocard(_1216030), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1216030, tc_HOL_Obool)), _1216032), _1216034))))], (23107 ^ _782435) ^ [_1216225, _1216227, _1216229] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216225), _1216227)), -(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(_1216225), _1216229)), hAPP(c_Finite__Set_Ocard(_1216225), _1216227))), hAPP(c_Finite__Set_Ocard(_1216225), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1216225, tc_HOL_Obool)), _1216229), _1216227)))))], (23113 ^ _782435) ^ [_1216386, _1216388, _1216390] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1216386), _1216388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1216386, tc_HOL_Obool)), _1216390), _1216388)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1216386), _1216390)), hAPP(c_Finite__Set_Ocard(_1216386), _1216388))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1216386, tc_HOL_Obool)), _1216390), _1216388)))], (23127 ^ _782435) ^ [_1216651] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216651)), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216651), c_Groups_Oone__class_Oone(tc_Nat_Onat))) = _1216651)], (23133 ^ _782435) ^ [_1216748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1216748)), -(_1216748 = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216748), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (23139 ^ _782435) ^ [_1216854, _1216856] : [_1216854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216854), _1216856) = _1216856)], (23145 ^ _782435) ^ [_1216937, _1216939] : [-(_1216937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1216937), _1216939) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1216937), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1216939)))], (23151 ^ _782435) ^ [_1216996] : [-(hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1216996)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat), _1216996)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1216996), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23153 ^ _782435) ^ [_1217040] : [-(hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217040)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat), _1217040)), hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1217040)), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (23155 ^ _782435) ^ [_1217096] : [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, _1217096)))))], (23157 ^ _782435) ^ [_1217130] : [-(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, _1217130)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23159 ^ _782435) ^ [_1217167, _1217169] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1217167), _1217169)), -(hAPP(c_Finite__Set_Ocard(_1217167), _1217169) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1217167, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1217167), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217169))], (23165 ^ _782435) ^ [_1217309, _1217311] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1217309), _1217311)), -(hAPP(c_Finite__Set_Ocard(_1217309), _1217311) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat, _1217309, c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), hAPP(c_COMBK(tc_Nat_Onat, _1217309), c_Groups_Oone__class_Oone(tc_Nat_Onat))), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217311))], (23171 ^ _782435) ^ [_1217436, _1217438] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1217436), _1217438))), -(hAPP(c_Finite__Set_Ocard(_1217436), _1217438) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23177 ^ _782435) ^ [_1217483, _1217485] : [class_Int_Oring__char__0(_1217483), hBOOL(hAPP(hAPP(c_member(_1217483), _1217485), c_Int_Oring__1__class_OInts(_1217483))), 23184 ^ _782435 : [(23185 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217483), _1217485), _1217485) = c_Groups_Ozero__class_Ozero(_1217483), -(_1217485 = c_Groups_Ozero__class_Ozero(_1217483))], (23191 ^ _782435) ^ [] : [_1217485 = c_Groups_Ozero__class_Ozero(_1217483), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217483), _1217485), _1217485) = c_Groups_Ozero__class_Ozero(_1217483))]]], (23197 ^ _782435) ^ [_1217794, _1217796, _1217798] : [class_Groups_Ocomm__monoid__add(_1217794), hAPP(_1217796, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(_1217794), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217794), _1217796), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1217798)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217794), _1217796), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1217798)))], (23207 ^ _782435) ^ [_1217983, _1217985, _1217987, _1217989] : [class_Groups_Ocomm__monoid__add(_1217983), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1217985), _1217987)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217983), _1217989), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1217985), _1217987)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1217983), hAPP(_1217989, _1217985)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1217983), _1217989), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1217985)), _1217987))))], (23217 ^ _782435) ^ [_1218216, _1218218, _1218220, _1218222] : [class_Groups_Ocomm__monoid__add(_1218216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218218), _1218220)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218216), _1218222), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1218218, _1218220)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1218216), hAPP(_1218222, _1218218)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1218216), _1218222), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1218218), _1218220))))], (23227 ^ _782435) ^ [_1218450, _1218452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218450), _1218452)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218450), hAPP(c_Nat_OSuc, _1218452)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1218452), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218450), _1218452)))], (23233 ^ _782435) ^ [_1218573, _1218575] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1218573), _1218575))), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1218573), hAPP(c_Nat_OSuc, _1218575)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (23239 ^ _782435) ^ [_1218625, _1218627, _1218629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218625), _1218627)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1218625), _1218629)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1218625, tc_HOL_Obool)), _1218627), _1218629) = c_Orderings_Obot__class_Obot(tc_fun(_1218625, tc_HOL_Obool)), -(hAPP(c_Finite__Set_Ocard(_1218625), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1218625, tc_HOL_Obool)), _1218627), _1218629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1218625), _1218627)), hAPP(c_Finite__Set_Ocard(_1218625), _1218629)))], (23253 ^ _782435) ^ [_1218924, _1218926, _1218928] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1218924), _1218926)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1218924), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1218924, tc_HOL_Obool)), _1218926), hAPP(hAPP(c_Set_Oinsert(_1218924), _1218928), c_Orderings_Obot__class_Obot(tc_fun(_1218924, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1218924), _1218926))))], (23259 ^ _782435) ^ [_1219089, _1219091, _1219093] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219089), _1219091)), -(hBOOL(hAPP(hAPP(c_member(_1219089), _1219093), _1219091))), -(hAPP(c_Finite__Set_Ocard(_1219089), hAPP(hAPP(c_Set_Oinsert(_1219089), _1219093), _1219091)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1219089), _1219091)))], (23269 ^ _782435) ^ [_1219247, _1219249, _1219251, _1219253, _1219255] : [c_Fun_Oinj__on(_1219247, _1219249, _1219251, _1219253), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219249, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219247, _1219249, _1219251), _1219253)), _1219255)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219249), _1219255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219247), _1219253)), hAPP(c_Finite__Set_Ocard(_1219249), _1219255))))], (23283 ^ _782435) ^ [_1219522, _1219524, _1219526, _1219528] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1219522), _1219524)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1219526), _1219528)), 23290 ^ _782435 : [(23301 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219522), _1219524)), hAPP(c_Finite__Set_Ocard(_1219526), _1219528))), 23305 ^ _782435 : [(23306 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1219522, _1219526, 23304 ^ [_1219522, _1219524, _1219526, _1219528], _1219524))], (23308 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219526, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219522, _1219526, 23304 ^ [_1219522, _1219524, _1219526, _1219528]), _1219524)), _1219528)))]]], (23291 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1219522), _1219524)), hAPP(c_Finite__Set_Ocard(_1219526), _1219528)))), 23292 ^ _782435 : [(23293 ^ _782435) ^ [_1219733] : [c_Fun_Oinj__on(_1219522, _1219526, _1219733, _1219524), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1219526, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1219522, _1219526, _1219733), _1219524)), _1219528))]]]]], (23310 ^ _782435) ^ [_1220049, _1220051] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1220051)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Nat__Transfer_Otsub(_1220049, _1220051))))], (23320 ^ _782435) ^ [_1220196, _1220198] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1220196), _1220198)), -(c_Nat__Transfer_Otsub(_1220198, _1220196) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1220198), _1220196))], (23326 ^ _782435) ^ [_1220301, _1220303] : [-(c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220301), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1220303)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1220301), _1220303)))], (23328 ^ _782435) ^ [_1220344] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220344)) = 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), _1220344))))], (23330 ^ _782435) ^ [_1220382, _1220384, _1220386, _1220388] : [class_Groups_Ocomm__monoid__add(_1220382), 23333 ^ _782435 : [(23334 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220384), _1220386)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220382), _1220388), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220386), hAPP(c_Nat_OSuc, _1220384))) = c_Groups_Ozero__class_Ozero(_1220382))], (23340 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1220384), _1220386))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220382), _1220388), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220386), hAPP(c_Nat_OSuc, _1220384))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220382), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220382), _1220388), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1220386), _1220384))), hAPP(_1220388, _1220384)))]]], (23346 ^ _782435) ^ [_1220712, _1220714, _1220716, _1220718] : [class_Groups_Ocomm__monoid__add(_1220712), 23349 ^ _782435 : [(23350 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220714)), _1220716)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220712), _1220718), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220716, hAPP(c_Nat_OSuc, _1220714))) = c_Groups_Ozero__class_Ozero(_1220712))], (23356 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1220714)), _1220716))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220712), _1220718), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220716, hAPP(c_Nat_OSuc, _1220714))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1220712), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1220712), _1220718), c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1220716, _1220714))), hAPP(_1220718, hAPP(c_Nat_OSuc, _1220714))))]]], (23362 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1221066, _1221068, _1221070] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221066), _1221068)), hBOOL(hAPP(hAPP(c_member(_1221066), _1221070), _1221068)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221066), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221066, tc_HOL_Obool)), _1221068), hAPP(hAPP(c_Set_Oinsert(_1221066), _1221070), c_Orderings_Obot__class_Obot(tc_fun(_1221066, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1221066), _1221068))))], (23374 ^ _782435) ^ [_1221299, _1221301, _1221303, _1221305] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221299), _1221301)), hBOOL(hAPP(hAPP(c_member(_1221299), _1221303), _1221301)), hBOOL(hAPP(hAPP(c_member(_1221299), _1221305), _1221301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221299), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221299, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221299, tc_HOL_Obool)), _1221301), hAPP(hAPP(c_Set_Oinsert(_1221299), _1221303), c_Orderings_Obot__class_Obot(tc_fun(_1221299, tc_HOL_Obool))))), hAPP(hAPP(c_Set_Oinsert(_1221299), _1221305), c_Orderings_Obot__class_Obot(tc_fun(_1221299, tc_HOL_Obool)))))), hAPP(c_Finite__Set_Ocard(_1221299), _1221301))))], (23388 ^ _782435) ^ [_1221654, _1221656] : [class_Int_Oring__char__0(_1221654), hBOOL(hAPP(hAPP(c_member(_1221654), _1221656), c_Int_Oring__1__class_OInts(_1221654))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221654), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1221654), c_Groups_Oone__class_Oone(_1221654)), _1221656)), _1221656) = c_Groups_Ozero__class_Ozero(_1221654)], (23398 ^ _782435) ^ [_1221840, _1221842, _1221844, _1221846] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1221840), _1221842)), hBOOL(hAPP(hAPP(c_member(_1221840), _1221844), _1221842)), -(hBOOL(hAPP(hAPP(c_member(_1221840), _1221844), _1221846))), -(hAPP(c_Finite__Set_Ocard(_1221840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221840, tc_HOL_Obool)), _1221842), hAPP(hAPP(c_Set_Oinsert(_1221840), _1221844), _1221846))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1221840), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1221840, tc_HOL_Obool)), _1221842), _1221846))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23412 ^ _782435) ^ [_1222120, _1222122, _1222124] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222120), _1222122)), -(hAPP(c_Finite__Set_Ocard(_1222120), hAPP(hAPP(c_Set_Oinsert(_1222120), _1222124), _1222122)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1222120), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222120, tc_HOL_Obool)), _1222122), hAPP(hAPP(c_Set_Oinsert(_1222120), _1222124), c_Orderings_Obot__class_Obot(tc_fun(_1222120, tc_HOL_Obool)))))))], (23418 ^ _782435) ^ [_1222297, _1222299, _1222301] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222297), _1222299)), hBOOL(hAPP(hAPP(c_member(_1222297), _1222301), _1222299)), -(hAPP(c_Finite__Set_Ocard(_1222297), _1222299) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1222297), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222297, tc_HOL_Obool)), _1222299), hAPP(hAPP(c_Set_Oinsert(_1222297), _1222301), c_Orderings_Obot__class_Obot(tc_fun(_1222297, tc_HOL_Obool)))))))], (23428 ^ _782435) ^ [_1222526, _1222528, _1222530] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222526), _1222528)), 23431 ^ _782435 : [(23432 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1222526), _1222530), _1222528)), -(hAPP(c_Finite__Set_Ocard(_1222526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222526, tc_HOL_Obool)), _1222528), hAPP(hAPP(c_Set_Oinsert(_1222526), _1222530), c_Orderings_Obot__class_Obot(tc_fun(_1222526, tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1222526), _1222528)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (23438 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222526), _1222530), _1222528))), -(hAPP(c_Finite__Set_Ocard(_1222526), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1222526, tc_HOL_Obool)), _1222528), hAPP(hAPP(c_Set_Oinsert(_1222526), _1222530), c_Orderings_Obot__class_Obot(tc_fun(_1222526, tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(_1222526), _1222528))]]], (23444 ^ _782435) ^ [_1222890, _1222892, _1222894] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1222890), _1222892)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1222890), _1222894)), 23454 ^ _782435 : [(23455 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1222890), 23453 ^ [_1222890, _1222892, _1222894]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1222890, tc_HOL_Obool)), _1222892), _1222894))))], (23457 ^ _782435) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1222890), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1222890, tc_HOL_Obool)), _1222892), _1222894)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1222890), _1222892)), hAPP(c_Finite__Set_Ocard(_1222890), _1222894)))], (23461 ^ _782435) ^ [_1223234, _1223236, _1223238, _1223240, _1223242] : [class_Groups_Oordered__ab__semigroup__add(_1223234), class_Rings_Osemiring__1(_1223234), 23471 ^ _782435 : [(23472 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1223236), 23470 ^ [_1223234, _1223236, _1223238, _1223240, _1223242]), _1223238)))], (23474 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223234), hAPP(_1223240, 23470 ^ [_1223234, _1223236, _1223238, _1223240, _1223242])), _1223242))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1223234), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1223236, _1223234), _1223240), _1223238)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1223234), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1223234), hAPP(c_Finite__Set_Ocard(_1223236), _1223238))), _1223242))))], (23478 ^ _782435) ^ [_1223642, _1223644, _1223646] : [hAPP(c_Finite__Set_Ocard(_1223642), _1223644) = hAPP(c_Nat_OSuc, _1223646), 23483 ^ _782435 : [(23484 ^ _782435) ^ [] : [-(_1223644 = hAPP(hAPP(c_Set_Oinsert(_1223642), 23481 ^ [_1223642, _1223644, _1223646]), 23482 ^ [_1223642, _1223644, _1223646]))], (23486 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1223642), 23481 ^ [_1223642, _1223644, _1223646]), 23482 ^ [_1223642, _1223644, _1223646]))], (23488 ^ _782435) ^ [] : [-(hAPP(c_Finite__Set_Ocard(_1223642), 23482 ^ [_1223642, _1223644, _1223646]) = _1223646)], (23490 ^ _782435) ^ [] : [_1223646 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(23482 ^ [_1223642, _1223644, _1223646] = c_Orderings_Obot__class_Obot(tc_fun(_1223642, tc_HOL_Obool)))]]], (23496 ^ _782435) ^ [_1224060, _1224062, _1224064] : [-(hAPP(c_Finite__Set_Ocard(_1224060), _1224062) = hAPP(c_Nat_OSuc, _1224064)), 23497 ^ _782435 : [(23498 ^ _782435) ^ [_1224160, _1224162] : [_1224062 = hAPP(hAPP(c_Set_Oinsert(_1224060), _1224162), _1224160), -(hBOOL(hAPP(hAPP(c_member(_1224060), _1224162), _1224160))), hAPP(c_Finite__Set_Ocard(_1224060), _1224160) = _1224064, 23509 ^ _782435 : [(23510 ^ _782435) ^ [] : [-(_1224064 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23512 ^ _782435) ^ [] : [_1224160 = c_Orderings_Obot__class_Obot(tc_fun(_1224060, tc_HOL_Obool))]]]]], (23526 ^ _782435) ^ [_1224702, _1224704, _1224706, _1224708] : [23527 ^ _782435 : [(23528 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1224702), _1224704)))], (23530 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1224706), _1224708)))]], -(hAPP(c_Finite__Set_Ocard(tc_sum(_1224702, _1224706)), c_Sum__Type_OPlus(_1224702, _1224706, _1224704, _1224708)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23516 ^ _782435) ^ [_1224497, _1224499, _1224501, _1224503] : [-(hAPP(c_Finite__Set_Ocard(tc_sum(_1224497, _1224501)), c_Sum__Type_OPlus(_1224497, _1224501, _1224499, _1224503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1224497), _1224499)), hAPP(c_Finite__Set_Ocard(_1224501), _1224503))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224497), _1224499)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224501), _1224503))], (23534 ^ _782435) ^ [_1224802] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224802)), -(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1224802) = 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, _1224802))))], (23540 ^ _782435) ^ [_1224905, _1224907, _1224909, _1224911, _1224913] : [class_Groups_Oordered__ab__group__add(_1224905), hBOOL(hAPP(c_Finite__Set_Ofinite(_1224907), _1224909)), 23550 ^ _782435 : [(23551 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1224907), 23549 ^ [_1224905, _1224907, _1224909, _1224911, _1224913]), _1224909)))], (23553 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1224905), c_Groups_Ozero__class_Ozero(_1224905)), hAPP(_1224911, 23549 ^ [_1224905, _1224907, _1224909, _1224911, _1224913])))]], hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1224907, _1224905), _1224911), _1224909) = c_Groups_Ozero__class_Ozero(_1224905), hBOOL(hAPP(hAPP(c_member(_1224907), _1224913), _1224909)), -(hAPP(_1224911, _1224913) = c_Groups_Ozero__class_Ozero(_1224905))], (23565 ^ _782435) ^ [_1225403] : [-(hAPP(c_Int_Onat, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1225403)) = _1225403)], (23567 ^ _782435) ^ [] : [-(hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23569 ^ _782435) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (23571 ^ _782435) ^ [_1225468, _1225470] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225468)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225470)), 23578 ^ _782435 : [(23579 ^ _782435) ^ [] : [hAPP(c_Int_Onat, _1225468) = hAPP(c_Int_Onat, _1225470), -(_1225468 = _1225470)], (23585 ^ _782435) ^ [] : [_1225468 = _1225470, -(hAPP(c_Int_Onat, _1225468) = hAPP(c_Int_Onat, _1225470))]]], (23591 ^ _782435) ^ [_1225753, _1225755] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225753)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1225755)), 23598 ^ _782435 : [(23599 ^ _782435) ^ [] : [hAPP(c_Int_Onat, _1225753) = hAPP(c_Int_Onat, _1225755), -(_1225753 = _1225755)], (23605 ^ _782435) ^ [] : [_1225753 = _1225755, -(hAPP(c_Int_Onat, _1225753) = hAPP(c_Int_Onat, _1225755))]]], (23622 ^ _782435) ^ [_1226235] : [23624 ^ _782435 : [(23625 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23623 ^ [_1226235])))], (23627 ^ _782435) ^ [] : [hBOOL(hAPP(_1226235, hAPP(c_Int_Onat, 23623 ^ [_1226235])))]], 23628 ^ _782435 : [(23629 ^ _782435) ^ [_1226368] : [-(hBOOL(hAPP(_1226235, _1226368)))]]], (23611 ^ _782435) ^ [_1226050] : [hBOOL(hAPP(_1226050, 23612 ^ [_1226050])), 23615 ^ _782435 : [(23616 ^ _782435) ^ [_1226144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226144)), -(hBOOL(hAPP(_1226050, hAPP(c_Int_Onat, _1226144))))]]], (23631 ^ _782435) ^ [_1226413] : [23632 ^ _782435 : [(23633 ^ _782435) ^ [_1226470] : [hBOOL(hAPP(_1226413, _1226470))]], 23635 ^ _782435 : [(23636 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 23634 ^ [_1226413])))], (23638 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1226413, hAPP(c_Int_Onat, 23634 ^ [_1226413]))))]]], (23640 ^ _782435) ^ [_1226556] : [-(hBOOL(hAPP(_1226556, 23647 ^ [_1226556]))), 23641 ^ _782435 : [(23642 ^ _782435) ^ [_1226608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1226608)), hBOOL(hAPP(_1226556, hAPP(c_Int_Onat, _1226608)))]]], (23651 ^ _782435) ^ [] : [-(c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (23653 ^ _782435) ^ [_1226753] : [-(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)), _1226753)) = _1226753)], (23655 ^ _782435) ^ [_1226782, _1226784] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1226782), _1226784) = 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)), _1226782)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1226784))))], (23657 ^ _782435) ^ [_1226828] : [-(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)), _1226828)) = hAPP(c_Int_Onat, _1226828))], (23659 ^ _782435) ^ [_1226860, _1226862] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1226860), _1226862)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226862), _1226860)))], (23661 ^ _782435) ^ [_1226903, _1226905] : [-(hAPP(c_Finite__Set_Ocard(tc_Int_Oint), c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1226903, _1226905)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1226905), _1226903)))], (23663 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1226974] : [hAPP(c_Int_Onat, _1226974) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1226974), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23671 ^ _782435) ^ [_1227061] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227061), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1227061) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23677 ^ _782435) ^ [_1227154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227154), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Onat, _1227154) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23683 ^ _782435) ^ [_1227260, _1227262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227260)), hAPP(c_Int_Onat, _1227262))), 23686 ^ _782435 : [(23687 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227262)))], (23689 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227260), _1227262)))]]], (23691 ^ _782435) ^ [_1227395, _1227397] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227395)), hAPP(c_Int_Onat, _1227397)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227397)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227395), _1227397))], (23701 ^ _782435) ^ [_1227562, _1227564] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227562)), 23704 ^ _782435 : [(23705 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227564)), hAPP(c_Int_Onat, _1227562))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227564), _1227562)))], (23711 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1227564), _1227562)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1227564)), hAPP(c_Int_Onat, _1227562))))]]], (23717 ^ _782435) ^ [_1227821, _1227823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227821)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1227823)), 23724 ^ _782435 : [(23725 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1227821)), hAPP(c_Int_Onat, _1227823))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227821), _1227823)))], (23731 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1227821), _1227823)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1227821)), hAPP(c_Int_Onat, _1227823))))]]], (23737 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1228154] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228154)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228154)) = _1228154)], (23745 ^ _782435) ^ [_1228260, _1228262] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228260) = _1228262, 23748 ^ _782435 : [(23749 ^ _782435) ^ [] : [-(_1228260 = hAPP(c_Int_Onat, _1228262))], (23751 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228262)))]]], (23753 ^ _782435) ^ [_1228375, _1228377] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228375) = _1228377), _1228375 = hAPP(c_Int_Onat, _1228377), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228377))], (23763 ^ _782435) ^ [_1228528] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228528)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228528)) = _1228528)], (23769 ^ _782435) ^ [_1228613] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1228613))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1228613)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (23775 ^ _782435) ^ [_1228672, _1228674] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228672), hAPP(c_Int_Onat, _1228674))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228672)), _1228674)))], (23781 ^ _782435) ^ [_1228777, _1228779] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228777)), _1228779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1228777), hAPP(c_Int_Onat, _1228779))))], (23787 ^ _782435) ^ [_1228888] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228888))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (23789 ^ _782435) ^ [_1228920, _1228922] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1228920, _1228922) = 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), _1228920), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1228922))))], (23791 ^ _782435) ^ [_1228962, _1228964, _1228966] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1228962), _1228964), _1228966) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1228962), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1228962, tc_Int_Oint), _1228964), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1228966))), class_Groups_Ocomm__monoid__add(_1228962), class_Groups_Ocomm__monoid__mult(_1228962)], (23801 ^ _782435) ^ [_1229165] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1229165))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229165)))], (23807 ^ _782435) ^ [_1229250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Int_Onat, _1229250))))], (23813 ^ _782435) ^ [_1229341, _1229343] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229341)), 23816 ^ _782435 : [(23817 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229341)), hAPP(c_Int_Onat, _1229343))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229341), _1229343)))], (23823 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229341), _1229343)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229341)), hAPP(c_Int_Onat, _1229343))))]]], (23829 ^ _782435) ^ [_1229600, _1229602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229600)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229602)), 23836 ^ _782435 : [(23837 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229600)), hAPP(c_Int_Onat, _1229602))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229600), _1229602)))], (23843 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1229600), _1229602)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onat, _1229600)), hAPP(c_Int_Onat, _1229602))))]]], (23865 ^ _782435) ^ [_1230122, _1230124] : [-(_1230122 = hAPP(c_Int_Onat, _1230124)), 23868 ^ _782435 : [(23869 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230124)))], (23871 ^ _782435) ^ [] : [_1230124 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230122)]], 23872 ^ _782435 : [(23873 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230124))], (23875 ^ _782435) ^ [] : [_1230122 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23849 ^ _782435) ^ [_1229930, _1229932] : [_1229930 = hAPP(c_Int_Onat, _1229932), 23852 ^ _782435 : [(23853 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229932)), -(_1229932 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1229930))], (23859 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1229932))), -(_1229930 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23895 ^ _782435) ^ [_1230553, _1230555] : [-(hAPP(c_Int_Onat, _1230553) = _1230555), 23898 ^ _782435 : [(23899 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230553)))], (23901 ^ _782435) ^ [] : [_1230553 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230555)]], 23902 ^ _782435 : [(23903 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230553))], (23905 ^ _782435) ^ [] : [_1230555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (23879 ^ _782435) ^ [_1230361, _1230363] : [hAPP(c_Int_Onat, _1230361) = _1230363, 23882 ^ _782435 : [(23883 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230361)), -(_1230361 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1230363))], (23889 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230361))), -(_1230363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (23909 ^ _782435) ^ [_1230777, _1230779] : [23910 ^ _782435 : [(23911 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230777))], (23913 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1230779))]], 23914 ^ _782435 : [(23915 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230777)), hAPP(c_Int_Onat, _1230779))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230777), _1230779)))], (23921 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1230777), _1230779)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onat, _1230777)), hAPP(c_Int_Onat, _1230779))))]]], (23943 ^ _782435) ^ [_1231356, _1231358] : [-(hBOOL(hAPP(_1231356, hAPP(c_Int_Onat, _1231358)))), 23947 ^ _782435 : [(23948 ^ _782435) ^ [] : [-(_1231358 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 23946 ^ [_1231356, _1231358]))], (23950 ^ _782435) ^ [] : [hBOOL(hAPP(_1231356, 23946 ^ [_1231356, _1231358]))]], 23951 ^ _782435 : [(23952 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231358), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (23954 ^ _782435) ^ [] : [hBOOL(hAPP(_1231356, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]], (23927 ^ _782435) ^ [_1231093, _1231095] : [hBOOL(hAPP(_1231093, hAPP(c_Int_Onat, _1231095))), 23930 ^ _782435 : [(23931 ^ _782435) ^ [_1231193] : [_1231095 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1231193), -(hBOOL(hAPP(_1231093, _1231193)))], (23937 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1231095), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(_1231093, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (23958 ^ _782435) ^ [_1231619, _1231621] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231619)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231621)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231619), _1231621)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231619)), hAPP(c_Int_Onat, _1231621)))], (23968 ^ _782435) ^ [_1231798, _1231800] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231798)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231800)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onat, _1231798)), hAPP(c_Int_Onat, _1231800)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1231798), _1231800)))], (23978 ^ _782435) ^ [_1231977, _1231979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1231977)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1231977), _1231979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1231977)), hAPP(c_Int_Onat, _1231979)))], (23984 ^ _782435) ^ [_1232100, _1232102] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1232102)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, _1232100)), hAPP(c_Int_Onat, _1232102)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1232100), _1232102)))], (23994 ^ _782435) ^ [_1232279, 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hAPP(c_Int_Oring__1__class_Oof__int(_1242831), _1242833)), c_Int_Oring__1__class_OInts(_1242831))))], (24628 ^ _782435) ^ [_1242934, _1242936, _1242938, _1242940] : [class_Rings_Oring__1(_1242934), -(hAPP(c_Int_Oring__1__class_Oof__int(_1242934), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1242936, tc_Int_Oint), _1242938), _1242940)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1242936, _1242934), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1242934, _1242936), c_Int_Oring__1__class_Oof__int(_1242934)), _1242938)), _1242940))], (24634 ^ _782435) ^ [_1243083, _1243085] : [class_Rings_Olinordered__idom(_1243083), 24637 ^ _782435 : [(24638 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243083), c_Groups_Ozero__class_Ozero(_1243083)), hAPP(c_Int_Oring__1__class_Oof__int(_1243083), _1243085))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243085)))], (24644 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243085)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243083), c_Groups_Ozero__class_Ozero(_1243083)), hAPP(c_Int_Oring__1__class_Oof__int(_1243083), _1243085))))]]], (24650 ^ _782435) ^ [_1243336, _1243338] : [class_Rings_Olinordered__idom(_1243336), 24653 ^ _782435 : [(24654 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243336), hAPP(c_Int_Oring__1__class_Oof__int(_1243336), _1243338)), c_Groups_Ozero__class_Ozero(_1243336))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243338), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24660 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1243338), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1243336), hAPP(c_Int_Oring__1__class_Oof__int(_1243336), _1243338)), c_Groups_Ozero__class_Ozero(_1243336))))]]], (24666 ^ _782435) ^ [_1243598, _1243600] : [class_Rings_Olinordered__idom(_1243598), 24669 ^ _782435 : [(24670 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243598), c_Groups_Ozero__class_Ozero(_1243598)), hAPP(c_Int_Oring__1__class_Oof__int(_1243598), _1243600))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243600)))], (24676 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1243600)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243598), c_Groups_Ozero__class_Ozero(_1243598)), hAPP(c_Int_Oring__1__class_Oof__int(_1243598), _1243600))))]]], (24682 ^ _782435) ^ [_1243851, _1243853] : [class_Rings_Olinordered__idom(_1243851), 24685 ^ _782435 : [(24686 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243851), hAPP(c_Int_Oring__1__class_Oof__int(_1243851), _1243853)), c_Groups_Ozero__class_Ozero(_1243851))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243853), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (24692 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1243853), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1243851), hAPP(c_Int_Oring__1__class_Oof__int(_1243851), _1243853)), c_Groups_Ozero__class_Ozero(_1243851))))]]], (24698 ^ _782435) ^ [_1244113, _1244115] : [class_Rings_Oring__1(_1244113), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244115)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1244113), hAPP(c_Int_Onat, _1244115)) = hAPP(c_Int_Oring__1__class_Oof__int(_1244113), _1244115))], (24708 ^ _782435) ^ [_1244270, _1244272, _1244274] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244270)), 24714 ^ _782435 : [(24715 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1244272, 24713 ^ [_1244270, _1244272, _1244274])))], (24717 ^ _782435) ^ [] : [hBOOL(hAPP(_1244272, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 24713 ^ [_1244270, _1244272, _1244274]), _1244270)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1244274)), 24722 ^ _782435 : [(24723 ^ _782435) ^ [_1244559] : [hBOOL(hAPP(_1244272, _1244559)), -(hBOOL(hAPP(_1244272, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1244559), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1244274), _1244270)))))]]], (24729 ^ _782435) ^ [_1244681, _1244683] : [-(hBOOL(hAPP(_1244681, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hBOOL(hAPP(_1244681, _1244683)), 24737 ^ _782435 : [(24738 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 24736 ^ [_1244681, _1244683]), _1244683)))], (24746 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1244681, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 24736 ^ [_1244681, _1244683]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (24740 ^ _782435) ^ [_1244919] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1244919), 24736 ^ [_1244681, _1244683])), hBOOL(hAPP(_1244681, _1244919))]]], (24748 ^ _782435) ^ [_1245071] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1245071)), 24752 ^ _782435 : [(24753 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 24751 ^ [_1245071])))], (24755 ^ _782435) ^ [] : [-(_1245071 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), 24751 ^ [_1245071]))]]], (24757 ^ _782435) ^ [_1245201, _1245203, _1245205, _1245207, _1245209] : [class_Groups_Ocomm__monoid__add(_1245201), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245203), _1245205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245203, tc_HOL_Obool)), _1245207), _1245205)), 24771 ^ _782435 : [(24772 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245203), 24770 ^ [_1245201, _1245203, _1245205, _1245207, _1245209]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1245203, tc_HOL_Obool)), _1245205), _1245207))))], (24774 ^ _782435) ^ [] : [hAPP(_1245209, 24770 ^ [_1245201, _1245203, _1245205, _1245207, _1245209]) = c_Groups_Ozero__class_Ozero(_1245201)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245203, _1245201), _1245209), _1245207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245203, _1245201), _1245209), _1245205))], (24778 ^ _782435) ^ [_1245652, _1245654, _1245656, _1245658, _1245660] : [class_Groups_Ocomm__monoid__add(_1245652), hBOOL(hAPP(c_Finite__Set_Ofinite(_1245654), _1245656)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1245654, tc_HOL_Obool)), _1245658), _1245656)), 24792 ^ _782435 : [(24793 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1245654), 24791 ^ [_1245652, _1245654, _1245656, _1245658, _1245660]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1245654, tc_HOL_Obool)), _1245656), _1245658))))], (24795 ^ _782435) ^ [] : [hAPP(_1245660, 24791 ^ [_1245652, _1245654, _1245656, _1245658, _1245660]) = c_Groups_Ozero__class_Ozero(_1245652)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245654, _1245652), _1245660), _1245656) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1245654, _1245652), _1245660), _1245658))], (24799 ^ _782435) ^ [_1246103, _1246105] : [class_Groups_Osgn__if(_1246103), 24802 ^ _782435 : [(24803 ^ _782435) ^ [] : [_1246105 = c_Groups_Ozero__class_Ozero(_1246103), -(c_Groups_Osgn__class_Osgn(_1246103, _1246105) = c_Groups_Ozero__class_Ozero(_1246103))], (24809 ^ _782435) ^ [] : [-(_1246105 = c_Groups_Ozero__class_Ozero(_1246103)), 24812 ^ _782435 : [(24813 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246103), c_Groups_Ozero__class_Ozero(_1246103)), _1246105)), -(c_Groups_Osgn__class_Osgn(_1246103, _1246105) = c_Groups_Oone__class_Oone(_1246103))], (24819 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246103), c_Groups_Ozero__class_Ozero(_1246103)), _1246105))), -(c_Groups_Osgn__class_Osgn(_1246103, _1246105) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246103), c_Groups_Oone__class_Oone(_1246103)))]]]]], (24825 ^ _782435) ^ [_1246500, _1246502] : [class_Rings_Olinordered__idom(_1246500), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246500), _1246502), c_Groups_Ozero__class_Ozero(_1246500))), -(c_Groups_Osgn__class_Osgn(_1246500, _1246502) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246500), c_Groups_Oone__class_Oone(_1246500)))], (24835 ^ _782435) ^ [_1246665, _1246667] : [class_Rings_Olinordered__idom(_1246665), 24838 ^ _782435 : [(24839 ^ _782435) ^ [] : [c_Groups_Osgn__class_Osgn(_1246665, _1246667) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246665), c_Groups_Oone__class_Oone(_1246665)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246665), _1246667), c_Groups_Ozero__class_Ozero(_1246665))))], (24845 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1246665), _1246667), c_Groups_Ozero__class_Ozero(_1246665))), -(c_Groups_Osgn__class_Osgn(_1246665, _1246667) = hAPP(c_Groups_Ouminus__class_Ouminus(_1246665), c_Groups_Oone__class_Oone(_1246665)))]]], (24851 ^ _782435) ^ [_1246927, _1246929, _1246931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1246927)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1246929), 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), _1246929), _1246931))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1246927))), _1246931)))], (24857 ^ _782435) ^ [_1247074, _1247076, _1247078] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1247074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1247076), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1247078), 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), _1247078), _1247076))), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1247074)))))], (24863 ^ _782435) ^ [_1247221, _1247223, _1247225, _1247227] : [class_Groups_Oordered__ab__group__add__abs(_1247221), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247221), hAPP(c_Groups_Oabs__class_Oabs(_1247221), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247223, _1247221), _1247225), _1247227))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247223, _1247221), hAPP(hAPP(c_COMBB(_1247221, _1247221, _1247223), c_Groups_Oabs__class_Oabs(_1247221)), _1247225)), _1247227))))], (24869 ^ _782435) ^ [_1247384, _1247386, _1247388, _1247390] : [class_Groups_Oordered__ab__group__add__abs(_1247384), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1247384), c_Groups_Ozero__class_Ozero(_1247384)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1247386, _1247384), hAPP(hAPP(c_COMBB(_1247384, _1247384, _1247386), c_Groups_Oabs__class_Oabs(_1247384)), _1247388)), _1247390))))], (24875 ^ _782435) ^ [_1247523, _1247525, _1247527] : [class_Groups_Oordered__ab__group__add__abs(_1247523), -(hAPP(c_Groups_Oabs__class_Oabs(_1247523), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247523), hAPP(c_Groups_Oabs__class_Oabs(_1247523), _1247525)), hAPP(c_Groups_Oabs__class_Oabs(_1247523), _1247527))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1247523), hAPP(c_Groups_Oabs__class_Oabs(_1247523), _1247525)), hAPP(c_Groups_Oabs__class_Oabs(_1247523), _1247527)))], (24881 ^ _782435) ^ [_1247682, _1247684] : [class_Rings_Olinordered__idom(_1247682), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247682), hAPP(c_Groups_Oabs__class_Oabs(_1247682), _1247684)), hAPP(c_Groups_Oabs__class_Oabs(_1247682), _1247684)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247682), _1247684), _1247684))], (24887 ^ _782435) ^ [_1247809, _1247811, _1247813] : [class_Rings_Olinordered__idom(_1247809), -(hAPP(c_Groups_Oabs__class_Oabs(_1247809), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247809), _1247811), _1247813)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1247809), hAPP(c_Groups_Oabs__class_Oabs(_1247809), _1247811)), hAPP(c_Groups_Oabs__class_Oabs(_1247809), _1247813)))], (24893 ^ _782435) ^ [_1247948, _1247950, _1247952] : [class_Groups_Oordered__ab__group__add__abs(_1247948), -(hAPP(c_Groups_Oabs__class_Oabs(_1247948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1247948), _1247950), _1247952)) = hAPP(c_Groups_Oabs__class_Oabs(_1247948), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1247948), _1247952), _1247950)))], (24899 ^ _782435) ^ [_1248077] : [class_Rings_Olinordered__idom(_1248077), -(hAPP(c_Groups_Oabs__class_Oabs(_1248077), c_Groups_Oone__class_Oone(_1248077)) = c_Groups_Oone__class_Oone(_1248077))], (24905 ^ _782435) ^ [_1248168, _1248170] : [class_Groups_Oordered__ab__group__add__abs(_1248168), -(hAPP(c_Groups_Oabs__class_Oabs(_1248168), hAPP(c_Groups_Ouminus__class_Ouminus(_1248168), _1248170)) = hAPP(c_Groups_Oabs__class_Oabs(_1248168), _1248170))], (24911 ^ _782435) ^ [_1248273, _1248275] : [class_Rings_Olinordered__idom(_1248273), -(hAPP(c_Groups_Oabs__class_Oabs(_1248273), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248273), _1248275)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1248273), _1248275))], (24917 ^ _782435) ^ [_1248378, _1248380, _1248382] : [class_Groups_Oordered__ab__group__add__abs(_1248378), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248378), hAPP(c_Groups_Oabs__class_Oabs(_1248378), _1248380)), _1248382)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248378), _1248380), _1248382)))], (24927 ^ _782435) ^ [_1248547, _1248549] : [class_Groups_Oordered__ab__group__add__abs(_1248547), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1248547), _1248549), hAPP(c_Groups_Oabs__class_Oabs(_1248547), _1248549))))], (24933 ^ _782435) ^ [_1248646, _1248648] : [class_Rings_Olinordered__idom(_1248646), -(c_Groups_Osgn__class_Osgn(_1248646, c_Groups_Osgn__class_Osgn(_1248646, _1248648)) = c_Groups_Osgn__class_Osgn(_1248646, _1248648))], (24939 ^ _782435) ^ [_1248739, _1248741] : [class_Groups_Oordered__ab__group__add__abs(_1248739), -(hAPP(c_Groups_Oabs__class_Oabs(_1248739), hAPP(c_Groups_Oabs__class_Oabs(_1248739), _1248741)) = hAPP(c_Groups_Oabs__class_Oabs(_1248739), _1248741))], (24945 ^ _782435) ^ [_1248844, _1248846] : [class_Rings_Olinordered__idom(_1248844), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248844), c_Groups_Osgn__class_Osgn(_1248844, _1248846)), hAPP(c_Groups_Oabs__class_Oabs(_1248844), _1248846)) = _1248846)], (24951 ^ _782435) ^ [_1248951, _1248953] : [class_Rings_Olinordered__idom(_1248951), -(hAPP(c_Groups_Oabs__class_Oabs(_1248951), _1248953) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1248951), _1248953), c_Groups_Osgn__class_Osgn(_1248951, _1248953)))], (24957 ^ _782435) ^ [_1249058, _1249060] : [class_Groups_Oordered__ab__group__add__abs(_1249058), 24960 ^ _782435 : [(24961 ^ _782435) ^ [] : [hAPP(c_Groups_Oabs__class_Oabs(_1249058), _1249060) = c_Groups_Ozero__class_Ozero(_1249058), -(_1249060 = c_Groups_Ozero__class_Ozero(_1249058))], (24967 ^ _782435) ^ [] : [_1249060 = c_Groups_Ozero__class_Ozero(_1249058), -(hAPP(c_Groups_Oabs__class_Oabs(_1249058), _1249060) = c_Groups_Ozero__class_Ozero(_1249058))]]], (24973 ^ _782435) ^ [_1249290] : [class_Groups_Oordered__ab__group__add__abs(_1249290), -(hAPP(c_Groups_Oabs__class_Oabs(_1249290), c_Groups_Ozero__class_Ozero(_1249290)) = c_Groups_Ozero__class_Ozero(_1249290))], (24979 ^ _782435) ^ [_1249381] : [-(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249381)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1249381))], (24981 ^ _782435) ^ [_1249413, _1249415, _1249417, _1249419] : [class_Groups_Oordered__ab__group__add__abs(_1249413), -(hAPP(c_Groups_Oabs__class_Oabs(_1249413), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249415, _1249413), hAPP(hAPP(c_COMBB(_1249413, _1249413, _1249415), c_Groups_Oabs__class_Oabs(_1249413)), _1249417)), _1249419)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1249415, _1249413), hAPP(hAPP(c_COMBB(_1249413, _1249413, _1249415), c_Groups_Oabs__class_Oabs(_1249413)), _1249417)), _1249419))], (24987 ^ _782435) ^ [_1249586, _1249588] : [class_Rings_Olinordered__idom(_1249586), 24990 ^ _782435 : [(24991 ^ _782435) ^ [] : [c_Groups_Osgn__class_Osgn(_1249586, _1249588) = c_Groups_Ozero__class_Ozero(_1249586), -(_1249588 = c_Groups_Ozero__class_Ozero(_1249586))], (24997 ^ _782435) ^ [] : [_1249588 = c_Groups_Ozero__class_Ozero(_1249586), -(c_Groups_Osgn__class_Osgn(_1249586, _1249588) = c_Groups_Ozero__class_Ozero(_1249586))]]], (25003 ^ _782435) ^ [_1249812] : [class_Groups_Osgn__if(_1249812), -(c_Groups_Osgn__class_Osgn(_1249812, c_Groups_Ozero__class_Ozero(_1249812)) = c_Groups_Ozero__class_Ozero(_1249812))], (25009 ^ _782435) ^ [_1249899, _1249901, _1249903] : [class_Rings_Olinordered__idom(_1249899), -(c_Groups_Osgn__class_Osgn(_1249899, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249899), _1249901), _1249903)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1249899), c_Groups_Osgn__class_Osgn(_1249899, _1249901)), c_Groups_Osgn__class_Osgn(_1249899, _1249903)))], (25015 ^ _782435) ^ [_1250026, _1250028] : [class_Groups_Oordered__ab__group__add__abs(_1250026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250026), c_Groups_Ozero__class_Ozero(_1250026)), _1250028)), -(hAPP(c_Groups_Oabs__class_Oabs(_1250026), _1250028) = _1250028)], (25025 ^ _782435) ^ [_1250181, _1250183] : [class_Groups_Oordered__ab__group__add__abs(_1250181), 25028 ^ _782435 : [(25029 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250181), hAPP(c_Groups_Oabs__class_Oabs(_1250181), _1250183)), c_Groups_Ozero__class_Ozero(_1250181))), -(_1250183 = c_Groups_Ozero__class_Ozero(_1250181))], (25035 ^ _782435) ^ [] : [_1250183 = c_Groups_Ozero__class_Ozero(_1250181), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250181), hAPP(c_Groups_Oabs__class_Oabs(_1250181), _1250183)), c_Groups_Ozero__class_Ozero(_1250181))))]]], (25041 ^ _782435) ^ [_1250434, _1250436] : [class_Groups_Oordered__ab__group__add__abs(_1250434), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1250434), c_Groups_Ozero__class_Ozero(_1250434)), hAPP(c_Groups_Oabs__class_Oabs(_1250434), _1250436))))], (25047 ^ _782435) ^ [_1250537, _1250539] : [class_Groups_Oordered__ab__group__add__abs(_1250537), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250537), c_Groups_Ozero__class_Ozero(_1250537)), _1250539)), -(hAPP(c_Groups_Oabs__class_Oabs(_1250537), _1250539) = _1250539)], (25057 ^ _782435) ^ [_1250692, _1250694] : [class_Groups_Oordered__ab__group__add__abs(_1250692), 25060 ^ _782435 : [(25061 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250692), c_Groups_Ozero__class_Ozero(_1250692)), hAPP(c_Groups_Oabs__class_Oabs(_1250692), _1250694))), _1250694 = c_Groups_Ozero__class_Ozero(_1250692)], (25067 ^ _782435) ^ [] : [-(_1250694 = c_Groups_Ozero__class_Ozero(_1250692)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250692), c_Groups_Ozero__class_Ozero(_1250692)), hAPP(c_Groups_Oabs__class_Oabs(_1250692), _1250694))))]]], (25073 ^ _782435) ^ [_1250907, _1250909] : [class_Groups_Oordered__ab__group__add__abs(_1250907), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1250907), hAPP(c_Groups_Oabs__class_Oabs(_1250907), _1250909)), c_Groups_Ozero__class_Ozero(_1250907)))], (25079 ^ _782435) ^ [_1251011, _1251013, _1251015] : [class_Groups_Oordered__ab__group__add__abs(_1251011), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251011), hAPP(c_Groups_Oabs__class_Oabs(_1251011), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251011), _1251013), _1251015))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1251011), hAPP(c_Groups_Oabs__class_Oabs(_1251011), _1251013)), hAPP(c_Groups_Oabs__class_Oabs(_1251011), _1251015)))))], (25085 ^ _782435) ^ [_1251164, _1251166, _1251168, _1251170, _1251172] : [class_Rings_Olinordered__idom(_1251164), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251164), hAPP(c_Groups_Oabs__class_Oabs(_1251164), _1251166)), _1251168)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251164), hAPP(c_Groups_Oabs__class_Oabs(_1251164), _1251170)), _1251172)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1251164), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251164), hAPP(c_Groups_Oabs__class_Oabs(_1251164), _1251166)), hAPP(c_Groups_Oabs__class_Oabs(_1251164), _1251170))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1251164), _1251168), _1251172))))], (25099 ^ _782435) ^ [_1251475, _1251477, _1251479] : [class_Groups_Oordered__ab__group__add__abs(_1251475), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251475), hAPP(c_Groups_Oabs__class_Oabs(_1251475), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251475), hAPP(c_Groups_Oabs__class_Oabs(_1251475), _1251477)), hAPP(c_Groups_Oabs__class_Oabs(_1251475), _1251479)))), hAPP(c_Groups_Oabs__class_Oabs(_1251475), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251475), _1251477), _1251479)))))], (25105 ^ _782435) ^ [_1251638, _1251640, _1251642] : [class_Groups_Oordered__ab__group__add__abs(_1251638), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251638), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251638), hAPP(c_Groups_Oabs__class_Oabs(_1251638), _1251640)), hAPP(c_Groups_Oabs__class_Oabs(_1251638), _1251642))), hAPP(c_Groups_Oabs__class_Oabs(_1251638), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251638), _1251640), _1251642)))))], (25111 ^ _782435) ^ [_1251791, _1251793, _1251795] : [class_Groups_Oordered__ab__group__add__abs(_1251791), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251791), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251791), hAPP(c_Groups_Oabs__class_Oabs(_1251791), _1251793)), hAPP(c_Groups_Oabs__class_Oabs(_1251791), _1251795))), hAPP(c_Groups_Oabs__class_Oabs(_1251791), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1251791), _1251795), _1251793)))))], (25117 ^ _782435) ^ [_1251944, _1251946, _1251948] : [class_Groups_Oordered__ab__group__add__abs(_1251944), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251944), hAPP(c_Groups_Oabs__class_Oabs(_1251944), _1251946)), _1251948)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1251944), hAPP(c_Groups_Ouminus__class_Ouminus(_1251944), _1251946)), _1251948)))], (25127 ^ _782435) ^ [_1252123, _1252125, _1252127] : [class_Groups_Oordered__ab__group__add__abs(_1252123), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252123), _1252125), _1252127)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252123), hAPP(c_Groups_Ouminus__class_Ouminus(_1252123), _1252125)), _1252127)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252123), hAPP(c_Groups_Oabs__class_Oabs(_1252123), _1252125)), _1252127)))], (25141 ^ _782435) ^ [_1252370, _1252372, _1252374] : [class_Groups_Oordered__ab__group__add__abs(_1252370), 25144 ^ _782435 : [(25145 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252370), hAPP(c_Groups_Oabs__class_Oabs(_1252370), _1252372)), _1252374)), 25148 ^ _782435 : [(25149 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252370), _1252372), _1252374)))], (25151 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252370), hAPP(c_Groups_Ouminus__class_Ouminus(_1252370), _1252372)), _1252374)))]]], (25153 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252370), hAPP(c_Groups_Oabs__class_Oabs(_1252370), _1252372)), _1252374))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252370), _1252372), _1252374)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252370), hAPP(c_Groups_Ouminus__class_Ouminus(_1252370), _1252372)), _1252374))]]], (25163 ^ _782435) ^ [_1252748, _1252750] : [class_Groups_Oordered__ab__group__add__abs(_1252748), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1252748), hAPP(c_Groups_Ouminus__class_Ouminus(_1252748), _1252750)), hAPP(c_Groups_Oabs__class_Oabs(_1252748), _1252750))))], (25169 ^ _782435) ^ [_1252857, _1252859, _1252861] : [class_Rings_Olinordered__idom(_1252857), 25172 ^ _782435 : [(25173 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252857), hAPP(c_Groups_Oabs__class_Oabs(_1252857), _1252859)), _1252861)), 25176 ^ _782435 : [(25177 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252857), _1252859), _1252861)))], (25179 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252857), hAPP(c_Groups_Ouminus__class_Ouminus(_1252857), _1252859)), _1252861)))]]], (25181 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252857), hAPP(c_Groups_Oabs__class_Oabs(_1252857), _1252859)), _1252861))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252857), _1252859), _1252861)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1252857), hAPP(c_Groups_Ouminus__class_Ouminus(_1252857), _1252859)), _1252861))]]], (25191 ^ _782435) ^ [_1253235, _1253237] : [hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1253235), _1253237)) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1253235) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25197 ^ _782435) ^ [_1253336, _1253338, _1253340] : [class_Rings_Olinordered__idom(_1253336), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253336), c_Groups_Ozero__class_Ozero(_1253336)), _1253338)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253336), hAPP(c_Groups_Oabs__class_Oabs(_1253336), _1253340)), _1253338) = hAPP(c_Groups_Oabs__class_Oabs(_1253336), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253336), _1253340), _1253338)))], (25207 ^ _782435) ^ [_1253537, _1253539, _1253541] : [class_Rings_Oordered__ring__abs(_1253537), -(hAPP(c_Groups_Oabs__class_Oabs(_1253537), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253537), _1253539), _1253541)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1253537), hAPP(c_Groups_Oabs__class_Oabs(_1253537), _1253539)), hAPP(c_Groups_Oabs__class_Oabs(_1253537), _1253541))), 25214 ^ _782435 : [(25215 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253537), c_Groups_Ozero__class_Ozero(_1253537)), _1253539))], (25217 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253537), _1253539), c_Groups_Ozero__class_Ozero(_1253537)))]], 25218 ^ _782435 : [(25219 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253537), c_Groups_Ozero__class_Ozero(_1253537)), _1253541))], (25221 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253537), _1253541), c_Groups_Ozero__class_Ozero(_1253537)))]]], (25225 ^ _782435) ^ [_1253932, _1253934, _1253936] : [class_Groups_Oordered__ab__group__add__abs(_1253932), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1253932), hAPP(c_Groups_Oabs__class_Oabs(_1253932), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1253932), _1253934), _1253936))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1253932), hAPP(c_Groups_Oabs__class_Oabs(_1253932), _1253934)), hAPP(c_Groups_Oabs__class_Oabs(_1253932), _1253936)))))], (25231 ^ _782435) ^ [_1254085, _1254087, _1254089, _1254091, _1254093] : [class_Groups_Oordered__ab__group__add__abs(_1254085), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254085), hAPP(c_Groups_Oabs__class_Oabs(_1254085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254085), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254085), _1254087), _1254089)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254085), _1254091), _1254093)))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1254085), hAPP(c_Groups_Oabs__class_Oabs(_1254085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254085), _1254087), _1254091))), hAPP(c_Groups_Oabs__class_Oabs(_1254085), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1254085), _1254089), _1254093))))))], (25237 ^ _782435) ^ [_1254306, _1254308] : [class_Groups_Oordered__ab__group__add__abs(_1254306), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254306), _1254308), c_Groups_Ozero__class_Ozero(_1254306))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254306), _1254308) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254306), _1254308))], (25247 ^ _782435) ^ [_1254471, _1254473] : [class_Groups_Oordered__ab__group__add__abs(_1254471), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1254471), hAPP(c_Groups_Ouminus__class_Ouminus(_1254471), hAPP(c_Groups_Oabs__class_Oabs(_1254471), _1254473))), c_Groups_Ozero__class_Ozero(_1254471))))], (25253 ^ _782435) ^ [_1254584, _1254586] : [class_Groups_Oordered__ab__group__add__abs(_1254584), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254584), _1254586), c_Groups_Ozero__class_Ozero(_1254584))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254584), _1254586) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254584), _1254586))], (25263 ^ _782435) ^ [_1254749, _1254751] : [class_Groups_Oabs__if(_1254749), 25266 ^ _782435 : [(25267 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254749), _1254751), c_Groups_Ozero__class_Ozero(_1254749))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254749), _1254751) = hAPP(c_Groups_Ouminus__class_Ouminus(_1254749), _1254751))], (25273 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1254749), _1254751), c_Groups_Ozero__class_Ozero(_1254749)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1254749), _1254751) = _1254751)]]], (25279 ^ _782435) ^ [_1255001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255001)), c_Groups_Oone__class_Oone(tc_Int_Oint))), -(_1255001 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25285 ^ _782435) ^ [_1255088] : [_1255088 = 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), _1255088)), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (25291 ^ _782435) ^ [_1255187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255187), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255187) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1255187))], (25297 ^ _782435) ^ [_1255278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1255278), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255278) = _1255278)], (25303 ^ _782435) ^ [_1255322, _1255324] : [-(hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1255322), _1255324))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255322))), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1255324))))], (25305 ^ _782435) ^ [_1255377, _1255379] : [class_Rings_Olinordered__idom(_1255377), 25308 ^ _782435 : [(25309 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255377), c_Groups_Osgn__class_Osgn(_1255377, _1255379)), c_Groups_Ozero__class_Ozero(_1255377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255377), _1255379), c_Groups_Ozero__class_Ozero(_1255377))))], (25315 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255377), _1255379), c_Groups_Ozero__class_Ozero(_1255377))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255377), c_Groups_Osgn__class_Osgn(_1255377, _1255379)), c_Groups_Ozero__class_Ozero(_1255377))))]]], (25321 ^ _782435) ^ [_1255645, _1255647] : [class_Rings_Olinordered__idom(_1255645), 25324 ^ _782435 : [(25325 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255645), c_Groups_Ozero__class_Ozero(_1255645)), c_Groups_Osgn__class_Osgn(_1255645, _1255647))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255645), c_Groups_Ozero__class_Ozero(_1255645)), _1255647)))], (25331 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255645), c_Groups_Ozero__class_Ozero(_1255645)), _1255647)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255645), c_Groups_Ozero__class_Ozero(_1255645)), c_Groups_Osgn__class_Osgn(_1255645, _1255647))))]]], (25337 ^ _782435) ^ [_1255913, _1255915] : [class_Rings_Olinordered__idom(_1255913), 25340 ^ _782435 : [(25341 ^ _782435) ^ [] : [c_Groups_Osgn__class_Osgn(_1255913, _1255915) = c_Groups_Oone__class_Oone(_1255913), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255913), c_Groups_Ozero__class_Ozero(_1255913)), _1255915)))], (25347 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1255913), c_Groups_Ozero__class_Ozero(_1255913)), _1255915)), -(c_Groups_Osgn__class_Osgn(_1255913, _1255915) = c_Groups_Oone__class_Oone(_1255913))]]], (25353 ^ _782435) ^ [_1256160, _1256162] : [class_Rings_Olinordered__idom(_1256160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1256160), c_Groups_Ozero__class_Ozero(_1256160)), _1256162)), -(c_Groups_Osgn__class_Osgn(_1256160, _1256162) = c_Groups_Oone__class_Oone(_1256160))], (25363 ^ _782435) ^ [_1256321] : [_1256321 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256321) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (25369 ^ _782435) ^ [_1256397] : [-(_1256397 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25372 ^ _782435 : [(25373 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256397)), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256397) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (25379 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1256397))), -(c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1256397) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (25385 ^ _782435) ^ [_1256589, _1256591] : [-(c_Nitpick_Oint__lcm(_1256589, _1256591) = 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), _1256589)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1256591)))))], (25387 ^ _782435) ^ [_1256635, _1256637, _1256639, _1256641, _1256643] : [class_Groups_Ocomm__monoid__add(_1256635), class_Groups_Ocomm__monoid__mult(_1256635), _1256637 = _1256639, c_Nat__Transfer_Onat__set(_1256639), 25405 ^ _782435 : [(25406 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 25404 ^ [_1256635, _1256637, _1256639, _1256641, _1256643])))], (25408 ^ _782435) ^ [] : [hAPP(_1256641, 25404 ^ [_1256635, _1256637, _1256639, _1256641, _1256643]) = hAPP(_1256643, 25404 ^ [_1256635, _1256637, _1256639, _1256641, _1256643])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256635), _1256641), _1256637) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1256635), _1256643), _1256639))], (25412 ^ _782435) ^ [_1257098, _1257100] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1257098), hAPP(c_Nat_OSuc, _1257100)) = 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), _1257098), _1257100)))], (25414 ^ _782435) ^ [_1257143, _1257145, _1257147] : [25416 ^ _782435 : [(25417 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25415 ^ [_1257143, _1257145, _1257147]), _1257143)))], (25419 ^ _782435) ^ [] : [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(_1257145, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25415 ^ [_1257143, _1257145, _1257147]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1257145, 25415 ^ [_1257143, _1257145, _1257147])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1257145, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257147)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257147), hAPP(_1257145, _1257143))), 25429 ^ _782435 : [(25430 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25428 ^ [_1257143, _1257145, _1257147]), _1257143)))], (25432 ^ _782435) ^ [] : [-(hAPP(_1257145, 25428 ^ [_1257143, _1257145, _1257147]) = _1257147)]]], (25434 ^ _782435) ^ [_1257593, _1257595, _1257597] : [25436 ^ _782435 : [(25437 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 25435 ^ [_1257593, _1257595, _1257597]), _1257593)))], (25439 ^ _782435) ^ [] : [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(_1257595, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 25435 ^ [_1257593, _1257595, _1257597]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1257595, 25435 ^ [_1257593, _1257595, _1257597])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1257595, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1257597)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1257597), hAPP(_1257595, _1257593))), 25449 ^ _782435 : [(25450 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 25448 ^ [_1257593, _1257595, _1257597]), _1257593)))], (25452 ^ _782435) ^ [] : [-(hAPP(_1257595, 25448 ^ [_1257593, _1257595, _1257597]) = _1257597)]]], (25454 ^ _782435) ^ [_1258043, _1258045, _1258047] : [-(c_Nat_Onat_Onat__case(_1258043, _1258045, _1258047, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1258045)], (25456 ^ _782435) ^ [_1258075, _1258077, _1258079, _1258081] : [-(c_Nat_Onat_Onat__case(_1258075, _1258077, _1258079, hAPP(c_Nat_OSuc, _1258081)) = hAPP(_1258079, _1258081))], (25458 ^ _782435) ^ [_1258115, _1258117] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258115)), -(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)), _1258115))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1258117))))) = 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)), _1258115))), 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, _1258117))))))], (25464 ^ _782435) ^ [_1258292, _1258294] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258292)), 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)), _1258292))), 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, _1258294))))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (25470 ^ _782435) ^ [_1258418, _1258420] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1258418))), -(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)), _1258418))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1258420)))) = 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)), _1258418))), 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, _1258420))))))], (25476 ^ _782435) ^ [_1258501, _1258503] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258501), _1258503)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1258501, 25479 ^ [_1258501, _1258503], c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, c_Groups_Oone__class_Oone(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1258501), _1258503)), _1258503))], (25483 ^ _782435) ^ [_1258622, _1258624] : [25485 ^ _782435 : [(25486 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 25484 ^ [_1258622, _1258624]), _1258622)))], (25488 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1258624), 25484 ^ [_1258622, _1258624]))]], -(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)), _1258624), _1258622))], (25492 ^ _782435) ^ [_1258797, _1258799, _1258801] : [hBOOL(hAPP(_1258797, _1258799)), -(hBOOL(hAPP(hAPP(c_member(_1258801), _1258799), hAPP(c_Set_OCollect(_1258801), _1258797))))], (25498 ^ _782435) ^ [_1258904, _1258906, _1258908] : [25499 ^ _782435 : [(25500 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258904), hAPP(c_Set_OCollect(_1258904), _1258906)))], (25502 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1258904), hAPP(c_Set_OCollect(_1258904), _1258908)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1258904), hAPP(c_Set_OCollect(_1258904), hAPP(hAPP(c_COMBS(_1258904, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1258904), c_fconj), _1258906)), _1258908)))))], (25506 ^ _782435) ^ [_1259115] : [-(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)), _1259115)))))], (25508 ^ _782435) ^ [_1259146] : [-(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)), _1259146)))))], (25510 ^ _782435) ^ [_1259177, _1259179] : [-(hAPP(c_Set_OCollect(_1259177), _1259179) = _1259179)], (25512 ^ _782435) ^ [_1259222, _1259224] : [c_Orderings_Obot__class_Obot(tc_fun(_1259222, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1259222), _1259224), 25515 ^ _782435 : [(25516 ^ _782435) ^ [_1259307] : [hBOOL(hAPP(_1259224, _1259307))]]], (25518 ^ _782435) ^ [_1259330, _1259332] : [-(hBOOL(hAPP(_1259332, 25519 ^ [_1259330, _1259332]))), -(c_Orderings_Obot__class_Obot(tc_fun(_1259330, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1259330), _1259332))], (25525 ^ _782435) ^ [_1259402, _1259404] : [hAPP(c_Set_OCollect(_1259402), _1259404) = c_Orderings_Obot__class_Obot(tc_fun(_1259402, tc_HOL_Obool)), 25528 ^ _782435 : [(25529 ^ _782435) ^ [_1259487] : [hBOOL(hAPP(_1259404, _1259487))]]], (25531 ^ _782435) ^ [_1259510, _1259512] : [-(hBOOL(hAPP(_1259512, 25532 ^ [_1259510, _1259512]))), -(hAPP(c_Set_OCollect(_1259510), _1259512) = c_Orderings_Obot__class_Obot(tc_fun(_1259510, tc_HOL_Obool)))], (25538 ^ _782435) ^ [_1259567, _1259569] : [-(hAPP(c_Set_OCollect(_1259567), hAPP(hAPP(c_COMBC(_1259567, tc_fun(_1259567, tc_HOL_Obool), tc_HOL_Obool), c_member(_1259567)), _1259569)) = _1259569)], (25540 ^ _782435) ^ [_1259630, _1259632, _1259634] : [hBOOL(hAPP(hAPP(c_member(_1259630), _1259632), hAPP(c_Set_OCollect(_1259630), _1259634))), -(hBOOL(hAPP(_1259634, _1259632)))], (25546 ^ _782435) ^ [_1259733, _1259735, _1259737] : [hBOOL(hAPP(_1259737, _1259735)), -(hBOOL(hAPP(hAPP(c_member(_1259733), _1259735), hAPP(c_Set_OCollect(_1259733), _1259737))))], (25552 ^ _782435) ^ [_1259842, _1259844, _1259846] : [hBOOL(hAPP(hAPP(c_member(_1259842), _1259844), hAPP(c_Set_OCollect(_1259842), _1259846))), -(hBOOL(hAPP(_1259846, _1259844)))], (25558 ^ _782435) ^ [_1259949, _1259951, _1259953] : [hBOOL(hAPP(hAPP(c_member(_1259949), _1259951), hAPP(c_Set_OCollect(_1259949), _1259953))), -(hBOOL(hAPP(_1259953, _1259951)))], (25564 ^ _782435) ^ [_1260056] : [-(c_Orderings_Obot__class_Obot(tc_fun(_1260056, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1260056), hAPP(c_COMBK(tc_HOL_Obool, _1260056), c_fFalse)))], (25566 ^ _782435) ^ [_1260113, _1260115, _1260117] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1260113), hAPP(c_Set_OCollect(_1260113), hAPP(hAPP(c_COMBS(_1260113, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260113), c_fdisj), _1260115)), _1260117)))), 25569 ^ _782435 : [(25570 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260113), hAPP(c_Set_OCollect(_1260113), _1260115))))], (25572 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260113), hAPP(c_Set_OCollect(_1260113), _1260117))))]]], (25574 ^ _782435) ^ [_1260308, _1260310, _1260312] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1260308), hAPP(c_Set_OCollect(_1260308), hAPP(hAPP(c_COMBS(_1260308, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260308), c_fdisj), _1260310)), _1260312))))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260308), hAPP(c_Set_OCollect(_1260308), _1260310))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1260308), hAPP(c_Set_OCollect(_1260308), _1260312)))], (25584 ^ _782435) ^ [_1260537, _1260539, _1260541] : [-(hAPP(hAPP(c_Set_Oinsert(_1260537), _1260539), hAPP(c_Set_OCollect(_1260537), _1260541)) = hAPP(c_Set_OCollect(_1260537), hAPP(hAPP(c_COMBS(_1260537, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260537), c_fimplies), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1260537), c_fNot), hAPP(hAPP(c_COMBC(_1260537, _1260537, tc_HOL_Obool), c_fequal), _1260539)))), _1260541)))], (25586 ^ _782435) ^ [_1260622] : [-(c_Orderings_Otop__class_Otop(tc_fun(_1260622, tc_HOL_Obool)) = hAPP(c_Set_OCollect(_1260622), hAPP(c_COMBK(tc_HOL_Obool, _1260622), c_fTrue)))], (25588 ^ _782435) ^ [_1260661, _1260663, _1260665] : [-(hAPP(c_Set_OCollect(_1260661), hAPP(hAPP(c_COMBS(_1260661, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260661), c_fdisj), _1260663)), _1260665)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1260661, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260661), _1260663)), hAPP(c_Set_OCollect(_1260661), _1260665)))], (25590 ^ _782435) ^ [_1260734, _1260736, _1260738] : [-(hAPP(c_Set_OCollect(_1260734), hAPP(hAPP(c_COMBS(_1260734, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260734), c_fconj), _1260736)), _1260738)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1260734, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260734), _1260736)), hAPP(c_Set_OCollect(_1260734), _1260738)))], (25592 ^ _782435) ^ [_1260807, _1260809] : [-(hAPP(c_Set_OCollect(_1260807), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1260807), c_fNot), _1260809)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1260807, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1260807), _1260809)))], (25594 ^ _782435) ^ [_1260860, _1260862, _1260864, _1260866] : [-(hAPP(c_Set_Ovimage(_1260860, _1260862, _1260864), hAPP(c_Set_OCollect(_1260862), _1260866)) = hAPP(c_Set_OCollect(_1260860), hAPP(hAPP(c_COMBB(_1260862, tc_HOL_Obool, _1260860), _1260866), _1260864)))], (25596 ^ _782435) ^ [_1260916, _1260918, _1260920] : [-(hAPP(hAPP(c_Set_Oinsert(_1260916), _1260918), _1260920) = hAPP(c_Set_OCollect(_1260916), hAPP(hAPP(c_COMBS(_1260916, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1260916), c_fdisj), hAPP(hAPP(c_COMBC(_1260916, _1260916, tc_HOL_Obool), c_fequal), _1260918))), hAPP(hAPP(c_COMBC(_1260916, tc_fun(_1260916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1260916)), _1260920))))], (25598 ^ _782435) ^ [_1261001, _1261003, _1261005] : [-(hAPP(hAPP(c_Set_Oinsert(_1261001), _1261003), _1261005) = hAPP(c_Set_OCollect(_1261001), hAPP(hAPP(c_COMBS(_1261001, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261001), c_fdisj), hAPP(hAPP(c_COMBC(_1261001, _1261001, tc_HOL_Obool), c_fequal), _1261003))), hAPP(hAPP(c_COMBC(_1261001, tc_fun(_1261001, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261001)), _1261005))))], (25600 ^ _782435) ^ [_1261086, _1261088, _1261090] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1261086, tc_HOL_Obool)), _1261088), _1261090) = hAPP(c_Set_OCollect(_1261086), hAPP(hAPP(c_COMBS(_1261086, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261086), c_fdisj), hAPP(hAPP(c_COMBC(_1261086, tc_fun(_1261086, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261086)), _1261088))), hAPP(hAPP(c_COMBC(_1261086, tc_fun(_1261086, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261086)), _1261090))))], (25602 ^ _782435) ^ [_1261179, _1261181, _1261183] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261179, tc_HOL_Obool)), _1261181), _1261183) = hAPP(c_Set_OCollect(_1261179), hAPP(hAPP(c_COMBS(_1261179, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261179), c_fconj), hAPP(hAPP(c_COMBC(_1261179, tc_fun(_1261179, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261179)), _1261181))), hAPP(hAPP(c_COMBC(_1261179, tc_fun(_1261179, tc_HOL_Obool), tc_HOL_Obool), c_member(_1261179)), _1261183))))], (25604 ^ _782435) ^ [_1261293, _1261295, _1261297, _1261299] : [hBOOL(hAPP(hAPP(c_member(_1261293), _1261295), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261293, tc_HOL_Obool)), _1261297), hAPP(c_Set_OCollect(_1261293), _1261299)))), 25607 ^ _782435 : [(25608 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1261293), _1261295), _1261297)))], (25610 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1261299, _1261295)))]]], (25612 ^ _782435) ^ [_1261460, _1261462, _1261464, _1261466] : [-(hBOOL(hAPP(hAPP(c_member(_1261460), _1261462), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1261460, tc_HOL_Obool)), _1261464), hAPP(c_Set_OCollect(_1261460), _1261466))))), hBOOL(hAPP(hAPP(c_member(_1261460), _1261462), _1261464)), hBOOL(hAPP(_1261466, _1261462))], (25622 ^ _782435) ^ [_1261663, _1261665] : [-(hAPP(c_Set_OCollect(_1261663), hAPP(c_fequal, _1261665)) = hAPP(hAPP(c_Set_Oinsert(_1261663), _1261665), c_Orderings_Obot__class_Obot(tc_fun(_1261663, tc_HOL_Obool))))], (25624 ^ _782435) ^ [_1261709, _1261711] : [-(hAPP(c_Set_OCollect(_1261709), hAPP(hAPP(c_COMBC(_1261709, _1261709, tc_HOL_Obool), c_fequal), _1261711)) = hAPP(hAPP(c_Set_Oinsert(_1261709), _1261711), c_Orderings_Obot__class_Obot(tc_fun(_1261709, tc_HOL_Obool))))], (25626 ^ _782435) ^ [_1261774, _1261776, _1261778] : [hBOOL(hAPP(_1261774, _1261776)), -(hAPP(c_Set_OCollect(_1261778), hAPP(hAPP(c_COMBS(_1261778, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261778), c_fconj), hAPP(c_fequal, _1261776))), _1261774)) = hAPP(hAPP(c_Set_Oinsert(_1261778), _1261776), c_Orderings_Obot__class_Obot(tc_fun(_1261778, tc_HOL_Obool))))], (25632 ^ _782435) ^ [_1261933, _1261935, _1261937] : [-(hBOOL(hAPP(_1261933, _1261935))), -(hAPP(c_Set_OCollect(_1261937), hAPP(hAPP(c_COMBS(_1261937, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1261937), c_fconj), hAPP(c_fequal, _1261935))), _1261933)) = c_Orderings_Obot__class_Obot(tc_fun(_1261937, tc_HOL_Obool)))], (25638 ^ _782435) ^ [_1262020, _1262022, _1262024] : [hBOOL(hAPP(_1262020, _1262022)), -(hAPP(c_Set_OCollect(_1262024), hAPP(hAPP(c_COMBS(_1262024, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262024), c_fconj), hAPP(hAPP(c_COMBC(_1262024, _1262024, tc_HOL_Obool), c_fequal), _1262022))), _1262020)) = hAPP(hAPP(c_Set_Oinsert(_1262024), _1262022), c_Orderings_Obot__class_Obot(tc_fun(_1262024, tc_HOL_Obool))))], (25644 ^ _782435) ^ [_1262193, _1262195, _1262197] : [-(hBOOL(hAPP(_1262193, _1262195))), -(hAPP(c_Set_OCollect(_1262197), hAPP(hAPP(c_COMBS(_1262197, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262197), c_fconj), hAPP(hAPP(c_COMBC(_1262197, _1262197, tc_HOL_Obool), c_fequal), _1262195))), _1262193)) = c_Orderings_Obot__class_Obot(tc_fun(_1262197, tc_HOL_Obool)))], (25650 ^ _782435) ^ [_1262275, _1262277, _1262279] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1262275, tc_HOL_Obool)), _1262277), _1262279) = hAPP(c_Set_OCollect(_1262275), hAPP(hAPP(c_COMBS(_1262275, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262275), c_fconj), hAPP(hAPP(c_COMBC(_1262275, tc_fun(_1262275, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262275)), _1262277))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262275), c_fNot), hAPP(hAPP(c_COMBC(_1262275, tc_fun(_1262275, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262275)), _1262279)))))], (25652 ^ _782435) ^ [_1262378, _1262380] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262378), hAPP(c_Set_OCollect(_1262378), _1262380))), 25655 ^ _782435 : [(25656 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262378), hAPP(c_Set_OCollect(_1262378), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262378), c_fNot), _1262380)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1262378), c_Orderings_Otop__class_Otop(tc_fun(_1262378, tc_HOL_Obool)))))], (25662 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1262378), c_Orderings_Otop__class_Otop(tc_fun(_1262378, tc_HOL_Obool)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1262378), hAPP(c_Set_OCollect(_1262378), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262378), c_fNot), _1262380)))))]]], (25668 ^ _782435) ^ [_1262687, _1262689, _1262691] : [-(hAPP(hAPP(c_Set_Oinsert(_1262687), _1262689), _1262691) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262687, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1262687), hAPP(hAPP(c_COMBC(_1262687, _1262687, tc_HOL_Obool), c_fequal), _1262689))), _1262691))], (25670 ^ _782435) ^ [_1262748, _1262750] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262748, tc_HOL_Obool)), _1262750) = hAPP(c_Set_OCollect(_1262748), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1262748), c_fNot), hAPP(hAPP(c_COMBC(_1262748, tc_fun(_1262748, tc_HOL_Obool), tc_HOL_Obool), c_member(_1262748)), _1262750))))], (25672 ^ _782435) ^ [_1262811, _1262813, _1262815, _1262817] : [-(hAPP(c_Set_Ovimage(_1262811, _1262813, _1262815), _1262817) = hAPP(c_Set_OCollect(_1262811), hAPP(hAPP(c_COMBC(_1262811, tc_fun(_1262813, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1262813, tc_fun(tc_fun(_1262813, tc_HOL_Obool), tc_HOL_Obool), _1262811), c_member(_1262813)), _1262815)), _1262817)))], (25674 ^ _782435) ^ [_1262883, _1262885, _1262887] : [-(hAPP(c_Set_OCollect(_1262883), hAPP(hAPP(c_COMBS(_1262883, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1262883), c_fimplies), _1262885)), _1262887)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1262883, tc_HOL_Obool)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1262883, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1262883), _1262885))), hAPP(c_Set_OCollect(_1262883), _1262887)))], (25676 ^ _782435) ^ [_1262964, _1262966] : [-(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), _1262964)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, tc_HOL_Obool), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), _1262966))))))], (25678 ^ _782435) ^ [_1263006, _1263008, _1263010, _1263012, _1263014, _1263016, _1263018] : [class_Groups_Ocomm__monoid__add(_1263006), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263008), _1263010)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263012), _1263014)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263008, _1263006), hAPP(hAPP(c_COMBS(_1263008, tc_fun(_1263012, tc_HOL_Obool), _1263006), hAPP(hAPP(c_COMBB(tc_fun(_1263012, _1263006), tc_fun(tc_fun(_1263012, tc_HOL_Obool), _1263006), _1263008), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263012, _1263006)), _1263016)), hAPP(hAPP(c_COMBB(tc_fun(_1263012, tc_HOL_Obool), tc_fun(_1263012, tc_HOL_Obool), _1263008), c_Set_OCollect(_1263012)), hAPP(hAPP(c_COMBB(tc_fun(_1263012, tc_HOL_Obool), tc_fun(_1263012, tc_HOL_Obool), _1263008), hAPP(c_COMBS(_1263012, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263012), c_fconj), hAPP(hAPP(c_COMBC(_1263012, tc_fun(_1263012, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263012)), _1263014)))), _1263018)))), _1263010) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263012, _1263006), hAPP(hAPP(c_COMBS(_1263012, tc_fun(_1263008, tc_HOL_Obool), _1263006), hAPP(hAPP(c_COMBB(tc_fun(_1263008, _1263006), tc_fun(tc_fun(_1263008, tc_HOL_Obool), _1263006), _1263012), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263008, _1263006)), hAPP(c_COMBC(_1263008, _1263012, _1263006), _1263016))), hAPP(hAPP(c_COMBB(tc_fun(_1263008, tc_HOL_Obool), tc_fun(_1263008, tc_HOL_Obool), _1263012), c_Set_OCollect(_1263008)), hAPP(hAPP(c_COMBB(tc_fun(_1263008, tc_HOL_Obool), tc_fun(_1263008, tc_HOL_Obool), _1263012), hAPP(c_COMBS(_1263008, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263008), c_fconj), hAPP(hAPP(c_COMBC(_1263008, tc_fun(_1263008, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263008)), _1263010)))), hAPP(c_COMBC(_1263008, _1263012, tc_HOL_Obool), _1263018))))), _1263014))], (25692 ^ _782435) ^ [_1263699, _1263701, _1263703, _1263705, _1263707, _1263709] : [-(hAPP(c_Set_Oimage(_1263699, _1263701, hAPP(hAPP(c_COMBS(_1263699, _1263701, _1263701), hAPP(hAPP(c_COMBS(_1263699, _1263701, tc_fun(_1263701, _1263701)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1263701, tc_fun(_1263701, _1263701)), _1263699), c_If(_1263701)), _1263703)), _1263705)), _1263707)), _1263709) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1263701, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1263699, _1263701, _1263705), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1263699, tc_HOL_Obool)), _1263709), hAPP(c_Set_OCollect(_1263699), _1263703)))), hAPP(c_Set_Oimage(_1263699, _1263701, _1263707), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1263699, tc_HOL_Obool)), _1263709), hAPP(c_Set_OCollect(_1263699), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1263699), c_fNot), _1263703))))))], (25694 ^ _782435) ^ [_1263847, _1263849, _1263851, _1263853] : [_1263847 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1263849, _1263851), 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)), _1263853))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1263849), _1263847)))], (25700 ^ _782435) ^ [_1263962, _1263964, _1263966, _1263968, _1263970] : [class_Groups_Ocomm__monoid__add(_1263962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1263964), _1263966)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263964, _1263962), _1263968), hAPP(c_Set_OCollect(_1263964), hAPP(hAPP(c_COMBS(_1263964, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1263964), c_fconj), hAPP(hAPP(c_COMBC(_1263964, tc_fun(_1263964, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263964)), _1263966))), hAPP(hAPP(c_COMBC(_1263964, tc_fun(_1263964, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263964)), _1263970)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1263964, _1263962), hAPP(hAPP(c_COMBC(_1263964, _1263962, _1263962), hAPP(hAPP(c_COMBS(_1263964, _1263962, tc_fun(_1263962, _1263962)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1263962, tc_fun(_1263962, _1263962)), _1263964), c_If(_1263962)), hAPP(hAPP(c_COMBC(_1263964, tc_fun(_1263964, tc_HOL_Obool), tc_HOL_Obool), c_member(_1263964)), _1263970))), _1263968)), c_Groups_Ozero__class_Ozero(_1263962))), _1263966))], (25710 ^ _782435) ^ [_1264371, _1264373, _1264375, _1264377, _1264379, _1264381] : [class_Groups_Ocomm__monoid__add(_1264371), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264373), _1264375)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264373, _1264371), _1264377), _1264375) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264379, _1264371), hAPP(hAPP(c_COMBB(tc_fun(_1264373, tc_HOL_Obool), _1264371, _1264379), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264373, _1264371), _1264377)), hAPP(hAPP(c_COMBB(tc_fun(_1264373, tc_HOL_Obool), tc_fun(_1264373, tc_HOL_Obool), _1264379), c_Set_OCollect(_1264373)), hAPP(hAPP(c_COMBB(tc_fun(_1264373, tc_HOL_Obool), tc_fun(_1264373, tc_HOL_Obool), _1264379), hAPP(c_COMBS(_1264373, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1264373), c_fconj), hAPP(hAPP(c_COMBC(_1264373, tc_fun(_1264373, tc_HOL_Obool), tc_HOL_Obool), c_member(_1264373)), _1264375)))), hAPP(c_COMBC(_1264373, _1264379, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1264379, tc_fun(_1264379, tc_HOL_Obool), _1264373), c_fequal), _1264381)))))), hAPP(c_Set_Oimage(_1264373, _1264379, _1264381), _1264375)))], (25720 ^ _782435) ^ [_1264782, _1264784, _1264786, _1264788, _1264790, _1264792] : [class_Groups_Ocomm__monoid__add(_1264782), hBOOL(hAPP(c_Finite__Set_Ofinite(_1264784), _1264786)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264784, _1264782), hAPP(hAPP(c_COMBS(_1264784, _1264782, _1264782), hAPP(hAPP(c_COMBS(_1264784, _1264782, tc_fun(_1264782, _1264782)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1264782, tc_fun(_1264782, _1264782)), _1264784), c_If(_1264782)), _1264788)), _1264790)), _1264792)), _1264786) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1264782), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264784, _1264782), _1264790), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264784, tc_HOL_Obool)), _1264786), hAPP(c_Set_OCollect(_1264784), _1264788)))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1264784, _1264782), _1264792), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1264784, tc_HOL_Obool)), _1264786), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1264784, tc_HOL_Obool)), hAPP(c_Set_OCollect(_1264784), _1264788))))))], (25730 ^ _782435) ^ [_1265180, _1265182] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1265180)), _1265182)), -(hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265180), _1265182)))], (25736 ^ _782435) ^ [_1265283, _1265285] : [hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool, c_fFalse, hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1265283), _1265285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1265283)), _1265285)))], (25742 ^ _782435) ^ [_1265392, _1265394, _1265396, _1265398, _1265400, _1265402] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1265392), _1265394)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1265396), _1265398)), 25752 ^ _782435 : [(25753 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1265396), 25751 ^ [_1265392, _1265394, _1265396, _1265398, _1265400, _1265402]), _1265398)))], (25755 ^ _782435) ^ [] : [hAPP(c_Finite__Set_Ocard(_1265392), hAPP(c_Set_OCollect(_1265392), hAPP(hAPP(c_COMBS(_1265392, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1265392), c_fconj), hAPP(hAPP(c_COMBC(_1265392, tc_fun(_1265392, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265392)), _1265394))), hAPP(hAPP(c_COMBC(_1265392, _1265396, tc_HOL_Obool), _1265400), 25751 ^ [_1265392, _1265394, _1265396, _1265398, _1265400, _1265402])))) = _1265402]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1265392, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1265396, tc_HOL_Obool), tc_Nat_Onat, _1265392), c_Finite__Set_Ocard(_1265396)), hAPP(hAPP(c_COMBB(tc_fun(_1265396, tc_HOL_Obool), tc_fun(_1265396, tc_HOL_Obool), _1265392), c_Set_OCollect(_1265396)), hAPP(hAPP(c_COMBB(tc_fun(_1265396, tc_HOL_Obool), tc_fun(_1265396, tc_HOL_Obool), _1265392), hAPP(c_COMBS(_1265396, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1265396), c_fconj), hAPP(hAPP(c_COMBC(_1265396, tc_fun(_1265396, tc_HOL_Obool), tc_HOL_Obool), c_member(_1265396)), _1265398)))), _1265400)))), _1265394) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1265402), hAPP(c_Finite__Set_Ocard(_1265396), _1265398)))], (25759 ^ _782435) ^ [_1266082, _1266084] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1266082), _1266084)), -(c_Fun_Obij__betw(tc_Nat_Onat, _1266082, 25762 ^ [_1266082, _1266084], hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1266082), _1266084)), _1266084))], (25766 ^ _782435) ^ [_1266201, _1266203, _1266205, _1266207] : [hBOOL(hAPP(hAPP(c_member(_1266201), _1266203), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266201, tc_HOL_Obool), _1266205))), c_Orderings_Oorder__class_Omono(tc_fun(_1266201, tc_HOL_Obool), tc_fun(_1266201, tc_HOL_Obool), _1266205), 25776 ^ _782435 : [(25777 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266201), 25775 ^ [_1266201, _1266203, _1266205, _1266207]), hAPP(_1266205, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266201, tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266201, tc_HOL_Obool), _1266205)), hAPP(c_Set_OCollect(_1266201), _1266207))))))], (25779 ^ _782435) ^ [] : [hBOOL(hAPP(_1266207, 25775 ^ [_1266201, _1266203, _1266205, _1266207]))]], -(hBOOL(hAPP(_1266207, _1266203)))], (25783 ^ _782435) ^ [_1266584, _1266586, _1266588, _1266590, _1266592] : [_1266584 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(_1266586, tc_HOL_Obool), _1266588), c_Orderings_Oorder__class_Omono(tc_fun(_1266586, tc_HOL_Obool), tc_fun(_1266586, tc_HOL_Obool), _1266588), hBOOL(hAPP(hAPP(c_member(_1266586), _1266590), _1266584)), 25797 ^ _782435 : [(25798 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1266586), 25796 ^ [_1266584, _1266586, _1266588, _1266590, _1266592]), hAPP(_1266588, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1266586, tc_HOL_Obool)), _1266584), hAPP(c_Set_OCollect(_1266586), _1266592))))))], (25800 ^ _782435) ^ [] : [hBOOL(hAPP(_1266592, 25796 ^ [_1266584, _1266586, _1266588, _1266590, _1266592]))]], -(hBOOL(hAPP(_1266592, _1266590)))], (25804 ^ _782435) ^ [_1267025, _1267027, _1267029, _1267031, _1267033] : [_1267025 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(_1267027, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1267027, tc_HOL_Obool), tc_fun(_1267027, tc_HOL_Obool), tc_fun(_1267027, tc_HOL_Obool)), c_Set_OCollect(_1267027)), _1267029)), c_Orderings_Oorder__class_Omono(tc_fun(_1267027, tc_HOL_Obool), tc_fun(_1267027, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1267027, tc_HOL_Obool), tc_fun(_1267027, tc_HOL_Obool), tc_fun(_1267027, tc_HOL_Obool)), c_Set_OCollect(_1267027)), _1267029)), hBOOL(hAPP(hAPP(c_member(_1267027), _1267031), _1267033)), 25818 ^ _782435 : [(25819 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267027), 25817 ^ [_1267025, _1267027, _1267029, _1267031, _1267033]), _1267033)))], (25821 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1267029, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1267027, tc_HOL_Obool)), _1267033), _1267025)), 25817 ^ [_1267025, _1267027, _1267029, _1267031, _1267033]))]], -(hBOOL(hAPP(hAPP(c_member(_1267027), _1267031), _1267025)))], (25825 ^ _782435) ^ [_1267565, _1267567] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267565), _1267567)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1267565, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_fun(_1267565, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1267565, tc_HOL_Obool), tc_fun(_1267565, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1267565, tc_HOL_Obool))), _1267567)))))], (25831 ^ _782435) ^ [_1267722, _1267724] : [-(hAPP(c_Set_OPow(_1267722), _1267724) = hAPP(c_Set_OCollect(tc_fun(_1267722, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_fun(_1267722, tc_HOL_Obool), tc_fun(_1267722, tc_HOL_Obool), tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(tc_fun(_1267722, tc_HOL_Obool))), _1267724)))], (25833 ^ _782435) ^ [_1267781] : [-(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)))), _1267781))))], (25835 ^ _782435) ^ [_1267809] : [-(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)))), _1267809)) = 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), _1267809), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))))], (25837 ^ _782435) ^ [_1267850] : [-(hAPP(c_Set_OCollect(tc_Nat_Onat), _1267850) = 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), _1267850), c_Int_Onat)))))], (25839 ^ _782435) ^ [_1267891, _1267893, _1267895, _1267897, _1267899, _1267901] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1267891), _1267893)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1267895), _1267897)), 25849 ^ _782435 : [(25850 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1267895), 25848 ^ [_1267891, _1267893, _1267895, _1267897, _1267899, _1267901]), _1267897)))], (25852 ^ _782435) ^ [] : [hAPP(c_Finite__Set_Ocard(_1267891), hAPP(c_Set_OCollect(_1267891), hAPP(hAPP(c_COMBS(_1267891, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1267891), c_fconj), hAPP(hAPP(c_COMBC(_1267891, tc_fun(_1267891, tc_HOL_Obool), tc_HOL_Obool), c_member(_1267891)), _1267893))), hAPP(hAPP(c_COMBC(_1267891, _1267895, tc_HOL_Obool), _1267899), 25848 ^ [_1267891, _1267893, _1267895, _1267897, _1267899, _1267901])))) = hAPP(_1267901, 25848 ^ [_1267891, _1267893, _1267895, _1267897, _1267899, _1267901])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267891, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1267895, tc_HOL_Obool), tc_Nat_Onat, _1267891), c_Finite__Set_Ocard(_1267895)), hAPP(hAPP(c_COMBB(tc_fun(_1267895, tc_HOL_Obool), tc_fun(_1267895, tc_HOL_Obool), _1267891), c_Set_OCollect(_1267895)), hAPP(hAPP(c_COMBB(tc_fun(_1267895, tc_HOL_Obool), tc_fun(_1267895, tc_HOL_Obool), _1267891), hAPP(c_COMBS(_1267895, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1267895), c_fconj), hAPP(hAPP(c_COMBC(_1267895, tc_fun(_1267895, tc_HOL_Obool), tc_HOL_Obool), c_member(_1267895)), _1267897)))), _1267899)))), _1267893) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1267895, tc_Nat_Onat), _1267901), _1267897))], (25856 ^ _782435) ^ [_1268601, _1268603, _1268605] : [class_Lattices_Odistrib__lattice(_1268601), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268601), _1268603)), -(_1268603 = c_Orderings_Obot__class_Obot(tc_fun(_1268601, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1268601), _1268605)), -(_1268605 = c_Orderings_Obot__class_Obot(tc_fun(_1268601, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1268601), c_Big__Operators_Olattice__class_OSup__fin(_1268601, _1268603)), c_Big__Operators_Olattice__class_OSup__fin(_1268601, _1268605)) = c_Big__Operators_Olattice__class_OSup__fin(_1268601, hAPP(c_Set_OCollect(_1268601), hAPP(hAPP(c_COMBB(tc_fun(_1268601, tc_HOL_Obool), tc_HOL_Obool, _1268601), c_HOL_OEx(_1268601)), hAPP(hAPP(c_COMBB(tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool)), tc_fun(_1268601, tc_HOL_Obool), _1268601), hAPP(c_COMBB(tc_fun(_1268601, tc_HOL_Obool), tc_HOL_Obool, _1268601), c_HOL_OEx(_1268601))), hAPP(hAPP(c_COMBC(_1268601, tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool)), tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268601, tc_fun(tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_HOL_Obool))), tc_fun(tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool)), tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool))), _1268601), c_COMBS(_1268601, tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268601, tc_fun(_1268601, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1268601, tc_fun(tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_HOL_Obool))), _1268601), hAPP(c_COMBB(tc_fun(_1268601, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_HOL_Obool)), _1268601), c_COMBS(_1268601, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool)), tc_fun(_1268601, tc_fun(_1268601, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1268601), hAPP(c_COMBB(tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1268601), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268601), c_fconj))), hAPP(hAPP(c_COMBC(_1268601, tc_fun(_1268601, tc_fun(_1268601, _1268601)), tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1268601, _1268601), tc_fun(_1268601, tc_HOL_Obool)), tc_fun(tc_fun(_1268601, tc_fun(_1268601, _1268601)), tc_fun(_1268601, tc_fun(_1268601, tc_HOL_Obool))), _1268601), c_COMBB(tc_fun(_1268601, _1268601), tc_fun(_1268601, tc_HOL_Obool), _1268601)), hAPP(hAPP(c_COMBB(tc_fun(_1268601, tc_HOL_Obool), tc_fun(tc_fun(_1268601, _1268601), tc_fun(_1268601, tc_HOL_Obool)), _1268601), c_COMBB(_1268601, tc_HOL_Obool, _1268601)), c_fequal))), c_Lattices_Osemilattice__inf__class_Oinf(_1268601)))))), hAPP(hAPP(c_COMBC(_1268601, tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1268601, tc_HOL_Obool), tc_fun(_1268601, tc_HOL_Obool)), _1268601), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1268601)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1268601), c_fconj), hAPP(hAPP(c_COMBC(_1268601, tc_fun(_1268601, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268601)), _1268603)))), hAPP(hAPP(c_COMBC(_1268601, tc_fun(_1268601, tc_HOL_Obool), tc_HOL_Obool), c_member(_1268601)), _1268605))))))))], (25878 ^ _782435) ^ [_1269700, _1269702, _1269704] : [class_Lattices_Odistrib__lattice(_1269700), hBOOL(hAPP(c_Finite__Set_Ofinite(_1269700), _1269702)), -(_1269702 = c_Orderings_Obot__class_Obot(tc_fun(_1269700, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1269700), _1269704), c_Big__Operators_Olattice__class_OSup__fin(_1269700, _1269702)) = c_Big__Operators_Olattice__class_OSup__fin(_1269700, hAPP(c_Set_OCollect(_1269700), hAPP(hAPP(c_COMBB(tc_fun(_1269700, tc_HOL_Obool), tc_HOL_Obool, _1269700), c_HOL_OEx(_1269700)), hAPP(hAPP(c_COMBC(_1269700, tc_fun(_1269700, tc_HOL_Obool), tc_fun(_1269700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269700, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1269700, tc_HOL_Obool), tc_fun(_1269700, tc_HOL_Obool)), _1269700), c_COMBS(_1269700, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269700, tc_HOL_Obool), tc_fun(_1269700, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1269700), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1269700), c_fconj)), hAPP(hAPP(c_COMBC(_1269700, tc_fun(_1269700, _1269700), tc_fun(_1269700, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1269700, tc_HOL_Obool), tc_fun(tc_fun(_1269700, _1269700), tc_fun(_1269700, tc_HOL_Obool)), _1269700), c_COMBB(_1269700, tc_HOL_Obool, _1269700)), c_fequal)), hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1269700), _1269704))))), hAPP(hAPP(c_COMBC(_1269700, tc_fun(_1269700, tc_HOL_Obool), tc_HOL_Obool), c_member(_1269700)), _1269702))))))], (25892 ^ _782435) ^ [_1270186, _1270188, _1270190] : [class_Lattices_Odistrib__lattice(_1270186), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270186), _1270188)), -(_1270188 = c_Orderings_Obot__class_Obot(tc_fun(_1270186, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1270186), _1270190)), -(_1270190 = c_Orderings_Obot__class_Obot(tc_fun(_1270186, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1270186), c_Big__Operators_Olattice__class_OInf__fin(_1270186, _1270188)), c_Big__Operators_Olattice__class_OInf__fin(_1270186, _1270190)) = c_Big__Operators_Olattice__class_OInf__fin(_1270186, hAPP(c_Set_OCollect(_1270186), hAPP(hAPP(c_COMBB(tc_fun(_1270186, tc_HOL_Obool), tc_HOL_Obool, _1270186), c_HOL_OEx(_1270186)), hAPP(hAPP(c_COMBB(tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool)), tc_fun(_1270186, tc_HOL_Obool), _1270186), hAPP(c_COMBB(tc_fun(_1270186, tc_HOL_Obool), tc_HOL_Obool, _1270186), c_HOL_OEx(_1270186))), hAPP(hAPP(c_COMBC(_1270186, tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool)), tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270186, tc_fun(tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_HOL_Obool))), tc_fun(tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool)), tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool))), _1270186), c_COMBS(_1270186, tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270186, tc_fun(_1270186, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1270186, tc_fun(tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_HOL_Obool))), _1270186), hAPP(c_COMBB(tc_fun(_1270186, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_HOL_Obool)), _1270186), c_COMBS(_1270186, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool)), tc_fun(_1270186, tc_fun(_1270186, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1270186), hAPP(c_COMBB(tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1270186), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270186), c_fconj))), hAPP(hAPP(c_COMBC(_1270186, tc_fun(_1270186, tc_fun(_1270186, _1270186)), tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1270186, _1270186), tc_fun(_1270186, tc_HOL_Obool)), tc_fun(tc_fun(_1270186, tc_fun(_1270186, _1270186)), tc_fun(_1270186, tc_fun(_1270186, tc_HOL_Obool))), _1270186), c_COMBB(tc_fun(_1270186, _1270186), tc_fun(_1270186, tc_HOL_Obool), _1270186)), hAPP(hAPP(c_COMBB(tc_fun(_1270186, tc_HOL_Obool), tc_fun(tc_fun(_1270186, _1270186), tc_fun(_1270186, tc_HOL_Obool)), _1270186), c_COMBB(_1270186, tc_HOL_Obool, _1270186)), c_fequal))), c_Lattices_Osemilattice__sup__class_Osup(_1270186)))))), hAPP(hAPP(c_COMBC(_1270186, tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1270186, tc_HOL_Obool), tc_fun(_1270186, tc_HOL_Obool)), _1270186), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1270186)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1270186), c_fconj), hAPP(hAPP(c_COMBC(_1270186, tc_fun(_1270186, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270186)), _1270188)))), hAPP(hAPP(c_COMBC(_1270186, tc_fun(_1270186, tc_HOL_Obool), tc_HOL_Obool), c_member(_1270186)), _1270190))))))))], (25914 ^ _782435) ^ [_1271285, _1271287, _1271289] : [class_Lattices_Odistrib__lattice(_1271285), hBOOL(hAPP(c_Finite__Set_Ofinite(_1271285), _1271287)), -(_1271287 = c_Orderings_Obot__class_Obot(tc_fun(_1271285, tc_HOL_Obool))), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271285), _1271289), c_Big__Operators_Olattice__class_OInf__fin(_1271285, _1271287)) = c_Big__Operators_Olattice__class_OInf__fin(_1271285, hAPP(c_Set_OCollect(_1271285), hAPP(hAPP(c_COMBB(tc_fun(_1271285, tc_HOL_Obool), tc_HOL_Obool, _1271285), c_HOL_OEx(_1271285)), hAPP(hAPP(c_COMBC(_1271285, tc_fun(_1271285, tc_HOL_Obool), tc_fun(_1271285, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271285, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1271285, tc_HOL_Obool), tc_fun(_1271285, tc_HOL_Obool)), _1271285), c_COMBS(_1271285, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271285, tc_HOL_Obool), tc_fun(_1271285, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1271285), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1271285), c_fconj)), hAPP(hAPP(c_COMBC(_1271285, tc_fun(_1271285, _1271285), tc_fun(_1271285, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271285, tc_HOL_Obool), tc_fun(tc_fun(_1271285, _1271285), tc_fun(_1271285, tc_HOL_Obool)), _1271285), c_COMBB(_1271285, tc_HOL_Obool, _1271285)), c_fequal)), hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1271285), _1271289))))), hAPP(hAPP(c_COMBC(_1271285, tc_fun(_1271285, tc_HOL_Obool), tc_HOL_Obool), c_member(_1271285)), _1271287))))))], (25928 ^ _782435) ^ [_1271771, _1271773, _1271775, _1271777] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1271771), hAPP(c_Set_OCollect(_1271771), _1271773))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1271775), hAPP(c_Set_OCollect(_1271775), hAPP(hAPP(c_COMBB(tc_fun(_1271771, tc_HOL_Obool), tc_HOL_Obool, _1271775), c_HOL_OEx(_1271771)), hAPP(hAPP(c_COMBC(_1271775, tc_fun(_1271771, tc_HOL_Obool), tc_fun(_1271771, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271771, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1271771, tc_HOL_Obool), tc_fun(_1271771, tc_HOL_Obool)), _1271775), c_COMBS(_1271771, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271771, tc_HOL_Obool), tc_fun(_1271771, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1271775), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1271771), c_fconj)), hAPP(hAPP(c_COMBC(_1271775, tc_fun(_1271771, _1271775), tc_fun(_1271771, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1271775, tc_HOL_Obool), tc_fun(tc_fun(_1271771, _1271775), tc_fun(_1271771, tc_HOL_Obool)), _1271775), c_COMBB(_1271775, tc_HOL_Obool, _1271771)), c_fequal)), _1271777)))), _1271773))))))], (25934 ^ _782435) ^ [_1272132, _1272134, _1272136, _1272138] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272132), hAPP(c_Set_OCollect(_1272132), _1272134))), 25937 ^ _782435 : [(25948 ^ _782435) ^ [] : [25950 ^ _782435 : [(25951 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1272134, 25949 ^ [_1272132, _1272134, _1272136, _1272138])))], (25953 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272136), hAPP(c_Set_OCollect(_1272136), hAPP(hAPP(c_COMBC(_1272136, _1272132, tc_HOL_Obool), _1272138), 25949 ^ [_1272132, _1272134, _1272136, _1272138]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272136), hAPP(c_Set_OCollect(_1272136), hAPP(hAPP(c_COMBB(tc_fun(_1272132, tc_HOL_Obool), tc_HOL_Obool, _1272136), c_HOL_OEx(_1272132)), hAPP(hAPP(c_COMBB(tc_fun(_1272132, tc_HOL_Obool), tc_fun(_1272132, tc_HOL_Obool), _1272136), hAPP(c_COMBS(_1272132, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272132), c_fconj), _1272134))), _1272138))))))], (25938 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1272136), hAPP(c_Set_OCollect(_1272136), hAPP(hAPP(c_COMBB(tc_fun(_1272132, tc_HOL_Obool), tc_HOL_Obool, _1272136), c_HOL_OEx(_1272132)), hAPP(hAPP(c_COMBB(tc_fun(_1272132, tc_HOL_Obool), tc_fun(_1272132, tc_HOL_Obool), _1272136), hAPP(c_COMBS(_1272132, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1272132), c_fconj), _1272134))), _1272138))))), 25941 ^ _782435 : [(25942 ^ _782435) ^ [_1272415] : [hBOOL(hAPP(_1272134, _1272415)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1272136), hAPP(c_Set_OCollect(_1272136), hAPP(hAPP(c_COMBC(_1272136, _1272132, tc_HOL_Obool), _1272138), _1272415)))))]]]]], (25957 ^ _782435) ^ [_1272780, _1272782] : [-(hAPP(c_Set_OPow(_1272780), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1272780, tc_HOL_Obool)), _1272782)) = hAPP(c_Set_OCollect(tc_fun(_1272780, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272780, tc_HOL_Obool)), c_HOL_OEx(tc_fun(_1272780, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(tc_fun(_1272780, tc_HOL_Obool), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1272780, tc_HOL_Obool)), c_COMBS(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1272780, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1272780, tc_HOL_Obool)), c_fconj)), hAPP(hAPP(c_COMBC(tc_fun(_1272780, tc_HOL_Obool), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_fun(_1272780, tc_HOL_Obool)), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_fun(_1272780, tc_HOL_Obool)), tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1272780, tc_HOL_Obool)), c_COMBB(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272780, tc_HOL_Obool))), c_fequal)), c_Groups_Ouminus__class_Ouminus(tc_fun(_1272780, tc_HOL_Obool)))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1272780, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1272780, tc_HOL_Obool)), hAPP(c_member(tc_fun(_1272780, tc_HOL_Obool)), _1272782)), c_Set_OPow(_1272780))))))], (25959 ^ _782435) ^ [_1273060, _1273062, _1273064] : [class_Groups_Olinordered__ab__semigroup__add(_1273060), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273060), _1273062)), -(_1273062 = c_Orderings_Obot__class_Obot(tc_fun(_1273060, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273060), _1273064), c_Big__Operators_Olinorder__class_OMin(_1273060, _1273062)) = c_Big__Operators_Olinorder__class_OMin(_1273060, hAPP(c_Set_OCollect(_1273060), hAPP(hAPP(c_COMBB(tc_fun(_1273060, tc_HOL_Obool), tc_HOL_Obool, _1273060), c_HOL_OEx(_1273060)), hAPP(hAPP(c_COMBC(_1273060, tc_fun(_1273060, tc_HOL_Obool), tc_fun(_1273060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273060, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1273060, tc_HOL_Obool), tc_fun(_1273060, tc_HOL_Obool)), _1273060), c_COMBS(_1273060, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273060, tc_HOL_Obool), tc_fun(_1273060, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1273060), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1273060), c_fconj)), hAPP(hAPP(c_COMBC(_1273060, tc_fun(_1273060, _1273060), tc_fun(_1273060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273060, tc_HOL_Obool), tc_fun(tc_fun(_1273060, _1273060), tc_fun(_1273060, tc_HOL_Obool)), _1273060), c_COMBB(_1273060, tc_HOL_Obool, _1273060)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1273060), _1273064))))), hAPP(hAPP(c_COMBC(_1273060, tc_fun(_1273060, tc_HOL_Obool), tc_HOL_Obool), c_member(_1273060)), _1273062))))))], (25973 ^ _782435) ^ [_1273546, _1273548, _1273550] : [class_Groups_Olinordered__ab__semigroup__add(_1273546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1273546), _1273548)), -(_1273548 = c_Orderings_Obot__class_Obot(tc_fun(_1273546, tc_HOL_Obool))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1273546), _1273550), c_Big__Operators_Olinorder__class_OMax(_1273546, _1273548)) = c_Big__Operators_Olinorder__class_OMax(_1273546, hAPP(c_Set_OCollect(_1273546), hAPP(hAPP(c_COMBB(tc_fun(_1273546, tc_HOL_Obool), tc_HOL_Obool, _1273546), c_HOL_OEx(_1273546)), hAPP(hAPP(c_COMBC(_1273546, tc_fun(_1273546, tc_HOL_Obool), tc_fun(_1273546, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273546, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1273546, tc_HOL_Obool), tc_fun(_1273546, tc_HOL_Obool)), _1273546), c_COMBS(_1273546, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273546, tc_HOL_Obool), tc_fun(_1273546, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1273546), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1273546), c_fconj)), hAPP(hAPP(c_COMBC(_1273546, tc_fun(_1273546, _1273546), tc_fun(_1273546, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1273546, tc_HOL_Obool), tc_fun(tc_fun(_1273546, _1273546), tc_fun(_1273546, tc_HOL_Obool)), _1273546), c_COMBB(_1273546, tc_HOL_Obool, _1273546)), c_fequal)), hAPP(c_Groups_Oplus__class_Oplus(_1273546), _1273550))))), hAPP(hAPP(c_COMBC(_1273546, tc_fun(_1273546, tc_HOL_Obool), tc_HOL_Obool), c_member(_1273546)), _1273548))))))], (25987 ^ _782435) ^ [_1274047, _1274049] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274047), _1274049)), -(_1274049 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1274047, 25991 ^ [_1274047, _1274049]), 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 ^ [_1274047, _1274049]))))], (25995 ^ _782435) ^ [_1274178, _1274180] : [25996 ^ _782435 : [(25997 ^ _782435) ^ [_1274242, _1274244] : [_1274180 = hAPP(c_Set_Oimage(tc_Nat_Onat, _1274178, _1274242), 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)), _1274244)))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274178), _1274180)))], (26001 ^ _782435) ^ [_1274313, _1274315, _1274317, _1274319] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1274313), _1274315))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1274317), hAPP(c_Set_Oimage(_1274313, _1274317, _1274319), _1274315))), 26009 ^ _782435 : [(26010 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1274313), 26008 ^ [_1274313, _1274315, _1274317, _1274319]), _1274315)))], (26012 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1274313), hAPP(c_Set_OCollect(_1274313), hAPP(hAPP(c_COMBS(_1274313, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1274313), c_fconj), hAPP(hAPP(c_COMBC(_1274313, tc_fun(_1274313, tc_HOL_Obool), tc_HOL_Obool), c_member(_1274313)), _1274315))), hAPP(hAPP(c_COMBC(_1274313, _1274317, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1274317, tc_fun(_1274317, tc_HOL_Obool), _1274313), c_fequal), _1274319)), hAPP(_1274319, 26008 ^ [_1274313, _1274315, _1274317, _1274319]))))))]]], (26014 ^ _782435) ^ [_1274787, _1274789] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1274787)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1274789)), hAPP(c_Int_Onat, _1274787)) = hAPP(c_Int_Onat, _1274789))], (26020 ^ _782435) ^ [_1274892, _1274894] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1274892))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onat, _1274894)), hAPP(c_Int_Onat, _1274892)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1274894), _1274892)), 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 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (26028 ^ _782435) ^ [_1274989] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1274989)))], (26030 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, c_Groups_Oone__class_Oone(tc_Int_Oint)))], (26032 ^ _782435) ^ [_1275041, _1275043] : [class_Groups_Olinordered__ab__group__add(_1275041), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275041), _1275043)), -(_1275043 = c_Orderings_Obot__class_Obot(tc_fun(_1275041, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275041), c_Big__Operators_Olinorder__class_OMin(_1275041, _1275043)) = c_Big__Operators_Olinorder__class_OMax(_1275041, hAPP(c_Set_Oimage(_1275041, _1275041, c_Groups_Ouminus__class_Ouminus(_1275041)), _1275043)))], (26046 ^ _782435) ^ [_1275241, _1275243] : [class_Groups_Olinordered__ab__group__add(_1275241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1275241), _1275243)), -(_1275243 = c_Orderings_Obot__class_Obot(tc_fun(_1275241, tc_HOL_Obool))), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1275241), c_Big__Operators_Olinorder__class_OMax(_1275241, _1275243)) = c_Big__Operators_Olinorder__class_OMin(_1275241, hAPP(c_Set_Oimage(_1275241, _1275241, c_Groups_Ouminus__class_Ouminus(_1275241)), _1275243)))], (26060 ^ _782435) ^ [_1275441, _1275443] : [class_Orderings_Olinorder(_1275441), -(c_Big__Operators_Olinorder__class_OMin(_1275441, hAPP(hAPP(c_Set_Oinsert(_1275441), _1275443), c_Orderings_Obot__class_Obot(tc_fun(_1275441, tc_HOL_Obool)))) = _1275443)], (26066 ^ _782435) ^ [_1275548, _1275550] : [class_Orderings_Olinorder(_1275548), -(c_Big__Operators_Olinorder__class_OMax(_1275548, hAPP(hAPP(c_Set_Oinsert(_1275548), _1275550), c_Orderings_Obot__class_Obot(tc_fun(_1275548, tc_HOL_Obool)))) = _1275550)], (26072 ^ _782435) ^ [_1275661] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275661))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275661)))], (26078 ^ _782435) ^ [_1275695] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1275695)), hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275695))], (26084 ^ _782435) ^ [_1275793] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275793)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275793), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (26090 ^ _782435) ^ [_1275878] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1275878), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275878)))], (26096 ^ _782435) ^ [_1275969] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, _1275969)), -(hAPP(c_Int_Onat, _1275969) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26102 ^ _782435) ^ [_1276050] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, _1276050))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onat, _1276050)) = _1276050)], (26108 ^ _782435) ^ [_1276092, _1276094, _1276096] : [class_Orderings_Olinorder(_1276092), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276092), _1276094)), hBOOL(hAPP(hAPP(c_member(_1276092), _1276096), _1276094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276092), _1276096), c_Big__Operators_Olinorder__class_OMax(_1276092, _1276094))))], (26122 ^ _782435) ^ [_1276319, _1276321, _1276323] : [class_Orderings_Olinorder(_1276319), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276319), _1276321)), hBOOL(hAPP(hAPP(c_member(_1276319), _1276323), _1276321)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276319), c_Big__Operators_Olinorder__class_OMin(_1276319, _1276321)), _1276323)))], (26136 ^ _782435) ^ [_1276546, _1276548] : [class_Orderings_Olinorder(_1276546), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276546), _1276548)), -(_1276548 = c_Orderings_Obot__class_Obot(tc_fun(_1276546, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1276546), c_Big__Operators_Olinorder__class_OMin(_1276546, _1276548)), _1276548)))], (26150 ^ _782435) ^ [_1276726, _1276728] : [class_Orderings_Olinorder(_1276726), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276726), _1276728)), -(_1276728 = c_Orderings_Obot__class_Obot(tc_fun(_1276726, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(_1276726), c_Big__Operators_Olinorder__class_OMax(_1276726, _1276728)), _1276728)))], (26164 ^ _782435) ^ [_1276906] : [-(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, _1276906))))))], (26166 ^ _782435) ^ [_1276940, _1276942, _1276944] : [class_Orderings_Olinorder(_1276940), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1276940, tc_HOL_Obool)), _1276942), _1276944)), -(_1276942 = c_Orderings_Obot__class_Obot(tc_fun(_1276940, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1276940), _1276944)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1276940), c_Big__Operators_Olinorder__class_OMax(_1276940, _1276942)), c_Big__Operators_Olinorder__class_OMax(_1276940, _1276944))))], (26184 ^ _782435) ^ [_1277246, _1277248, _1277250] : [class_Orderings_Olinorder(_1277246), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1277246, tc_HOL_Obool)), _1277248), _1277250)), -(_1277248 = c_Orderings_Obot__class_Obot(tc_fun(_1277246, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277246), _1277250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1277246), c_Big__Operators_Olinorder__class_OMin(_1277246, _1277250)), c_Big__Operators_Olinorder__class_OMin(_1277246, _1277248))))], (26202 ^ _782435) ^ [_1277552, _1277554, _1277556] : [class_Orderings_Olinorder(_1277552), hBOOL(hAPP(c_Finite__Set_Ofinite(_1277552), _1277554)), hBOOL(hAPP(hAPP(c_member(_1277552), _1277556), _1277554)), 26213 ^ _782435 : [(26214 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277552, tc_HOL_Obool)), _1277554), hAPP(hAPP(c_Set_Oinsert(_1277552), _1277556), c_Orderings_Obot__class_Obot(tc_fun(_1277552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1277552, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1277552, _1277554) = _1277556)], (26220 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277552, tc_HOL_Obool)), _1277554), hAPP(hAPP(c_Set_Oinsert(_1277552), _1277556), c_Orderings_Obot__class_Obot(tc_fun(_1277552, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1277552, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1277552, _1277554) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1277552), _1277556), c_Big__Operators_Olinorder__class_OMin(_1277552, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1277552, tc_HOL_Obool)), _1277554), hAPP(hAPP(c_Set_Oinsert(_1277552), _1277556), c_Orderings_Obot__class_Obot(tc_fun(_1277552, tc_HOL_Obool)))))))]]], (26226 ^ _782435) ^ [_1278058, _1278060, _1278062] : [class_Orderings_Olinorder(_1278058), hBOOL(hAPP(c_Finite__Set_Ofinite(_1278058), _1278060)), hBOOL(hAPP(hAPP(c_member(_1278058), _1278062), _1278060)), 26237 ^ _782435 : [(26238 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278058, tc_HOL_Obool)), _1278060), hAPP(hAPP(c_Set_Oinsert(_1278058), _1278062), c_Orderings_Obot__class_Obot(tc_fun(_1278058, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278058, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1278058, _1278060) = _1278062)], (26244 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278058, tc_HOL_Obool)), _1278060), hAPP(hAPP(c_Set_Oinsert(_1278058), _1278062), c_Orderings_Obot__class_Obot(tc_fun(_1278058, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1278058, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1278058, _1278060) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1278058), _1278062), c_Big__Operators_Olinorder__class_OMax(_1278058, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1278058, tc_HOL_Obool)), _1278060), hAPP(hAPP(c_Set_Oinsert(_1278058), _1278062), c_Orderings_Obot__class_Obot(tc_fun(_1278058, tc_HOL_Obool)))))))]]], (26250 ^ _782435) ^ [_1278564, _1278566, _1278568, _1278570] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1278564, tc_Nat_Onat), _1278566), _1278568) = hAPP(c_Nat_OSuc, _1278570), 26254 ^ _782435 : [(26255 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1278564), 26253 ^ [_1278564, _1278566, _1278568, _1278570]), _1278568)))], (26257 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1278566, 26253 ^ [_1278564, _1278566, _1278568, _1278570]))))]]], (26259 ^ _782435) ^ [_1278746, _1278748, _1278750, _1278752, _1278754, _1278756] : [c_Fun_Oinj__on(_1278746, _1278748, _1278750, _1278752), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278748, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278746, _1278748, _1278750), _1278752)), _1278754)), c_Fun_Oinj__on(_1278748, _1278746, _1278756, _1278754), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1278746, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1278748, _1278746, _1278756), _1278754)), _1278752)), -(c_Fun_Obij__betw(_1278746, _1278748, 26274 ^ [_1278746, _1278748, _1278750, _1278752, _1278754, _1278756], _1278752, _1278754))], (26278 ^ _782435) ^ [_1279113, _1279115, _1279117, _1279119, _1279121] : [class_Groups_Ocomm__monoid__mult(_1279113), hBOOL(hAPP(c_Finite__Set_Ofinite(_1279115), _1279117)), hBOOL(hAPP(hAPP(c_member(_1279115), _1279119), _1279117)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279115, _1279113), _1279121), _1279117) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1279113), hAPP(_1279121, _1279119)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279115, _1279113), _1279121), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1279115, tc_HOL_Obool)), _1279117), hAPP(hAPP(c_Set_Oinsert(_1279115), _1279119), c_Orderings_Obot__class_Obot(tc_fun(_1279115, tc_HOL_Obool)))))))], (26292 ^ _782435) ^ [_1279438, _1279440, _1279442, _1279444, _1279446] : [class_Orderings_Olinorder(_1279438), class_Orderings_Olinorder(_1279440), c_Orderings_Oorder__class_Omono(_1279440, _1279438, _1279442), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279438), hAPP(_1279442, _1279444)), hAPP(_1279442, _1279446)) = hAPP(_1279442, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1279440), _1279444), _1279446)))], (26306 ^ _782435) ^ [_1279687, _1279689, _1279691, _1279693, _1279695] : [class_Orderings_Olinorder(_1279687), class_Orderings_Olinorder(_1279689), c_Orderings_Oorder__class_Omono(_1279689, _1279687, _1279691), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279687), hAPP(_1279691, _1279693)), hAPP(_1279691, _1279695)) = hAPP(_1279691, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1279689), _1279693), _1279695)))], (26320 ^ _782435) ^ [_1279936, _1279938, _1279940, _1279942] : [-(hAPP(c_Int_Oring__1__class_Oof__int(_1279936), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279938, tc_Int_Oint), _1279940), _1279942)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1279938, _1279936), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1279936, _1279938), c_Int_Oring__1__class_Oof__int(_1279936)), _1279940)), _1279942)), class_Groups_Ocomm__monoid__mult(_1279936), class_Rings_Oring__1(_1279936)], (26330 ^ _782435) ^ [_1280139, _1280141, _1280143] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280139, tc_Nat_Onat), _1280141), _1280143) = hAPP(c_Int_Onat, hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1280139, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1280139), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1280141)), _1280143)))], (26332 ^ _782435) ^ [_1280197, _1280199, _1280201, _1280203] : [class_Orderings_Olinorder(_1280197), 26335 ^ _782435 : [(26346 ^ _782435) ^ [] : [26347 ^ _782435 : [(26348 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), _1280201))], (26350 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), _1280203))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280197), _1280201), _1280203))))], (26336 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280197), _1280201), _1280203))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), _1280201))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280197), _1280199), _1280203)))]]], (26354 ^ _782435) ^ [_1280546, _1280548, _1280550, _1280552] : [class_Orderings_Olinorder(_1280546), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280546), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280546), _1280548), _1280550)), _1280552)), 26361 ^ _782435 : [(26362 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280546), _1280548), _1280552)))], (26364 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280546), _1280550), _1280552)))]]], (26366 ^ _782435) ^ [_1280769, _1280771, _1280773, _1280775, _1280777] : [class_Orderings_Olinorder(_1280769), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280769), _1280771), _1280773)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280769), _1280775), _1280777)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1280769), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280769), _1280771), _1280775)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1280769), _1280773), _1280777))))], (26380 ^ _782435) ^ [_1281040, _1281042, _1281044, _1281046] : [class_Orderings_Olinorder(_1281040), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281040), _1281042), _1281044)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281040), _1281046), _1281044)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281040), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281040), _1281042), _1281046)), _1281044)))], (26394 ^ _782435) ^ [_1281289, _1281291, _1281293, _1281295] : [class_Orderings_Olinorder(_1281289), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281289), _1281291), _1281293)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281289), _1281295), _1281293)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281289), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281289), _1281291), _1281295)), _1281293)))], (26408 ^ _782435) ^ [_1281538, _1281540, _1281542] : [class_Orderings_Olinorder(_1281538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281538), _1281540), _1281542)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281538), _1281542), _1281540) = _1281542)], (26418 ^ _782435) ^ [_1281699, _1281701, _1281703] : [class_Orderings_Olinorder(_1281699), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281699), _1281701), _1281703)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281699), _1281701), _1281703) = _1281703)], (26428 ^ _782435) ^ [_1281860, _1281862, _1281864, _1281866] : [class_Orderings_Olinorder(_1281860), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281860), _1281862), _1281864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1281860), _1281862), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1281860), _1281866), _1281864))))], (26438 ^ _782435) ^ [_1282039, _1282041, _1282043, _1282045] : [class_Orderings_Olinorder(_1282039), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282039), _1282041), _1282043)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282039), _1282041), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282039), _1282043), _1282045))))], (26448 ^ _782435) ^ [_1282218, _1282220, _1282222, _1282224] : [class_Orderings_Olinorder(_1282218), 26451 ^ _782435 : [(26452 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282218), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282218), _1282220), _1282222)), _1282224)), 26455 ^ _782435 : [(26456 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282218), _1282220), _1282224)))], (26458 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282218), _1282222), _1282224)))]]], (26460 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282218), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282218), _1282220), _1282222)), _1282224))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282218), _1282220), _1282224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282218), _1282222), _1282224))]]], (26470 ^ _782435) ^ [_1282598, _1282600, _1282602] : [class_Orderings_Olinorder(_1282598), 26473 ^ _782435 : [(26474 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282598), _1282600), _1282602)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282598), _1282600), _1282602) = _1282602)], (26480 ^ _782435) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282598), _1282600), _1282602) = _1282602, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282598), _1282600), _1282602)))]]], (26486 ^ _782435) ^ [_1282854, _1282856, _1282858] : [class_Orderings_Olinorder(_1282854), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282854), _1282856), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282854), _1282858), _1282856))))], (26492 ^ _782435) ^ [_1282961, _1282963, _1282965] : [class_Orderings_Olinorder(_1282961), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1282961), _1282963), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1282961), _1282963), _1282965))))], (26498 ^ _782435) ^ [_1283068, _1283070, _1283072, _1283074] : [class_Orderings_Olinorder(_1283068), 26501 ^ _782435 : [(26512 ^ _782435) ^ [] : [26513 ^ _782435 : [(26514 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283068), _1283070), _1283074))], (26516 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283068), _1283072), _1283074))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283068), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283068), _1283070), _1283072)), _1283074)))], (26502 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283068), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283068), _1283070), _1283072)), _1283074)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283068), _1283070), _1283074))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283068), _1283072), _1283074)))]]], (26520 ^ _782435) ^ [_1283417, _1283419, _1283421, _1283423] : [class_Orderings_Olinorder(_1283417), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283417), _1283419), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283417), _1283421), _1283423))), 26527 ^ _782435 : [(26528 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283417), _1283419), _1283421)))], (26530 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283417), _1283419), _1283423)))]]], (26532 ^ _782435) ^ [_1283640, _1283642, _1283644, _1283646, _1283648] : [class_Orderings_Olinorder(_1283640), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283640), _1283642), _1283644)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283640), _1283646), _1283648)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283640), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283640), _1283642), _1283646)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283640), _1283644), _1283648))))], (26546 ^ _782435) ^ [_1283911, _1283913, _1283915, _1283917] : [class_Orderings_Olinorder(_1283911), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283911), _1283913), _1283915)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283911), _1283913), _1283917)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1283911), _1283913), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1283911), _1283915), _1283917))))], (26560 ^ _782435) ^ [_1284160, _1284162, _1284164, _1284166] : [class_Orderings_Olinorder(_1284160), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284160), _1284162), _1284164)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284160), _1284162), _1284166)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284160), _1284162), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284160), _1284164), _1284166))))], (26574 ^ _782435) ^ [_1284409, _1284411, _1284413] : [class_Orderings_Olinorder(_1284409), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284409), _1284411), _1284413)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284409), _1284413), _1284411) = _1284411)], (26584 ^ _782435) ^ [_1284570, _1284572, _1284574] : [class_Orderings_Olinorder(_1284570), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284570), _1284572), _1284574)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284570), _1284572), _1284574) = _1284572)], (26594 ^ _782435) ^ [_1284731, _1284733, _1284735, _1284737] : [class_Orderings_Olinorder(_1284731), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284731), _1284733), _1284735)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284731), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284731), _1284737), _1284733)), _1284735)))], (26604 ^ _782435) ^ [_1284910, _1284912, _1284914, _1284916] : [class_Orderings_Olinorder(_1284910), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284910), _1284912), _1284914)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1284910), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1284910), _1284912), _1284916)), _1284914)))], (26614 ^ _782435) ^ [_1285089, _1285091, _1285093, _1285095] : [class_Orderings_Olinorder(_1285089), 26617 ^ _782435 : [(26618 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285089), _1285091), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285089), _1285093), _1285095))), 26621 ^ _782435 : [(26622 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285089), _1285091), _1285093)))], (26624 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285089), _1285091), _1285095)))]]], (26626 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285089), _1285091), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285089), _1285093), _1285095)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285089), _1285091), _1285093)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285089), _1285091), _1285095))]]], (26636 ^ _782435) ^ [_1285469, _1285471, _1285473] : [class_Orderings_Olinorder(_1285469), 26639 ^ _782435 : [(26640 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285469), _1285471), _1285473)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285469), _1285471), _1285473) = _1285471)], (26646 ^ _782435) ^ [] : [hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285469), _1285471), _1285473) = _1285471, -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285469), _1285471), _1285473)))]]], (26652 ^ _782435) ^ [_1285725, _1285727, _1285729] : [class_Orderings_Olinorder(_1285725), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285725), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285725), _1285727), _1285729)), _1285729)))], (26658 ^ _782435) ^ [_1285832, _1285834, _1285836] : [class_Orderings_Olinorder(_1285832), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1285832), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1285832), _1285834), _1285836)), _1285834)))], (26664 ^ _782435) ^ [_1285939, _1285941, _1285943, _1285945] : [class_Orderings_Olinorder(_1285939), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285939), _1285941), _1285943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1285939), _1285941), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1285939), _1285945), _1285943))))], (26674 ^ _782435) ^ [_1286118, _1286120, _1286122, _1286124] : [class_Orderings_Olinorder(_1286118), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286118), _1286120), _1286122)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286118), _1286120), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286118), _1286122), _1286124))))], (26684 ^ _782435) ^ [_1286297, _1286299, _1286301, _1286303] : [class_Orderings_Olinorder(_1286297), 26687 ^ _782435 : [(26688 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286297), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286297), _1286299), _1286301)), _1286303)), 26691 ^ _782435 : [(26692 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286297), _1286299), _1286303)))], (26694 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286297), _1286301), _1286303)))]]], (26696 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286297), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286297), _1286299), _1286301)), _1286303))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286297), _1286299), _1286303)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286297), _1286301), _1286303))]]], (26706 ^ _782435) ^ [_1286677, _1286679, _1286681, _1286683] : [class_Orderings_Olinorder(_1286677), 26709 ^ _782435 : [(26720 ^ _782435) ^ [] : [26721 ^ _782435 : [(26722 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286677), _1286679), _1286681))], (26724 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286677), _1286679), _1286683))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286677), _1286679), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286677), _1286681), _1286683))))], (26710 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286677), _1286679), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1286677), _1286681), _1286683))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286677), _1286679), _1286681))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1286677), _1286679), _1286683)))]]], (26728 ^ _782435) ^ [_1287026, _1287028, _1287030, _1287032] : [class_Orderings_Olinorder(_1287026), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287026), _1287028), _1287030)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287026), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287026), _1287032), _1287028)), _1287030)))], (26738 ^ _782435) ^ [_1287205, _1287207, _1287209, _1287211] : [class_Orderings_Olinorder(_1287205), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287205), _1287207), _1287209)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287205), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287205), _1287207), _1287211)), _1287209)))], (26748 ^ _782435) ^ [_1287384, _1287386, _1287388, _1287390] : [class_Orderings_Olinorder(_1287384), 26751 ^ _782435 : [(26762 ^ _782435) ^ [] : [26763 ^ _782435 : [(26764 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287384), _1287386), _1287390))], (26766 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287384), _1287388), _1287390))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287384), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287384), _1287386), _1287388)), _1287390)))], (26752 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287384), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287384), _1287386), _1287388)), _1287390)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287384), _1287386), _1287390))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287384), _1287388), _1287390)))]]], (26770 ^ _782435) ^ [_1287733, _1287735, _1287737, _1287739] : [class_Orderings_Olinorder(_1287733), 26773 ^ _782435 : [(26774 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287733), _1287735), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287733), _1287737), _1287739))), 26777 ^ _782435 : [(26778 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287733), _1287735), _1287737)))], (26780 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287733), _1287735), _1287739)))]]], (26782 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287733), _1287735), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1287733), _1287737), _1287739)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287733), _1287735), _1287737)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1287733), _1287735), _1287739))]]], (26792 ^ _782435) ^ [_1288113, _1288115, _1288117, _1288119] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1288113), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288113), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288113), _1288115), _1288117)), _1288119) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288113), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288113), _1288115), _1288119)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288113), _1288117), _1288119)))], (26798 ^ _782435) ^ [_1288272, _1288274, _1288276, _1288278] : [class_Groups_Oordered__ab__semigroup__add__imp__le(_1288272), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288272), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288272), _1288274), _1288276)), _1288278) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288272), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288272), _1288274), _1288278)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1288272), _1288276), _1288278)))], (26804 ^ _782435) ^ [_1288431, _1288433, _1288435, _1288437] : [class_Groups_Oordered__ab__group__add(_1288431), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288431), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288431), _1288433), _1288435)), _1288437) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288431), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288431), _1288433), _1288437)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288431), _1288435), _1288437)))], (26810 ^ _782435) ^ [_1288590, _1288592, _1288594, _1288596] : [class_Groups_Oordered__ab__group__add(_1288590), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288590), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288590), _1288592), _1288594)), _1288596) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288590), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288590), _1288592), _1288596)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1288590), _1288594), _1288596)))], (26816 ^ _782435) ^ [_1288749] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288749) = _1288749)], (26818 ^ _782435) ^ [_1288775] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1288775), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1288775)], (26820 ^ _782435) ^ [_1288804] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1288804) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26822 ^ _782435) ^ [_1288830] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1288830), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (26824 ^ _782435) ^ [_1288859, _1288861] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288859)), hAPP(c_Nat_OSuc, _1288861)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1288859), _1288861)))], (26826 ^ _782435) ^ [_1288905, _1288907] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1288905)), hAPP(c_Nat_OSuc, _1288907)) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1288905), _1288907)))], (26828 ^ _782435) ^ [_1288951, _1288953, _1288955, _1288957] : [class_Orderings_Olinorder(_1288951), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1288951), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288951), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288951), _1288953), _1288955)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288951), _1288953), _1288957))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1288951), _1288953), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1288951), _1288955), _1288957)))))], (26834 ^ _782435) ^ [_1289124, _1289126, _1289128, _1289130] : [class_Orderings_Olinorder(_1289124), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1289124), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289124), _1289126), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289124), _1289128), _1289130))), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289124), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289124), _1289126), _1289128)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289124), _1289126), _1289130)))))], (26840 ^ _782435) ^ [_1289297, _1289299] : [class_Orderings_Olinorder(_1289297), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289297), _1289299), _1289299) = _1289299)], (26846 ^ _782435) ^ [_1289388, _1289390] : [class_Orderings_Olinorder(_1289388), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289388), _1289390), _1289390) = _1289390)], (26852 ^ _782435) ^ [_1289479, _1289481] : [class_Orderings_Olinorder(_1289479), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289479), _1289481), _1289481) = _1289481)], (26858 ^ _782435) ^ [_1289570, _1289572] : [class_Orderings_Olinorder(_1289570), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289570), _1289572), _1289572) = _1289572)], (26864 ^ _782435) ^ [_1289661, _1289663, _1289665] : [class_Orderings_Olinorder(_1289661), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289661), _1289663), _1289665) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289661), _1289665), _1289663))], (26870 ^ _782435) ^ [_1289770, _1289772, _1289774] : [class_Orderings_Olinorder(_1289770), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289770), _1289772), _1289774) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1289770), _1289774), _1289772))], (26876 ^ _782435) ^ [_1289879, _1289881, _1289883] : [class_Orderings_Olinorder(_1289879), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289879), _1289881), _1289883) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289879), _1289883), _1289881))], (26882 ^ _782435) ^ [_1289988, _1289990, _1289992] : [class_Orderings_Olinorder(_1289988), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289988), _1289990), _1289992) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1289988), _1289992), _1289990))], (26888 ^ _782435) ^ [_1290097, _1290099, _1290101] : [class_Orderings_Olinorder(_1290097), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290097), _1290099), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290097), _1290099), _1290101)) = _1290099)], (26894 ^ _782435) ^ [_1290206, _1290208, _1290210] : [class_Orderings_Olinorder(_1290206), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290206), _1290208), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290206), _1290208), _1290210)) = _1290208)], (26900 ^ _782435) ^ [_1290315, _1290317, _1290319] : [class_Orderings_Olinorder(_1290315), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290315), _1290317), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290315), _1290317), _1290319)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290315), _1290317), _1290319))], (26906 ^ _782435) ^ [_1290440, _1290442, _1290444] : [class_Orderings_Olinorder(_1290440), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290440), _1290442), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290440), _1290442), _1290444)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290440), _1290442), _1290444))], (26912 ^ _782435) ^ [_1290565, _1290567, _1290569] : [class_Orderings_Olinorder(_1290565), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290565), _1290567), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290565), _1290567), _1290569)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290565), _1290567), _1290569))], (26918 ^ _782435) ^ [_1290690, _1290692, _1290694] : [class_Orderings_Olinorder(_1290690), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290690), _1290692), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290690), _1290692), _1290694)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1290690), _1290692), _1290694))], (26924 ^ _782435) ^ [_1290815, _1290817, _1290819, _1290821] : [class_Orderings_Olinorder(_1290815), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290815), _1290817), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290815), _1290819), _1290821)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290815), _1290819), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290815), _1290817), _1290821)))], (26930 ^ _782435) ^ [_1290958, _1290960, _1290962, _1290964] : [class_Orderings_Olinorder(_1290958), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290958), _1290960), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290958), _1290962), _1290964)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290958), _1290962), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1290958), _1290960), _1290964)))], (26936 ^ _782435) ^ [_1291101, _1291103, _1291105, _1291107] : [class_Orderings_Olinorder(_1291101), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291101), _1291103), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291101), _1291105), _1291107)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291101), _1291105), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291101), _1291103), _1291107)))], (26942 ^ _782435) ^ [_1291244, _1291246, _1291248, _1291250] : [class_Orderings_Olinorder(_1291244), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291244), _1291246), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291244), _1291248), _1291250)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291244), _1291248), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291244), _1291246), _1291250)))], (26948 ^ _782435) ^ [_1291387, _1291389, _1291391, _1291393] : [class_Orderings_Olinorder(_1291387), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291387), _1291389), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291387), _1291391), _1291393)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291387), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291387), _1291389), _1291391)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291387), _1291389), _1291393)))], (26954 ^ _782435) ^ [_1291546, _1291548, _1291550, _1291552] : [class_Orderings_Olinorder(_1291546), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291546), _1291548), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291546), _1291550), _1291552)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291546), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291546), _1291548), _1291550)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291546), _1291548), _1291552)))], (26960 ^ _782435) ^ [_1291705, _1291707, _1291709, _1291711] : [class_Orderings_Olinorder(_1291705), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291705), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291705), _1291707), _1291709)), _1291711) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291705), _1291707), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291705), _1291709), _1291711)))], (26966 ^ _782435) ^ [_1291848, _1291850, _1291852, _1291854] : [class_Orderings_Olinorder(_1291848), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291848), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291848), _1291850), _1291852)), _1291854) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291848), _1291850), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1291848), _1291852), _1291854)))], (26972 ^ _782435) ^ [_1291991, _1291993, _1291995, _1291997] : [class_Orderings_Olinorder(_1291991), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291991), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291991), _1291993), _1291995)), _1291997) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291991), _1291993), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1291991), _1291995), _1291997)))], (26978 ^ _782435) ^ [_1292134, _1292136, _1292138, _1292140] : [class_Orderings_Olinorder(_1292134), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292134), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292134), _1292136), _1292138)), _1292140) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292134), _1292136), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292134), _1292138), _1292140)))], (26984 ^ _782435) ^ [_1292277, _1292279, _1292281, _1292283] : [class_Orderings_Olinorder(_1292277), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292277), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292277), _1292279), _1292281)), _1292283) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292277), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292277), _1292279), _1292283)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292277), _1292281), _1292283)))], (26990 ^ _782435) ^ [_1292436, _1292438, _1292440, _1292442] : [class_Orderings_Olinorder(_1292436), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292436), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292436), _1292438), _1292440)), _1292442) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292436), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292436), _1292438), _1292442)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292436), _1292440), _1292442)))], (26996 ^ _782435) ^ [_1292595, _1292597, _1292599] : [class_Groups_Olinordered__ab__group__add(_1292595), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292595), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292595), _1292597), _1292599)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292595), hAPP(c_Groups_Ouminus__class_Ouminus(_1292595), _1292597)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292595), _1292599)))], (27002 ^ _782435) ^ [_1292734, _1292736, _1292738] : [class_Groups_Olinordered__ab__group__add(_1292734), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1292734), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1292734), _1292736), _1292738)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1292734), hAPP(c_Groups_Ouminus__class_Ouminus(_1292734), _1292736)), hAPP(c_Groups_Ouminus__class_Ouminus(_1292734), _1292738)))], (27008 ^ _782435) ^ [_1292873, _1292875, _1292877, _1292879] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1292873), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292875, tc_Nat_Onat), _1292877), _1292879)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1292875, _1292873), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1292873, _1292875), c_Nat_Osemiring__1__class_Oof__nat(_1292873)), _1292877)), _1292879)), class_Groups_Ocomm__monoid__mult(_1292873), class_Rings_Osemiring__1(_1292873)], (27018 ^ _782435) ^ [_1293076, _1293078, _1293080] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293076, tc_Nat_Onat), _1293078), _1293080)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1293076, tc_Int_Oint), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Int_Oint, _1293076), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1293078)), _1293080))], (27020 ^ _782435) ^ [_1293134, _1293136, _1293138] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1293134), _1293136)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1293138), _1293136)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1293134), _1293138)), _1293136))], (27022 ^ _782435) ^ [_1293191, _1293193, _1293195, _1293197, _1293199] : [class_Orderings_Olinorder(_1293191), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293191, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293191, _1293193), _1293195)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293191, _1293197), _1293199)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1293191, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293191), _1293193), _1293197)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293191), _1293195), _1293199)))], (27028 ^ _782435) ^ [_1293362, _1293364, _1293366, _1293368, _1293370] : [class_Orderings_Olinorder(_1293362), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293362, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1293362, _1293364, _1293366)), c_SetInterval_Oord__class_OatLeastAtMost(_1293362, _1293368, _1293370)) = c_SetInterval_Oord__class_OatLeastAtMost(_1293362, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293362), _1293364), _1293368), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293362), _1293366), _1293370)))], (27034 ^ _782435) ^ [_1293521, _1293523, _1293525, _1293527, _1293529] : [class_Orderings_Olinorder(_1293521), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293521, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293521, _1293523, _1293525)), c_SetInterval_Oord__class_OgreaterThanAtMost(_1293521, _1293527, _1293529)) = c_SetInterval_Oord__class_OgreaterThanAtMost(_1293521, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293521), _1293523), _1293527), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293521), _1293525), _1293529)))], (27040 ^ _782435) ^ [_1293680] : [-(c_Lattices_Osemilattice__inf__class_Oinf(_1293680) = c_Orderings_Oord__class_Omin(_1293680)), class_Lattices_Osemilattice__inf(_1293680), class_Orderings_Olinorder(_1293680)], (27050 ^ _782435) ^ [_1293809] : [-(c_Lattices_Osemilattice__sup__class_Osup(_1293809) = c_Orderings_Oord__class_Omax(_1293809)), class_Lattices_Osemilattice__sup(_1293809), class_Orderings_Olinorder(_1293809)], (27060 ^ _782435) ^ [_1293938, _1293940, _1293942, _1293944, _1293946] : [class_Orderings_Olinorder(_1293938), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1293938, tc_HOL_Obool)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1293938, _1293940, _1293942)), c_SetInterval_Oord__class_OgreaterThanLessThan(_1293938, _1293944, _1293946)) = c_SetInterval_Oord__class_OgreaterThanLessThan(_1293938, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1293938), _1293940), _1293944), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1293938), _1293942), _1293946)))], (27066 ^ _782435) ^ [_1294097, _1294099, _1294101, _1294103, _1294105] : [class_Groups_Ocomm__monoid__mult(_1294097), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294099, _1294097), hAPP(hAPP(c_COMBS(_1294099, _1294097, _1294097), hAPP(hAPP(c_COMBB(_1294097, tc_fun(_1294097, _1294097), _1294099), c_Groups_Otimes__class_Otimes(_1294097)), _1294101)), _1294103)), _1294105) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1294097), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294099, _1294097), _1294101), _1294105)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294099, _1294097), _1294103), _1294105)))], (27072 ^ _782435) ^ [_1294298, _1294300, _1294302] : [class_Groups_Ocomm__monoid__mult(_1294298), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294300, _1294298), hAPP(c_COMBK(_1294298, _1294300), c_Groups_Oone__class_Oone(_1294298))), _1294302) = c_Groups_Oone__class_Oone(_1294298))], (27078 ^ _782435) ^ [_1294413, _1294415, _1294417, _1294419] : [class_Fields_Olinordered__field(_1294413), -(hAPP(c_Groups_Oabs__class_Oabs(_1294413), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294415, _1294413), _1294417), _1294419)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294415, _1294413), hAPP(hAPP(c_COMBB(_1294413, _1294413, _1294415), c_Groups_Oabs__class_Oabs(_1294413)), _1294417)), _1294419))], (27084 ^ _782435) ^ [_1294562] : [class_Orderings_Olinorder(_1294562), -(c_Finite__Set_Ofun__left__comm__idem(_1294562, _1294562, c_Orderings_Oord__class_Omax(_1294562)))], (27090 ^ _782435) ^ [_1294641] : [class_Orderings_Olinorder(_1294641), -(c_Finite__Set_Ofun__left__comm__idem(_1294641, _1294641, c_Orderings_Oord__class_Omin(_1294641)))], (27096 ^ _782435) ^ [_1294720, _1294722, _1294724] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1294720), _1294722), _1294724) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1294720), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1294720, tc_Int_Oint), _1294722), c_Int_Onat)), hAPP(c_Set_Oimage(tc_Nat_Onat, tc_Int_Oint, c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1294724))), class_Groups_Ocomm__monoid__add(_1294720), class_Groups_Ocomm__monoid__mult(_1294720)], (27106 ^ _782435) ^ [_1294911, _1294913, _1294915, _1294917] : [class_Rings_Ocomm__semiring__1(_1294911), hBOOL(hAPP(c_Finite__Set_Ofinite(_1294913), _1294915)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1294913, _1294911), _1294917), _1294915) = c_Groups_Ozero__class_Ozero(_1294911)), 27115 ^ _782435 : [(27116 ^ _782435) ^ [_1295092] : [hBOOL(hAPP(hAPP(c_member(_1294913), _1295092), _1294915)), hAPP(_1294917, _1295092) = c_Groups_Ozero__class_Ozero(_1294911)]]], (27124 ^ _782435) ^ [_1295241, _1295243, _1295245, _1295247] : [class_Rings_Ocomm__semiring__1(_1295241), class_Rings_Ono__zero__divisors(_1295241), hBOOL(hAPP(c_Finite__Set_Ofinite(_1295243), _1295245)), 27135 ^ _782435 : [(27136 ^ _782435) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295243, _1295241), _1295247), _1295245) = c_Groups_Ozero__class_Ozero(_1295241), 27140 ^ _782435 : [(27141 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1295243), 27139 ^ [_1295241, _1295243, _1295245, _1295247]), _1295245)))], (27143 ^ _782435) ^ [] : [-(hAPP(_1295247, 27139 ^ [_1295241, _1295243, _1295245, _1295247]) = c_Groups_Ozero__class_Ozero(_1295241))]]], (27145 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295243, _1295241), _1295247), _1295245) = c_Groups_Ozero__class_Ozero(_1295241)), 27146 ^ _782435 : [(27147 ^ _782435) ^ [_1295619] : [hBOOL(hAPP(hAPP(c_member(_1295243), _1295619), _1295245)), hAPP(_1295247, _1295619) = c_Groups_Ozero__class_Ozero(_1295241)]]]]], (27155 ^ _782435) ^ [_1295774, _1295776, _1295778] : [class_Groups_Ocomm__monoid__mult(_1295774), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295776, _1295774), _1295778), c_Orderings_Obot__class_Obot(tc_fun(_1295776, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1295774))], (27161 ^ _782435) ^ [_1295883, _1295885, _1295887] : [class_Groups_Ocomm__monoid__mult(_1295883), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295885, _1295883), _1295887), c_Orderings_Obot__class_Obot(tc_fun(_1295885, tc_HOL_Obool))) = c_Groups_Oone__class_Oone(_1295883))], (27167 ^ _782435) ^ [_1295992, _1295994, _1295996, _1295998] : [class_Groups_Ocomm__monoid__mult(_1295992), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1295994), _1295996))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1295994, _1295992), _1295998), _1295996) = c_Groups_Oone__class_Oone(_1295992))], (27177 ^ _782435) ^ [_1296116, _1296118, _1296120, _1296122] : [class_Groups_Ocomm__monoid__mult(_1296116), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1296118), _1296120))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296118, _1296116), _1296122), _1296120) = c_Groups_Oone__class_Oone(_1296116))], (27187 ^ _782435) ^ [_1296240, _1296242, _1296244] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1296240), _1296242)), 27190 ^ _782435 : [(27201 ^ _782435) ^ [] : [27203 ^ _782435 : [(27204 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1296240), 27202 ^ [_1296240, _1296242, _1296244]), _1296242)))], (27206 ^ _782435) ^ [] : [hAPP(_1296244, 27202 ^ [_1296240, _1296242, _1296244]) = c_Groups_Oone__class_Oone(tc_Nat_Onat)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296240, tc_Nat_Onat), _1296244), _1296242) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (27191 ^ _782435) ^ [] : [hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296240, tc_Nat_Onat), _1296244), _1296242) = c_Groups_Oone__class_Oone(tc_Nat_Onat), 27194 ^ _782435 : [(27195 ^ _782435) ^ [_1296402] : [hBOOL(hAPP(hAPP(c_member(_1296240), _1296402), _1296242)), -(hAPP(_1296244, _1296402) = c_Groups_Oone__class_Oone(tc_Nat_Onat))]]]]], (27210 ^ _782435) ^ [_1296660, _1296662, _1296664] : [class_Groups_Ocomm__monoid__add(_1296660), class_Groups_Ocomm__monoid__mult(_1296660), c_Nat__Transfer_Onat__set(_1296662), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1296660), _1296664), _1296662) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat, _1296660), hAPP(hAPP(c_COMBB(tc_Int_Oint, _1296660, tc_Nat_Onat), _1296664), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))), hAPP(c_Set_Oimage(tc_Int_Oint, tc_Nat_Onat, c_Int_Onat), _1296662)))], (27224 ^ _782435) ^ [_1296905, _1296907] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1296905), _1296907)), _1296907) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1296905), _1296907))], (27226 ^ _782435) ^ [_1296948, _1296950, _1296952, _1296954, _1296956] : [class_Groups_Ocomm__monoid__mult(_1296948), hBOOL(hAPP(c_Finite__Set_Ofinite(_1296950), _1296952)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296950, _1296948), hAPP(hAPP(c_COMBS(_1296950, _1296948, _1296948), hAPP(hAPP(c_COMBB(_1296948, tc_fun(_1296948, _1296948), _1296950), c_Groups_Otimes__class_Otimes(_1296948)), _1296954)), _1296956)), _1296952) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1296948), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296950, _1296948), _1296954), _1296952)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1296950, _1296948), _1296956), _1296952)))], (27236 ^ _782435) ^ [_1297215, _1297217, _1297219] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1297215), _1297217)), 27239 ^ _782435 : [(27250 ^ _782435) ^ [] : [27252 ^ _782435 : [(27253 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1297215), 27251 ^ [_1297215, _1297217, _1297219]), _1297217)))], (27255 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1297219, 27251 ^ [_1297215, _1297217, _1297219])))]], -(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(_1297215, tc_Nat_Onat), _1297219), _1297217))))], (27240 ^ _782435) ^ [] : [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(_1297215, tc_Nat_Onat), _1297219), _1297217))), 27243 ^ _782435 : [(27244 ^ _782435) ^ [_1297383] : [hBOOL(hAPP(hAPP(c_member(_1297215), _1297383), _1297217)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1297219, _1297383))))]]]]], (27259 ^ _782435) ^ [_1297651, _1297653, _1297655, _1297657, _1297659, _1297661, _1297663, _1297665] : [class_Groups_Ocomm__monoid__mult(_1297651), c_Fun_Oinj__on(_1297653, _1297655, _1297657, _1297659), _1297661 = hAPP(c_Set_Oimage(_1297653, _1297655, _1297657), _1297659), _1297663 = hAPP(c_Fun_Ocomp(_1297655, _1297651, _1297653, _1297665), _1297657), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297655, _1297651), _1297665), _1297661) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1297653, _1297651), _1297663), _1297659))], (27277 ^ _782435) ^ [_1298000, _1298002, _1298004, _1298006, _1298008, _1298010] : [class_Groups_Ocomm__monoid__mult(_1298000), c_Fun_Oinj__on(_1298002, _1298004, _1298006, _1298008), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298004, _1298000), _1298010), hAPP(c_Set_Oimage(_1298002, _1298004, _1298006), _1298008)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298002, _1298000), hAPP(c_Fun_Ocomp(_1298004, _1298000, _1298002, _1298010), _1298006)), _1298008))], (27287 ^ _782435) ^ [_1298213, _1298215] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1298213)), _1298215) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298213), 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), _1298213)), _1298215))], (27289 ^ _782435) ^ [_1298261, _1298263] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), _1298261), hAPP(c_Nat_OSuc, _1298263)) = c_Nat_Onat_Onat__case(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1298263), 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)), _1298263)), _1298261))], (27291 ^ _782435) ^ [_1298309, _1298311, _1298313, _1298315, _1298317] : [class_Groups_Ocomm__monoid__mult(_1298309), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298311), _1298313)), 27298 ^ _782435 : [(27299 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298311), _1298315), _1298313)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298311, _1298309), hAPP(hAPP(c_COMBC(_1298311, _1298309, _1298309), hAPP(hAPP(c_COMBS(_1298311, _1298309, tc_fun(_1298309, _1298309)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298309, tc_fun(_1298309, _1298309)), _1298311), c_If(_1298309)), hAPP(c_fequal, _1298315))), _1298317)), c_Groups_Oone__class_Oone(_1298309))), _1298313) = hAPP(_1298317, _1298315))], (27305 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298311), _1298315), _1298313))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298311, _1298309), hAPP(hAPP(c_COMBC(_1298311, _1298309, _1298309), hAPP(hAPP(c_COMBS(_1298311, _1298309, tc_fun(_1298309, _1298309)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298309, tc_fun(_1298309, _1298309)), _1298311), c_If(_1298309)), hAPP(c_fequal, _1298315))), _1298317)), c_Groups_Oone__class_Oone(_1298309))), _1298313) = c_Groups_Oone__class_Oone(_1298309))]]], (27311 ^ _782435) ^ [_1298819, _1298821, _1298823, _1298825, _1298827] : [class_Groups_Ocomm__monoid__mult(_1298819), hBOOL(hAPP(c_Finite__Set_Ofinite(_1298821), _1298823)), 27318 ^ _782435 : [(27319 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1298821), _1298825), _1298823)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298821, _1298819), hAPP(hAPP(c_COMBC(_1298821, _1298819, _1298819), hAPP(hAPP(c_COMBS(_1298821, _1298819, tc_fun(_1298819, _1298819)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298819, tc_fun(_1298819, _1298819)), _1298821), c_If(_1298819)), hAPP(hAPP(c_COMBC(_1298821, _1298821, tc_HOL_Obool), c_fequal), _1298825))), _1298827)), c_Groups_Oone__class_Oone(_1298819))), _1298823) = hAPP(_1298827, _1298825))], (27325 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1298821), _1298825), _1298823))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1298821, _1298819), hAPP(hAPP(c_COMBC(_1298821, _1298819, _1298819), hAPP(hAPP(c_COMBS(_1298821, _1298819, tc_fun(_1298819, _1298819)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1298819, tc_fun(_1298819, _1298819)), _1298821), c_If(_1298819)), hAPP(hAPP(c_COMBC(_1298821, _1298821, tc_HOL_Obool), c_fequal), _1298825))), _1298827)), c_Groups_Oone__class_Oone(_1298819))), _1298823) = c_Groups_Oone__class_Oone(_1298819))]]], (27331 ^ _782435) ^ [_1299357, _1299359, _1299361] : [class_Orderings_Olinorder(_1299357), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299357), _1299359)), hBOOL(hAPP(hAPP(c_member(_1299357), _1299361), _1299359)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299357), _1299361), c_Big__Operators_Olinorder__class_OMax(_1299357, _1299359)) = c_Big__Operators_Olinorder__class_OMax(_1299357, _1299359))], (27345 ^ _782435) ^ [_1299592, _1299594, _1299596] : [class_Orderings_Olinorder(_1299592), hBOOL(hAPP(c_Finite__Set_Ofinite(_1299592), _1299594)), hBOOL(hAPP(hAPP(c_member(_1299592), _1299596), _1299594)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1299592), _1299596), c_Big__Operators_Olinorder__class_OMin(_1299592, _1299594)) = c_Big__Operators_Olinorder__class_OMin(_1299592, _1299594))], (27359 ^ _782435) ^ [_1299827, _1299829, _1299831, _1299833, _1299835] : [class_Lattices_Osemilattice__sup(_1299827), class_Orderings_Olinorder(_1299829), c_Orderings_Oorder__class_Omono(_1299829, _1299827, _1299831), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1299827), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1299827), hAPP(_1299831, _1299833)), hAPP(_1299831, _1299835))), hAPP(_1299831, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1299829), _1299833), _1299835)))))], (27373 ^ _782435) ^ [_1300090, _1300092, _1300094, _1300096, _1300098] : [class_Lattices_Osemilattice__inf(_1300090), class_Orderings_Olinorder(_1300092), c_Orderings_Oorder__class_Omono(_1300092, _1300090, _1300094), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1300090), hAPP(_1300094, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300092), _1300096), _1300098))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1300090), hAPP(_1300094, _1300096)), hAPP(_1300094, _1300098)))))], (27387 ^ _782435) ^ [_1300353, _1300355, _1300357, _1300359] : [class_Orderings_Olinorder(_1300353), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300353, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatMost(_1300353), _1300355)), c_SetInterval_Oord__class_OatLeastAtMost(_1300353, _1300357, _1300359)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300353, _1300357, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300353), _1300355), _1300359)))], (27393 ^ _782435) ^ [_1300496, _1300498, _1300500, _1300502] : [class_Orderings_Olinorder(_1300496), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300496, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300496, _1300498, _1300500)), hAPP(c_SetInterval_Oord__class_OatMost(_1300496), _1300502)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300496, _1300498, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1300496), _1300500), _1300502)))], (27399 ^ _782435) ^ [_1300639, _1300641, _1300643, _1300645] : [class_Orderings_Olinorder(_1300639), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300639, tc_HOL_Obool)), hAPP(c_SetInterval_Oord__class_OatLeast(_1300639), _1300641)), c_SetInterval_Oord__class_OatLeastAtMost(_1300639, _1300643, _1300645)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300639, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300639), _1300641), _1300643), _1300645))], (27405 ^ _782435) ^ [_1300782, _1300784, _1300786, _1300788] : [class_Orderings_Olinorder(_1300782), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1300782, tc_HOL_Obool)), c_SetInterval_Oord__class_OatLeastAtMost(_1300782, _1300784, _1300786)), hAPP(c_SetInterval_Oord__class_OatLeast(_1300782), _1300788)) = c_SetInterval_Oord__class_OatLeastAtMost(_1300782, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1300782), _1300784), _1300788), _1300786))], (27411 ^ _782435) ^ [_1300925, _1300927] : [class_Orderings_Olinorder(_1300925), hBOOL(hAPP(c_Finite__Set_Ofinite(_1300925), _1300927)), -(c_Big__Operators_Olinorder__class_OMax(_1300925, _1300927) = hAPP(c_Finite__Set_Ofold1(_1300925, c_Orderings_Oord__class_Omax(_1300925)), _1300927))], (27421 ^ _782435) ^ [_1301082, _1301084] : [class_Orderings_Olinorder(_1301082), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301082), _1301084)), -(c_Big__Operators_Olinorder__class_OMin(_1301082, _1301084) = hAPP(c_Finite__Set_Ofold1(_1301082, c_Orderings_Oord__class_Omin(_1301082)), _1301084))], (27431 ^ _782435) ^ [_1301239, _1301241, _1301243, _1301245, _1301247] : [class_Groups_Ocomm__monoid__mult(_1301239), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301241), _1301243)), -(hBOOL(hAPP(hAPP(c_member(_1301241), _1301245), _1301243))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301241, _1301239), _1301247), hAPP(hAPP(c_Set_Oinsert(_1301241), _1301245), _1301243)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301239), hAPP(_1301247, _1301245)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301241, _1301239), _1301247), _1301243)))], (27445 ^ _782435) ^ [_1301489, _1301491, _1301493, _1301495, _1301497] : [class_Groups_Ocomm__monoid__mult(_1301489), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301491), _1301493)), -(hBOOL(hAPP(hAPP(c_member(_1301491), _1301495), _1301493))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301491, _1301489), _1301497), hAPP(hAPP(c_Set_Oinsert(_1301491), _1301495), _1301493)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301489), hAPP(_1301497, _1301495)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301491, _1301489), _1301497), _1301493)))], (27459 ^ _782435) ^ [_1301739, _1301741, _1301743, _1301745, _1301747] : [class_Groups_Ocomm__monoid__mult(_1301739), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301741), _1301743)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1301741), _1301745)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301739), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301741, _1301739), _1301747), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1301741, tc_HOL_Obool)), _1301743), _1301745))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301741, _1301739), _1301747), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1301741, tc_HOL_Obool)), _1301743), _1301745))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1301739), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301741, _1301739), _1301747), _1301743)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1301741, _1301739), _1301747), _1301745)))], (27473 ^ _782435) ^ [_1302100, _1302102, _1302104, _1302106, _1302108] : [class_Groups_Ocomm__monoid__mult(_1302100), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302102), _1302104)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302102), _1302106)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302100), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302102, _1302100), _1302108), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1302102, tc_HOL_Obool)), _1302104), _1302106))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302102, _1302100), _1302108), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1302102, tc_HOL_Obool)), _1302104), _1302106))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1302100), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302102, _1302100), _1302108), _1302104)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302102, _1302100), _1302108), _1302106)))], (27487 ^ _782435) ^ [_1302461, _1302463, _1302465, _1302467, _1302469] : [class_Groups_Ocomm__monoid__mult(_1302461), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302463), _1302465)), c_Fun_Oinj__on(_1302463, _1302463, _1302467, _1302465), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302463, _1302461), _1302469), hAPP(c_Set_Oimage(_1302463, _1302463, _1302467), _1302465)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302463, _1302461), hAPP(c_Fun_Ocomp(_1302463, _1302461, _1302463, _1302469), _1302467)), _1302465))], (27501 ^ _782435) ^ [_1302736, _1302738, _1302740, _1302742] : [class_Groups_Ocomm__monoid__mult(_1302736), hBOOL(hAPP(c_Finite__Set_Ofinite(_1302738), _1302740)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302738, _1302736), _1302742), _1302740) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1302736, _1302738, c_Groups_Otimes__class_Otimes(_1302736)), _1302742), c_Groups_Oone__class_Oone(_1302736)), _1302740))], (27511 ^ _782435) ^ [_1302931, _1302933, _1302935, _1302937] : [class_Groups_Ocomm__monoid__mult(_1302931), 27514 ^ _782435 : [(27515 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1302933), _1302935)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302933, _1302931), _1302937), _1302935) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1302931, _1302933, c_Groups_Otimes__class_Otimes(_1302931)), _1302937), c_Groups_Oone__class_Oone(_1302931)), _1302935))], (27521 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1302933), _1302935))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1302933, _1302931), _1302937), _1302935) = c_Groups_Oone__class_Oone(_1302931))]]], (27527 ^ _782435) ^ [_1303203, _1303205] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1303203)), _1303205) = 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), _1303203)), _1303205))], (27529 ^ _782435) ^ [_1303248, _1303250] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1303248), hAPP(c_Nat_OSuc, _1303250)) = 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)), _1303250)), _1303248))], (27531 ^ _782435) ^ [_1303293, _1303295, _1303297] : [class_Orderings_Olinorder(_1303293), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303293), _1303295)), hBOOL(hAPP(hAPP(c_member(_1303293), _1303297), _1303295)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303293), hAPP(c_Finite__Set_Ofold1(_1303293, c_Orderings_Oord__class_Omin(_1303293)), _1303295)), _1303297)))], (27545 ^ _782435) ^ [_1303530, _1303532, _1303534] : [class_Orderings_Olinorder(_1303530), hBOOL(hAPP(c_Finite__Set_Ofinite(_1303530), _1303532)), -(_1303532 = c_Orderings_Obot__class_Obot(tc_fun(_1303530, tc_HOL_Obool))), 27556 ^ _782435 : [(27557 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303530), hAPP(c_Finite__Set_Ofold1(_1303530, c_Orderings_Oord__class_Omin(_1303530)), _1303532)), _1303534)), 27561 ^ _782435 : [(27562 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1303530), 27560 ^ [_1303530, _1303532, _1303534]), _1303532)))], (27564 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303530), 27560 ^ [_1303530, _1303532, _1303534]), _1303534)))]]], (27566 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303530), hAPP(c_Finite__Set_Ofold1(_1303530, c_Orderings_Oord__class_Omin(_1303530)), _1303532)), _1303534))), 27567 ^ _782435 : [(27568 ^ _782435) ^ [_1303919] : [hBOOL(hAPP(hAPP(c_member(_1303530), _1303919), _1303532)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1303530), _1303919), _1303534))]]]]], (27576 ^ _782435) ^ [_1304080, _1304082, _1304084] : [class_Orderings_Olinorder(_1304080), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304080), _1304082)), -(_1304082 = c_Orderings_Obot__class_Obot(tc_fun(_1304080, tc_HOL_Obool))), 27587 ^ _782435 : [(27598 ^ _782435) ^ [] : [27600 ^ _782435 : [(27601 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304080), 27599 ^ [_1304080, _1304082, _1304084]), _1304082)))], (27603 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304080), _1304084), 27599 ^ [_1304080, _1304082, _1304084]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304080), _1304084), hAPP(c_Finite__Set_Ofold1(_1304080, c_Orderings_Oord__class_Omin(_1304080)), _1304082))))], (27588 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304080), _1304084), hAPP(c_Finite__Set_Ofold1(_1304080, c_Orderings_Oord__class_Omin(_1304080)), _1304082))), 27591 ^ _782435 : [(27592 ^ _782435) ^ [_1304373] : [hBOOL(hAPP(hAPP(c_member(_1304080), _1304373), _1304082)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1304080), _1304084), _1304373)))]]]]], (27607 ^ _782435) ^ [_1304658, _1304660, _1304662] : [class_Orderings_Olinorder(_1304658), hBOOL(hAPP(c_Finite__Set_Ofinite(_1304658), _1304660)), -(_1304660 = c_Orderings_Obot__class_Obot(tc_fun(_1304658, tc_HOL_Obool))), 27618 ^ _782435 : [(27619 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304658), hAPP(c_Finite__Set_Ofold1(_1304658, c_Orderings_Oord__class_Omin(_1304658)), _1304660)), _1304662)), 27623 ^ _782435 : [(27624 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1304658), 27622 ^ [_1304658, _1304660, _1304662]), _1304660)))], (27626 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304658), 27622 ^ [_1304658, _1304660, _1304662]), _1304662)))]]], (27628 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304658), hAPP(c_Finite__Set_Ofold1(_1304658, c_Orderings_Oord__class_Omin(_1304658)), _1304660)), _1304662))), 27629 ^ _782435 : [(27630 ^ _782435) ^ [_1305047] : [hBOOL(hAPP(hAPP(c_member(_1304658), _1305047), _1304660)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1304658), _1305047), _1304662))]]]]], (27638 ^ _782435) ^ [_1305208, _1305210, _1305212] : [class_Orderings_Olinorder(_1305208), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305208), _1305210)), -(_1305210 = c_Orderings_Obot__class_Obot(tc_fun(_1305208, tc_HOL_Obool))), 27649 ^ _782435 : [(27660 ^ _782435) ^ [] : [27662 ^ _782435 : [(27663 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1305208), 27661 ^ [_1305208, _1305210, _1305212]), _1305210)))], (27665 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305208), _1305212), 27661 ^ [_1305208, _1305210, _1305212]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305208), _1305212), hAPP(c_Finite__Set_Ofold1(_1305208, c_Orderings_Oord__class_Omin(_1305208)), _1305210))))], (27650 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305208), _1305212), hAPP(c_Finite__Set_Ofold1(_1305208, c_Orderings_Oord__class_Omin(_1305208)), _1305210))), 27653 ^ _782435 : [(27654 ^ _782435) ^ [_1305501] : [hBOOL(hAPP(hAPP(c_member(_1305208), _1305501), _1305210)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1305208), _1305212), _1305501)))]]]]], (27669 ^ _782435) ^ [_1305786, _1305788, _1305790] : [class_Orderings_Olinorder(_1305786), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305786), _1305788)), -(_1305788 = c_Orderings_Obot__class_Obot(tc_fun(_1305786, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1305786, hAPP(hAPP(c_Set_Oinsert(_1305786), _1305790), _1305788)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1305786), _1305790), c_Big__Operators_Olinorder__class_OMax(_1305786, _1305788)))], (27683 ^ _782435) ^ [_1305994, _1305996, _1305998] : [class_Orderings_Olinorder(_1305994), hBOOL(hAPP(c_Finite__Set_Ofinite(_1305994), _1305996)), -(_1305996 = c_Orderings_Obot__class_Obot(tc_fun(_1305994, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1305994, hAPP(hAPP(c_Set_Oinsert(_1305994), _1305998), _1305996)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1305994), _1305998), c_Big__Operators_Olinorder__class_OMin(_1305994, _1305996)))], (27697 ^ _782435) ^ [_1306202, _1306204, _1306206] : [class_Orderings_Olinorder(_1306202), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306202), _1306204)), -(_1306206 = c_Orderings_Obot__class_Obot(tc_fun(_1306202, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306202, tc_HOL_Obool)), _1306206), _1306204)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306202), c_Big__Operators_Olinorder__class_OMax(_1306202, _1306206)), c_Big__Operators_Olinorder__class_OMax(_1306202, _1306204)) = c_Big__Operators_Olinorder__class_OMax(_1306202, _1306204))], (27715 ^ _782435) ^ [_1306516, _1306518, _1306520] : [class_Orderings_Olinorder(_1306516), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306516), _1306518)), -(_1306520 = c_Orderings_Obot__class_Obot(tc_fun(_1306516, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1306516, tc_HOL_Obool)), _1306520), _1306518)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1306516), c_Big__Operators_Olinorder__class_OMin(_1306516, _1306520)), c_Big__Operators_Olinorder__class_OMin(_1306516, _1306518)) = c_Big__Operators_Olinorder__class_OMin(_1306516, _1306518))], (27733 ^ _782435) ^ [_1306830, _1306832, _1306834] : [class_Orderings_Olinorder(_1306830), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306830), _1306832)), -(_1306832 = c_Orderings_Obot__class_Obot(tc_fun(_1306830, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1306830), _1306834)), -(_1306834 = c_Orderings_Obot__class_Obot(tc_fun(_1306830, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1306830, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1306830, tc_HOL_Obool)), _1306832), _1306834)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1306830), c_Big__Operators_Olinorder__class_OMax(_1306830, _1306832)), c_Big__Operators_Olinorder__class_OMax(_1306830, _1306834)))], (27755 ^ _782435) ^ [_1307179, _1307181, _1307183] : [class_Orderings_Olinorder(_1307179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307179), _1307181)), -(_1307181 = c_Orderings_Obot__class_Obot(tc_fun(_1307179, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307179), _1307183)), -(_1307183 = c_Orderings_Obot__class_Obot(tc_fun(_1307179, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1307179, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307179, tc_HOL_Obool)), _1307181), _1307183)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1307179), c_Big__Operators_Olinorder__class_OMin(_1307179, _1307181)), c_Big__Operators_Olinorder__class_OMin(_1307179, _1307183)))], (27777 ^ _782435) ^ [_1307528, _1307530, _1307532, _1307534, _1307536] : [class_Groups_Ocomm__monoid__mult(_1307528), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307530), _1307532)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307530, _1307528), _1307534), hAPP(hAPP(c_Set_Oinsert(_1307530), _1307536), _1307532)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307528), hAPP(_1307534, _1307536)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307530, _1307528), _1307534), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1307530, tc_HOL_Obool)), _1307532), hAPP(hAPP(c_Set_Oinsert(_1307530), _1307536), c_Orderings_Obot__class_Obot(tc_fun(_1307530, tc_HOL_Obool)))))))], (27787 ^ _782435) ^ [_1307797, _1307799, _1307801, _1307803, _1307805] : [class_Groups_Ocomm__monoid__mult(_1307797), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307799), _1307801)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1307799), _1307803)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1307799, tc_HOL_Obool)), _1307801), _1307803) = c_Orderings_Obot__class_Obot(tc_fun(_1307799, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307799, _1307797), _1307805), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1307799, tc_HOL_Obool)), _1307801), _1307803)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1307797), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307799, _1307797), _1307805), _1307801)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1307799, _1307797), _1307805), _1307803)))], (27805 ^ _782435) ^ [_1308192, _1308194, _1308196, _1308198, _1308200] : [class_Groups_Ocomm__monoid__mult(_1308192), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308194), _1308196)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308194), _1308198)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1308194, tc_HOL_Obool)), _1308196), _1308198) = c_Orderings_Obot__class_Obot(tc_fun(_1308194, tc_HOL_Obool)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308194, _1308192), _1308200), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1308194, tc_HOL_Obool)), _1308196), _1308198)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1308192), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308194, _1308192), _1308200), _1308196)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1308194, _1308192), _1308200), _1308198)))], (27823 ^ _782435) ^ [_1308587, _1308589, _1308591] : [class_Orderings_Olinorder(_1308587), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308587), _1308589)), -(hBOOL(hAPP(hAPP(c_member(_1308587), _1308591), _1308589))), -(_1308589 = c_Orderings_Obot__class_Obot(tc_fun(_1308587, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1308587, hAPP(hAPP(c_Set_Oinsert(_1308587), _1308591), _1308589)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1308587), _1308591), c_Big__Operators_Olinorder__class_OMax(_1308587, _1308589)))], (27841 ^ _782435) ^ [_1308824, _1308826, _1308828] : [class_Orderings_Olinorder(_1308824), hBOOL(hAPP(c_Finite__Set_Ofinite(_1308824), _1308826)), -(hBOOL(hAPP(hAPP(c_member(_1308824), _1308828), _1308826))), -(_1308826 = c_Orderings_Obot__class_Obot(tc_fun(_1308824, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1308824, hAPP(hAPP(c_Set_Oinsert(_1308824), _1308828), _1308826)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1308824), _1308828), c_Big__Operators_Olinorder__class_OMin(_1308824, _1308826)))], (27859 ^ _782435) ^ [_1309061, _1309063, _1309065] : [class_Orderings_Olinorder(_1309061), -(_1309063 = c_Orderings_Obot__class_Obot(tc_fun(_1309061, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1309061, tc_HOL_Obool)), _1309063), _1309065)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309061), _1309065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1309061), hAPP(c_Finite__Set_Ofold1(_1309061, c_Orderings_Oord__class_Omin(_1309061)), _1309065)), hAPP(c_Finite__Set_Ofold1(_1309061, c_Orderings_Oord__class_Omin(_1309061)), _1309063))))], (27877 ^ _782435) ^ [_1309387, _1309389, _1309391] : [class_Orderings_Olinorder(_1309387), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309387), _1309389)), 27884 ^ _782435 : [(27885 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309387, tc_HOL_Obool)), _1309389), hAPP(hAPP(c_Set_Oinsert(_1309387), _1309391), c_Orderings_Obot__class_Obot(tc_fun(_1309387, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309387, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1309387, hAPP(hAPP(c_Set_Oinsert(_1309387), _1309391), _1309389)) = _1309391)], (27891 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309387, tc_HOL_Obool)), _1309389), hAPP(hAPP(c_Set_Oinsert(_1309387), _1309391), c_Orderings_Obot__class_Obot(tc_fun(_1309387, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1309387, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMax(_1309387, hAPP(hAPP(c_Set_Oinsert(_1309387), _1309391), _1309389)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309387), _1309391), c_Big__Operators_Olinorder__class_OMax(_1309387, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1309387, tc_HOL_Obool)), _1309389), hAPP(hAPP(c_Set_Oinsert(_1309387), _1309391), c_Orderings_Obot__class_Obot(tc_fun(_1309387, tc_HOL_Obool)))))))]]], (27897 ^ _782435) ^ [_1309857, _1309859, _1309861] : [class_Orderings_Olinorder(_1309857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309857), _1309859)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1309857), _1309861)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309857, tc_HOL_Obool)), _1309859), _1309861) = c_Orderings_Obot__class_Obot(tc_fun(_1309857, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309857), c_Big__Operators_Olinorder__class_OMax(_1309857, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1309857, tc_HOL_Obool)), _1309859), _1309861))), c_Big__Operators_Olinorder__class_OMax(_1309857, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1309857, tc_HOL_Obool)), _1309859), _1309861))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1309857), c_Big__Operators_Olinorder__class_OMax(_1309857, _1309859)), c_Big__Operators_Olinorder__class_OMax(_1309857, _1309861)))], (27915 ^ _782435) ^ [_1310205, _1310207, _1310209] : [class_Orderings_Olinorder(_1310205), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310205), _1310207)), -(_1310207 = c_Orderings_Obot__class_Obot(tc_fun(_1310205, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310205), _1310209)), -(_1310209 = c_Orderings_Obot__class_Obot(tc_fun(_1310205, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1310205, tc_HOL_Obool)), _1310207), _1310209) = c_Orderings_Obot__class_Obot(tc_fun(_1310205, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMax(_1310205, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1310205, tc_HOL_Obool)), _1310207), _1310209)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1310205), c_Big__Operators_Olinorder__class_OMax(_1310205, _1310207)), c_Big__Operators_Olinorder__class_OMax(_1310205, _1310209)))], (27941 ^ _782435) ^ [_1310682, _1310684, _1310686] : [class_Orderings_Olinorder(_1310682), hBOOL(hAPP(c_Finite__Set_Ofinite(_1310682), _1310684)), 27948 ^ _782435 : [(27949 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310682, tc_HOL_Obool)), _1310684), hAPP(hAPP(c_Set_Oinsert(_1310682), _1310686), c_Orderings_Obot__class_Obot(tc_fun(_1310682, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310682, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1310682, hAPP(hAPP(c_Set_Oinsert(_1310682), _1310686), _1310684)) = _1310686)], (27955 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310682, tc_HOL_Obool)), _1310684), hAPP(hAPP(c_Set_Oinsert(_1310682), _1310686), c_Orderings_Obot__class_Obot(tc_fun(_1310682, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1310682, tc_HOL_Obool))), -(c_Big__Operators_Olinorder__class_OMin(_1310682, hAPP(hAPP(c_Set_Oinsert(_1310682), _1310686), _1310684)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1310682), _1310686), c_Big__Operators_Olinorder__class_OMin(_1310682, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1310682, tc_HOL_Obool)), _1310684), hAPP(hAPP(c_Set_Oinsert(_1310682), _1310686), c_Orderings_Obot__class_Obot(tc_fun(_1310682, tc_HOL_Obool)))))))]]], (27961 ^ _782435) ^ [_1311152, _1311154, _1311156] : [class_Orderings_Olinorder(_1311152), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311152), _1311154)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311152), _1311156)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311152, tc_HOL_Obool)), _1311154), _1311156) = c_Orderings_Obot__class_Obot(tc_fun(_1311152, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311152), c_Big__Operators_Olinorder__class_OMin(_1311152, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311152, tc_HOL_Obool)), _1311154), _1311156))), c_Big__Operators_Olinorder__class_OMin(_1311152, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311152, tc_HOL_Obool)), _1311154), _1311156))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311152), c_Big__Operators_Olinorder__class_OMin(_1311152, _1311154)), c_Big__Operators_Olinorder__class_OMin(_1311152, _1311156)))], (27979 ^ _782435) ^ [_1311500, _1311502, _1311504] : [class_Orderings_Olinorder(_1311500), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311500), _1311502)), -(_1311502 = c_Orderings_Obot__class_Obot(tc_fun(_1311500, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1311500), _1311504)), -(_1311504 = c_Orderings_Obot__class_Obot(tc_fun(_1311500, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1311500, tc_HOL_Obool)), _1311502), _1311504) = c_Orderings_Obot__class_Obot(tc_fun(_1311500, tc_HOL_Obool)), -(c_Big__Operators_Olinorder__class_OMin(_1311500, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1311500, tc_HOL_Obool)), _1311502), _1311504)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1311500), c_Big__Operators_Olinorder__class_OMin(_1311500, _1311502)), c_Big__Operators_Olinorder__class_OMin(_1311500, _1311504)))], (28005 ^ _782435) ^ [_1311977] : [class_Orderings_Olinorder(_1311977), -(c_Orderings_Oord_Omin(_1311977, hAPP(c_COMBC(_1311977, _1311977, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1311977))) = c_Orderings_Oord__class_Omax(_1311977))], (28011 ^ _782435) ^ [_1312078] : [class_Orderings_Olinorder(_1312078), -(c_Orderings_Oord_Omax(_1312078, hAPP(c_COMBC(_1312078, _1312078, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1312078))) = c_Orderings_Oord__class_Omin(_1312078))], (28017 ^ _782435) ^ [_1312179] : [class_Orderings_Oord(_1312179), -(c_Orderings_Oord__class_Omax(_1312179) = c_Orderings_Oord_Omax(_1312179, c_Orderings_Oord__class_Oless__eq(_1312179)))], (28023 ^ _782435) ^ [_1312266] : [class_Orderings_Oord(_1312266), -(c_Orderings_Oord__class_Omin(_1312266) = c_Orderings_Oord_Omin(_1312266, c_Orderings_Oord__class_Oless__eq(_1312266)))], (28029 ^ _782435) ^ [_1312353, _1312355, _1312357] : [class_Orderings_Olinorder(_1312353), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312353), _1312355)), -(_1312355 = c_Orderings_Obot__class_Obot(tc_fun(_1312353, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1312353), _1312357), c_Big__Operators_Olattice_OInf__fin(_1312353, c_Orderings_Oord__class_Omin(_1312353), _1312355)) = c_Big__Operators_Olattice_OInf__fin(_1312353, c_Orderings_Oord__class_Omin(_1312353), hAPP(c_Set_OCollect(_1312353), hAPP(hAPP(c_COMBB(tc_fun(_1312353, tc_HOL_Obool), tc_HOL_Obool, _1312353), c_HOL_OEx(_1312353)), hAPP(hAPP(c_COMBC(_1312353, tc_fun(_1312353, tc_HOL_Obool), tc_fun(_1312353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312353, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1312353, tc_HOL_Obool), tc_fun(_1312353, tc_HOL_Obool)), _1312353), c_COMBS(_1312353, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312353, tc_HOL_Obool), tc_fun(_1312353, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1312353), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1312353), c_fconj)), hAPP(hAPP(c_COMBC(_1312353, tc_fun(_1312353, _1312353), tc_fun(_1312353, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1312353, tc_HOL_Obool), tc_fun(tc_fun(_1312353, _1312353), tc_fun(_1312353, tc_HOL_Obool)), _1312353), c_COMBB(_1312353, tc_HOL_Obool, _1312353)), c_fequal)), hAPP(c_Orderings_Oord__class_Omax(_1312353), _1312357))))), hAPP(hAPP(c_COMBC(_1312353, tc_fun(_1312353, tc_HOL_Obool), tc_HOL_Obool), c_member(_1312353)), _1312355))))))], (28043 ^ _782435) ^ [] : [-(c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat))], (28045 ^ _782435) ^ [] : [-(c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat))], (28047 ^ _782435) ^ [_1312887, _1312889, _1312891] : [class_Orderings_Olinorder(_1312887), hBOOL(hAPP(c_Finite__Set_Ofinite(_1312887), _1312889)), hBOOL(hAPP(hAPP(c_member(_1312887), _1312891), _1312889)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1312887), _1312891), c_Big__Operators_Olattice_OInf__fin(_1312887, c_Orderings_Oord__class_Omin(_1312887), _1312889)) = c_Big__Operators_Olattice_OInf__fin(_1312887, c_Orderings_Oord__class_Omin(_1312887), _1312889))], (28061 ^ _782435) ^ [_1313134, _1313136] : [class_Orderings_Olinorder(_1313134), -(c_Big__Operators_Olattice_OInf__fin(_1313134, c_Orderings_Oord__class_Omin(_1313134), hAPP(hAPP(c_Set_Oinsert(_1313134), _1313136), c_Orderings_Obot__class_Obot(tc_fun(_1313134, tc_HOL_Obool)))) = _1313136)], (28067 ^ _782435) ^ [_1313247, _1313249] : [class_Orderings_Olinorder(_1313247), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313247), _1313249)), -(c_Big__Operators_Olattice_OInf__fin(_1313247, c_Orderings_Oord__class_Omin(_1313247), _1313249) = hAPP(c_Finite__Set_Ofold1(_1313247, c_Orderings_Oord__class_Omin(_1313247)), _1313249))], (28077 ^ _782435) ^ [_1313410, _1313412, _1313414] : [class_Orderings_Olinorder(_1313410), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313410), _1313412)), -(_1313412 = c_Orderings_Obot__class_Obot(tc_fun(_1313410, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1313410, c_Orderings_Oord__class_Omin(_1313410), hAPP(hAPP(c_Set_Oinsert(_1313410), _1313414), _1313412)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313410), _1313414), c_Big__Operators_Olattice_OInf__fin(_1313410, c_Orderings_Oord__class_Omin(_1313410), _1313412)))], (28091 ^ _782435) ^ [_1313630, _1313632, _1313634] : [class_Orderings_Olinorder(_1313630), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313630), _1313632)), -(_1313634 = c_Orderings_Obot__class_Obot(tc_fun(_1313630, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1313630, tc_HOL_Obool)), _1313634), _1313632)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1313630), c_Big__Operators_Olattice_OInf__fin(_1313630, c_Orderings_Oord__class_Omin(_1313630), _1313634)), c_Big__Operators_Olattice_OInf__fin(_1313630, c_Orderings_Oord__class_Omin(_1313630), _1313632)) = c_Big__Operators_Olattice_OInf__fin(_1313630, c_Orderings_Oord__class_Omin(_1313630), _1313632))], (28109 ^ _782435) ^ [_1313962, _1313964, _1313966] : [class_Orderings_Olinorder(_1313962), hBOOL(hAPP(c_Finite__Set_Ofinite(_1313962), _1313964)), hBOOL(hAPP(hAPP(c_member(_1313962), _1313966), _1313964)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1313962), _1313966), c_Big__Operators_Olattice_OInf__fin(_1313962, c_Orderings_Oord__class_Omin(_1313962), _1313964)) = _1313966)], (28123 ^ _782435) ^ [_1314197, _1314199, _1314201] : [class_Orderings_Olinorder(_1314197), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314197), _1314199)), -(_1314199 = c_Orderings_Obot__class_Obot(tc_fun(_1314197, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314197), _1314201)), -(_1314201 = c_Orderings_Obot__class_Obot(tc_fun(_1314197, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314197, c_Orderings_Oord__class_Omin(_1314197), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1314197, tc_HOL_Obool)), _1314199), _1314201)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314197), c_Big__Operators_Olattice_OInf__fin(_1314197, c_Orderings_Oord__class_Omin(_1314197), _1314199)), c_Big__Operators_Olattice_OInf__fin(_1314197, c_Orderings_Oord__class_Omin(_1314197), _1314201)))], (28145 ^ _782435) ^ [_1314564, _1314566, _1314568] : [class_Orderings_Olinorder(_1314564), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314564), _1314566)), -(hBOOL(hAPP(hAPP(c_member(_1314564), _1314568), _1314566))), -(_1314566 = c_Orderings_Obot__class_Obot(tc_fun(_1314564, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314564, c_Orderings_Oord__class_Omin(_1314564), hAPP(hAPP(c_Set_Oinsert(_1314564), _1314568), _1314566)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314564), _1314568), c_Big__Operators_Olattice_OInf__fin(_1314564, c_Orderings_Oord__class_Omin(_1314564), _1314566)))], (28163 ^ _782435) ^ [_1314813, _1314815, _1314817] : [class_Orderings_Olinorder(_1314813), hBOOL(hAPP(c_Finite__Set_Ofinite(_1314813), _1314815)), 28170 ^ _782435 : [(28171 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314813, tc_HOL_Obool)), _1314815), hAPP(hAPP(c_Set_Oinsert(_1314813), _1314817), c_Orderings_Obot__class_Obot(tc_fun(_1314813, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314813, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1314813, c_Orderings_Oord__class_Omin(_1314813), hAPP(hAPP(c_Set_Oinsert(_1314813), _1314817), _1314815)) = _1314817)], (28177 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314813, tc_HOL_Obool)), _1314815), hAPP(hAPP(c_Set_Oinsert(_1314813), _1314817), c_Orderings_Obot__class_Obot(tc_fun(_1314813, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1314813, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1314813, c_Orderings_Oord__class_Omin(_1314813), hAPP(hAPP(c_Set_Oinsert(_1314813), _1314817), _1314815)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1314813), _1314817), c_Big__Operators_Olattice_OInf__fin(_1314813, c_Orderings_Oord__class_Omin(_1314813), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1314813, tc_HOL_Obool)), _1314815), hAPP(hAPP(c_Set_Oinsert(_1314813), _1314817), c_Orderings_Obot__class_Obot(tc_fun(_1314813, tc_HOL_Obool)))))))]]], (28183 ^ _782435) ^ [_1315301, _1315303, _1315305] : [class_Orderings_Olinorder(_1315301), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315301), _1315303)), -(_1315303 = c_Orderings_Obot__class_Obot(tc_fun(_1315301, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315301), _1315305)), -(_1315305 = c_Orderings_Obot__class_Obot(tc_fun(_1315301, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315301, tc_HOL_Obool)), _1315303), _1315305) = c_Orderings_Obot__class_Obot(tc_fun(_1315301, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1315301, c_Orderings_Oord__class_Omin(_1315301), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315301, tc_HOL_Obool)), _1315303), _1315305)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315301), c_Big__Operators_Olattice_OInf__fin(_1315301, c_Orderings_Oord__class_Omin(_1315301), _1315303)), c_Big__Operators_Olattice_OInf__fin(_1315301, c_Orderings_Oord__class_Omin(_1315301), _1315305)))], (28209 ^ _782435) ^ [_1315796, _1315798, _1315800] : [class_Orderings_Olinorder(_1315796), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315796), _1315798)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1315796), _1315800)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315796, tc_HOL_Obool)), _1315798), _1315800) = c_Orderings_Obot__class_Obot(tc_fun(_1315796, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315796), c_Big__Operators_Olattice_OInf__fin(_1315796, c_Orderings_Oord__class_Omin(_1315796), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1315796, tc_HOL_Obool)), _1315798), _1315800))), c_Big__Operators_Olattice_OInf__fin(_1315796, c_Orderings_Oord__class_Omin(_1315796), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1315796, tc_HOL_Obool)), _1315798), _1315800))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1315796), c_Big__Operators_Olattice_OInf__fin(_1315796, c_Orderings_Oord__class_Omin(_1315796), _1315798)), c_Big__Operators_Olattice_OInf__fin(_1315796, c_Orderings_Oord__class_Omin(_1315796), _1315800)))], (28227 ^ _782435) ^ [_1316168, _1316170, _1316172] : [class_Orderings_Olinorder(_1316168), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316168), _1316170)), hBOOL(hAPP(hAPP(c_member(_1316168), _1316172), _1316170)), 28238 ^ _782435 : [(28239 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316168, tc_HOL_Obool)), _1316170), hAPP(hAPP(c_Set_Oinsert(_1316168), _1316172), c_Orderings_Obot__class_Obot(tc_fun(_1316168, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1316168, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OInf__fin(_1316168, c_Orderings_Oord__class_Omin(_1316168), _1316170) = _1316172)], (28245 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316168, tc_HOL_Obool)), _1316170), hAPP(hAPP(c_Set_Oinsert(_1316168), _1316172), c_Orderings_Obot__class_Obot(tc_fun(_1316168, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1316168, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OInf__fin(_1316168, c_Orderings_Oord__class_Omin(_1316168), _1316170) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1316168), _1316172), c_Big__Operators_Olattice_OInf__fin(_1316168, c_Orderings_Oord__class_Omin(_1316168), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1316168, tc_HOL_Obool)), _1316170), hAPP(hAPP(c_Set_Oinsert(_1316168), _1316172), c_Orderings_Obot__class_Obot(tc_fun(_1316168, tc_HOL_Obool)))))))]]], (28251 ^ _782435) ^ [_1316692, _1316694, _1316696] : [class_Orderings_Olinorder(_1316692), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316692), _1316694)), -(_1316694 = c_Orderings_Obot__class_Obot(tc_fun(_1316692, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1316692), _1316696)), -(_1316696 = c_Orderings_Obot__class_Obot(tc_fun(_1316692, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1316692), c_Big__Operators_Olattice_OInf__fin(_1316692, c_Orderings_Oord__class_Omin(_1316692), _1316694)), c_Big__Operators_Olattice_OInf__fin(_1316692, c_Orderings_Oord__class_Omin(_1316692), _1316696)) = c_Big__Operators_Olattice_OInf__fin(_1316692, c_Orderings_Oord__class_Omin(_1316692), hAPP(c_Set_OCollect(_1316692), hAPP(hAPP(c_COMBB(tc_fun(_1316692, tc_HOL_Obool), tc_HOL_Obool, _1316692), c_HOL_OEx(_1316692)), hAPP(hAPP(c_COMBB(tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool)), tc_fun(_1316692, tc_HOL_Obool), _1316692), hAPP(c_COMBB(tc_fun(_1316692, tc_HOL_Obool), tc_HOL_Obool, _1316692), c_HOL_OEx(_1316692))), hAPP(hAPP(c_COMBC(_1316692, tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool)), tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316692, tc_fun(tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_HOL_Obool))), tc_fun(tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool)), tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool))), _1316692), c_COMBS(_1316692, tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316692, tc_fun(_1316692, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1316692, tc_fun(tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_HOL_Obool))), _1316692), hAPP(c_COMBB(tc_fun(_1316692, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_HOL_Obool)), _1316692), c_COMBS(_1316692, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool)), tc_fun(_1316692, tc_fun(_1316692, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1316692), hAPP(c_COMBB(tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1316692), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1316692), c_fconj))), hAPP(hAPP(c_COMBC(_1316692, tc_fun(_1316692, tc_fun(_1316692, _1316692)), tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1316692, _1316692), tc_fun(_1316692, tc_HOL_Obool)), tc_fun(tc_fun(_1316692, tc_fun(_1316692, _1316692)), tc_fun(_1316692, tc_fun(_1316692, tc_HOL_Obool))), _1316692), c_COMBB(tc_fun(_1316692, _1316692), tc_fun(_1316692, tc_HOL_Obool), _1316692)), hAPP(hAPP(c_COMBB(tc_fun(_1316692, tc_HOL_Obool), tc_fun(tc_fun(_1316692, _1316692), tc_fun(_1316692, tc_HOL_Obool)), _1316692), c_COMBB(_1316692, tc_HOL_Obool, _1316692)), c_fequal))), c_Orderings_Oord__class_Omax(_1316692)))))), hAPP(hAPP(c_COMBC(_1316692, tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1316692, tc_HOL_Obool), tc_fun(_1316692, tc_HOL_Obool)), _1316692), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1316692)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1316692), c_fconj), hAPP(hAPP(c_COMBC(_1316692, tc_fun(_1316692, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316692)), _1316694)))), hAPP(hAPP(c_COMBC(_1316692, tc_fun(_1316692, tc_HOL_Obool), tc_HOL_Obool), c_member(_1316692)), _1316696))))))))], (28273 ^ _782435) ^ [_1317809, _1317811, _1317813] : [28275 ^ _782435 : [(28276 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1317809), 28274 ^ [_1317809, _1317811, _1317813]), _1317811)))], (28278 ^ _782435) ^ [] : [c_Nat__Transfer_Ois__nat(hAPP(_1317813, 28274 ^ [_1317809, _1317811, _1317813]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317809, tc_Int_Oint), _1317813), _1317811) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1317809, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_Nat_Onat, _1317809), c_Int_Onat), _1317813)), _1317811)))], (28282 ^ _782435) ^ [_1318039, _1318041, _1318043] : [class_Orderings_Olinorder(_1318039), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318039), _1318041)), -(_1318041 = c_Orderings_Obot__class_Obot(tc_fun(_1318039, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1318039), _1318043)), -(_1318043 = c_Orderings_Obot__class_Obot(tc_fun(_1318039, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1318039), c_Big__Operators_Olattice_OSup__fin(_1318039, c_Orderings_Oord__class_Omax(_1318039), _1318041)), c_Big__Operators_Olattice_OSup__fin(_1318039, c_Orderings_Oord__class_Omax(_1318039), _1318043)) = c_Big__Operators_Olattice_OSup__fin(_1318039, c_Orderings_Oord__class_Omax(_1318039), hAPP(c_Set_OCollect(_1318039), hAPP(hAPP(c_COMBB(tc_fun(_1318039, tc_HOL_Obool), tc_HOL_Obool, _1318039), c_HOL_OEx(_1318039)), hAPP(hAPP(c_COMBB(tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool)), tc_fun(_1318039, tc_HOL_Obool), _1318039), hAPP(c_COMBB(tc_fun(_1318039, tc_HOL_Obool), tc_HOL_Obool, _1318039), c_HOL_OEx(_1318039))), hAPP(hAPP(c_COMBC(_1318039, tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool)), tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318039, tc_fun(tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_HOL_Obool))), tc_fun(tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool)), tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool))), _1318039), c_COMBS(_1318039, tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318039, tc_fun(_1318039, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1318039, tc_fun(tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_HOL_Obool))), _1318039), hAPP(c_COMBB(tc_fun(_1318039, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_HOL_Obool)), _1318039), c_COMBS(_1318039, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool)), tc_fun(_1318039, tc_fun(_1318039, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1318039), hAPP(c_COMBB(tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1318039), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1318039), c_fconj))), hAPP(hAPP(c_COMBC(_1318039, tc_fun(_1318039, tc_fun(_1318039, _1318039)), tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1318039, _1318039), tc_fun(_1318039, tc_HOL_Obool)), tc_fun(tc_fun(_1318039, tc_fun(_1318039, _1318039)), tc_fun(_1318039, tc_fun(_1318039, tc_HOL_Obool))), _1318039), c_COMBB(tc_fun(_1318039, _1318039), tc_fun(_1318039, tc_HOL_Obool), _1318039)), hAPP(hAPP(c_COMBB(tc_fun(_1318039, tc_HOL_Obool), tc_fun(tc_fun(_1318039, _1318039), tc_fun(_1318039, tc_HOL_Obool)), _1318039), c_COMBB(_1318039, tc_HOL_Obool, _1318039)), c_fequal))), c_Orderings_Oord__class_Omin(_1318039)))))), hAPP(hAPP(c_COMBC(_1318039, tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1318039, tc_HOL_Obool), tc_fun(_1318039, tc_HOL_Obool)), _1318039), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1318039)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1318039), c_fconj), hAPP(hAPP(c_COMBC(_1318039, tc_fun(_1318039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318039)), _1318041)))), hAPP(hAPP(c_COMBC(_1318039, tc_fun(_1318039, tc_HOL_Obool), tc_HOL_Obool), c_member(_1318039)), _1318043))))))))], (28304 ^ _782435) ^ [_1319156, _1319158, _1319160] : [class_Orderings_Olinorder(_1319156), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319156), _1319158)), -(_1319158 = c_Orderings_Obot__class_Obot(tc_fun(_1319156, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319156), _1319160), c_Big__Operators_Olattice_OSup__fin(_1319156, c_Orderings_Oord__class_Omax(_1319156), _1319158)) = c_Big__Operators_Olattice_OSup__fin(_1319156, c_Orderings_Oord__class_Omax(_1319156), hAPP(c_Set_OCollect(_1319156), hAPP(hAPP(c_COMBB(tc_fun(_1319156, tc_HOL_Obool), tc_HOL_Obool, _1319156), c_HOL_OEx(_1319156)), hAPP(hAPP(c_COMBC(_1319156, tc_fun(_1319156, tc_HOL_Obool), tc_fun(_1319156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319156, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1319156, tc_HOL_Obool), tc_fun(_1319156, tc_HOL_Obool)), _1319156), c_COMBS(_1319156, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319156, tc_HOL_Obool), tc_fun(_1319156, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1319156), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1319156), c_fconj)), hAPP(hAPP(c_COMBC(_1319156, tc_fun(_1319156, _1319156), tc_fun(_1319156, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1319156, tc_HOL_Obool), tc_fun(tc_fun(_1319156, _1319156), tc_fun(_1319156, tc_HOL_Obool)), _1319156), c_COMBB(_1319156, tc_HOL_Obool, _1319156)), c_fequal)), hAPP(c_Orderings_Oord__class_Omin(_1319156), _1319160))))), hAPP(hAPP(c_COMBC(_1319156, tc_fun(_1319156, tc_HOL_Obool), tc_HOL_Obool), c_member(_1319156)), _1319158))))))], (28318 ^ _782435) ^ [_1319654, _1319656] : [class_Orderings_Olinorder(_1319654), hBOOL(hAPP(c_Finite__Set_Ofinite(_1319654), _1319656)), -(_1319656 = c_Orderings_Obot__class_Obot(tc_fun(_1319654, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1319654), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1319654), 28331 ^ [_1319654, _1319656]), 28332 ^ [_1319654, _1319656])), hAPP(hAPP(c_Set_Oinsert(_1319654), 28331 ^ [_1319654, _1319656]), hAPP(hAPP(c_Set_Oinsert(_1319654), 28332 ^ [_1319654, _1319656]), c_Orderings_Obot__class_Obot(tc_fun(_1319654, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1319654), c_Big__Operators_Olattice_OInf__fin(_1319654, c_Orderings_Oord__class_Omin(_1319654), _1319656)), _1319656)))], (28338 ^ _782435) ^ [_1320104, _1320106, _1320108] : [class_Orderings_Olinorder(_1320104), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320104), _1320106)), hBOOL(hAPP(hAPP(c_member(_1320104), _1320108), _1320106)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320104), _1320108), c_Big__Operators_Olattice_OSup__fin(_1320104, c_Orderings_Oord__class_Omax(_1320104), _1320106)) = c_Big__Operators_Olattice_OSup__fin(_1320104, c_Orderings_Oord__class_Omax(_1320104), _1320106))], (28352 ^ _782435) ^ [_1320351, _1320353] : [class_Orderings_Olinorder(_1320351), -(c_Big__Operators_Olattice_OSup__fin(_1320351, c_Orderings_Oord__class_Omax(_1320351), hAPP(hAPP(c_Set_Oinsert(_1320351), _1320353), c_Orderings_Obot__class_Obot(tc_fun(_1320351, tc_HOL_Obool)))) = _1320353)], (28358 ^ _782435) ^ [_1320464, _1320466] : [class_Orderings_Olinorder(_1320464), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320464), _1320466)), -(c_Big__Operators_Olattice_OSup__fin(_1320464, c_Orderings_Oord__class_Omax(_1320464), _1320466) = hAPP(c_Finite__Set_Ofold1(_1320464, c_Orderings_Oord__class_Omax(_1320464)), _1320466))], (28368 ^ _782435) ^ [_1320627, _1320629, _1320631] : [class_Orderings_Olinorder(_1320627), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320627), _1320629)), -(_1320629 = c_Orderings_Obot__class_Obot(tc_fun(_1320627, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1320627, c_Orderings_Oord__class_Omax(_1320627), hAPP(hAPP(c_Set_Oinsert(_1320627), _1320631), _1320629)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320627), _1320631), c_Big__Operators_Olattice_OSup__fin(_1320627, c_Orderings_Oord__class_Omax(_1320627), _1320629)))], (28382 ^ _782435) ^ [_1320847, _1320849, _1320851] : [class_Orderings_Olinorder(_1320847), hBOOL(hAPP(c_Finite__Set_Ofinite(_1320847), _1320849)), -(_1320851 = c_Orderings_Obot__class_Obot(tc_fun(_1320847, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1320847, tc_HOL_Obool)), _1320851), _1320849)), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1320847), c_Big__Operators_Olattice_OSup__fin(_1320847, c_Orderings_Oord__class_Omax(_1320847), _1320851)), c_Big__Operators_Olattice_OSup__fin(_1320847, c_Orderings_Oord__class_Omax(_1320847), _1320849)) = c_Big__Operators_Olattice_OSup__fin(_1320847, c_Orderings_Oord__class_Omax(_1320847), _1320849))], (28400 ^ _782435) ^ [_1321179, _1321181, _1321183] : [class_Orderings_Olinorder(_1321179), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321179), _1321181)), hBOOL(hAPP(hAPP(c_member(_1321179), _1321183), _1321181)), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1321179), _1321183), c_Big__Operators_Olattice_OSup__fin(_1321179, c_Orderings_Oord__class_Omax(_1321179), _1321181)) = _1321183)], (28414 ^ _782435) ^ [_1321414, _1321416, _1321418] : [class_Orderings_Olinorder(_1321414), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321414), _1321416)), -(_1321416 = c_Orderings_Obot__class_Obot(tc_fun(_1321414, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321414), _1321418)), -(_1321418 = c_Orderings_Obot__class_Obot(tc_fun(_1321414, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321414, c_Orderings_Oord__class_Omax(_1321414), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1321414, tc_HOL_Obool)), _1321416), _1321418)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321414), c_Big__Operators_Olattice_OSup__fin(_1321414, c_Orderings_Oord__class_Omax(_1321414), _1321416)), c_Big__Operators_Olattice_OSup__fin(_1321414, c_Orderings_Oord__class_Omax(_1321414), _1321418)))], (28436 ^ _782435) ^ [_1321781, _1321783, _1321785] : [class_Orderings_Olinorder(_1321781), hBOOL(hAPP(c_Finite__Set_Ofinite(_1321781), _1321783)), -(hBOOL(hAPP(hAPP(c_member(_1321781), _1321785), _1321783))), -(_1321783 = c_Orderings_Obot__class_Obot(tc_fun(_1321781, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1321781, c_Orderings_Oord__class_Omax(_1321781), hAPP(hAPP(c_Set_Oinsert(_1321781), _1321785), _1321783)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1321781), _1321785), c_Big__Operators_Olattice_OSup__fin(_1321781, c_Orderings_Oord__class_Omax(_1321781), _1321783)))], (28454 ^ _782435) ^ [_1322030, _1322032, _1322034] : [class_Orderings_Olinorder(_1322030), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322030), _1322032)), 28461 ^ _782435 : [(28462 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322030, tc_HOL_Obool)), _1322032), hAPP(hAPP(c_Set_Oinsert(_1322030), _1322034), c_Orderings_Obot__class_Obot(tc_fun(_1322030, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322030, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1322030, c_Orderings_Oord__class_Omax(_1322030), hAPP(hAPP(c_Set_Oinsert(_1322030), _1322034), _1322032)) = _1322034)], (28468 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322030, tc_HOL_Obool)), _1322032), hAPP(hAPP(c_Set_Oinsert(_1322030), _1322034), c_Orderings_Obot__class_Obot(tc_fun(_1322030, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1322030, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1322030, c_Orderings_Oord__class_Omax(_1322030), hAPP(hAPP(c_Set_Oinsert(_1322030), _1322034), _1322032)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322030), _1322034), c_Big__Operators_Olattice_OSup__fin(_1322030, c_Orderings_Oord__class_Omax(_1322030), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1322030, tc_HOL_Obool)), _1322032), hAPP(hAPP(c_Set_Oinsert(_1322030), _1322034), c_Orderings_Obot__class_Obot(tc_fun(_1322030, tc_HOL_Obool)))))))]]], (28474 ^ _782435) ^ [_1322518, _1322520, _1322522] : [class_Orderings_Olinorder(_1322518), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322518), _1322520)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322518), _1322522)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322518, tc_HOL_Obool)), _1322520), _1322522) = c_Orderings_Obot__class_Obot(tc_fun(_1322518, tc_HOL_Obool))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322518), c_Big__Operators_Olattice_OSup__fin(_1322518, c_Orderings_Oord__class_Omax(_1322518), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322518, tc_HOL_Obool)), _1322520), _1322522))), c_Big__Operators_Olattice_OSup__fin(_1322518, c_Orderings_Oord__class_Omax(_1322518), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322518, tc_HOL_Obool)), _1322520), _1322522))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322518), c_Big__Operators_Olattice_OSup__fin(_1322518, c_Orderings_Oord__class_Omax(_1322518), _1322520)), c_Big__Operators_Olattice_OSup__fin(_1322518, c_Orderings_Oord__class_Omax(_1322518), _1322522)))], (28492 ^ _782435) ^ [_1322890, _1322892, _1322894] : [class_Orderings_Olinorder(_1322890), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322890), _1322892)), -(_1322892 = c_Orderings_Obot__class_Obot(tc_fun(_1322890, tc_HOL_Obool))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1322890), _1322894)), -(_1322894 = c_Orderings_Obot__class_Obot(tc_fun(_1322890, tc_HOL_Obool))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1322890, tc_HOL_Obool)), _1322892), _1322894) = c_Orderings_Obot__class_Obot(tc_fun(_1322890, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1322890, c_Orderings_Oord__class_Omax(_1322890), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1322890, tc_HOL_Obool)), _1322892), _1322894)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1322890), c_Big__Operators_Olattice_OSup__fin(_1322890, c_Orderings_Oord__class_Omax(_1322890), _1322892)), c_Big__Operators_Olattice_OSup__fin(_1322890, c_Orderings_Oord__class_Omax(_1322890), _1322894)))], (28518 ^ _782435) ^ [_1323385, _1323387, _1323389] : [class_Orderings_Olinorder(_1323385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323385), _1323387)), hBOOL(hAPP(hAPP(c_member(_1323385), _1323389), _1323387)), 28529 ^ _782435 : [(28530 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323385, tc_HOL_Obool)), _1323387), hAPP(hAPP(c_Set_Oinsert(_1323385), _1323389), c_Orderings_Obot__class_Obot(tc_fun(_1323385, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323385, tc_HOL_Obool)), -(c_Big__Operators_Olattice_OSup__fin(_1323385, c_Orderings_Oord__class_Omax(_1323385), _1323387) = _1323389)], (28536 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323385, tc_HOL_Obool)), _1323387), hAPP(hAPP(c_Set_Oinsert(_1323385), _1323389), c_Orderings_Obot__class_Obot(tc_fun(_1323385, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(_1323385, tc_HOL_Obool))), -(c_Big__Operators_Olattice_OSup__fin(_1323385, c_Orderings_Oord__class_Omax(_1323385), _1323387) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1323385), _1323389), c_Big__Operators_Olattice_OSup__fin(_1323385, c_Orderings_Oord__class_Omax(_1323385), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1323385, tc_HOL_Obool)), _1323387), hAPP(hAPP(c_Set_Oinsert(_1323385), _1323389), c_Orderings_Obot__class_Obot(tc_fun(_1323385, tc_HOL_Obool)))))))]]], (28542 ^ _782435) ^ [_1323909, _1323911] : [class_Orderings_Olinorder(_1323909), hBOOL(hAPP(c_Finite__Set_Ofinite(_1323909), _1323911)), -(_1323911 = c_Orderings_Obot__class_Obot(tc_fun(_1323909, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1323909), c_Big__Operators_Olattice_OInf__fin(_1323909, c_Orderings_Oord__class_Omin(_1323909), _1323911)), c_Big__Operators_Olattice_OSup__fin(_1323909, c_Orderings_Oord__class_Omax(_1323909), _1323911))))], (28556 ^ _782435) ^ [_1324107, _1324109] : [class_Orderings_Olinorder(_1324107), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324107), _1324109)), -(_1324109 = c_Orderings_Obot__class_Obot(tc_fun(_1324107, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324107), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324107), 28569 ^ [_1324107, _1324109]), 28570 ^ [_1324107, _1324109])), hAPP(hAPP(c_Set_Oinsert(_1324107), 28569 ^ [_1324107, _1324109]), hAPP(hAPP(c_Set_Oinsert(_1324107), 28570 ^ [_1324107, _1324109]), c_Orderings_Obot__class_Obot(tc_fun(_1324107, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324107), c_Big__Operators_Olattice_OSup__fin(_1324107, c_Orderings_Oord__class_Omax(_1324107), _1324109)), _1324109)))], (28576 ^ _782435) ^ [_1324557, _1324559] : [class_Orderings_Olinorder(_1324557), hBOOL(hAPP(c_Finite__Set_Ofinite(_1324557), _1324559)), -(_1324559 = c_Orderings_Obot__class_Obot(tc_fun(_1324557, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1324557), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1324557), 28589 ^ [_1324557, _1324559]), 28590 ^ [_1324557, _1324559])), hAPP(hAPP(c_Set_Oinsert(_1324557), 28589 ^ [_1324557, _1324559]), hAPP(hAPP(c_Set_Oinsert(_1324557), 28590 ^ [_1324557, _1324559]), c_Orderings_Obot__class_Obot(tc_fun(_1324557, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1324557), c_Big__Operators_Olinorder__class_OMax(_1324557, _1324559)), _1324559)))], (28596 ^ _782435) ^ [_1325001, _1325003] : [class_Orderings_Olinorder(_1325001), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325001), _1325003)), -(_1325003 = c_Orderings_Obot__class_Obot(tc_fun(_1325001, tc_HOL_Obool))), hBOOL(hAPP(hAPP(c_member(_1325001), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1325001), 28609 ^ [_1325001, _1325003]), 28610 ^ [_1325001, _1325003])), hAPP(hAPP(c_Set_Oinsert(_1325001), 28609 ^ [_1325001, _1325003]), hAPP(hAPP(c_Set_Oinsert(_1325001), 28610 ^ [_1325001, _1325003]), c_Orderings_Obot__class_Obot(tc_fun(_1325001, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(_1325001), c_Big__Operators_Olinorder__class_OMin(_1325001, _1325003)), _1325003)))], (28616 ^ _782435) ^ [_1325445, _1325447, _1325449, _1325451, _1325453] : [class_Groups_Ocomm__monoid__mult(_1325445), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325447), _1325449)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325447), _1325451)), 28630 ^ _782435 : [(28631 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325447), 28629 ^ [_1325445, _1325447, _1325449, _1325451, _1325453]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325447, tc_HOL_Obool)), _1325449), _1325451))))], (28633 ^ _782435) ^ [] : [hAPP(_1325453, 28629 ^ [_1325445, _1325447, _1325449, _1325451, _1325453]) = c_Groups_Oone__class_Oone(_1325445)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325447, _1325445), _1325453), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325447, tc_HOL_Obool)), _1325449), _1325451)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325445), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325447, _1325445), _1325453), _1325449)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325447, _1325445), _1325453), _1325451)))], (28637 ^ _782435) ^ [_1325940, _1325942, _1325944, _1325946, _1325948] : [class_Groups_Ocomm__monoid__mult(_1325940), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325942), _1325944)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1325942), _1325946)), 28651 ^ _782435 : [(28652 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1325942), 28650 ^ [_1325940, _1325942, _1325944, _1325946, _1325948]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1325942, tc_HOL_Obool)), _1325944), _1325946))))], (28654 ^ _782435) ^ [] : [hAPP(_1325948, 28650 ^ [_1325940, _1325942, _1325944, _1325946, _1325948]) = c_Groups_Oone__class_Oone(_1325940)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325942, _1325940), _1325948), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1325942, tc_HOL_Obool)), _1325944), _1325946)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1325940), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325942, _1325940), _1325948), _1325944)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1325942, _1325940), _1325948), _1325946)))], (28658 ^ _782435) ^ [_1326435, _1326437, _1326439, _1326441, _1326443, _1326445] : [class_Groups_Ocomm__monoid__mult(_1326435), hBOOL(hAPP(c_Finite__Set_Ofinite(_1326437), _1326439)), 28665 ^ _782435 : [(28666 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1326437), _1326441), _1326439)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1326437, _1326435), hAPP(hAPP(c_COMBC(_1326437, _1326435, _1326435), hAPP(hAPP(c_COMBS(_1326437, _1326435, tc_fun(_1326435, _1326435)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1326435, tc_fun(_1326435, _1326435)), _1326437), c_If(_1326435)), hAPP(hAPP(c_COMBC(_1326437, _1326437, tc_HOL_Obool), c_fequal), _1326441))), _1326443)), _1326445)), _1326439) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1326435), hAPP(_1326443, _1326441)), hAPP(hAPP(c_Power_Opower__class_Opower(_1326435), _1326445), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1326437), _1326439)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (28672 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1326437), _1326441), _1326439))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1326437, _1326435), hAPP(hAPP(c_COMBC(_1326437, _1326435, _1326435), hAPP(hAPP(c_COMBS(_1326437, _1326435, tc_fun(_1326435, _1326435)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1326435, tc_fun(_1326435, _1326435)), _1326437), c_If(_1326435)), hAPP(hAPP(c_COMBC(_1326437, _1326437, tc_HOL_Obool), c_fequal), _1326441))), _1326443)), _1326445)), _1326439) = hAPP(hAPP(c_Power_Opower__class_Opower(_1326435), _1326445), hAPP(c_Finite__Set_Ocard(_1326437), _1326439)))]]], (28678 ^ _782435) ^ [_1327047, _1327049, _1327051, _1327053, _1327055] : [class_Fields_Ofield(_1327047), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327049), _1327051)), -(hAPP(_1327053, _1327055) = c_Groups_Ozero__class_Ozero(_1327047)), 28689 ^ _782435 : [(28690 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1327049), _1327055), _1327051)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327049, _1327047), _1327053), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327049, tc_HOL_Obool)), _1327051), hAPP(hAPP(c_Set_Oinsert(_1327049), _1327055), c_Orderings_Obot__class_Obot(tc_fun(_1327049, tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1327047), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327049, _1327047), _1327053), _1327051)), hAPP(_1327053, _1327055)))], (28696 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1327049), _1327055), _1327051))), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327049, _1327047), _1327053), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1327049, tc_HOL_Obool)), _1327051), hAPP(hAPP(c_Set_Oinsert(_1327049), _1327055), c_Orderings_Obot__class_Obot(tc_fun(_1327049, tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1327049, _1327047), _1327053), _1327051))]]], (28702 ^ _782435) ^ [_1327588, _1327590, _1327592] : [class_Orderings_Olinorder(_1327588), hAPP(_1327590, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327588), 28707 ^ [_1327588, _1327590, _1327592]), 28708 ^ [_1327588, _1327590, _1327592])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1327588), hAPP(_1327590, 28707 ^ [_1327588, _1327590, _1327592])), hAPP(_1327590, 28708 ^ [_1327588, _1327590, _1327592])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1327588), _1327592)), -(_1327592 = c_Orderings_Obot__class_Obot(tc_fun(_1327588, tc_HOL_Obool))), -(hAPP(_1327590, c_Big__Operators_Olattice_OSup__fin(_1327588, c_Orderings_Oord__class_Omax(_1327588), _1327592)) = c_Big__Operators_Olattice_OSup__fin(_1327588, c_Orderings_Oord__class_Omax(_1327588), hAPP(c_Set_Oimage(_1327588, _1327588, _1327590), _1327592)))], (28722 ^ _782435) ^ [_1328003, _1328005] : [c_Nat__Transfer_Ois__nat(_1328003), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328003), _1328005)))], (28728 ^ _782435) ^ [_1328088, _1328090, _1328092] : [class_Rings_Oring__1(_1328088), -(hAPP(c_Int_Oring__1__class_Oof__int(_1328088), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328090), _1328092)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1328088), hAPP(c_Int_Oring__1__class_Oof__int(_1328088), _1328090)), _1328092))], (28734 ^ _782435) ^ [_1328213, _1328215] : [class_Rings_Ocomm__semiring__1(_1328213), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1328213), _1328215), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1328215)], (28740 ^ _782435) ^ [_1328304, _1328306, _1328308] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328304), _1328306)), _1328308) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1328304), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1328306), _1328308)))], (28742 ^ _782435) ^ [_1328355, _1328357] : [class_Rings_Odivision__ring__inverse__zero(_1328355), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328355), _1328357), c_Groups_Ozero__class_Ozero(_1328355)) = c_Groups_Ozero__class_Ozero(_1328355))], (28748 ^ _782435) ^ [_1328454, _1328456] : [class_Rings_Odivision__ring(_1328454), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328454), c_Groups_Ozero__class_Ozero(_1328454)), _1328456) = c_Groups_Ozero__class_Ozero(_1328454))], (28754 ^ _782435) ^ [_1328553, _1328555, _1328557, _1328559] : [class_Rings_Odivision__ring(_1328553), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328553), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328553), _1328555), _1328557)), _1328559) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1328553), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328553), _1328555), _1328559)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328553), _1328557), _1328559)))], (28760 ^ _782435) ^ [_1328712, _1328714, _1328716, _1328718] : [class_Rings_Odivision__ring(_1328712), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328712), _1328714), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328712), _1328716), _1328718)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328712), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1328712), _1328714), _1328716)), _1328718))], (28766 ^ _782435) ^ [_1328855, _1328857, _1328859, _1328861] : [class_Rings_Odivision__ring(_1328855), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328855), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1328855), _1328857), _1328859)), _1328861) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1328855), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328855), _1328857), _1328861)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1328855), _1328859), _1328861)))], (28772 ^ _782435) ^ [_1329014, _1329016, _1329018, _1329020] : [class_Rings_Ocomm__semiring__1(_1329014), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1329014), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329014), _1329016), _1329018)), _1329020) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1329014), hAPP(hAPP(c_Power_Opower__class_Opower(_1329014), _1329016), _1329020)), hAPP(hAPP(c_Power_Opower__class_Opower(_1329014), _1329018), _1329020)))], (28778 ^ _782435) ^ [_1329173, _1329175] : [class_Rings_Odivision__ring(_1329173), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329173), _1329175), c_Groups_Oone__class_Oone(_1329173)) = _1329175)], (28784 ^ _782435) ^ [_1329268, _1329270, _1329272] : [class_Rings_Odivision__ring(_1329268), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1329268), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329268), _1329270), _1329272)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329268), hAPP(c_Groups_Ouminus__class_Ouminus(_1329268), _1329270)), _1329272))], (28790 ^ _782435) ^ [_1329397, _1329399] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329397), _1329399)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329397)), _1329399))], (28792 ^ _782435) ^ [_1329440, _1329442] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329440)), _1329442) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329440), _1329442)))], (28794 ^ _782435) ^ [_1329483, _1329485] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1329483)), _1329485) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1329483), _1329485)))], (28796 ^ _782435) ^ [_1329526, _1329528, _1329530, _1329532] : [class_Rings_Ocomm__semiring__1(_1329526), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1329526), hAPP(hAPP(c_Power_Opower__class_Opower(_1329526), _1329528), _1329530)), _1329532) = hAPP(hAPP(c_Power_Opower__class_Opower(_1329526), _1329528), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1329530), _1329532)))], (28802 ^ _782435) ^ [_1329665, _1329667] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329665)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1329665)), _1329667) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1329665), _1329667)))], (28808 ^ _782435) ^ [_1329782, _1329784] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1329782)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1329782), _1329784)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onat, _1329782)), _1329784))], (28814 ^ _782435) ^ [_1329899, _1329901, _1329903, _1329905, _1329907] : [class_Fields_Ofield(_1329899), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1329899), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329901, _1329899), _1329903), _1329905)), _1329907) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1329901, _1329899), hAPP(hAPP(c_COMBC(_1329901, _1329899, _1329899), hAPP(hAPP(c_COMBB(_1329899, tc_fun(_1329899, _1329899), _1329901), c_Rings_Oinverse__class_Odivide(_1329899)), _1329903)), _1329907)), _1329905))], (28820 ^ _782435) ^ [_1330082, _1330084, _1330086, _1330088] : [class_Rings_Odivision__ring(_1330082), -(_1330084 = c_Groups_Ozero__class_Ozero(_1330082)), 28827 ^ _782435 : [(28828 ^ _782435) ^ [] : [_1330086 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330082), _1330088), _1330084), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330082), _1330086), _1330084) = _1330088)], (28834 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330082), _1330086), _1330084) = _1330088, -(_1330086 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330082), _1330088), _1330084))]]], (28840 ^ _782435) ^ [_1330410, _1330412, _1330414, _1330416] : [class_Rings_Odivision__ring(_1330410), -(_1330412 = c_Groups_Ozero__class_Ozero(_1330410)), 28847 ^ _782435 : [(28848 ^ _782435) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330410), _1330414), _1330412) = _1330416, -(_1330414 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330410), _1330416), _1330412))], (28854 ^ _782435) ^ [] : [_1330414 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330410), _1330416), _1330412), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330410), _1330414), _1330412) = _1330416)]]], (28860 ^ _782435) ^ [_1330738, _1330740, _1330742, _1330744] : [class_Rings_Odivision__ring(_1330738), -(_1330740 = c_Groups_Ozero__class_Ozero(_1330738)), _1330742 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330738), _1330744), _1330740), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330738), _1330742), _1330740) = _1330744)], (28874 ^ _782435) ^ [_1330968, _1330970, _1330972, _1330974] : [class_Rings_Odivision__ring(_1330968), -(_1330970 = c_Groups_Ozero__class_Ozero(_1330968)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1330968), _1330972), _1330970) = _1330974, -(_1330972 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1330968), _1330974), _1330970))], (28888 ^ _782435) ^ [_1331198, _1331200] : [class_Rings_Odivision__ring__inverse__zero(_1331198), 28891 ^ _782435 : [(28892 ^ _782435) ^ [] : [_1331200 = c_Groups_Ozero__class_Ozero(_1331198), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331198), _1331200), _1331200) = c_Groups_Ozero__class_Ozero(_1331198))], (28898 ^ _782435) ^ [] : [-(_1331200 = c_Groups_Ozero__class_Ozero(_1331198)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331198), _1331200), _1331200) = c_Groups_Oone__class_Oone(_1331198))]]], (28904 ^ _782435) ^ [_1331420, _1331422] : [class_Rings_Odivision__ring(_1331420), -(_1331422 = c_Groups_Ozero__class_Ozero(_1331420)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331420), _1331422), _1331422) = c_Groups_Oone__class_Oone(_1331420))], (28914 ^ _782435) ^ [_1331534, _1331536, _1331538] : [class_Rings_Odivision__ring(_1331534), -(_1331536 = c_Groups_Ozero__class_Ozero(_1331534)), 28921 ^ _782435 : [(28922 ^ _782435) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331534), _1331538), _1331536) = c_Groups_Oone__class_Oone(_1331534), -(_1331538 = _1331536)], (28928 ^ _782435) ^ [] : [_1331538 = _1331536, -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331534), _1331538), _1331536) = c_Groups_Oone__class_Oone(_1331534))]]], (28934 ^ _782435) ^ [_1331836, _1331838, _1331840] : [class_Rings_Odivision__ring(_1331836), -(_1331838 = c_Groups_Ozero__class_Ozero(_1331836)), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1331836), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331836), _1331840), _1331838)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331836), _1331840), hAPP(c_Groups_Ouminus__class_Ouminus(_1331836), _1331838)))], (28944 ^ _782435) ^ [_1331984, _1331986, _1331988] : [class_Rings_Odivision__ring(_1331984), -(_1331986 = c_Groups_Ozero__class_Ozero(_1331984)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331984), hAPP(c_Groups_Ouminus__class_Ouminus(_1331984), _1331988)), hAPP(c_Groups_Ouminus__class_Ouminus(_1331984), _1331986)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1331984), _1331988), _1331986))], (28954 ^ _782435) ^ [_1332132, _1332134, _1332136] : [class_Rings_Ocomm__semiring__1(_1332132), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332132), hAPP(hAPP(c_Power_Opower__class_Opower(_1332132), _1332134), _1332136)), _1332134) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332132), _1332134), hAPP(c_Nat_OSuc, _1332136)))], (28960 ^ _782435) ^ [_1332263, _1332265, _1332267] : [class_Rings_Ocomm__semiring__1(_1332263), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332263), _1332265), hAPP(hAPP(c_Power_Opower__class_Opower(_1332263), _1332265), _1332267)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332263), _1332265), hAPP(c_Nat_OSuc, _1332267)))], (28966 ^ _782435) ^ [_1332394, _1332396, _1332398] : [class_Rings_Ocomm__semiring__1(_1332394), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1332394), _1332396), hAPP(c_Nat_OSuc, _1332398)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332394), _1332396), hAPP(hAPP(c_Power_Opower__class_Opower(_1332394), _1332396), _1332398)))], (28972 ^ _782435) ^ [_1332525, _1332527] : [class_Rings_Ocomm__semiring__1(_1332525), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1332525), _1332527), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1332525))], (28978 ^ _782435) ^ [_1332620, _1332622, _1332624, _1332626] : [class_Rings_Ocomm__semiring__1(_1332620), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1332620), hAPP(hAPP(c_Power_Opower__class_Opower(_1332620), _1332622), _1332624)), hAPP(hAPP(c_Power_Opower__class_Opower(_1332620), _1332622), _1332626)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1332620), _1332622), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332624), _1332626)))], (28984 ^ _782435) ^ [_1332775, _1332777] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1332775)), -(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), _1332775), _1332777))))], (28990 ^ _782435) ^ [_1332872, _1332874, _1332876] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332872), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1332874), _1332876)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332872), _1332874)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1332872), _1332876)))], (28992 ^ _782435) ^ [_1332929, _1332931, _1332933] : [class_Rings_Oring__1(_1332929), hBOOL(hAPP(hAPP(c_member(_1332929), _1332931), c_Int_Oring__1__class_OInts(_1332929))), -(hBOOL(hAPP(hAPP(c_member(_1332929), hAPP(hAPP(c_Power_Opower__class_Opower(_1332929), _1332931), _1332933)), c_Int_Oring__1__class_OInts(_1332929))))], (29002 ^ _782435) ^ [_1333112, _1333114, _1333116, _1333118, _1333120] : [class_Fields_Ofield__inverse__zero(_1333112), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333114), _1333116)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333114, _1333112), hAPP(hAPP(c_COMBS(_1333114, _1333112, _1333112), hAPP(hAPP(c_COMBB(_1333112, tc_fun(_1333112, _1333112), _1333114), c_Rings_Oinverse__class_Odivide(_1333112)), _1333118)), _1333120)), _1333116) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333112), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333114, _1333112), _1333118), _1333116)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333114, _1333112), _1333120), _1333116)))], (29012 ^ _782435) ^ [_1333379, _1333381, _1333383] : [class_Fields_Ofield(_1333379), -(_1333381 = c_Groups_Oone__class_Oone(_1333379)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1333379), hAPP(c_Power_Opower__class_Opower(_1333379), _1333381)), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1333383)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1333379), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1333379), hAPP(hAPP(c_Power_Opower__class_Opower(_1333379), _1333381), _1333383)), c_Groups_Oone__class_Oone(_1333379))), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1333379), _1333381), c_Groups_Oone__class_Oone(_1333379))))], (29022 ^ _782435) ^ [_1333581, _1333583] : [-(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), _1333581)), _1333583))))], (29024 ^ _782435) ^ [_1333617, _1333619, _1333621, _1333623] : [class_Groups_Ocomm__monoid__mult(_1333617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1333619), _1333621)), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1333619, _1333617), hAPP(c_COMBK(_1333617, _1333619), _1333623)), _1333621) = hAPP(hAPP(c_Power_Opower__class_Opower(_1333617), _1333623), hAPP(c_Finite__Set_Ocard(_1333619), _1333621)))], (29034 ^ _782435) ^ [_1333825, _1333827] : [_1333825 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333827), _1333825) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (29040 ^ _782435) ^ [_1333908, _1333910] : [-(_1333908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333910), _1333908) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1333910), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1333910), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1333908), c_Groups_Oone__class_Oone(tc_Nat_Onat)))))], (29056 ^ _782435) ^ [_1334134, _1334136] : [29057 ^ _782435 : [(29058 ^ _782435) ^ [] : [-(_1334134 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (29060 ^ _782435) ^ [] : [_1334136 = 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), _1334134)), _1334136))))], (29046 ^ _782435) ^ [_1333985, _1333987] : [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), _1333985)), _1333987))), _1333985 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1333987 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29064 ^ _782435) ^ [_1334270, _1334272] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1334270), _1334272)), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1334270, tc_HOL_Obool)), hAPP(c_Set_OPow(_1334270), _1334272)) = 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(_1334270), _1334272)))], (29070 ^ _782435) ^ [_1334397, _1334399, _1334401, _1334403] : [class_Rings_Olinordered__semidom(_1334397), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334397), _1334399), _1334401)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1334397), c_Groups_Ozero__class_Ozero(_1334397)), _1334399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1334403)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1334397), hAPP(hAPP(c_Power_Opower__class_Opower(_1334397), _1334399), _1334403)), hAPP(hAPP(c_Power_Opower__class_Opower(_1334397), _1334401), _1334403))))], (29088 ^ _782435) ^ [_1334726, _1334728, _1334730, _1334732] : [class_Fields_Ofield(_1334726), -(_1334728 = c_Groups_Ozero__class_Ozero(_1334726)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1334730), _1334732)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1334726), _1334728), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1334732), _1334730)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1334726), hAPP(hAPP(c_Power_Opower__class_Opower(_1334726), _1334728), _1334732)), hAPP(hAPP(c_Power_Opower__class_Opower(_1334726), _1334728), _1334730)))], (29102 ^ _782435) ^ [_1335010, _1335012, _1335014] : [class_Rings_Olinordered__semidom(_1335010), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335010), c_Groups_Oone__class_Oone(_1335010)), _1335012)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1335014)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335010), c_Groups_Oone__class_Oone(_1335010)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335010), _1335012), _1335014))))], (29116 ^ _782435) ^ [_1335251, _1335253, _1335255, _1335257] : [class_Rings_Olinordered__semidom(_1335251), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1335251), c_Groups_Oone__class_Oone(_1335251)), _1335253)), 29123 ^ _782435 : [(29124 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335251), hAPP(hAPP(c_Power_Opower__class_Opower(_1335251), _1335253), _1335255)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335251), _1335253), _1335257))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335255), _1335257)))], (29130 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1335255), _1335257)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1335251), hAPP(hAPP(c_Power_Opower__class_Opower(_1335251), _1335253), _1335255)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335251), _1335253), _1335257))))]]], (29136 ^ _782435) ^ [_1335626, _1335628, _1335630] : [class_Rings_Oring__1__no__zero__divisors(_1335626), -(_1335628 = c_Groups_Ozero__class_Ozero(_1335626)), hAPP(hAPP(c_Power_Opower__class_Opower(_1335626), _1335628), _1335630) = c_Groups_Ozero__class_Ozero(_1335626)], (29146 ^ _782435) ^ [_1335785] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1335785) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29158 ^ _782435) ^ [_1335924, _1335926] : [29159 ^ _782435 : [(29160 ^ _782435) ^ [] : [_1335926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (29162 ^ _782435) ^ [] : [_1335924 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1335924), _1335926) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29148 ^ _782435) ^ [_1335826, _1335828] : [hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1335826), _1335828) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1335828 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1335826 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (29166 ^ _782435) ^ [_1336053, _1336055, _1336057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336053)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336053), _1336055)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336053), _1336057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1336055), _1336057)))], (29186 ^ _782435) ^ [_1336355, _1336357] : [29187 ^ _782435 : [(29188 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336355))], (29190 ^ _782435) ^ [] : [_1336357 = 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), _1336355), _1336357))))], (29176 ^ _782435) ^ [_1336249, _1336251] : [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), _1336249), _1336251))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1336249))), -(_1336251 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (29194 ^ _782435) ^ [_1336492, _1336494, _1336496, _1336498] : [class_Groups_Ocomm__monoid__mult(_1336492), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1336492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336492), _1336494), _1336496)), _1336498) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336492), hAPP(hAPP(c_Power_Opower__class_Opower(_1336492), _1336494), _1336498)), hAPP(hAPP(c_Power_Opower__class_Opower(_1336492), _1336496), _1336498)))], (29200 ^ _782435) ^ [_1336651, _1336653, _1336655] : [class_Groups_Omonoid__mult(_1336651), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336651), hAPP(hAPP(c_Power_Opower__class_Opower(_1336651), _1336653), _1336655)), _1336653) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1336651), _1336653), hAPP(hAPP(c_Power_Opower__class_Opower(_1336651), _1336653), _1336655)))], (29206 ^ _782435) ^ [_1336792, _1336794] : [class_Groups_Omonoid__mult(_1336792), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1336792), c_Groups_Oone__class_Oone(_1336792)), _1336794) = c_Groups_Oone__class_Oone(_1336792))], (29212 ^ _782435) ^ [_1336891, _1336893, _1336895] : [class_Rings_Osemiring__1(_1336891), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336891), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1336893), _1336895)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1336891), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1336891), _1336893)), _1336895))], (29218 ^ _782435) ^ [_1337016, _1337018, _1337020, _1337022] : [class_Groups_Omonoid__mult(_1337016), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337016), _1337018), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1337020), _1337022)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337016), hAPP(hAPP(c_Power_Opower__class_Opower(_1337016), _1337018), _1337020)), _1337022))], (29224 ^ _782435) ^ [_1337155, _1337157, _1337159, _1337161] : [class_Fields_Ofield__inverse__zero(_1337155), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337155), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337155), _1337157), _1337159)), _1337161) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1337155), hAPP(hAPP(c_Power_Opower__class_Opower(_1337155), _1337157), _1337161)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337155), _1337159), _1337161)))], (29230 ^ _782435) ^ [_1337314, _1337316, _1337318] : [class_Rings_Olinordered__idom(_1337314), -(hAPP(c_Groups_Oabs__class_Oabs(_1337314), hAPP(hAPP(c_Power_Opower__class_Opower(_1337314), _1337316), _1337318)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1337314), hAPP(c_Groups_Oabs__class_Oabs(_1337314), _1337316)), _1337318))], (29236 ^ _782435) ^ [_1337443, _1337445] : [class_Groups_Omonoid__mult(_1337443), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1337443), _1337445), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = _1337445)], (29242 ^ _782435) ^ [_1337534, _1337536, _1337538] : [class_Rings_Olinordered__semidom(_1337534), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337534), c_Groups_Ozero__class_Ozero(_1337534)), _1337536)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337534), c_Groups_Ozero__class_Ozero(_1337534)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337534), _1337536), _1337538))))], (29252 ^ _782435) ^ [_1337717, _1337719, _1337721, _1337723] : [class_Rings_Olinordered__semidom(_1337717), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337717), _1337719), _1337721)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337717), c_Groups_Ozero__class_Ozero(_1337717)), _1337719)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1337717), hAPP(hAPP(c_Power_Opower__class_Opower(_1337717), _1337719), _1337723)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337717), _1337721), _1337723))))], (29266 ^ _782435) ^ [_1337986, _1337988, _1337990] : [class_Rings_Olinordered__semidom(_1337986), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337986), c_Groups_Ozero__class_Ozero(_1337986)), _1337988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1337986), c_Groups_Ozero__class_Ozero(_1337986)), hAPP(hAPP(c_Power_Opower__class_Opower(_1337986), _1337988), _1337990))))], (29276 ^ _782435) ^ [_1338169, _1338171, _1338173] : [class_Power_Opower(_1338169), class_Rings_Omult__zero(_1338169), class_Rings_Ono__zero__divisors(_1338169), class_Rings_Ozero__neq__one(_1338169), 29291 ^ _782435 : [(29292 ^ _782435) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1338169), _1338171), _1338173) = c_Groups_Ozero__class_Ozero(_1338169), 29295 ^ _782435 : [(29296 ^ _782435) ^ [] : [-(_1338171 = c_Groups_Ozero__class_Ozero(_1338169))], (29298 ^ _782435) ^ [] : [_1338173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (29300 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1338169), _1338171), _1338173) = c_Groups_Ozero__class_Ozero(_1338169)), _1338171 = c_Groups_Ozero__class_Ozero(_1338169), -(_1338173 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (29310 ^ _782435) ^ [_1338661, _1338663, _1338665] : [class_Rings_Olinordered__semidom(_1338661), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338661), c_Groups_Oone__class_Oone(_1338661)), _1338663)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1338661), c_Groups_Oone__class_Oone(_1338661)), hAPP(hAPP(c_Power_Opower__class_Opower(_1338661), _1338663), _1338665))))], (29320 ^ _782435) ^ [_1338844, _1338846] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1338844), c_Groups_Ozero__class_Ozero(_1338844)), hAPP(c_Nat_OSuc, _1338846)) = c_Groups_Ozero__class_Ozero(_1338844)), class_Power_Opower(_1338844), class_Rings_Osemiring__0(_1338844)], (29330 ^ _782435) ^ [_1338999, _1339001, _1339003, _1339005] : [class_Rings_Olinordered__semidom(_1338999), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1338999), c_Groups_Oone__class_Oone(_1338999)), _1339001)), 29337 ^ _782435 : [(29338 ^ _782435) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1338999), _1339001), _1339003) = hAPP(hAPP(c_Power_Opower__class_Opower(_1338999), _1339001), _1339005), -(_1339003 = _1339005)], (29344 ^ _782435) ^ [] : [_1339003 = _1339005, -(hAPP(hAPP(c_Power_Opower__class_Opower(_1338999), _1339001), _1339003) = hAPP(hAPP(c_Power_Opower__class_Opower(_1338999), _1339001), _1339005))]]], (29350 ^ _782435) ^ [_1339338, _1339340, _1339342] : [class_Power_Opower(_1339338), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339338), _1339340), hAPP(c_Nat_OSuc, _1339342)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339338), _1339340), hAPP(hAPP(c_Power_Opower__class_Opower(_1339338), _1339340), _1339342)))], (29356 ^ _782435) ^ [_1339469, _1339471, _1339473] : [class_Groups_Omonoid__mult(_1339469), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339469), _1339471), hAPP(c_Nat_OSuc, _1339473)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339469), hAPP(hAPP(c_Power_Opower__class_Opower(_1339469), _1339471), _1339473)), _1339471))], (29362 ^ _782435) ^ [_1339600, _1339602] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1339600)), -(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), _1339600), _1339602))))], (29368 ^ _782435) ^ [_1339697, _1339699] : [class_Power_Opower(_1339697), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339697), _1339699), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(_1339697))], (29374 ^ _782435) ^ [_1339792, _1339794, _1339796, _1339798] : [class_Groups_Omonoid__mult(_1339792), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339792), _1339794), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1339796), _1339798)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1339792), hAPP(hAPP(c_Power_Opower__class_Opower(_1339792), _1339794), _1339796)), hAPP(hAPP(c_Power_Opower__class_Opower(_1339792), _1339794), _1339798)))], (29380 ^ _782435) ^ [_1339947, _1339949, _1339951, _1339953] : [class_Fields_Ofield(_1339947), -(_1339949 = c_Groups_Ozero__class_Ozero(_1339947)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1339947), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339947), _1339951), _1339949)), _1339953) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1339947), hAPP(hAPP(c_Power_Opower__class_Opower(_1339947), _1339951), _1339953)), hAPP(hAPP(c_Power_Opower__class_Opower(_1339947), _1339949), _1339953)))], (29390 ^ _782435) ^ [_1340125, _1340127, _1340129] : [class_Fields_Ofield__inverse__zero(_1340125), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340125), c_Groups_Oone__class_Oone(_1340125)), hAPP(hAPP(c_Power_Opower__class_Opower(_1340125), _1340127), _1340129)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340125), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1340125), c_Groups_Oone__class_Oone(_1340125)), _1340127)), _1340129))], (29396 ^ _782435) ^ [_1340274, _1340276, _1340278] : [class_Rings_Olinordered__idom(_1340274), -(hAPP(c_Groups_Oabs__class_Oabs(_1340274), hAPP(hAPP(c_Power_Opower__class_Opower(_1340274), hAPP(c_Groups_Ouminus__class_Ouminus(_1340274), _1340276)), _1340278)) = hAPP(c_Groups_Oabs__class_Oabs(_1340274), hAPP(hAPP(c_Power_Opower__class_Opower(_1340274), _1340276), _1340278)))], (29402 ^ _782435) ^ [_1340413, _1340415, _1340417, _1340419] : [class_Rings_Olinordered__semidom(_1340413), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340413), hAPP(hAPP(c_Power_Opower__class_Opower(_1340413), _1340415), _1340417)), hAPP(hAPP(c_Power_Opower__class_Opower(_1340413), _1340419), _1340417))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340413), c_Groups_Ozero__class_Ozero(_1340413)), _1340419)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1340413), _1340415), _1340419)))], (29416 ^ _782435) ^ [_1340682, _1340684, _1340686, _1340688] : [class_Rings_Olinordered__semidom(_1340682), hAPP(hAPP(c_Power_Opower__class_Opower(_1340682), _1340684), hAPP(c_Nat_OSuc, _1340686)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1340682), _1340688), hAPP(c_Nat_OSuc, _1340686)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340682), c_Groups_Ozero__class_Ozero(_1340682)), _1340684)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1340682), c_Groups_Ozero__class_Ozero(_1340682)), _1340688)), -(_1340684 = _1340688)], (29434 ^ _782435) ^ [_1341009, _1341011, _1341013, _1341015] : [class_Rings_Olinordered__semidom(_1341009), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341009), hAPP(hAPP(c_Power_Opower__class_Opower(_1341009), _1341011), hAPP(c_Nat_OSuc, _1341013))), hAPP(hAPP(c_Power_Opower__class_Opower(_1341009), _1341015), hAPP(c_Nat_OSuc, _1341013)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341009), c_Groups_Ozero__class_Ozero(_1341009)), _1341015)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1341009), _1341011), _1341015)))], (29448 ^ _782435) ^ [_1341290, _1341292, _1341294] : [class_Rings_Olinordered__semidom(_1341290), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341290), c_Groups_Oone__class_Oone(_1341290)), _1341292)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341290), hAPP(hAPP(c_Power_Opower__class_Opower(_1341290), _1341292), _1341294)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341290), _1341292), hAPP(hAPP(c_Power_Opower__class_Opower(_1341290), _1341292), _1341294)))))], (29458 ^ _782435) ^ [_1341501, _1341503, _1341505] : [class_Rings_Olinordered__semidom(_1341501), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341501), c_Groups_Oone__class_Oone(_1341501)), _1341503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341501), c_Groups_Oone__class_Oone(_1341501)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1341501), _1341503), hAPP(hAPP(c_Power_Opower__class_Opower(_1341501), _1341503), _1341505)))))], (29468 ^ _782435) ^ [_1341700, _1341702] : [class_Power_Opower(_1341700), class_Rings_Osemiring__0(_1341700), 29475 ^ _782435 : [(29476 ^ _782435) ^ [] : [_1341702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341700), c_Groups_Ozero__class_Ozero(_1341700)), _1341702) = c_Groups_Oone__class_Oone(_1341700))], (29482 ^ _782435) ^ [] : [-(_1341702 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1341700), c_Groups_Ozero__class_Ozero(_1341700)), _1341702) = c_Groups_Ozero__class_Ozero(_1341700))]]], (29488 ^ _782435) ^ [_1341974, _1341976, _1341978] : [class_Rings_Olinordered__semidom(_1341974), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341974), c_Groups_Oone__class_Oone(_1341974)), _1341976)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1341974), c_Groups_Oone__class_Oone(_1341974)), hAPP(hAPP(c_Power_Opower__class_Opower(_1341974), _1341976), hAPP(c_Nat_OSuc, _1341978)))))], (29498 ^ _782435) ^ [_1342163, _1342165, _1342167, _1342169] : [class_Rings_Olinordered__semidom(_1342163), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342163), c_Groups_Oone__class_Oone(_1342163)), _1342165)), 29505 ^ _782435 : [(29506 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342163), hAPP(hAPP(c_Power_Opower__class_Opower(_1342163), _1342165), _1342167)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342163), _1342165), _1342169))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342167), _1342169)))], (29512 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342167), _1342169)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342163), hAPP(hAPP(c_Power_Opower__class_Opower(_1342163), _1342165), _1342167)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342163), _1342165), _1342169))))]]], (29518 ^ _782435) ^ [_1342538, _1342540, _1342542, _1342544] : [class_Rings_Olinordered__semidom(_1342538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342538), c_Groups_Oone__class_Oone(_1342538)), _1342540)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342538), hAPP(hAPP(c_Power_Opower__class_Opower(_1342538), _1342540), _1342542)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342538), _1342540), _1342544))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342542), _1342544)))], (29532 ^ _782435) ^ [_1342803, _1342805, _1342807, _1342809] : [class_Rings_Olinordered__semidom(_1342803), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1342805), _1342807)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342803), c_Groups_Oone__class_Oone(_1342803)), _1342809)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1342803), hAPP(hAPP(c_Power_Opower__class_Opower(_1342803), _1342809), _1342805)), hAPP(hAPP(c_Power_Opower__class_Opower(_1342803), _1342809), _1342807))))], (29546 ^ _782435) ^ [_1343068, _1343070, _1343072] : [class_Rings_Olinordered__idom(_1343068), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343068), c_Groups_Ozero__class_Ozero(_1343068)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343068), hAPP(c_Groups_Oabs__class_Oabs(_1343068), _1343070)), _1343072))))], (29552 ^ _782435) ^ [_1343189, _1343191, _1343193, _1343195] : [class_Rings_Olinordered__semidom(_1343189), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1343191), _1343193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343189), c_Groups_Oone__class_Oone(_1343189)), _1343195)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343189), hAPP(hAPP(c_Power_Opower__class_Opower(_1343189), _1343195), _1343191)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343189), _1343195), _1343193))))], (29566 ^ _782435) ^ [_1343454, _1343456, _1343458] : [class_Rings_Oring__1(_1343454), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1343454), hAPP(c_Groups_Ouminus__class_Ouminus(_1343454), _1343456)), _1343458) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343454), hAPP(hAPP(c_Power_Opower__class_Opower(_1343454), hAPP(c_Groups_Ouminus__class_Ouminus(_1343454), c_Groups_Oone__class_Oone(_1343454))), _1343458)), hAPP(hAPP(c_Power_Opower__class_Opower(_1343454), _1343456), _1343458)))], (29572 ^ _782435) ^ [_1343619, _1343621, _1343623] : [class_Rings_Olinordered__semidom(_1343619), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343619), c_Groups_Ozero__class_Ozero(_1343619)), _1343621)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343619), _1343621), c_Groups_Oone__class_Oone(_1343619))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1343619), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1343619), _1343621), hAPP(hAPP(c_Power_Opower__class_Opower(_1343619), _1343621), _1343623))), hAPP(hAPP(c_Power_Opower__class_Opower(_1343619), _1343621), _1343623))))], (29586 ^ _782435) ^ [_1343902, _1343904, _1343906, _1343908] : [class_Rings_Olinordered__semidom(_1343902), hAPP(hAPP(c_Power_Opower__class_Opower(_1343902), _1343904), _1343906) = hAPP(hAPP(c_Power_Opower__class_Opower(_1343902), _1343908), _1343906), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343902), c_Groups_Ozero__class_Ozero(_1343902)), _1343904)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1343902), c_Groups_Ozero__class_Ozero(_1343902)), _1343908)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1343906)), -(_1343904 = _1343908)], (29608 ^ _782435) ^ [_1344277, _1344279, _1344281] : [class_Rings_Olinordered__semidom(_1344277), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344277), c_Groups_Ozero__class_Ozero(_1344277)), _1344279)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344277), _1344279), c_Groups_Oone__class_Oone(_1344277))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344277), hAPP(hAPP(c_Power_Opower__class_Opower(_1344277), _1344279), hAPP(c_Nat_OSuc, _1344281))), c_Groups_Oone__class_Oone(_1344277))))], (29622 ^ _782435) ^ [_1344538, _1344540, _1344542, _1344544] : [class_Rings_Olinordered__semidom(_1344538), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1344540), _1344542)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344538), c_Groups_Ozero__class_Ozero(_1344538)), _1344544)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344538), _1344544), c_Groups_Oone__class_Oone(_1344538))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1344538), hAPP(hAPP(c_Power_Opower__class_Opower(_1344538), _1344544), _1344542)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344538), _1344544), _1344540))))], (29640 ^ _782435) ^ [_1344877, _1344879, _1344881, _1344883] : [class_Rings_Olinordered__semidom(_1344877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1344879), _1344881)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344877), c_Groups_Ozero__class_Ozero(_1344877)), _1344883)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344877), _1344883), c_Groups_Oone__class_Oone(_1344877))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1344877), hAPP(hAPP(c_Power_Opower__class_Opower(_1344877), _1344883), _1344881)), hAPP(hAPP(c_Power_Opower__class_Opower(_1344877), _1344883), _1344879))))], (29658 ^ _782435) ^ [_1345216, _1345218, _1345220, _1345222] : [class_Rings_Olinordered__semidom(_1345216), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345216), c_Groups_Oone__class_Oone(_1345216)), _1345218)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345216), hAPP(hAPP(c_Power_Opower__class_Opower(_1345216), _1345218), _1345220)), hAPP(hAPP(c_Power_Opower__class_Opower(_1345216), _1345218), _1345222))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1345220), _1345222)))], (29672 ^ _782435) ^ [_1345481, _1345483, _1345485, _1345487] : [class_Fields_Olinordered__field__inverse__zero(_1345481), 29675 ^ _782435 : [(29702 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), _1345483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345481), _1345485), _1345487)))), 29705 ^ _782435 : [(29706 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), c_Groups_Ozero__class_Ozero(_1345481)), _1345487)))], (29708 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345481), _1345483), _1345487)), _1345485))]], 29709 ^ _782435 : [(29710 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), c_Groups_Ozero__class_Ozero(_1345481)), _1345487))], (29712 ^ _782435) ^ [] : [29713 ^ _782435 : [(29714 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), _1345487), c_Groups_Ozero__class_Ozero(_1345481))))], (29716 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), _1345485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345481), _1345483), _1345487)))]], 29717 ^ _782435 : [(29718 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), _1345487), c_Groups_Ozero__class_Ozero(_1345481)))], (29720 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), _1345483), c_Groups_Ozero__class_Ozero(_1345481)))]]]]], (29676 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), _1345483), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1345481), _1345485), _1345487))), 29679 ^ _782435 : [(29680 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), c_Groups_Ozero__class_Ozero(_1345481)), _1345487)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345481), _1345483), _1345487)), _1345485)))], (29686 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), c_Groups_Ozero__class_Ozero(_1345481)), _1345487))), 29689 ^ _782435 : [(29690 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), _1345487), c_Groups_Ozero__class_Ozero(_1345481))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), _1345485), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1345481), _1345483), _1345487))))], (29696 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1345481), _1345487), c_Groups_Ozero__class_Ozero(_1345481)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1345481), _1345483), c_Groups_Ozero__class_Ozero(_1345481))))]]]]]]], (29724 ^ _782435) ^ [_1346434, _1346436, _1346438, _1346440] : [class_Fields_Olinordered__field__inverse__zero(_1346434), 29727 ^ _782435 : [(29754 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346434), _1346436), _1346438)), _1346440))), 29757 ^ _782435 : [(29758 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), c_Groups_Ozero__class_Ozero(_1346434)), _1346438)))], (29760 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), _1346436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346434), _1346440), _1346438)))]], 29761 ^ _782435 : [(29762 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), c_Groups_Ozero__class_Ozero(_1346434)), _1346438))], (29764 ^ _782435) ^ [] : [29765 ^ _782435 : [(29766 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), _1346438), c_Groups_Ozero__class_Ozero(_1346434))))], (29768 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346434), _1346440), _1346438)), _1346436))]], 29769 ^ _782435 : [(29770 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), _1346438), c_Groups_Ozero__class_Ozero(_1346434)))], (29772 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), c_Groups_Ozero__class_Ozero(_1346434)), _1346440))]]]]], (29728 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1346434), _1346436), _1346438)), _1346440)), 29731 ^ _782435 : [(29732 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), c_Groups_Ozero__class_Ozero(_1346434)), _1346438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), _1346436), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346434), _1346440), _1346438))))], (29738 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), c_Groups_Ozero__class_Ozero(_1346434)), _1346438))), 29741 ^ _782435 : [(29742 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), _1346438), c_Groups_Ozero__class_Ozero(_1346434))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1346434), _1346440), _1346438)), _1346436)))], (29748 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1346434), _1346438), c_Groups_Ozero__class_Ozero(_1346434)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1346434), c_Groups_Ozero__class_Ozero(_1346434)), _1346440)))]]]]]]], (29776 ^ _782435) ^ [_1347387, _1347389, _1347391, _1347393] : [class_Fields_Olinordered__field(_1347387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347387), c_Groups_Ozero__class_Ozero(_1347387)), _1347389)), 29783 ^ _782435 : [(29784 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347387), _1347391), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347387), _1347393), _1347389))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347387), _1347391), _1347389)), _1347393)))], (29790 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347387), _1347391), _1347389)), _1347393)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347387), _1347391), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347387), _1347393), _1347389))))]]], (29796 ^ _782435) ^ [_1347768, _1347770, _1347772, _1347774] : [class_Fields_Olinordered__field(_1347768), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1347768), c_Groups_Ozero__class_Ozero(_1347768)), _1347770)), 29803 ^ _782435 : [(29804 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347768), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347768), _1347772), _1347770)), _1347774)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347768), _1347772), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347768), _1347774), _1347770))))], (29810 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347768), _1347772), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1347768), _1347774), _1347770))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1347768), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1347768), _1347772), _1347770)), _1347774)))]]], (29816 ^ _782435) ^ [_1348149, _1348151, _1348153, _1348155, _1348157] : [class_Fields_Ofield__inverse__zero(_1348149), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348149), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348149), _1348151), _1348153)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348149), _1348155), _1348157)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348149), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348149), _1348151), _1348155)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1348149), _1348153), _1348157)))], (29822 ^ _782435) ^ [_1348326, _1348328, _1348330] : [class_Fields_Ofield__inverse__zero(_1348326), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348326), hAPP(c_Groups_Ouminus__class_Ouminus(_1348326), _1348328)), hAPP(c_Groups_Ouminus__class_Ouminus(_1348326), _1348330)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348326), _1348328), _1348330))], (29828 ^ _782435) ^ [_1348455, _1348457, _1348459] : [class_Fields_Ofield__inverse__zero(_1348455), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1348455), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348455), _1348457), _1348459)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348455), _1348457), hAPP(c_Groups_Ouminus__class_Ouminus(_1348455), _1348459)))], (29834 ^ _782435) ^ [_1348584, _1348586, _1348588] : [class_Fields_Olinordered__field__inverse__zero(_1348584), -(hAPP(c_Groups_Oabs__class_Oabs(_1348584), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348584), _1348586), _1348588)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348584), hAPP(c_Groups_Oabs__class_Oabs(_1348584), _1348586)), hAPP(c_Groups_Oabs__class_Oabs(_1348584), _1348588)))], (29840 ^ _782435) ^ [_1348723, _1348725, _1348727, _1348729] : [class_Fields_Olinordered__field__inverse__zero(_1348723), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348723), _1348725), _1348727)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348723), _1348729), c_Groups_Ozero__class_Ozero(_1348723))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348723), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348723), _1348727), _1348729)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348723), _1348725), _1348729))))], (29854 ^ _782435) ^ [_1348992, _1348994, _1348996, _1348998] : [class_Fields_Olinordered__field__inverse__zero(_1348992), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348992), _1348994), _1348996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348992), c_Groups_Ozero__class_Ozero(_1348992)), _1348998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1348992), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348992), _1348994), _1348998)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1348992), _1348996), _1348998))))], (29868 ^ _782435) ^ [_1349261, _1349263, _1349265] : [class_Fields_Olinordered__field__inverse__zero(_1349261), 29871 ^ _782435 : [(29872 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349261), _1349263), _1349265)), c_Groups_Ozero__class_Ozero(_1349261))), 29877 ^ _782435 : [(29878 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), c_Groups_Ozero__class_Ozero(_1349261)), _1349263)))], (29880 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), _1349265), c_Groups_Ozero__class_Ozero(_1349261))))]], 29881 ^ _782435 : [(29882 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), _1349263), c_Groups_Ozero__class_Ozero(_1349261))))], (29884 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), c_Groups_Ozero__class_Ozero(_1349261)), _1349265)))]]], (29886 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349261), _1349263), _1349265)), c_Groups_Ozero__class_Ozero(_1349261)))), 29887 ^ _782435 : [(29888 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), c_Groups_Ozero__class_Ozero(_1349261)), _1349263)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), _1349265), c_Groups_Ozero__class_Ozero(_1349261)))], (29894 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), _1349263), c_Groups_Ozero__class_Ozero(_1349261))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349261), c_Groups_Ozero__class_Ozero(_1349261)), _1349265))]]]]], (29902 ^ _782435) ^ [_1349851, _1349853, _1349855] : [class_Fields_Olinordered__field__inverse__zero(_1349851), 29905 ^ _782435 : [(29906 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), c_Groups_Ozero__class_Ozero(_1349851)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349851), _1349853), _1349855))), 29911 ^ _782435 : [(29912 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), c_Groups_Ozero__class_Ozero(_1349851)), _1349853)))], (29914 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), c_Groups_Ozero__class_Ozero(_1349851)), _1349855)))]], 29915 ^ _782435 : [(29916 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), _1349853), c_Groups_Ozero__class_Ozero(_1349851))))], (29918 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), _1349855), c_Groups_Ozero__class_Ozero(_1349851))))]]], (29920 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), c_Groups_Ozero__class_Ozero(_1349851)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1349851), _1349853), _1349855)))), 29921 ^ _782435 : [(29922 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), c_Groups_Ozero__class_Ozero(_1349851)), _1349853)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), c_Groups_Ozero__class_Ozero(_1349851)), _1349855))], (29928 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), _1349853), c_Groups_Ozero__class_Ozero(_1349851))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1349851), _1349855), c_Groups_Ozero__class_Ozero(_1349851)))]]]]], (29936 ^ _782435) ^ [_1350441, _1350443, _1350445, _1350447] : [class_Fields_Olinordered__field(_1350441), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350441), _1350443), _1350445)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350441), _1350447), c_Groups_Ozero__class_Ozero(_1350441))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350441), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350441), _1350445), _1350447)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350441), _1350443), _1350447))))], (29950 ^ _782435) ^ [_1350710, _1350712, _1350714, _1350716] : [class_Fields_Olinordered__field(_1350710), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350710), _1350712), _1350714)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350710), c_Groups_Ozero__class_Ozero(_1350710)), _1350716)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350710), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350710), _1350712), _1350716)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350710), _1350714), _1350716))))], (29964 ^ _782435) ^ [_1350979, _1350981, _1350983] : [class_Fields_Olinordered__field(_1350979), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350979), _1350981), c_Groups_Ozero__class_Ozero(_1350979))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350979), _1350983), c_Groups_Ozero__class_Ozero(_1350979))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1350979), c_Groups_Ozero__class_Ozero(_1350979)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1350979), _1350981), _1350983))))], (29978 ^ _782435) ^ [_1351234, _1351236, _1351238] : [class_Fields_Olinordered__field(_1351234), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351234), _1351236), c_Groups_Ozero__class_Ozero(_1351234))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351234), c_Groups_Ozero__class_Ozero(_1351234)), _1351238)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351234), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351234), _1351236), _1351238)), c_Groups_Ozero__class_Ozero(_1351234))))], (29992 ^ _782435) ^ [_1351489, _1351491, _1351493] : [class_Fields_Olinordered__field(_1351489), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351489), c_Groups_Ozero__class_Ozero(_1351489)), _1351491)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351489), _1351493), c_Groups_Ozero__class_Ozero(_1351489))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351489), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351489), _1351491), _1351493)), c_Groups_Ozero__class_Ozero(_1351489))))], (30006 ^ _782435) ^ [_1351744, _1351746, _1351748] : [class_Fields_Olinordered__field(_1351744), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351744), c_Groups_Ozero__class_Ozero(_1351744)), _1351746)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351744), c_Groups_Ozero__class_Ozero(_1351744)), _1351748)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351744), c_Groups_Ozero__class_Ozero(_1351744)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351744), _1351746), _1351748))))], (30020 ^ _782435) ^ [_1351999, _1352001, _1352003] : [class_Fields_Olinordered__field__inverse__zero(_1351999), 30023 ^ _782435 : [(30024 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351999), _1352001), _1352003)), c_Groups_Ozero__class_Ozero(_1351999))), 30029 ^ _782435 : [(30030 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), c_Groups_Ozero__class_Ozero(_1351999)), _1352001)))], (30032 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), _1352003), c_Groups_Ozero__class_Ozero(_1351999))))]], 30033 ^ _782435 : [(30034 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), _1352001), c_Groups_Ozero__class_Ozero(_1351999))))], (30036 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), c_Groups_Ozero__class_Ozero(_1351999)), _1352003)))]]], (30038 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1351999), _1352001), _1352003)), c_Groups_Ozero__class_Ozero(_1351999)))), 30039 ^ _782435 : [(30040 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), c_Groups_Ozero__class_Ozero(_1351999)), _1352001)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), _1352003), c_Groups_Ozero__class_Ozero(_1351999)))], (30046 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), _1352001), c_Groups_Ozero__class_Ozero(_1351999))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1351999), c_Groups_Ozero__class_Ozero(_1351999)), _1352003))]]]]], (30054 ^ _782435) ^ [_1352589, _1352591, _1352593] : [class_Fields_Olinordered__field__inverse__zero(_1352589), 30057 ^ _782435 : [(30058 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), c_Groups_Ozero__class_Ozero(_1352589)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352589), _1352591), _1352593))), 30063 ^ _782435 : [(30064 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), c_Groups_Ozero__class_Ozero(_1352589)), _1352591)))], (30066 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), c_Groups_Ozero__class_Ozero(_1352589)), _1352593)))]], 30067 ^ _782435 : [(30068 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), _1352591), c_Groups_Ozero__class_Ozero(_1352589))))], (30070 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), _1352593), c_Groups_Ozero__class_Ozero(_1352589))))]]], (30072 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), c_Groups_Ozero__class_Ozero(_1352589)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1352589), _1352591), _1352593)))), 30073 ^ _782435 : [(30074 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), c_Groups_Ozero__class_Ozero(_1352589)), _1352591)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), c_Groups_Ozero__class_Ozero(_1352589)), _1352593))], (30080 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), _1352591), c_Groups_Ozero__class_Ozero(_1352589))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1352589), _1352593), c_Groups_Ozero__class_Ozero(_1352589)))]]]]], (30088 ^ _782435) ^ [_1353179, _1353181, _1353183, _1353185] : [class_Fields_Ofield__inverse__zero(_1353179), 30091 ^ _782435 : [(30108 ^ _782435) ^ [] : [-(_1353181 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353179), _1353183), _1353185)), 30111 ^ _782435 : [(30112 ^ _782435) ^ [] : [_1353185 = c_Groups_Ozero__class_Ozero(_1353179)], (30114 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353179), _1353181), _1353185) = _1353183]], 30115 ^ _782435 : [(30116 ^ _782435) ^ [] : [-(_1353185 = c_Groups_Ozero__class_Ozero(_1353179))], (30118 ^ _782435) ^ [] : [_1353181 = c_Groups_Ozero__class_Ozero(_1353179)]]], (30092 ^ _782435) ^ [] : [_1353181 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353179), _1353183), _1353185), 30095 ^ _782435 : [(30096 ^ _782435) ^ [] : [-(_1353185 = c_Groups_Ozero__class_Ozero(_1353179)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353179), _1353181), _1353185) = _1353183)], (30102 ^ _782435) ^ [] : [_1353185 = c_Groups_Ozero__class_Ozero(_1353179), -(_1353181 = c_Groups_Ozero__class_Ozero(_1353179))]]]]], (30122 ^ _782435) ^ [_1353673, _1353675, _1353677, _1353679] : [class_Fields_Ofield__inverse__zero(_1353673), 30125 ^ _782435 : [(30142 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353673), _1353675), _1353677) = _1353679), 30145 ^ _782435 : [(30146 ^ _782435) ^ [] : [_1353677 = c_Groups_Ozero__class_Ozero(_1353673)], (30148 ^ _782435) ^ [] : [_1353675 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353673), _1353679), _1353677)]], 30149 ^ _782435 : [(30150 ^ _782435) ^ [] : [-(_1353677 = c_Groups_Ozero__class_Ozero(_1353673))], (30152 ^ _782435) ^ [] : [_1353679 = c_Groups_Ozero__class_Ozero(_1353673)]]], (30126 ^ _782435) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1353673), _1353675), _1353677) = _1353679, 30129 ^ _782435 : [(30130 ^ _782435) ^ [] : [-(_1353677 = c_Groups_Ozero__class_Ozero(_1353673)), -(_1353675 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1353673), _1353679), _1353677))], (30136 ^ _782435) ^ [] : [_1353677 = c_Groups_Ozero__class_Ozero(_1353673), -(_1353679 = c_Groups_Ozero__class_Ozero(_1353673))]]]]], (30156 ^ _782435) ^ [_1354167, _1354169, _1354171, _1354173] : [class_Fields_Ofield__inverse__zero(_1354167), -(_1354169 = c_Groups_Ozero__class_Ozero(_1354167)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354167), _1354171), _1354169)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354167), _1354173), _1354169)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354167), _1354171), _1354173))], (30166 ^ _782435) ^ [_1354329, _1354331, _1354333, _1354335] : [class_Fields_Ofield__inverse__zero(_1354329), -(_1354331 = c_Groups_Ozero__class_Ozero(_1354329)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354329), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354329), _1354331), _1354333)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354329), _1354331), _1354335)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354329), _1354333), _1354335))], (30176 ^ _782435) ^ [_1354491, _1354493, _1354495, _1354497, _1354499] : [class_Fields_Ofield(_1354491), -(_1354493 = c_Groups_Ozero__class_Ozero(_1354491)), -(_1354495 = c_Groups_Ozero__class_Ozero(_1354491)), 30187 ^ _782435 : [(30188 ^ _782435) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354491), _1354497), _1354493) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354491), _1354499), _1354495), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354491), _1354497), _1354495) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354491), _1354499), _1354493))], (30194 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354491), _1354497), _1354495) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1354491), _1354499), _1354493), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354491), _1354497), _1354493) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354491), _1354499), _1354495))]]], (30200 ^ _782435) ^ [_1354940, _1354942, _1354944] : [class_Fields_Olinordered__field(_1354940), -(_1354942 = c_Groups_Ozero__class_Ozero(_1354940)), -(hAPP(c_Groups_Oabs__class_Oabs(_1354940), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354940), _1354944), _1354942)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1354940), hAPP(c_Groups_Oabs__class_Oabs(_1354940), _1354944)), hAPP(c_Groups_Oabs__class_Oabs(_1354940), _1354942)))], (30210 ^ _782435) ^ [_1355098, _1355100, _1355102] : [class_Fields_Olinordered__field(_1355098), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355098), c_Groups_Ozero__class_Ozero(_1355098)), _1355100)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355098), c_Groups_Ozero__class_Ozero(_1355098)), _1355102)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355098), c_Groups_Ozero__class_Ozero(_1355098)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355098), _1355100), _1355102))))], (30224 ^ _782435) ^ [_1355353, _1355355, _1355357] : [class_Fields_Olinordered__field(_1355353), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355353), c_Groups_Ozero__class_Ozero(_1355353)), _1355355)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355353), _1355357), c_Groups_Ozero__class_Ozero(_1355353))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355353), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355353), _1355355), _1355357)), c_Groups_Ozero__class_Ozero(_1355353))))], (30238 ^ _782435) ^ [_1355608, _1355610, _1355612, _1355614, _1355616] : [class_Fields_Olinordered__field(_1355608), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355608), c_Groups_Ozero__class_Ozero(_1355608)), _1355610)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1355608), _1355610), _1355612)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355608), c_Groups_Ozero__class_Ozero(_1355608)), _1355614)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355608), _1355614), _1355616)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1355608), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355608), _1355610), _1355616)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1355608), _1355612), _1355614))))], (30260 ^ _782435) ^ [_1356031, _1356033, _1356035, _1356037, _1356039] : [class_Fields_Olinordered__field(_1356031), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356031), c_Groups_Ozero__class_Ozero(_1356031)), _1356033)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356031), _1356033), _1356035)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356031), c_Groups_Ozero__class_Ozero(_1356031)), _1356037)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356031), _1356037), _1356039)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356031), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356031), _1356033), _1356039)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356031), _1356035), _1356037))))], (30282 ^ _782435) ^ [_1356454, _1356456, _1356458, _1356460, _1356462] : [class_Fields_Olinordered__field(_1356454), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356454), c_Groups_Ozero__class_Ozero(_1356454)), _1356456)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356454), _1356456), _1356458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356454), c_Groups_Ozero__class_Ozero(_1356454)), _1356460)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356454), _1356460), _1356462)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356454), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356454), _1356456), _1356462)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356454), _1356458), _1356460))))], (30304 ^ _782435) ^ [_1356877, _1356879, _1356881] : [class_Fields_Olinordered__field(_1356877), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356877), _1356879), c_Groups_Ozero__class_Ozero(_1356877))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1356877), c_Groups_Ozero__class_Ozero(_1356877)), _1356881)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1356877), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1356877), _1356879), _1356881)), c_Groups_Ozero__class_Ozero(_1356877))))], (30318 ^ _782435) ^ [_1357132, _1357134, _1357136] : [class_Fields_Olinordered__field(_1357132), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357132), _1357134), c_Groups_Ozero__class_Ozero(_1357132))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357132), _1357136), c_Groups_Ozero__class_Ozero(_1357132))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1357132), c_Groups_Ozero__class_Ozero(_1357132)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357132), _1357134), _1357136))))], (30332 ^ _782435) ^ [_1357387, _1357389, _1357391, _1357393] : [class_Fields_Olinordered__field(_1357387), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357387), _1357389), _1357391)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357387), _1357393), c_Groups_Ozero__class_Ozero(_1357387))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357387), c_Groups_Ozero__class_Ozero(_1357387)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357387), _1357389), _1357391))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357387), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357387), _1357393), _1357389)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357387), _1357393), _1357391))))], (30350 ^ _782435) ^ [_1357746, _1357748, _1357750, _1357752] : [class_Fields_Olinordered__field(_1357746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357746), _1357748), _1357750)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357746), c_Groups_Ozero__class_Ozero(_1357746)), _1357752)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357746), c_Groups_Ozero__class_Ozero(_1357746)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1357746), _1357750), _1357748))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1357746), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357746), _1357752), _1357750)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1357746), _1357752), _1357748))))], (30368 ^ _782435) ^ [_1358105, _1358107, _1358109, _1358111] : [class_Fields_Olinordered__field(_1358105), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358105), _1358107), c_Groups_Ozero__class_Ozero(_1358105))), 30375 ^ _782435 : [(30376 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358105), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358105), _1358109), _1358107)), _1358111)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358105), _1358111), _1358107)), _1358109)))], (30382 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358105), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358105), _1358111), _1358107)), _1358109)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358105), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358105), _1358109), _1358107)), _1358111)))]]], (30388 ^ _782435) ^ [_1358486, _1358488, _1358490, _1358492] : [class_Fields_Olinordered__field(_1358486), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358486), _1358488), c_Groups_Ozero__class_Ozero(_1358486))), 30395 ^ _782435 : [(30396 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358486), _1358490), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358486), _1358492), _1358488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358486), _1358492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358486), _1358490), _1358488))))], (30402 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358486), _1358492), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358486), _1358490), _1358488))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358486), _1358490), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358486), _1358492), _1358488))))]]], (30408 ^ _782435) ^ [_1358867, _1358869, _1358871, _1358873] : [class_Fields_Olinordered__field(_1358867), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358867), c_Groups_Ozero__class_Ozero(_1358867)), _1358869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358867), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1358867), _1358871), _1358869)), _1358873)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1358867), _1358871), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1358867), _1358873), _1358869))))], (30422 ^ _782435) ^ [_1359136, _1359138, _1359140, _1359142] : [class_Fields_Olinordered__field(_1359136), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359136), c_Groups_Ozero__class_Ozero(_1359136)), _1359138)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359136), _1359140), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359136), _1359142), _1359138))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359136), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359136), _1359140), _1359138)), _1359142)))], (30436 ^ _782435) ^ [_1359405, _1359407, _1359409, _1359411] : [class_Fields_Olinordered__field(_1359405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359405), c_Groups_Ozero__class_Ozero(_1359405)), _1359407)), 30443 ^ _782435 : [(30444 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359405), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359405), _1359409), _1359407)), _1359411)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359405), _1359409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359405), _1359411), _1359407))))], (30450 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359405), _1359409), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359405), _1359411), _1359407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359405), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359405), _1359409), _1359407)), _1359411)))]]], (30456 ^ _782435) ^ [_1359786, _1359788, _1359790, _1359792] : [class_Fields_Olinordered__field(_1359786), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359786), c_Groups_Ozero__class_Ozero(_1359786)), _1359788)), 30463 ^ _782435 : [(30464 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359786), _1359790), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359786), _1359792), _1359788))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359786), _1359790), _1359788)), _1359792)))], (30470 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359786), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1359786), _1359790), _1359788)), _1359792)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1359786), _1359790), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1359786), _1359792), _1359788))))]]], (30476 ^ _782435) ^ [_1360167, _1360169, _1360171, _1360173] : [class_Fields_Olinordered__field__inverse__zero(_1360167), 30479 ^ _782435 : [(30506 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360167), _1360169), _1360171)), _1360173))), 30509 ^ _782435 : [(30510 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), c_Groups_Ozero__class_Ozero(_1360167)), _1360171)))], (30512 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), _1360169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360167), _1360173), _1360171)))]], 30513 ^ _782435 : [(30514 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), c_Groups_Ozero__class_Ozero(_1360167)), _1360171))], (30516 ^ _782435) ^ [] : [30517 ^ _782435 : [(30518 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), _1360171), c_Groups_Ozero__class_Ozero(_1360167))))], (30520 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360167), _1360173), _1360171)), _1360169))]], 30521 ^ _782435 : [(30522 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), _1360171), c_Groups_Ozero__class_Ozero(_1360167)))], (30524 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), c_Groups_Ozero__class_Ozero(_1360167)), _1360173))]]]]], (30480 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1360167), _1360169), _1360171)), _1360173)), 30483 ^ _782435 : [(30484 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), c_Groups_Ozero__class_Ozero(_1360167)), _1360171)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), _1360169), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360167), _1360173), _1360171))))], (30490 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), c_Groups_Ozero__class_Ozero(_1360167)), _1360171))), 30493 ^ _782435 : [(30494 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), _1360171), c_Groups_Ozero__class_Ozero(_1360167))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1360167), _1360173), _1360171)), _1360169)))], (30500 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), _1360171), c_Groups_Ozero__class_Ozero(_1360167)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1360167), c_Groups_Ozero__class_Ozero(_1360167)), _1360173)))]]]]]]], (30528 ^ _782435) ^ [_1361120, _1361122, _1361124, _1361126] : [class_Fields_Olinordered__field__inverse__zero(_1361120), 30531 ^ _782435 : [(30558 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361122), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361120), _1361124), _1361126)))), 30561 ^ _782435 : [(30562 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), c_Groups_Ozero__class_Ozero(_1361120)), _1361126)))], (30564 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361120), _1361122), _1361126)), _1361124))]], 30565 ^ _782435 : [(30566 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), c_Groups_Ozero__class_Ozero(_1361120)), _1361126))], (30568 ^ _782435) ^ [] : [30569 ^ _782435 : [(30570 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361126), c_Groups_Ozero__class_Ozero(_1361120))))], (30572 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361120), _1361122), _1361126)))]], 30573 ^ _782435 : [(30574 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361126), c_Groups_Ozero__class_Ozero(_1361120)))], (30576 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361122), c_Groups_Ozero__class_Ozero(_1361120)))]]]]], (30532 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361122), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1361120), _1361124), _1361126))), 30535 ^ _782435 : [(30536 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), c_Groups_Ozero__class_Ozero(_1361120)), _1361126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361120), _1361122), _1361126)), _1361124)))], (30542 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), c_Groups_Ozero__class_Ozero(_1361120)), _1361126))), 30545 ^ _782435 : [(30546 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361126), c_Groups_Ozero__class_Ozero(_1361120))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361124), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1361120), _1361122), _1361126))))], (30552 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361126), c_Groups_Ozero__class_Ozero(_1361120)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1361120), _1361122), c_Groups_Ozero__class_Ozero(_1361120))))]]]]]]], (30580 ^ _782435) ^ [_1362073, _1362075, _1362077, _1362079] : [class_Fields_Ofield__inverse__zero(_1362073), -(_1362075 = c_Groups_Ozero__class_Ozero(_1362073)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362073), _1362077), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362073), _1362079), _1362075)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362073), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362073), _1362079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362073), _1362077), _1362075))), _1362075))], (30590 ^ _782435) ^ [_1362251, _1362253, _1362255, _1362257] : [class_Fields_Ofield(_1362251), -(_1362253 = c_Groups_Ozero__class_Ozero(_1362251)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362251), _1362255), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362251), _1362257), _1362253)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362251), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362251), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362251), _1362253), _1362255)), _1362257)), _1362253))], (30600 ^ _782435) ^ [_1362429, _1362431, _1362433, _1362435] : [class_Fields_Ofield__inverse__zero(_1362429), -(_1362431 = c_Groups_Ozero__class_Ozero(_1362429)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362429), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362429), _1362433), _1362431)), _1362435) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362429), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362429), _1362433), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362429), _1362435), _1362431))), _1362431))], (30610 ^ _782435) ^ [_1362607, _1362609, _1362611, _1362613] : [class_Fields_Ofield(_1362607), -(_1362609 = c_Groups_Ozero__class_Ozero(_1362607)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362607), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362607), _1362611), _1362609)), _1362613) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362607), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362607), _1362611), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362607), _1362609), _1362613))), _1362609))], (30620 ^ _782435) ^ [_1362785, _1362787, _1362789, _1362791, _1362793] : [class_Fields_Ofield(_1362785), -(_1362787 = c_Groups_Ozero__class_Ozero(_1362785)), -(_1362789 = c_Groups_Ozero__class_Ozero(_1362785)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362785), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362785), _1362791), _1362787)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362785), _1362793), _1362789)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1362785), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1362785), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362785), _1362791), _1362789)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362785), _1362793), _1362787))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1362785), _1362787), _1362789)))], (30634 ^ _782435) ^ [_1363032, _1363034, _1363036, _1363038] : [class_Fields_Ofield(_1363032), -(_1363034 = c_Groups_Ozero__class_Ozero(_1363032)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363032), _1363036), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363032), _1363038), _1363034)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363032), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363032), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363032), _1363034), _1363036)), _1363038)), _1363034))], (30644 ^ _782435) ^ [_1363210, _1363212, _1363214, _1363216] : [class_Fields_Ofield(_1363210), -(_1363212 = c_Groups_Ozero__class_Ozero(_1363210)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363210), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363210), _1363214), _1363212)), _1363216) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363210), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363210), _1363214), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363210), _1363212), _1363216))), _1363212))], (30654 ^ _782435) ^ [_1363388, _1363390, _1363392, _1363394, _1363396] : [class_Fields_Ofield(_1363388), -(_1363390 = c_Groups_Ozero__class_Ozero(_1363388)), -(_1363392 = c_Groups_Ozero__class_Ozero(_1363388)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363388), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363388), _1363394), _1363390)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363388), _1363396), _1363392)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363388), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1363388), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363388), _1363394), _1363392)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363388), _1363396), _1363390))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1363388), _1363390), _1363392)))], (30668 ^ _782435) ^ [_1363635, _1363637, _1363639] : [class_Fields_Olinordered__field(_1363635), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363635), _1363637), _1363639)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363635), _1363637), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363635), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363635), _1363637), _1363639)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363635), c_Groups_Oone__class_Oone(_1363635)), c_Groups_Oone__class_Oone(_1363635))))))], (30678 ^ _782435) ^ [_1363850, _1363852, _1363854] : [class_Fields_Olinordered__field(_1363850), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363850), _1363852), _1363854)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1363850), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1363850), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363850), _1363852), _1363854)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1363850), c_Groups_Oone__class_Oone(_1363850)), c_Groups_Oone__class_Oone(_1363850)))), _1363854)))], (30688 ^ _782435) ^ [_1364065, _1364067, _1364069] : [class_Fields_Olinordered__field__inverse__zero(_1364065), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364065), c_Groups_Ozero__class_Ozero(_1364065)), _1364067)), -(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364065), hAPP(c_Groups_Oabs__class_Oabs(_1364065), _1364069)), _1364067) = hAPP(c_Groups_Oabs__class_Oabs(_1364065), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364065), _1364069), _1364067)))], (30698 ^ _782435) ^ [_1364266, _1364268, _1364270, _1364272] : [class_Fields_Olinordered__field__inverse__zero(_1364266), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364266), _1364268), _1364270)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364266), _1364272), c_Groups_Ozero__class_Ozero(_1364266))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364266), c_Groups_Ozero__class_Ozero(_1364266)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364266), _1364268), _1364270))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364266), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364266), _1364272), _1364268)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364266), _1364272), _1364270))))], (30716 ^ _782435) ^ [_1364625, _1364627, _1364629, _1364631] : [class_Fields_Olinordered__field(_1364625), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364625), _1364627), _1364629)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364625), c_Groups_Ozero__class_Ozero(_1364625)), _1364631)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364625), c_Groups_Ozero__class_Ozero(_1364625)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364625), _1364629), _1364627))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364625), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364625), _1364631), _1364629)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364625), _1364631), _1364627))))], (30734 ^ _782435) ^ [_1364984, _1364986, _1364988, _1364990] : [class_Fields_Olinordered__field(_1364984), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1364984), _1364986), c_Groups_Ozero__class_Ozero(_1364984))), 30741 ^ _782435 : [(30742 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364984), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364984), _1364988), _1364986)), _1364990)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364984), _1364990), _1364986)), _1364988)))], (30748 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364984), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1364984), _1364990), _1364986)), _1364988)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1364984), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1364984), _1364988), _1364986)), _1364990)))]]], (30754 ^ _782435) ^ [_1365365, _1365367, _1365369, _1365371] : [class_Fields_Olinordered__field(_1365365), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365365), _1365367), c_Groups_Ozero__class_Ozero(_1365365))), 30761 ^ _782435 : [(30762 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365365), _1365369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365365), _1365371), _1365367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365365), _1365371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365365), _1365369), _1365367))))], (30768 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365365), _1365371), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365365), _1365369), _1365367))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365365), _1365369), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365365), _1365371), _1365367))))]]], (30774 ^ _782435) ^ [_1365746, _1365748, _1365750, _1365752] : [class_Fields_Olinordered__field(_1365746), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1365746), c_Groups_Ozero__class_Ozero(_1365746)), _1365748)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365746), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1365746), _1365750), _1365748)), _1365752)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1365746), _1365750), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1365746), _1365752), _1365748))))], (30788 ^ _782435) ^ [_1366015, _1366017, _1366019, _1366021] : [class_Fields_Olinordered__field(_1366015), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1366015), c_Groups_Ozero__class_Ozero(_1366015)), _1366017)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366015), _1366019), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366015), _1366021), _1366017))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1366015), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366015), _1366019), _1366017)), _1366021)))], (30802 ^ _782435) ^ [_1366284, _1366286, _1366288, _1366290, _1366292] : [class_Fields_Ofield(_1366284), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366286), _1366288)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1366286), _1366290)), 30816 ^ _782435 : [(30817 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1366286), 30815 ^ [_1366284, _1366286, _1366288, _1366290, _1366292]), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366286, tc_HOL_Obool)), _1366288), _1366290))))], (30819 ^ _782435) ^ [] : [-(hAPP(_1366292, 30815 ^ [_1366284, _1366286, _1366288, _1366290, _1366292]) = c_Groups_Ozero__class_Ozero(_1366284))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366286, _1366284), _1366292), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1366286, tc_HOL_Obool)), _1366288), _1366290)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1366284), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1366284), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366286, _1366284), _1366292), _1366288)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366286, _1366284), _1366292), _1366290))), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1366286, _1366284), _1366292), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1366286, tc_HOL_Obool)), _1366288), _1366290))))], (30823 ^ _782435) ^ [_1366780] : [class_Power_Opower(_1366780), -(c_Power_Opower__class_Opower(_1366780) = c_Power_Opower_Opower(_1366780, c_Groups_Oone__class_Oone(_1366780), c_Groups_Otimes__class_Otimes(_1366780)))], (30829 ^ _782435) ^ [_1366873, _1366875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1366873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1366875)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366875), _1366873)), _1366875) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1366875), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1366873), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (30839 ^ _782435) ^ [_1367058, _1367060, _1367062] : [class_Orderings_Olinorder(_1367058), hAPP(_1367060, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367058), 30844 ^ [_1367058, _1367060, _1367062]), 30845 ^ [_1367058, _1367060, _1367062])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1367058), hAPP(_1367060, 30844 ^ [_1367058, _1367060, _1367062])), hAPP(_1367060, 30845 ^ [_1367058, _1367060, _1367062])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1367058), _1367062)), -(_1367062 = c_Orderings_Obot__class_Obot(tc_fun(_1367058, tc_HOL_Obool))), -(hAPP(_1367060, c_Big__Operators_Olattice_OInf__fin(_1367058, c_Orderings_Oord__class_Omin(_1367058), _1367062)) = c_Big__Operators_Olattice_OInf__fin(_1367058, c_Orderings_Oord__class_Omin(_1367058), hAPP(c_Set_Oimage(_1367058, _1367058, _1367060), _1367062)))], (30859 ^ _782435) ^ [_1367473] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1367473) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (30861 ^ _782435) ^ [_1367499, _1367501] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367499), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367501)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367499)), _1367501))], (30863 ^ _782435) ^ [_1367542, _1367544] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367542)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1367544)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367542), _1367544))], (30865 ^ _782435) ^ [_1367585, _1367587] : [class_Divides_Osemiring__div(_1367585), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367585), c_Groups_Ozero__class_Ozero(_1367585)), _1367587) = c_Groups_Ozero__class_Ozero(_1367585))], (30871 ^ _782435) ^ [_1367684, _1367686] : [class_Divides_Osemiring__div(_1367684), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367684), _1367686), c_Groups_Ozero__class_Ozero(_1367684)) = c_Groups_Ozero__class_Ozero(_1367684))], (30877 ^ _782435) ^ [_1367783, _1367785] : [c_Nat__Transfer_Ois__nat(_1367783), c_Nat__Transfer_Ois__nat(_1367785), -(c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1367783), _1367785)))], (30887 ^ _782435) ^ [_1367918, _1367920] : [class_Divides_Osemiring__div(_1367918), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1367918), _1367920), c_Groups_Oone__class_Oone(_1367918)) = _1367920)], (30893 ^ _782435) ^ [_1368013, _1368015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368013)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368015)), -(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), _1368013), _1368015))))], (30903 ^ _782435) ^ [_1368166, _1368168] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368166), 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)), _1368168)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368166), _1368168)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30913 ^ _782435) ^ [_1368331, _1368333] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368331), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 30916 ^ _782435 : [(30917 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368333), _1368331)), 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)), _1368333)))], (30923 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368333)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368333), _1368331)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30929 ^ _782435) ^ [_1368587, _1368589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1368587)), 30932 ^ _782435 : [(30933 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368589), _1368587)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368589), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (30939 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1368589), 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), _1368589), _1368587)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (30945 ^ _782435) ^ [_1368842] : [-(_1368842 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1368842), _1368842) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (30951 ^ _782435) ^ [_1368882, _1368884, _1368886, _1368888] : [class_Divides_Osemiring__div(_1368882), 30954 ^ _782435 : [(30955 ^ _782435) ^ [] : [_1368884 = c_Groups_Ozero__class_Ozero(_1368882), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368882), _1368884), _1368886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368882), _1368884), _1368888)) = c_Groups_Ozero__class_Ozero(_1368882))], (30961 ^ _782435) ^ [] : [-(_1368884 = c_Groups_Ozero__class_Ozero(_1368882)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368882), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368882), _1368884), _1368886)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1368882), _1368884), _1368888)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1368882), _1368886), _1368888))]]], (30967 ^ _782435) ^ [_1369188, _1369190, _1369192] : [class_Divides_Osemiring__div(_1369188), -(_1369190 = c_Groups_Ozero__class_Ozero(_1369188)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369188), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369188), _1369192), _1369190)), _1369190) = _1369192)], (30977 ^ _782435) ^ [_1369316, _1369318, _1369320] : [class_Divides_Osemiring__div(_1369316), -(_1369318 = c_Groups_Ozero__class_Ozero(_1369316)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369316), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369316), _1369318), _1369320)), _1369318) = _1369320)], (30987 ^ _782435) ^ [_1369444, _1369446, _1369448, _1369450] : [class_Divides_Osemiring__div(_1369444), -(_1369446 = c_Groups_Ozero__class_Ozero(_1369444)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369444), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369444), _1369448), _1369446)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369444), _1369450), _1369446)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369444), _1369448), _1369450))], (30997 ^ _782435) ^ [_1369606, _1369608, _1369610, _1369612] : [class_Divides_Osemiring__div(_1369606), -(_1369608 = c_Groups_Ozero__class_Ozero(_1369606)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369606), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369606), _1369608), _1369610)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1369606), _1369608), _1369612)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369606), _1369610), _1369612))], (31007 ^ _782435) ^ [_1369768, _1369770] : [class_Divides_Osemiring__div(_1369768), -(_1369770 = c_Groups_Ozero__class_Ozero(_1369768)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1369768), _1369770), _1369770) = c_Groups_Oone__class_Oone(_1369768))], (31017 ^ _782435) ^ [_1369897, _1369899] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1369897), _1369899) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1369899 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31026 ^ _782435 : [(31027 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1369897)))], (31029 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369897), _1369899)))]], 31030 ^ _782435 : [(31031 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1369897), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31033 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1369899), _1369897)))]]], (31035 ^ _782435) ^ [_1370128, _1370130] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1370128), _1370130) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31036 ^ _782435 : [(31037 ^ _782435) ^ [] : [_1370130 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (31039 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370128)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370128), _1370130))], (31045 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370128), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1370130), _1370128))]]], (31053 ^ _782435) ^ [_1370423, _1370425] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370423)), 31056 ^ _782435 : [(31057 ^ _782435) ^ [] : [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), _1370425), _1370423))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370425)))], (31063 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370425)), -(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), _1370425), _1370423))))]]], (31069 ^ _782435) ^ [_1370664, _1370666] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370664)), 31072 ^ _782435 : [(31073 ^ _782435) ^ [] : [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), _1370666), _1370664))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370664), _1370666)))], (31079 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370664), _1370666)), -(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), _1370666), _1370664))))]]], (31085 ^ _782435) ^ [_1370914, _1370916] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370914)), 31088 ^ _782435 : [(31089 ^ _782435) ^ [] : [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), _1370914), _1370916))), 31092 ^ _782435 : [(31093 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370916), _1370914)))], (31095 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370916)))]]], (31097 ^ _782435) ^ [] : [-(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), _1370914), _1370916)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1370916), _1370914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1370916))]]], (31107 ^ _782435) ^ [_1371242, _1371244, _1371246] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371242)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371244)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371244), _1371246)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371242), _1371246)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371242), _1371244))))], (31121 ^ _782435) ^ [_1371481, _1371483] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371481)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371483), 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), _1371481), _1371483)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31131 ^ _782435) ^ [_1371646, _1371648] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1371646)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371646), _1371648)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1371646), _1371648) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31141 ^ _782435) ^ [_1371801, _1371803] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1371801), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31144 ^ _782435 : [(31145 ^ _782435) ^ [] : [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), _1371803), _1371801))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371803), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31151 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1371803), 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), _1371803), _1371801))))]]], (31157 ^ _782435) ^ [_1372057, _1372059] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372057), 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)), _1372059)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372057), _1372059)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31167 ^ _782435) ^ [_1372222, _1372224, _1372226] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372222), 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)), _1372224)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372224), _1372226)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372222), _1372224)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372222), _1372226))))], (31181 ^ _782435) ^ [_1372467, _1372469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372467), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372469), _1372467)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372467), _1372469) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31191 ^ _782435) ^ [_1372628, _1372630, _1372632] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372628), _1372630)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1372632)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372628), _1372632)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372630), _1372632))))], (31201 ^ _782435) ^ [_1372809, _1372811, _1372813] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1372809), _1372811)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1372813), 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), _1372811), _1372813)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372809), _1372813))))], (31211 ^ _782435) ^ [_1372996, _1372998] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1372996)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1372998)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1372996), _1372998)), _1372996)))], (31221 ^ _782435) ^ [_1373155, _1373157, _1373159] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1373155)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373157), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1373159), _1373155)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1373157), _1373159)), _1373155))], (31227 ^ _782435) ^ [_1373286, _1373288, _1373290, _1373292] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1373286, _1373288, _1373290), _1373292), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1373288)], (31229 ^ _782435) ^ [_1373325, _1373327, _1373329, _1373331, _1373333] : [-(hAPP(hAPP(c_Power_Opower_Opower(_1373325, _1373327, _1373329), _1373331), hAPP(c_Nat_OSuc, _1373333)) = hAPP(hAPP(_1373329, _1373331), hAPP(hAPP(c_Power_Opower_Opower(_1373325, _1373327, _1373329), _1373331), _1373333)))], (31231 ^ _782435) ^ [_1373385, _1373387, _1373389, _1373391] : [class_Divides_Osemiring__div(_1373385), -(_1373387 = c_Groups_Ozero__class_Ozero(_1373385)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373385), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373385), _1373389), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373385), _1373391), _1373387))), _1373387) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373385), _1373391), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373385), _1373389), _1373387)))], (31241 ^ _782435) ^ [_1373563, _1373565, _1373567, _1373569] : [class_Divides_Osemiring__div(_1373563), -(_1373565 = c_Groups_Ozero__class_Ozero(_1373563)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373563), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373563), _1373567), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1373563), _1373565), _1373569))), _1373565) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373563), _1373569), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373563), _1373567), _1373565)))], (31251 ^ _782435) ^ [_1373741, _1373743, _1373745] : [class_Divides_Osemiring__div(_1373741), -(_1373743 = c_Groups_Ozero__class_Ozero(_1373741)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373741), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373741), _1373743), _1373745)), _1373743) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373741), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373741), _1373745), _1373743)), c_Groups_Oone__class_Oone(_1373741)))], (31261 ^ _782435) ^ [_1373905, _1373907, _1373909] : [class_Divides_Osemiring__div(_1373905), -(_1373907 = c_Groups_Ozero__class_Ozero(_1373905)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373905), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373905), _1373909), _1373907)), _1373907) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1373905), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1373905), _1373909), _1373907)), c_Groups_Oone__class_Oone(_1373905)))], (31271 ^ _782435) ^ [_1374069, _1374071, _1374073, _1374075] : [_1374069 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374071), _1374073)), _1374075), -(_1374071 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1374069), _1374071) = _1374073), 31278 ^ _782435 : [(31279 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374071)))], (31281 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374075), _1374071))]], 31286 ^ _782435 : [(31287 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374071))], (31289 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374071), _1374075)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1374075), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (31347 ^ _782435) ^ [_1375516, _1375518, _1375520] : [-(hBOOL(hAPP(_1375516, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1375518), _1375520)))), 31350 ^ _782435 : [(31351 ^ _782435) ^ [] : [-(_1375520 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (31353 ^ _782435) ^ [] : [hBOOL(hAPP(_1375516, c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 31356 ^ _782435 : [(31357 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1375520)))], (31361 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31359 ^ [_1375516, _1375518, _1375520])))], (31363 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 31359 ^ [_1375516, _1375518, _1375520]), _1375520)))], (31365 ^ _782435) ^ [] : [-(_1375518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1375520), 31358 ^ [_1375516, _1375518, _1375520])), 31359 ^ [_1375516, _1375518, _1375520]))], (31367 ^ _782435) ^ [] : [hBOOL(hAPP(_1375516, 31358 ^ [_1375516, _1375518, _1375520]))]], 31368 ^ _782435 : [(31369 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375520), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31373 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1375520), 31371 ^ [_1375516, _1375518, _1375520])))], (31375 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31371 ^ [_1375516, _1375518, _1375520]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31377 ^ _782435) ^ [] : [-(_1375518 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1375520), 31370 ^ [_1375516, _1375518, _1375520])), 31371 ^ [_1375516, _1375518, _1375520]))], (31379 ^ _782435) ^ [] : [hBOOL(hAPP(_1375516, 31370 ^ [_1375516, _1375518, _1375520]))]]], (31301 ^ _782435) ^ [_1374556, _1374558, _1374560] : [hBOOL(hAPP(_1374556, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1374558), _1374560))), 31304 ^ _782435 : [(31305 ^ _782435) ^ [] : [_1374560 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1374556, c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31311 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374560)), 31314 ^ _782435 : [(31315 ^ _782435) ^ [_1374890] : [-(hBOOL(hAPP(_1374556, _1374890))), 31316 ^ _782435 : [(31317 ^ _782435) ^ [_1374961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1374961)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374961), _1374560)), _1374558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374560), _1374890)), _1374961)]]]]], (31329 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374560), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31332 ^ _782435 : [(31333 ^ _782435) ^ [_1375220] : [-(hBOOL(hAPP(_1374556, _1375220))), 31334 ^ _782435 : [(31335 ^ _782435) ^ [_1375294] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1374560), _1375294)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1375294), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1374558 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1374560), _1375220)), _1375294)]]]]]]], (31383 ^ _782435) ^ [_1376239, _1376241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376239)), -(c_SMT_Oz3div(_1376241, _1376239) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376241), _1376239))], (31389 ^ _782435) ^ [_1376332, _1376334] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1376332))), -(c_SMT_Oz3div(_1376334, _1376332) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1376334), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1376332))))], (31395 ^ _782435) ^ [_1376387, _1376389, _1376391] : [class_Orderings_Olinorder(_1376387), hAPP(_1376389, hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376387), 31400 ^ [_1376387, _1376389, _1376391]), 31401 ^ [_1376387, _1376389, _1376391])) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1376387), hAPP(_1376389, 31400 ^ [_1376387, _1376389, _1376391])), hAPP(_1376389, 31401 ^ [_1376387, _1376389, _1376391])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376387), _1376391)), -(_1376391 = c_Orderings_Obot__class_Obot(tc_fun(_1376387, tc_HOL_Obool))), -(hAPP(_1376389, c_Big__Operators_Olinorder__class_OMax(_1376387, _1376391)) = c_Big__Operators_Olinorder__class_OMax(_1376387, hAPP(c_Set_Oimage(_1376387, _1376387, _1376389), _1376391)))], (31415 ^ _782435) ^ [_1376790, _1376792, _1376794] : [class_Orderings_Olinorder(_1376790), hAPP(_1376792, hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376790), 31420 ^ [_1376790, _1376792, _1376794]), 31421 ^ [_1376790, _1376792, _1376794])) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1376790), hAPP(_1376792, 31420 ^ [_1376790, _1376792, _1376794])), hAPP(_1376792, 31421 ^ [_1376790, _1376792, _1376794])), hBOOL(hAPP(c_Finite__Set_Ofinite(_1376790), _1376794)), -(_1376794 = c_Orderings_Obot__class_Obot(tc_fun(_1376790, tc_HOL_Obool))), -(hAPP(_1376792, c_Big__Operators_Olinorder__class_OMin(_1376790, _1376794)) = c_Big__Operators_Olinorder__class_OMin(_1376790, hAPP(c_Set_Oimage(_1376790, _1376790, _1376792), _1376794)))], (31435 ^ _782435) ^ [_1377193, _1377195, _1377197, _1377199, _1377201, _1377203, _1377205, _1377207] : [class_Groups_Ocomm__monoid__mult(_1377193), c_Fun_Oinj__on(_1377195, _1377197, _1377199, _1377201), _1377203 = hAPP(c_Set_Oimage(_1377195, _1377197, _1377199), _1377201), 31449 ^ _782435 : [(31450 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1377195), 31448 ^ [_1377193, _1377195, _1377197, _1377199, _1377201, _1377203, _1377205, _1377207]), _1377201)))], (31452 ^ _782435) ^ [] : [hAPP(_1377205, 31448 ^ [_1377193, _1377195, _1377197, _1377199, _1377201, _1377203, _1377205, _1377207]) = hAPP(hAPP(c_Fun_Ocomp(_1377197, _1377193, _1377195, _1377207), _1377199), 31448 ^ [_1377193, _1377195, _1377197, _1377199, _1377201, _1377203, _1377205, _1377207])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377197, _1377193), _1377207), _1377203) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1377195, _1377193), _1377205), _1377201))], (31456 ^ _782435) ^ [_1377701, _1377703, _1377705] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377701), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1377703), _1377705)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377701), _1377703)), _1377705))], (31458 ^ _782435) ^ [_1377752, _1377754, _1377756] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1377752), _1377754)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377752), _1377756)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377754), _1377756))))], (31464 ^ _782435) ^ [_1377875, _1377877] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377875), _1377877)), _1377875)))], (31466 ^ _782435) ^ [_1377911] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377911), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = _1377911)], (31468 ^ _782435) ^ [_1377940, _1377942] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1377940), _1377942)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1377940), _1377942) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31474 ^ _782435) ^ [_1378051, _1378053, _1378055] : [_1378051 = 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), _1378051), _1378053)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378051), _1378055)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31480 ^ _782435) ^ [_1378160, _1378162, _1378164] : [-(_1378160 = 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), _1378160), _1378162)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378160), _1378164)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378162), _1378164))], (31486 ^ _782435) ^ [_1378224, _1378226] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378224), _1378226)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378224)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378226)))], (31488 ^ _782435) ^ [_1378270, _1378272] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378270)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1378272)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378270), _1378272)))], (31490 ^ _782435) ^ [_1378316, _1378318, _1378320] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378316)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1378316), _1378318)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378320), _1378318)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378320), _1378316))))], (31500 ^ _782435) ^ [_1378497, _1378499, _1378501] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378497)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378497), _1378499)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378497), _1378501)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378499), _1378501))], (31506 ^ _782435) ^ [_1378628, _1378630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378628)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378628), _1378630)), _1378628) = _1378630)], (31512 ^ _782435) ^ [_1378733, _1378735] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378733)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1378735), _1378733)), _1378733) = _1378735)], (31518 ^ _782435) ^ [_1378838, _1378840] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1378838)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378840)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378840), _1378838)), _1378840)))], (31528 ^ _782435) ^ [_1378997, _1378999] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1378997)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1378999), _1378997))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1378999), _1378997) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1378999), _1378997)), _1378997)))], (31538 ^ _782435) ^ [_1379145, _1379147] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1379145)), 31541 ^ _782435 : [(31542 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379147), _1379145)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379147), _1379145) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31548 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379147), _1379145))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379147), _1379145) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1379147), _1379145)), _1379145)))]]], (31578 ^ _782435) ^ [_1379854, _1379856, _1379858] : [-(hBOOL(hAPP(_1379854, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379856), _1379858)))), 31581 ^ _782435 : [(31582 ^ _782435) ^ [] : [-(_1379858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31584 ^ _782435) ^ [] : [hBOOL(hAPP(_1379854, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]], 31585 ^ _782435 : [(31586 ^ _782435) ^ [] : [_1379858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (31590 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 31588 ^ [_1379854, _1379856, _1379858]), _1379858)))], (31592 ^ _782435) ^ [] : [-(_1379856 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1379858), 31587 ^ [_1379854, _1379856, _1379858])), 31588 ^ [_1379854, _1379856, _1379858]))], (31594 ^ _782435) ^ [] : [hBOOL(hAPP(_1379854, 31587 ^ [_1379854, _1379856, _1379858]))]]], (31554 ^ _782435) ^ [_1379417, _1379419, _1379421] : [hBOOL(hAPP(_1379417, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1379419), _1379421))), 31557 ^ _782435 : [(31558 ^ _782435) ^ [] : [_1379421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1379417, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (31564 ^ _782435) ^ [] : [-(_1379421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 31567 ^ _782435 : [(31568 ^ _782435) ^ [_1379669, _1379671] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1379669), _1379421)), _1379419 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1379421), _1379671)), _1379669), -(hBOOL(hAPP(_1379417, _1379671)))]]]]], (31598 ^ _782435) ^ [_1380276, _1380278] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380276)), -(hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1380276), _1380278)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1380276)), hAPP(c_Int_Onat, _1380278)))], (31604 ^ _782435) ^ [_1380399, _1380401] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1380401)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onat, _1380399)), hAPP(c_Int_Onat, _1380401)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1380399), _1380401)))], (31614 ^ _782435) ^ [_1380578, _1380580] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1380578)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1380578), _1380580)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1380580), _1380578) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1380580), _1380578)), _1380578)))], (31624 ^ _782435) ^ [_1380781, _1380783, _1380785] : [hBOOL(hAPP(_1380781, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1380783), _1380785))), 31629 ^ _782435 : [(31630 ^ _782435) ^ [] : [-(_1380785 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (31632 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1380781, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]], 31634 ^ _782435 : [(31635 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380785), 31633 ^ [_1380781, _1380783, _1380785])), _1380783)))], (31637 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1380783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1380785), hAPP(c_Nat_OSuc, 31633 ^ [_1380781, _1380783, _1380785])))))], (31639 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1380781, 31633 ^ [_1380781, _1380783, _1380785])))]]], (31641 ^ _782435) ^ [_1381085, _1381087, _1381089] : [-(hBOOL(hAPP(_1381085, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381087), _1381089)))), 31642 ^ _782435 : [(31643 ^ _782435) ^ [] : [_1381089 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hBOOL(hAPP(_1381085, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (31649 ^ _782435) ^ [_1381253] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381089), _1381253)), _1381087)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381087), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381089), hAPP(c_Nat_OSuc, _1381253)))), hBOOL(hAPP(_1381085, _1381253))]]], (31661 ^ _782435) ^ [_1381483, _1381485, _1381487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1381483)), 31664 ^ _782435 : [(31675 ^ _782435) ^ [] : [_1381485 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381487), _1381483), 31678 ^ _782435 : [(31679 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381483), _1381485)), _1381487)))], (31681 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381483), hAPP(c_Nat_OSuc, _1381485)))))]]], (31665 ^ _782435) ^ [] : [-(_1381485 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1381487), _1381483)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381483), _1381485)), _1381487)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1381487), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381483), hAPP(c_Nat_OSuc, _1381485))))]]], (31683 ^ _782435) ^ [_1381867, _1381869] : [-(c_Nitpick_Onat__lcm(_1381867, _1381869) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1381867), _1381869)), c_Nitpick_Onat__gcd(_1381867, _1381869)))], (31685 ^ _782435) ^ [_1381910, _1381912, _1381914, _1381916, _1381918] : [class_Groups_Ocomm__monoid__mult(_1381910), hBOOL(hAPP(c_Finite__Set_Ofinite(_1381912), _1381914)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1381912, tc_HOL_Obool)), _1381916), _1381914)), 31699 ^ _782435 : [(31700 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1381912), 31698 ^ [_1381910, _1381912, _1381914, _1381916, _1381918]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1381912, tc_HOL_Obool)), _1381914), _1381916))))], (31702 ^ _782435) ^ [] : [hAPP(_1381918, 31698 ^ [_1381910, _1381912, _1381914, _1381916, _1381918]) = c_Groups_Oone__class_Oone(_1381910)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381912, _1381910), _1381918), _1381916) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1381912, _1381910), _1381918), _1381914))], (31706 ^ _782435) ^ [_1382361, _1382363, _1382365, _1382367, _1382369] : [class_Groups_Ocomm__monoid__mult(_1382361), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382363), _1382365)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1382363, tc_HOL_Obool)), _1382367), _1382365)), 31720 ^ _782435 : [(31721 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1382363), 31719 ^ [_1382361, _1382363, _1382365, _1382367, _1382369]), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1382363, tc_HOL_Obool)), _1382365), _1382367))))], (31723 ^ _782435) ^ [] : [hAPP(_1382369, 31719 ^ [_1382361, _1382363, _1382365, _1382367, _1382369]) = c_Groups_Oone__class_Oone(_1382361)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382363, _1382361), _1382369), _1382365) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1382363, _1382361), _1382369), _1382367))], (31727 ^ _782435) ^ [_1382812, _1382814, _1382816] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1382812, tc_HOL_Obool)), _1382814)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1382812), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1382812, tc_HOL_Obool), _1382814))), 31737 ^ _782435 : [(31738 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382812, tc_HOL_Obool)), 31736 ^ [_1382812, _1382814, _1382816]), _1382814)))], (31740 ^ _782435) ^ [] : [hAPP(c_Finite__Set_Ocard(_1382812), 31736 ^ [_1382812, _1382814, _1382816]) = _1382816]], 31744 ^ _782435 : [(31745 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382812, tc_HOL_Obool)), 31743 ^ [_1382812, _1382814, _1382816]), _1382814)))], (31748 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1382812, tc_HOL_Obool)), 31746 ^ [_1382812, _1382814, _1382816]), _1382814)))], (31750 ^ _782435) ^ [] : [31743 ^ [_1382812, _1382814, _1382816] = 31746 ^ [_1382812, _1382814, _1382816]], (31752 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1382812, tc_HOL_Obool)), 31743 ^ [_1382812, _1382814, _1382816]), 31746 ^ [_1382812, _1382814, _1382816]) = c_Orderings_Obot__class_Obot(tc_fun(_1382812, tc_HOL_Obool))]], -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1382816), hAPP(c_Finite__Set_Ocard(tc_fun(_1382812, tc_HOL_Obool)), _1382814)) = hAPP(c_Finite__Set_Ocard(_1382812), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1382812, tc_HOL_Obool), _1382814)))], (31756 ^ _782435) ^ [_1383594, _1383596] : [-(hAPP(hAPP(c_Nitpick_Oint__gcd, _1383594), _1383596) = 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), _1383594)), hAPP(c_Int_Onat, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1383596)))))], (31758 ^ _782435) ^ [_1383643, _1383645, _1383647] : [class_Fields_Olinordered__field__inverse__zero(_1383643), 31764 ^ _782435 : [(31765 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383643), c_Groups_Ozero__class_Ozero(_1383643)), 31763 ^ [_1383643, _1383645, _1383647])))], (31767 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1383643), 31763 ^ [_1383643, _1383645, _1383647]), c_Groups_Oone__class_Oone(_1383643))))], (31769 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383643), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1383643), 31763 ^ [_1383643, _1383645, _1383647]), _1383645)), _1383647))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1383643), _1383645), _1383647)))], (31773 ^ _782435) ^ [_1383992, _1383994, _1383996, _1383998, _1384000] : [class_Groups_Ocomm__monoid__add(_1383992), class_Groups_Ocomm__monoid__mult(_1383992), _1383994 = _1383996, c_Nat__Transfer_Onat__set(_1383996), 31791 ^ _782435 : [(31792 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 31790 ^ [_1383992, _1383994, _1383996, _1383998, _1384000])))], (31794 ^ _782435) ^ [] : [hAPP(_1383998, 31790 ^ [_1383992, _1383994, _1383996, _1383998, _1384000]) = hAPP(_1384000, 31790 ^ [_1383992, _1383994, _1383996, _1383998, _1384000])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1383992), _1383998), _1383994) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint, _1383992), _1384000), _1383996))], (31798 ^ _782435) ^ [_1384455, _1384457, _1384459] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384455), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 31801 ^ _782435 : [(31820 ^ _782435) ^ [] : [31823 ^ _782435 : [(31824 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384455), 31822 ^ [_1384455, _1384457, _1384459])))], (31826 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 31822 ^ [_1384455, _1384457, _1384459]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (31828 ^ _782435) ^ [] : [-(_1384459 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384455), 31821 ^ [_1384455, _1384457, _1384459])), 31822 ^ [_1384455, _1384457, _1384459]))], (31830 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1384457, 31821 ^ [_1384455, _1384457, _1384459]), 31822 ^ [_1384455, _1384457, _1384459]))]], -(hBOOL(hAPP(hAPP(_1384457, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384459), _1384455)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384459, _1384455))))], (31802 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1384457, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1384459), _1384455)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1384459, _1384455))), 31805 ^ _782435 : [(31806 ^ _782435) ^ [_1384665, _1384667] : [-(hBOOL(hAPP(hAPP(_1384457, _1384667), _1384665))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1384455), _1384665)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1384665), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1384459 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1384455), _1384667)), _1384665)]]]]], (31834 ^ _782435) ^ [_1385188, _1385190, _1385192] : [-(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, _1385188, _1385190)), _1385192), _1385190) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1385188), _1385192), _1385190))], (31836 ^ _782435) ^ [_1385239, _1385241] : [c_Nat__Transfer_Ois__nat(_1385239), c_Nat__Transfer_Ois__nat(_1385241), -(c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385239, _1385241)))], (31846 ^ _782435) ^ [_1385370, _1385372, _1385374] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385370), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385372, _1385374)), _1385374) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385370), _1385372), _1385374))], (31848 ^ _782435) ^ [_1385421, _1385423, _1385425] : [-(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, _1385421, _1385423)), _1385425), _1385423) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1385421), _1385425), _1385423))], (31850 ^ _782435) ^ [_1385472, _1385474] : [-(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, _1385472, _1385474)), _1385474) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385472), _1385474))], (31852 ^ _782435) ^ [_1385515, _1385517] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385515), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385517)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385515, _1385517)))], (31854 ^ _782435) ^ [_1385557, _1385559] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1385557, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1385559)) = 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), _1385557), _1385559)))], (31856 ^ _782435) ^ [_1385599, _1385601, _1385603, _1385605, _1385607, _1385609] : [class_Divides_Osemiring__div(_1385599), c_Divides_Odiv__class_Omod(_1385599, _1385601, _1385603) = c_Divides_Odiv__class_Omod(_1385599, _1385605, _1385603), c_Divides_Odiv__class_Omod(_1385599, _1385607, _1385603) = c_Divides_Odiv__class_Omod(_1385599, _1385609, _1385603), -(c_Divides_Odiv__class_Omod(_1385599, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385599), _1385601), _1385607), _1385603) = c_Divides_Odiv__class_Omod(_1385599, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385599), _1385605), _1385609), _1385603))], (31870 ^ _782435) ^ [_1385882, _1385884, _1385886, _1385888] : [class_Divides_Osemiring__div(_1385882), -(c_Divides_Odiv__class_Omod(_1385882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385882), c_Divides_Odiv__class_Omod(_1385882, _1385884, _1385886)), _1385888), _1385886) = c_Divides_Odiv__class_Omod(_1385882, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1385882), _1385884), _1385888), _1385886))], (31876 ^ _782435) ^ [_1386017, _1386019, _1386021, _1386023] : [class_Divides_Osemiring__div(_1386017), -(c_Divides_Odiv__class_Omod(_1386017, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386017), _1386019), c_Divides_Odiv__class_Omod(_1386017, _1386021, _1386023)), _1386023) = c_Divides_Odiv__class_Omod(_1386017, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386017), _1386019), _1386021), _1386023))], (31882 ^ _782435) ^ [_1386152, _1386154, _1386156, _1386158] : [class_Divides_Osemiring__div(_1386152), -(c_Divides_Odiv__class_Omod(_1386152, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386152), _1386154), _1386156), _1386158) = c_Divides_Odiv__class_Omod(_1386152, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386152), c_Divides_Odiv__class_Omod(_1386152, _1386154, _1386158)), c_Divides_Odiv__class_Omod(_1386152, _1386156, _1386158)), _1386158))], (31888 ^ _782435) ^ [_1386295, _1386297, _1386299, _1386301] : [class_Divides_Osemiring__div(_1386295), -(c_Divides_Odiv__class_Omod(_1386295, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386295), _1386297), _1386299), _1386301) = c_Divides_Odiv__class_Omod(_1386295, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386295), c_Divides_Odiv__class_Omod(_1386295, _1386297, _1386301)), _1386299), _1386301))], (31894 ^ _782435) ^ [_1386430, _1386432, _1386434, _1386436] : [class_Divides_Osemiring__div(_1386430), -(c_Divides_Odiv__class_Omod(_1386430, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386430), _1386432), _1386434), _1386436) = c_Divides_Odiv__class_Omod(_1386430, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386430), _1386432), c_Divides_Odiv__class_Omod(_1386430, _1386434, _1386436)), _1386436))], (31900 ^ _782435) ^ [_1386565, _1386567, _1386569] : [class_Divides_Osemiring__div(_1386565), -(c_Divides_Odiv__class_Omod(_1386565, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386565), _1386567), _1386569), _1386567) = c_Divides_Odiv__class_Omod(_1386565, _1386569, _1386567))], (31906 ^ _782435) ^ [_1386674, _1386676, _1386678] : [class_Divides_Osemiring__div(_1386674), -(c_Divides_Odiv__class_Omod(_1386674, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1386674), _1386676), _1386678), _1386678) = c_Divides_Odiv__class_Omod(_1386674, _1386676, _1386678))], (31912 ^ _782435) ^ [_1386783, _1386785, _1386787, _1386789, _1386791, _1386793] : [class_Divides_Osemiring__div(_1386783), c_Divides_Odiv__class_Omod(_1386783, _1386785, _1386787) = c_Divides_Odiv__class_Omod(_1386783, _1386789, _1386787), c_Divides_Odiv__class_Omod(_1386783, _1386791, _1386787) = c_Divides_Odiv__class_Omod(_1386783, _1386793, _1386787), -(c_Divides_Odiv__class_Omod(_1386783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386783), _1386785), _1386791), _1386787) = c_Divides_Odiv__class_Omod(_1386783, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1386783), _1386789), _1386793), _1386787))], (31926 ^ _782435) ^ [_1387066, _1387068, _1387070, _1387072] : [class_Divides_Osemiring__div(_1387066), -(c_Divides_Odiv__class_Omod(_1387066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387066), c_Divides_Odiv__class_Omod(_1387066, _1387068, _1387070)), _1387072), _1387070) = c_Divides_Odiv__class_Omod(_1387066, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387066), _1387068), _1387072), _1387070))], (31932 ^ _782435) ^ [_1387201, _1387203, _1387205, _1387207] : [class_Divides_Osemiring__div(_1387201), -(c_Divides_Odiv__class_Omod(_1387201, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387201), _1387203), _1387205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387201), _1387207), _1387205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387201), c_Divides_Odiv__class_Omod(_1387201, _1387203, _1387207)), _1387205))], (31938 ^ _782435) ^ [_1387344, _1387346, _1387348, _1387350] : [class_Divides_Osemiring__div(_1387344), -(c_Divides_Odiv__class_Omod(_1387344, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387344), _1387346), _1387348), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387344), _1387346), _1387350)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387344), _1387346), c_Divides_Odiv__class_Omod(_1387344, _1387348, _1387350)))], (31944 ^ _782435) ^ [_1387487, _1387489, _1387491, _1387493] : [class_Divides_Osemiring__div(_1387487), -(c_Divides_Odiv__class_Omod(_1387487, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387487), _1387489), _1387491), _1387493) = c_Divides_Odiv__class_Omod(_1387487, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387487), c_Divides_Odiv__class_Omod(_1387487, _1387489, _1387493)), c_Divides_Odiv__class_Omod(_1387487, _1387491, _1387493)), _1387493))], (31950 ^ _782435) ^ [_1387630, _1387632, _1387634, _1387636] : [class_Divides_Osemiring__div(_1387630), -(c_Divides_Odiv__class_Omod(_1387630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387630), _1387632), _1387634), _1387636) = c_Divides_Odiv__class_Omod(_1387630, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387630), c_Divides_Odiv__class_Omod(_1387630, _1387632, _1387636)), _1387634), _1387636))], (31956 ^ _782435) ^ [_1387765, _1387767, _1387769, _1387771] : [class_Divides_Osemiring__div(_1387765), -(c_Divides_Odiv__class_Omod(_1387765, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387765), _1387767), _1387769), _1387771) = c_Divides_Odiv__class_Omod(_1387765, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1387765), _1387767), c_Divides_Odiv__class_Omod(_1387765, _1387769, _1387771)), _1387771))], (31962 ^ _782435) ^ [_1387900, _1387902, _1387904, _1387906] : [class_Divides_Oring__div(_1387900), -(c_Divides_Odiv__class_Omod(_1387900, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387900), _1387902), _1387904), _1387906) = c_Divides_Odiv__class_Omod(_1387900, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1387900), _1387902), c_Divides_Odiv__class_Omod(_1387900, _1387904, _1387906)), _1387906))], (31968 ^ _782435) ^ [_1388035, _1388037, _1388039, _1388041] : [class_Divides_Oring__div(_1388035), -(c_Divides_Odiv__class_Omod(_1388035, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388035), _1388037), _1388039), _1388041) = c_Divides_Odiv__class_Omod(_1388035, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388035), c_Divides_Odiv__class_Omod(_1388035, _1388037, _1388041)), _1388039), _1388041))], (31974 ^ _782435) ^ [_1388170, _1388172, _1388174, _1388176] : [class_Divides_Oring__div(_1388170), -(c_Divides_Odiv__class_Omod(_1388170, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388170), _1388172), _1388174), _1388176) = c_Divides_Odiv__class_Omod(_1388170, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388170), c_Divides_Odiv__class_Omod(_1388170, _1388172, _1388176)), c_Divides_Odiv__class_Omod(_1388170, _1388174, _1388176)), _1388176))], (31980 ^ _782435) ^ [_1388313, _1388315, _1388317, _1388319, _1388321, _1388323] : [class_Divides_Oring__div(_1388313), c_Divides_Odiv__class_Omod(_1388313, _1388315, _1388317) = c_Divides_Odiv__class_Omod(_1388313, _1388319, _1388317), c_Divides_Odiv__class_Omod(_1388313, _1388321, _1388317) = c_Divides_Odiv__class_Omod(_1388313, _1388323, _1388317), -(c_Divides_Odiv__class_Omod(_1388313, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388313), _1388315), _1388321), _1388317) = c_Divides_Odiv__class_Omod(_1388313, hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1388313), _1388319), _1388323), _1388317))], (31994 ^ _782435) ^ [_1388596, _1388598, _1388600] : [class_Divides_Oring__div(_1388596), -(c_Divides_Odiv__class_Omod(_1388596, hAPP(c_Groups_Ouminus__class_Ouminus(_1388596), _1388598), _1388600) = c_Divides_Odiv__class_Omod(_1388596, hAPP(c_Groups_Ouminus__class_Ouminus(_1388596), c_Divides_Odiv__class_Omod(_1388596, _1388598, _1388600)), _1388600))], (32000 ^ _782435) ^ [_1388717, _1388719, _1388721, _1388723] : [class_Divides_Oring__div(_1388717), c_Divides_Odiv__class_Omod(_1388717, _1388719, _1388721) = c_Divides_Odiv__class_Omod(_1388717, _1388723, _1388721), -(c_Divides_Odiv__class_Omod(_1388717, hAPP(c_Groups_Ouminus__class_Ouminus(_1388717), _1388719), _1388721) = c_Divides_Odiv__class_Omod(_1388717, hAPP(c_Groups_Ouminus__class_Ouminus(_1388717), _1388723), _1388721))], (32010 ^ _782435) ^ [_1388904] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1388904, _1388904) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32012 ^ _782435) ^ [_1388931] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1388931) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32014 ^ _782435) ^ [_1388958, _1388960] : [class_Divides_Osemiring__div(_1388958), -(c_Divides_Odiv__class_Omod(_1388958, _1388960, _1388960) = c_Groups_Ozero__class_Ozero(_1388958))], (32020 ^ _782435) ^ [_1389045, _1389047] : [class_Divides_Osemiring__div(_1389045), -(c_Divides_Odiv__class_Omod(_1389045, _1389047, c_Groups_Ozero__class_Ozero(_1389045)) = _1389047)], (32026 ^ _782435) ^ [_1389132, _1389134] : [class_Divides_Osemiring__div(_1389132), -(c_Divides_Odiv__class_Omod(_1389132, c_Groups_Ozero__class_Ozero(_1389132), _1389134) = c_Groups_Ozero__class_Ozero(_1389132))], (32032 ^ _782435) ^ [_1389223, _1389225, _1389227] : [class_Divides_Osemiring__div(_1389223), -(c_Divides_Odiv__class_Omod(_1389223, c_Divides_Odiv__class_Omod(_1389223, _1389225, _1389227), _1389227) = c_Divides_Odiv__class_Omod(_1389223, _1389225, _1389227))], (32038 ^ _782435) ^ [_1389324, _1389326, _1389328] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389324), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1389326, _1389328)), _1389328) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389324), _1389326), _1389328))], (32040 ^ _782435) ^ [_1389375, _1389377, _1389379] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389375), _1389377), _1389379) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1389375), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1389377, _1389379)), _1389379))], (32042 ^ _782435) ^ [_1389426, _1389428, _1389430] : [class_Divides_Osemiring__div(_1389426), -(c_Divides_Odiv__class_Omod(_1389426, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389426), _1389428), _1389430), _1389428) = c_Groups_Ozero__class_Ozero(_1389426))], (32048 ^ _782435) ^ [_1389531, _1389533, _1389535] : [class_Divides_Osemiring__div(_1389531), -(c_Divides_Odiv__class_Omod(_1389531, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389531), _1389533), _1389535), _1389535) = c_Groups_Ozero__class_Ozero(_1389531))], (32054 ^ _782435) ^ [_1389636, _1389638, _1389640, _1389642] : [class_Divides_Osemiring__div(_1389636), -(c_Divides_Odiv__class_Omod(_1389636, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389636), _1389638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389636), _1389640), _1389642)), _1389640) = c_Divides_Odiv__class_Omod(_1389636, _1389638, _1389640))], (32060 ^ _782435) ^ [_1389763, _1389765, _1389767, _1389769] : [class_Divides_Osemiring__div(_1389763), -(c_Divides_Odiv__class_Omod(_1389763, hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1389763), _1389765), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1389763), _1389767), _1389769)), _1389769) = c_Divides_Odiv__class_Omod(_1389763, _1389765, _1389769))], (32066 ^ _782435) ^ [_1389890, _1389892] : [class_Divides_Osemiring__div(_1389890), -(c_Divides_Odiv__class_Omod(_1389890, _1389892, c_Groups_Oone__class_Oone(_1389890)) = c_Groups_Ozero__class_Ozero(_1389890))], (32072 ^ _782435) ^ [_1389981, _1389983, _1389985] : [class_Divides_Osemiring__div(_1389981), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1389981), c_Divides_Odiv__class_Omod(_1389981, _1389983, _1389985)), _1389985) = c_Groups_Ozero__class_Ozero(_1389981))], (32078 ^ _782435) ^ [_1390086, _1390088] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390086)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390086, _1390088)), _1390086)))], (32084 ^ _782435) ^ [_1390185, _1390187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390185)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390187)), -(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, _1390185, _1390187))))], (32094 ^ _782435) ^ [_1390334, _1390336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1390334)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390336, _1390334)), _1390334)))], (32100 ^ _782435) ^ [_1390433, _1390435] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390433), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1390433), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390435, _1390433))))], (32106 ^ _782435) ^ [_1390553, _1390555] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390553, _1390555) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(_1390553 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390555), 32109 ^ [_1390553, _1390555]))], (32113 ^ _782435) ^ [_1390658, _1390660] : [32114 ^ _782435 : [(32115 ^ _782435) ^ [_1390707] : [_1390658 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1390660), _1390707)]], -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390658, _1390660) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32119 ^ _782435) ^ [_1390769, _1390771] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390769), _1390771) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390769, _1390771) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32125 ^ _782435) ^ [_1390859, _1390861] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390859, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1390861)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390859, _1390861) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (32131 ^ _782435) ^ [_1390950, _1390952] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1390950, _1390952)), _1390952) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32133 ^ _782435) ^ [_1390983] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1390983), c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32135 ^ _782435) ^ [_1391009] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391009, c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = _1391009)], (32137 ^ _782435) ^ [_1391038, _1391040, _1391042] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1391038), _1391040)), _1391042) = 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), _1391038), _1391042)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1391040), _1391042))), 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, _1391038, _1391042)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391040, _1391042))), _1391042)))], (32139 ^ _782435) ^ [_1391121, _1391123, _1391125] : [class_Divides_Osemiring__div(_1391121), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391121), c_Divides_Odiv__class_Omod(_1391121, _1391123, _1391125)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391121), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391121), _1391123), _1391125)), _1391125)) = _1391123)], (32145 ^ _782435) ^ [_1391254, _1391256, _1391258] : [class_Divides_Osemiring__div(_1391254), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391254), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391254), _1391256), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391254), _1391258), _1391256))), c_Divides_Odiv__class_Omod(_1391254, _1391258, _1391256)) = _1391258)], (32151 ^ _782435) ^ [_1391387, _1391389, _1391391] : [class_Divides_Osemiring__div(_1391387), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391387), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391387), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391387), _1391389), _1391391)), _1391391)), c_Divides_Odiv__class_Omod(_1391387, _1391389, _1391391)) = _1391389)], (32157 ^ _782435) ^ [_1391520, _1391522, _1391524, _1391526] : [class_Divides_Osemiring__div(_1391520), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391520), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391520), _1391522), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391520), _1391524), _1391522))), c_Divides_Odiv__class_Omod(_1391520, _1391524, _1391522))), _1391526) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391520), _1391524), _1391526))], (32163 ^ _782435) ^ [_1391687, _1391689, _1391691, _1391693] : [class_Divides_Osemiring__div(_1391687), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391687), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391687), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1391687), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1391687), _1391689), _1391691)), _1391691)), c_Divides_Odiv__class_Omod(_1391687, _1391689, _1391691))), _1391693) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1391687), _1391689), _1391693))], (32169 ^ _782435) ^ [_1391854, _1391856] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1391854), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1391856), _1391854)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1391854, _1391856) = _1391854)], (32179 ^ _782435) ^ [_1392011, _1392013] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392011), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 32182 ^ _782435 : [(32183 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392013, _1392011)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32185 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392011), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392013, _1392011))))]]], (32187 ^ _782435) ^ [_1392160, _1392162] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392160), 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, _1392162, _1392160)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32193 ^ _782435) ^ [_1392265, _1392267] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392265)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1392265), _1392267)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392265, _1392267) = _1392265)], (32203 ^ _782435) ^ [_1392416, _1392418] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392416)), 32206 ^ _782435 : [(32207 ^ _782435) ^ [] : [-(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, _1392418, _1392416))))], (32209 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392418, _1392416)), _1392416)))]]], (32211 ^ _782435) ^ [_1392553, _1392555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1392553)), -(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, _1392555, _1392553))))], (32217 ^ _782435) ^ [_1392655, _1392657] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392655, _1392657) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392655, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392657)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32223 ^ _782435) ^ [_1392748, _1392750] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392748, _1392750) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392748, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1392750)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392748, _1392750)), _1392750))], (32229 ^ _782435) ^ [_1392816, _1392818] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392816, _1392818) = 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), _1392816), _1392818) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32235 ^ _782435) ^ [_1392909, _1392911] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392909, _1392911) = 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), _1392909), _1392911) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1392911), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392909, _1392911)))], (32241 ^ _782435) ^ [_1392968, _1392970] : [-(_1392968 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1392970), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1392968), _1392970))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1392968, _1392970)))], (32243 ^ _782435) ^ [_1393015, _1393017, _1393019] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393015), _1393017)), _1393019) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393015), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393017), _1393019))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393015), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393017, _1393019))), _1393019)))], (32245 ^ _782435) ^ [_1393088, _1393090, _1393092] : [-(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), _1393088), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393090), _1393088))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393090, _1393088))), _1393092) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393090), _1393092))], (32247 ^ _782435) ^ [_1393149, _1393151, _1393153] : [-(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), _1393149), _1393151)), _1393151)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393149, _1393151))), _1393153) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393149), _1393153))], (32249 ^ _782435) ^ [_1393210, _1393212] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393210), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393212), _1393210)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1393212), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393212, _1393210)))], (32251 ^ _782435) ^ [_1393257, _1393259] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393257, _1393259) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1393257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1393257), _1393259)), _1393259)))], (32253 ^ _782435) ^ [_1393304, _1393306] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393304)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393304), _1393306)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393304, _1393306) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1393304), _1393306))], (32309 ^ _782435) ^ [_1394374, _1394376, _1394378] : [-(hBOOL(hAPP(_1394374, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1394376, _1394378)))), 32312 ^ _782435 : [(32313 ^ _782435) ^ [] : [-(_1394378 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (32315 ^ _782435) ^ [] : [hBOOL(hAPP(_1394374, _1394376))]], 32318 ^ _782435 : [(32319 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1394378)))], (32323 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32321 ^ [_1394374, _1394376, _1394378])))], (32325 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32321 ^ [_1394374, _1394376, _1394378]), _1394378)))], (32327 ^ _782435) ^ [] : [-(_1394376 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394378), 32320 ^ [_1394374, _1394376, _1394378])), 32321 ^ [_1394374, _1394376, _1394378]))], (32329 ^ _782435) ^ [] : [hBOOL(hAPP(_1394374, 32321 ^ [_1394374, _1394376, _1394378]))]], 32330 ^ _782435 : [(32331 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394378), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32335 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1394378), 32333 ^ [_1394374, _1394376, _1394378])))], (32337 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 32333 ^ [_1394374, _1394376, _1394378]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32339 ^ _782435) ^ [] : [-(_1394376 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1394378), 32332 ^ [_1394374, _1394376, _1394378])), 32333 ^ [_1394374, _1394376, _1394378]))], (32341 ^ _782435) ^ [] : [hBOOL(hAPP(_1394374, 32333 ^ [_1394374, _1394376, _1394378]))]]], (32263 ^ _782435) ^ [_1393497, _1393499, _1393501] : [hBOOL(hAPP(_1393497, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1393499, _1393501))), 32266 ^ _782435 : [(32267 ^ _782435) ^ [] : [_1393501 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hBOOL(hAPP(_1393497, _1393499)))], (32273 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393501)), 32276 ^ _782435 : [(32277 ^ _782435) ^ [_1393827, _1393829] : [-(hBOOL(hAPP(_1393497, _1393827))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1393827)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393827), _1393501)), _1393499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393501), _1393829)), _1393827)]]], (32291 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393501), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), 32294 ^ _782435 : [(32295 ^ _782435) ^ [_1394119, _1394121] : [-(hBOOL(hAPP(_1393497, _1394119))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1393501), _1394119)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1394119), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), _1393499 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1393501), _1394121)), _1394119)]]]]], (32345 ^ _782435) ^ [_1395086, _1395088, _1395090, _1395092] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395086)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395088)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395088), _1395090)), -(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), _1395090), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395092, _1395086))), _1395088))))], (32359 ^ _782435) ^ [_1395333, _1395335, _1395337, _1395339] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395333)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395335)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395335), _1395337)), -(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), _1395337), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395339, _1395333))), _1395335)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1395337), _1395333))))], (32373 ^ _782435) ^ [_1395598, _1395600, _1395602, _1395604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395598)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395600), _1395602)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395602), 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), _1395600), _1395598)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1395600), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395604, _1395598))), _1395602))))], (32387 ^ _782435) ^ [_1395869, _1395871, _1395873, _1395875] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1395869)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1395871), _1395873)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1395873), 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), _1395871), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1395875, _1395869))), _1395873)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (32401 ^ _782435) ^ [_1396128, _1396130, _1396132, _1396134] : [_1396128 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396130), _1396132)), _1396134), -(_1396130 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396128, _1396130) = _1396134), 32408 ^ _782435 : [(32409 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396130)))], (32411 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396134), _1396130))]], 32416 ^ _782435 : [(32417 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396130))], (32419 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1396130), _1396134)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1396134), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (32431 ^ _782435) ^ [_1396593, _1396595, _1396597] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1396593)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396595, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396597), _1396593)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1396597), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396595), _1396597), _1396593))), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396595, _1396597)))], (32437 ^ _782435) ^ [_1396747, _1396749] : [-(_1396747 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32440 ^ _782435 : [(32441 ^ _782435) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396749, _1396747) = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396749), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396747)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396749), _1396747)))], (32447 ^ _782435) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1396749, _1396747) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1396749), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1396747)) = 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), _1396749), _1396747))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (32453 ^ _782435) ^ [_1397020, _1397022] : [-(_1397020 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32456 ^ _782435 : [(32457 ^ _782435) ^ [] : [c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397022, _1397020) = 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), _1397022)), _1397020) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397022), _1397020)))], (32463 ^ _782435) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397022, _1397020) = 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), _1397022)), _1397020) = 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), _1397022), _1397020))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]]], (32469 ^ _782435) ^ [_1397294, _1397296, _1397298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397294)), 32472 ^ _782435 : [(32491 ^ _782435) ^ [] : [32494 ^ _782435 : [(32495 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 32493 ^ [_1397294, _1397296, _1397298])))], (32497 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 32493 ^ [_1397294, _1397296, _1397298]), _1397294)))], (32499 ^ _782435) ^ [] : [-(_1397298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1397294), 32492 ^ [_1397294, _1397296, _1397298])), 32493 ^ [_1397294, _1397296, _1397298]))], (32501 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1397296, 32492 ^ [_1397294, _1397296, _1397298]), 32493 ^ [_1397294, _1397296, _1397298]))]], -(hBOOL(hAPP(hAPP(_1397296, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397298), _1397294)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397298, _1397294))))], (32473 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1397296, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1397298), _1397294)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1397298, _1397294))), 32476 ^ _782435 : [(32477 ^ _782435) ^ [_1397495, _1397497] : [-(hBOOL(hAPP(hAPP(_1397296, _1397497), _1397495))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1397495)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1397495), _1397294)), _1397298 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1397294), _1397497)), _1397495)]]]]], (32505 ^ _782435) ^ [_1398018, _1398020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398018)), -(c_SMT_Oz3mod(_1398020, _1398018) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1398020, _1398018))], (32511 ^ _782435) ^ [_1398107, _1398109] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1398107))), -(c_SMT_Oz3mod(_1398109, _1398107) = c_Divides_Odiv__class_Omod(tc_Int_Oint, _1398109, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1398107)))], (32517 ^ _782435) ^ [_1398157, _1398159, _1398161] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398157), _1398159)), 32523 ^ _782435 : [(32524 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1398157), 32522 ^ [_1398157, _1398159, _1398161]), _1398159)))], (32526 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(_1398161, 32522 ^ [_1398157, _1398159, _1398161])))]], -(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(_1398157, tc_Nat_Onat), _1398161), _1398159))))], (32530 ^ _782435) ^ [_1398418, _1398420, _1398422] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398418), _1398420)), c_Fun_Oinj__on(_1398418, tc_fun(tc_fun(_1398418, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1398418, tc_fun(tc_prod(_1398418, _1398418), tc_HOL_Obool), tc_fun(tc_fun(_1398418, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1398418, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1398418, _1398418), tc_HOL_Obool), tc_fun(tc_fun(_1398418, tc_HOL_Obool), tc_HOL_Obool)), _1398418), c_Equiv__Relations_Oquotient(_1398418)), hAPP(hAPP(c_COMBC(_1398418, tc_fun(_1398418, tc_HOL_Obool), tc_fun(_1398418, tc_HOL_Obool)), c_Set_Oinsert(_1398418)), c_Orderings_Obot__class_Obot(tc_fun(_1398418, tc_HOL_Obool))))), _1398422), _1398420), -(hAPP(c_Finite__Set_Ocard(tc_fun(_1398418, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1398418), _1398420), _1398422)) = hAPP(c_Finite__Set_Ocard(_1398418), _1398420))], (32540 ^ _782435) ^ [_1398767, _1398769] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1398767), _1398769)), -(c_Fun_Obij__betw(_1398767, tc_Nat_Onat, 32543 ^ [_1398767, _1398769], _1398769, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), hAPP(c_Finite__Set_Ocard(_1398767), _1398769))))], (32547 ^ _782435) ^ [_1398886, _1398888] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1398886), _1398888) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1398886, _1398888)), _1398888))], (32549 ^ _782435) ^ [_1398929, _1398931] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1398929), _1398931)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1398929, _1398931) = _1398929)], (32555 ^ _782435) ^ [_1399024, _1399026, _1399028] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399024, _1399026)), _1399028) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399024), _1399028), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399026), _1399028)))], (32557 ^ _782435) ^ [_1399077, _1399079, _1399081] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399077), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399079, _1399081)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399077), _1399079), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1399077), _1399081)))], (32559 ^ _782435) ^ [_1399130, _1399132] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399130, _1399132)), _1399130)))], (32561 ^ _782435) ^ [_1399164, _1399166] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399164), c_Orderings_Obot__class_Obot(tc_fun(_1399164, tc_HOL_Obool))), _1399166) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399164, tc_HOL_Obool), tc_HOL_Obool)))], (32563 ^ _782435) ^ [_1399228, _1399230, _1399232] : [c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399228, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399228), _1399230), _1399232), -(_1399230 = c_Orderings_Obot__class_Obot(tc_fun(_1399228, tc_HOL_Obool)))], (32569 ^ _782435) ^ [_1399345, _1399347, _1399349] : [_1399347 = c_Orderings_Obot__class_Obot(tc_fun(_1399345, tc_HOL_Obool)), -(c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399345, tc_HOL_Obool), tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399345), _1399347), _1399349))], (32575 ^ _782435) ^ [_1399486, _1399488, _1399490] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399486), _1399488), _1399490) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399486, tc_HOL_Obool), tc_HOL_Obool)), -(_1399488 = c_Orderings_Obot__class_Obot(tc_fun(_1399486, tc_HOL_Obool)))], (32581 ^ _782435) ^ [_1399603, _1399605, _1399607] : [_1399605 = c_Orderings_Obot__class_Obot(tc_fun(_1399603, tc_HOL_Obool)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1399603), _1399605), _1399607) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1399603, tc_HOL_Obool), tc_HOL_Obool)))], (32587 ^ _782435) ^ [_1399726] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399726, hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32589 ^ _782435) ^ [_1399762, _1399764] : [hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399762, _1399764)) = _1399764, -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399762), _1399764) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32595 ^ _782435) ^ [_1399861, _1399863] : [-(hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399861, _1399863)) = _1399863), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1399861), _1399863) = hAPP(c_Nat_OSuc, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399861, _1399863)))], (32601 ^ _782435) ^ [_1399920, _1399922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1399920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1399922, _1399920)), _1399920)))], (32607 ^ _782435) ^ [_1400034, _1400036] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400034, _1400036) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1400034 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1400036), 32610 ^ [_1400034, _1400036]))], (32614 ^ _782435) ^ [_1400139, _1400141] : [32615 ^ _782435 : [(32616 ^ _782435) ^ [_1400188] : [_1400139 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1400141), _1400188)]], -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400139, _1400141) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32620 ^ _782435) ^ [_1400260, _1400262] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400260), _1400262)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400260, _1400262) = _1400260)], (32626 ^ _782435) ^ [_1400349, _1400351] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400349), _1400351))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400349, _1400351) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400349), _1400351), _1400351))], (32632 ^ _782435) ^ [_1400402, _1400404] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1400402), _1400404))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400402, _1400404) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400402), _1400404), _1400404))], (32638 ^ _782435) ^ [_1400457, _1400459, _1400461] : [-(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), _1400457), _1400459)), _1400461), _1400459) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400461, _1400459))], (32640 ^ _782435) ^ [_1400504, _1400506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1400504), _1400506)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400506, _1400504) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1400506), _1400504), _1400504))], (32646 ^ _782435) ^ [_1400619, _1400621] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400619), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400621)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400619, _1400621)))], (32648 ^ _782435) ^ [_1400661, _1400663] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400661, _1400663)) = c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400661), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1400663)))], (32650 ^ _782435) ^ [_1400703, _1400705, _1400707] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1400703), _1400705)), _1400707) = 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), _1400703), _1400707)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1400705), _1400707))), 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, _1400703, _1400707)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400705, _1400707))), _1400707)))], (32652 ^ _782435) ^ [_1400795, _1400797] : [_1400795 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1400797, _1400795) = _1400797)], (32658 ^ _782435) ^ [_1400872, _1400874] : [-(_1400872 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1400874, _1400872) = c_Nitpick_Onat__gcd(_1400872, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400874, _1400872)))], (32664 ^ _782435) ^ [_1400920, _1400922] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1400920)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1400922, _1400920)), _1400920)))], (32670 ^ _782435) ^ [_1401019, _1401021, _1401023] : [-(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), _1401019), _1401021)), _1401023)), _1401021) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, _1401023), _1401021))], (32672 ^ _782435) ^ [_1401072, _1401074, _1401076] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401072, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401074), _1401076)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401074), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401072), _1401074), _1401076))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401072, _1401074)))], (32674 ^ _782435) ^ [_1401135, _1401137, _1401139] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401135), _1401137)), _1401139) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401135), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401137), _1401139))), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401135), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401137, _1401139))), _1401139)))], (32676 ^ _782435) ^ [_1401208, _1401210] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401208), _1401210)), _1401210) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401208), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401208, _1401210)))], (32678 ^ _782435) ^ [_1401255, _1401257] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401255), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401257), _1401255)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401257), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401257, _1401255)))], (32680 ^ _782435) ^ [_1401302, _1401304] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401302, _1401304) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1401302), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1401302), _1401304)), _1401304)))], (32682 ^ _782435) ^ [_1401349, _1401351, _1401353, _1401355] : [c_Fun_Oinj__on(_1401349, tc_fun(tc_fun(_1401349, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1401349, tc_fun(tc_prod(_1401349, _1401349), tc_HOL_Obool), tc_fun(tc_fun(_1401349, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1401349, tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1401349, _1401349), tc_HOL_Obool), tc_fun(tc_fun(_1401349, tc_HOL_Obool), tc_HOL_Obool)), _1401349), c_Equiv__Relations_Oquotient(_1401349)), hAPP(hAPP(c_COMBC(_1401349, tc_fun(_1401349, tc_HOL_Obool), tc_fun(_1401349, tc_HOL_Obool)), c_Set_Oinsert(_1401349)), c_Orderings_Obot__class_Obot(tc_fun(_1401349, tc_HOL_Obool))))), _1401351), _1401353), hBOOL(hAPP(hAPP(c_member(_1401349), _1401355), _1401353)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401349), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1401349, tc_HOL_Obool)), _1401353), hAPP(hAPP(c_Set_Oinsert(_1401349), _1401355), c_Orderings_Obot__class_Obot(tc_fun(_1401349, tc_HOL_Obool))))), _1401351) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(_1401349, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401349), _1401353), _1401351)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1401349), hAPP(hAPP(c_Set_Oinsert(_1401349), _1401355), c_Orderings_Obot__class_Obot(tc_fun(_1401349, tc_HOL_Obool)))), _1401351)))], (32716 ^ _782435) ^ [_1402267, _1402269, _1402271] : [-(hBOOL(hAPP(_1402267, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1402269, _1402271)))), 32719 ^ _782435 : [(32720 ^ _782435) ^ [] : [-(_1402271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32722 ^ _782435) ^ [] : [hBOOL(hAPP(_1402267, _1402269))]], 32723 ^ _782435 : [(32724 ^ _782435) ^ [] : [_1402271 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (32728 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32726 ^ [_1402267, _1402269, _1402271]), _1402271)))], (32730 ^ _782435) ^ [] : [-(_1402269 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402271), 32725 ^ [_1402267, _1402269, _1402271])), 32726 ^ [_1402267, _1402269, _1402271]))], (32732 ^ _782435) ^ [] : [hBOOL(hAPP(_1402267, 32726 ^ [_1402267, _1402269, _1402271]))]]], (32692 ^ _782435) ^ [_1401834, _1401836, _1401838] : [hBOOL(hAPP(_1401834, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1401836, _1401838))), 32695 ^ _782435 : [(32696 ^ _782435) ^ [] : [_1401838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(_1401834, _1401836)))], (32702 ^ _782435) ^ [] : [-(_1401838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 32705 ^ _782435 : [(32706 ^ _782435) ^ [_1402082, _1402084] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402082), _1401838)), _1401836 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1401838), _1402084)), _1402082), -(hBOOL(hAPP(_1401834, _1402082)))]]]]], (32736 ^ _782435) ^ [_1402676, _1402678, _1402680, _1402682] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1402676)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1402678), _1402680)), -(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), _1402680), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1402682, _1402676))), _1402678)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402680), _1402676))))], (32746 ^ _782435) ^ [_1402881, _1402883] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1402881)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1402881), _1402883)), _1402881) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (32752 ^ _782435) ^ [_1402988, _1402990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1402988)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1402990)), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1402988), hAPP(c_Int_Onat, _1402990)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1402988, _1402990)))], (32762 ^ _782435) ^ [_1403159, _1403161] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403159)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1403161)), -(hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, _1403159, _1403161)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onat, _1403159), hAPP(c_Int_Onat, _1403161)))], (32772 ^ _782435) ^ [_1403330, _1403332, _1403334] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403330), _1403332), _1403334) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1403330, tc_fun(tc_fun(_1403330, tc_HOL_Obool), tc_HOL_Obool)), _1403332), hAPP(hAPP(c_COMBC(_1403330, tc_fun(tc_fun(_1403330, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1403330, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1403330, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1403330, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1403330, tc_HOL_Obool), tc_HOL_Obool)), _1403330), c_Set_Oinsert(tc_fun(_1403330, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1403330, tc_HOL_Obool), tc_fun(_1403330, tc_HOL_Obool), _1403330), c_Relation_OImage(_1403330, _1403330, _1403334)), hAPP(hAPP(c_COMBC(_1403330, tc_fun(_1403330, tc_HOL_Obool), tc_fun(_1403330, tc_HOL_Obool)), c_Set_Oinsert(_1403330)), c_Orderings_Obot__class_Obot(tc_fun(_1403330, tc_HOL_Obool)))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1403330, tc_HOL_Obool), tc_HOL_Obool)))))], (32774 ^ _782435) ^ [_1403486, _1403488, _1403490] : [-(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403486), hAPP(hAPP(c_Set_Oinsert(_1403486), _1403488), c_Orderings_Obot__class_Obot(tc_fun(_1403486, tc_HOL_Obool)))), _1403490) = hAPP(hAPP(c_Set_Oinsert(tc_fun(_1403486, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403486, _1403486, _1403490), hAPP(hAPP(c_Set_Oinsert(_1403486), _1403488), c_Orderings_Obot__class_Obot(tc_fun(_1403486, tc_HOL_Obool))))), c_Orderings_Obot__class_Obot(tc_fun(tc_fun(_1403486, tc_HOL_Obool), tc_HOL_Obool))))], (32776 ^ _782435) ^ [_1403573, _1403575, _1403577, _1403579] : [hBOOL(hAPP(hAPP(c_member(_1403573), _1403575), _1403577)), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1403573, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1403573, _1403573, _1403579), hAPP(hAPP(c_Set_Oinsert(_1403573), _1403575), c_Orderings_Obot__class_Obot(tc_fun(_1403573, tc_HOL_Obool))))), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1403573), _1403577), _1403579))))], (32782 ^ _782435) ^ [_1403744, _1403746, _1403748, _1403750] : [class_Groups_Ocomm__monoid__mult(_1403744), hBOOL(hAPP(c_Finite__Set_Ofinite(_1403746), _1403748)), 32792 ^ _782435 : [(32793 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1403746), 32791 ^ [_1403744, _1403746, _1403748, _1403750]), _1403748)))], (32795 ^ _782435) ^ [] : [hAPP(_1403750, 32791 ^ [_1403744, _1403746, _1403748, _1403750]) = c_Groups_Oone__class_Oone(_1403744)]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1403744, _1403746, c_Groups_Otimes__class_Otimes(_1403744)), _1403750), c_Groups_Oone__class_Oone(_1403744)), _1403748) = c_Groups_Oone__class_Oone(_1403744))], (32799 ^ _782435) ^ [_1404085, _1404087, _1404089, _1404091] : [-(hAPP(c_Relation_OImage(_1404085, _1404087, _1404089), _1404091) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404085, tc_fun(_1404087, tc_HOL_Obool)), _1404091), hAPP(hAPP(c_COMBB(tc_fun(_1404085, tc_HOL_Obool), tc_fun(_1404087, tc_HOL_Obool), _1404085), c_Relation_OImage(_1404085, _1404087, _1404089)), hAPP(hAPP(c_COMBC(_1404085, tc_fun(_1404085, tc_HOL_Obool), tc_fun(_1404085, tc_HOL_Obool)), c_Set_Oinsert(_1404085)), c_Orderings_Obot__class_Obot(tc_fun(_1404085, tc_HOL_Obool))))))], (32801 ^ _782435) ^ [_1404176, _1404178, _1404180, _1404182, _1404184, _1404186] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404176, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404178, _1404176, _1404180), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404182, tc_fun(_1404178, tc_HOL_Obool)), _1404184), _1404186))), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1404182, tc_fun(_1404176, tc_HOL_Obool)), _1404184), hAPP(hAPP(c_COMBB(tc_fun(_1404178, tc_HOL_Obool), tc_fun(_1404176, tc_HOL_Obool), _1404182), c_Relation_OImage(_1404178, _1404176, _1404180)), _1404186)))))], (32803 ^ _782435) ^ [_1404270, _1404272, _1404274, _1404276, _1404278] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404270, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404272, _1404270, _1404274), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404272, tc_HOL_Obool)), _1404276), _1404278))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1404270, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404272, _1404270, _1404274), _1404276)), hAPP(c_Relation_OImage(_1404272, _1404270, _1404274), _1404278)))))], (32805 ^ _782435) ^ [_1404354, _1404356, _1404358, _1404360, _1404362, _1404364] : [-(hAPP(c_Relation_OImage(_1404354, _1404356, _1404358), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404360, tc_fun(_1404354, tc_HOL_Obool)), _1404362), _1404364)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1404360, tc_fun(_1404356, tc_HOL_Obool)), _1404362), hAPP(hAPP(c_COMBB(tc_fun(_1404354, tc_HOL_Obool), tc_fun(_1404356, tc_HOL_Obool), _1404360), c_Relation_OImage(_1404354, _1404356, _1404358)), _1404364)))], (32807 ^ _782435) ^ [_1404438, _1404440, _1404442] : [-(hAPP(c_Relation_OImage(_1404438, _1404440, _1404442), c_Orderings_Obot__class_Obot(tc_fun(_1404438, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1404440, tc_HOL_Obool)))], (32809 ^ _782435) ^ [_1404482, _1404484, _1404486, _1404488, _1404490, _1404492] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1404482, _1404484), tc_HOL_Obool)), _1404486), _1404488)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404482, tc_HOL_Obool)), _1404490), _1404492)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1404484, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404482, _1404484, _1404486), _1404490)), hAPP(c_Relation_OImage(_1404482, _1404484, _1404488), _1404492))))], (32819 ^ _782435) ^ [_1404721, _1404723, _1404725, _1404727, _1404729] : [-(hAPP(c_Relation_OImage(_1404721, _1404723, _1404725), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404721, tc_HOL_Obool)), _1404727), _1404729)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404723, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404721, _1404723, _1404725), _1404727)), hAPP(c_Relation_OImage(_1404721, _1404723, _1404725), _1404729)))], (32821 ^ _782435) ^ [_1404795, _1404797, _1404799, _1404801, _1404803] : [-(hAPP(c_Relation_OImage(_1404795, _1404797, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1404795, _1404797), tc_HOL_Obool)), _1404799), _1404801)), _1404803) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1404797, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1404795, _1404797, _1404799), _1404803)), hAPP(c_Relation_OImage(_1404795, _1404797, _1404801), _1404803)))], (32823 ^ _782435) ^ [_1404872, _1404874, _1404876, _1404878] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1404872, tc_HOL_Obool)), _1404874), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1404872), _1404876), _1404878))), 32827 ^ _782435 : [(32828 ^ _782435) ^ [] : [-(_1404874 = hAPP(c_Relation_OImage(_1404872, _1404872, _1404878), hAPP(hAPP(c_Set_Oinsert(_1404872), 32826 ^ [_1404872, _1404874, _1404876, _1404878]), c_Orderings_Obot__class_Obot(tc_fun(_1404872, tc_HOL_Obool)))))], (32830 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1404872), 32826 ^ [_1404872, _1404874, _1404876, _1404878]), _1404876)))]]], (32832 ^ _782435) ^ [_1405100, _1405102, _1405104] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1405100, _1405102) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1405104, _1405102), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1405104), _1405100)), -(_1405100 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1405104), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1405102), 32839 ^ [_1405100, _1405102, _1405104])))], (32843 ^ _782435) ^ [_1405297, _1405299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1405297), _1405299)), 32849 ^ _782435 : [(32850 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405297), 32848 ^ [_1405297, _1405299]), _1405299)))], (32852 ^ _782435) ^ [] : [c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_Finite__Set_Ocard(_1405297), _1405299) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (32856 ^ _782435) ^ [_1405497, _1405499, _1405501] : [32858 ^ _782435 : [(32859 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 32857 ^ [_1405497, _1405499, _1405501]), _1405497)))], (32861 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1405499, 32857 ^ [_1405497, _1405499, _1405501])))], (32863 ^ _782435) ^ [] : [hBOOL(hAPP(_1405499, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, 32857 ^ [_1405497, _1405499, _1405501]), _1405497)))]], hBOOL(hAPP(_1405499, _1405501)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1405501), _1405497)), -(hBOOL(hAPP(_1405499, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (32875 ^ _782435) ^ [_1405859, _1405861, _1405863] : [_1405859 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1405861, _1405861), tc_HOL_Obool)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1405861, _1405861), tc_HOL_Obool)), _1405859), _1405863)))], (32881 ^ _782435) ^ [_1405980, _1405982, _1405984, _1405986, _1405988, _1405990] : [class_Groups_Oab__semigroup__mult(_1405980), hBOOL(hAPP(c_Finite__Set_Ofinite(_1405982), _1405984)), 32891 ^ _782435 : [(32892 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1405982), 32890 ^ [_1405980, _1405982, _1405984, _1405986, _1405988, _1405990]), _1405984)))], (32894 ^ _782435) ^ [] : [hAPP(_1405986, 32890 ^ [_1405980, _1405982, _1405984, _1405986, _1405988, _1405990]) = hAPP(_1405988, 32890 ^ [_1405980, _1405982, _1405984, _1405986, _1405988, _1405990])]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1405980, _1405982, c_Groups_Otimes__class_Otimes(_1405980)), _1405986), _1405990), _1405984) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1405980, _1405982, c_Groups_Otimes__class_Otimes(_1405980)), _1405988), _1405990), _1405984))], (32898 ^ _782435) ^ [_1406385, _1406387, _1406389] : [class_Orderings_Olinorder(_1406385), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406385), _1406387)), 32908 ^ _782435 : [(32909 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406385), 32907 ^ [_1406385, _1406387, _1406389]), _1406387)))], (32911 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406385), 32907 ^ [_1406385, _1406387, _1406389]), _1406389))]], hBOOL(hAPP(hAPP(c_member(_1406385), _1406389), _1406387)), -(c_Big__Operators_Olinorder__class_OMax(_1406385, _1406387) = _1406389)], (32919 ^ _782435) ^ [_1406757, _1406759, _1406761] : [class_Orderings_Olinorder(_1406757), hBOOL(hAPP(c_Finite__Set_Ofinite(_1406757), _1406759)), 32929 ^ _782435 : [(32930 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1406757), 32928 ^ [_1406757, _1406759, _1406761]), _1406759)))], (32932 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1406757), _1406761), 32928 ^ [_1406757, _1406759, _1406761]))]], hBOOL(hAPP(hAPP(c_member(_1406757), _1406761), _1406759)), -(c_Big__Operators_Olinorder__class_OMin(_1406757, _1406759) = _1406761)], (32940 ^ _782435) ^ [_1407129] : [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), _1407129))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407129) = hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407129)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (32946 ^ _782435) ^ [_1407244, _1407246] : [class_Int_Onumber__ring(_1407244), 32949 ^ _782435 : [(32950 ^ _782435) ^ [] : [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), _1407246))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407244), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407246)) = hAPP(c_Int_Onumber__class_Onumber__of(_1407244), _1407246))], (32956 ^ _782435) ^ [] : [-(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), _1407246)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1407244), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1407246)) = c_Groups_Ozero__class_Ozero(_1407244))]]], (32962 ^ _782435) ^ [_1407484, _1407486] : [class_Int_Onumber__ring(_1407484), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407484), _1407486) = hAPP(c_Int_Oring__1__class_Oof__int(_1407484), _1407486))], (32968 ^ _782435) ^ [_1407579, _1407581, _1407583] : [class_Int_Onumber__ring(_1407579), class_Int_Oring__char__0(_1407579), 32975 ^ _782435 : [(32976 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1407579), _1407581) = hAPP(c_Int_Onumber__class_Onumber__of(_1407579), _1407583), -(_1407581 = _1407583)], (32982 ^ _782435) ^ [] : [_1407581 = _1407583, -(hAPP(c_Int_Onumber__class_Onumber__of(_1407579), _1407581) = hAPP(c_Int_Onumber__class_Onumber__of(_1407579), _1407583))]]], (32988 ^ _782435) ^ [_1407874, _1407876, _1407878] : [class_Int_Onumber(_1407874), 32991 ^ _782435 : [(32992 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1407874), _1407876) = _1407878, -(_1407878 = hAPP(c_Int_Onumber__class_Onumber__of(_1407874), _1407876))], (32998 ^ _782435) ^ [] : [_1407878 = hAPP(c_Int_Onumber__class_Onumber__of(_1407874), _1407876), -(hAPP(c_Int_Onumber__class_Onumber__of(_1407874), _1407876) = _1407878)]]], (33004 ^ _782435) ^ [_1408115, _1408117] : [class_Int_Onumber__ring(_1408115), -(hAPP(c_Int_Oring__1__class_Oof__int(_1408115), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408117)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408115), _1408117))], (33010 ^ _782435) ^ [_1408216, _1408218] : [class_Int_Onumber__ring(_1408216), 33013 ^ _782435 : [(33014 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408218))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408218)) = c_Groups_Ozero__class_Ozero(_1408216))], (33020 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1408218)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1408216), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1408218)) = hAPP(c_Int_Onumber__class_Onumber__of(_1408216), _1408218))]]], (33026 ^ _782435) ^ [_1408456, _1408458, _1408460] : [class_Int_Onumber(_1408456), class_Orderings_Olinorder(_1408456), 33033 ^ _782435 : [(33034 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408456), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408458)), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408460))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408456), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408460)), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408458)))], (33040 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1408456), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408460)), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408458)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1408456), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408458)), hAPP(c_Int_Onumber__class_Onumber__of(_1408456), _1408460))))]]], (33046 ^ _782435) ^ [_1408783, _1408785, _1408787, _1408789] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408783), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408783), _1408785), _1408787)), hAPP(c_Int_Onumber__class_Onumber__of(_1408783), _1408789)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1408783), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408783), _1408785), hAPP(c_Int_Onumber__class_Onumber__of(_1408783), _1408789))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1408783), _1408787), hAPP(c_Int_Onumber__class_Onumber__of(_1408783), _1408789)))), class_Int_Onumber(_1408783), class_Rings_Osemiring(_1408783)], (33056 ^ _782435) ^ [_1409026, _1409028, _1409030, _1409032] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409026), hAPP(c_Int_Onumber__class_Onumber__of(_1409026), _1409028)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409026), _1409030), _1409032)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1409026), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409026), hAPP(c_Int_Onumber__class_Onumber__of(_1409026), _1409028)), _1409030)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409026), hAPP(c_Int_Onumber__class_Onumber__of(_1409026), _1409028)), _1409032))), class_Int_Onumber(_1409026), class_Rings_Osemiring(_1409026)], (33066 ^ _782435) ^ [_1409269, _1409271, _1409273, _1409275] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409269), hAPP(c_Int_Onumber__class_Onumber__of(_1409269), _1409271)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409269), _1409273), _1409275)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409269), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409269), hAPP(c_Int_Onumber__class_Onumber__of(_1409269), _1409271)), _1409273)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409269), hAPP(c_Int_Onumber__class_Onumber__of(_1409269), _1409271)), _1409275))), class_Int_Onumber(_1409269), class_Rings_Oring(_1409269)], (33076 ^ _782435) ^ [_1409512, _1409514, _1409516, _1409518] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409512), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409512), _1409514), _1409516)), hAPP(c_Int_Onumber__class_Onumber__of(_1409512), _1409518)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1409512), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409512), _1409514), hAPP(c_Int_Onumber__class_Onumber__of(_1409512), _1409518))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1409512), _1409516), hAPP(c_Int_Onumber__class_Onumber__of(_1409512), _1409518)))), class_Int_Onumber(_1409512), class_Rings_Oring(_1409512)], (33086 ^ _782435) ^ [_1409755, _1409757, _1409759] : [class_Int_Onumber__ring(_1409755), class_Rings_Olinordered__idom(_1409755), 33093 ^ _782435 : [(33094 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409755), hAPP(c_Int_Onumber__class_Onumber__of(_1409755), _1409757)), hAPP(c_Int_Onumber__class_Onumber__of(_1409755), _1409759))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409757), _1409759)))], (33100 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1409757), _1409759)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1409755), hAPP(c_Int_Onumber__class_Onumber__of(_1409755), _1409757)), hAPP(c_Int_Onumber__class_Onumber__of(_1409755), _1409759))))]]], (33106 ^ _782435) ^ [_1410086, _1410088, _1410090] : [class_Int_Onumber__ring(_1410086), class_Rings_Olinordered__idom(_1410086), 33113 ^ _782435 : [(33114 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410086), hAPP(c_Int_Onumber__class_Onumber__of(_1410086), _1410088)), hAPP(c_Int_Onumber__class_Onumber__of(_1410086), _1410090))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410088), _1410090)))], (33120 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1410088), _1410090)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1410086), hAPP(c_Int_Onumber__class_Onumber__of(_1410086), _1410088)), hAPP(c_Int_Onumber__class_Onumber__of(_1410086), _1410090))))]]], (33126 ^ _782435) ^ [_1410417, _1410419, _1410421] : [class_Int_Onumber(_1410417), class_Orderings_Oord(_1410417), 33133 ^ _782435 : [(33134 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410417), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410419)), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410421))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410417), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410419)), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410421)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410419))], (33140 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410417), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410419)), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410421)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omin(_1410417), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410419)), hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410421)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410417), _1410421))]]], (33146 ^ _782435) ^ [_1410809, _1410811, _1410813] : [class_Int_Onumber(_1410809), class_Orderings_Oord(_1410809), 33153 ^ _782435 : [(33154 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410809), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410811)), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410813))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410809), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410811)), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410813)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410813))], (33160 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1410809), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410811)), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410813)))), -(hAPP(hAPP(c_Orderings_Oord__class_Omax(_1410809), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410811)), hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410813)) = hAPP(c_Int_Onumber__class_Onumber__of(_1410809), _1410811))]]], (33166 ^ _782435) ^ [_1411201, _1411203, _1411205] : [class_Int_Onumber__ring(_1411201), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411201), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411203), _1411205)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411201), hAPP(c_Int_Onumber__class_Onumber__of(_1411201), _1411203)), hAPP(c_Int_Onumber__class_Onumber__of(_1411201), _1411205)))], (33172 ^ _782435) ^ [_1411336, _1411338, _1411340] : [class_Int_Onumber__ring(_1411336), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411336), hAPP(c_Int_Onumber__class_Onumber__of(_1411336), _1411338)), hAPP(c_Int_Onumber__class_Onumber__of(_1411336), _1411340)) = hAPP(c_Int_Onumber__class_Onumber__of(_1411336), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411338), _1411340)))], (33178 ^ _782435) ^ [_1411471, _1411473, _1411475, _1411477] : [class_Int_Onumber__ring(_1411471), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411471), hAPP(c_Int_Onumber__class_Onumber__of(_1411471), _1411473)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411471), hAPP(c_Int_Onumber__class_Onumber__of(_1411471), _1411475)), _1411477)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1411471), hAPP(c_Int_Onumber__class_Onumber__of(_1411471), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1411473), _1411475))), _1411477))], (33184 ^ _782435) ^ [_1411640, _1411642, _1411644] : [class_Int_Onumber__ring(_1411640), -(hAPP(c_Int_Onumber__class_Onumber__of(_1411640), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411642), _1411644)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411640), hAPP(c_Int_Onumber__class_Onumber__of(_1411640), _1411642)), hAPP(c_Int_Onumber__class_Onumber__of(_1411640), _1411644)))], (33190 ^ _782435) ^ [_1411775, _1411777, _1411779] : [class_Int_Onumber__ring(_1411775), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411775), hAPP(c_Int_Onumber__class_Onumber__of(_1411775), _1411777)), hAPP(c_Int_Onumber__class_Onumber__of(_1411775), _1411779)) = hAPP(c_Int_Onumber__class_Onumber__of(_1411775), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411777), _1411779)))], (33196 ^ _782435) ^ [_1411910, _1411912, _1411914, _1411916] : [class_Int_Onumber__ring(_1411910), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411910), hAPP(c_Int_Onumber__class_Onumber__of(_1411910), _1411912)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411910), hAPP(c_Int_Onumber__class_Onumber__of(_1411910), _1411914)), _1411916)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1411910), hAPP(c_Int_Onumber__class_Onumber__of(_1411910), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1411912), _1411914))), _1411916))], (33202 ^ _782435) ^ [_1412079, _1412081, _1412083] : [class_Int_Onumber__ring(_1412079), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412079), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1412081), _1412083)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1412079), hAPP(c_Int_Onumber__class_Onumber__of(_1412079), _1412081)), hAPP(c_Int_Onumber__class_Onumber__of(_1412079), _1412083)))], (33208 ^ _782435) ^ [_1412214, _1412216] : [class_Int_Onumber__ring(_1412214), -(hAPP(c_Int_Onumber__class_Onumber__of(_1412214), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412216)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1412214), hAPP(c_Int_Onumber__class_Onumber__of(_1412214), _1412216)))], (33214 ^ _782435) ^ [_1412325, _1412327] : [class_Int_Onumber__ring(_1412325), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1412325), hAPP(c_Int_Onumber__class_Onumber__of(_1412325), _1412327)) = hAPP(c_Int_Onumber__class_Onumber__of(_1412325), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1412327)))], (33220 ^ _782435) ^ [_1412436, _1412438] : [class_Int_Onumber__ring(_1412436), -(hBOOL(hAPP(hAPP(c_member(_1412436), hAPP(c_Int_Onumber__class_Onumber__of(_1412436), _1412438)), c_Int_Oring__1__class_OInts(_1412436))))], (33226 ^ _782435) ^ [_1412539, _1412541, _1412543, _1412545] : [class_Fields_Ofield__inverse__zero(_1412539), class_Int_Onumber(_1412539), 33233 ^ _782435 : [(33250 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1412539), _1412541), hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543)) = _1412545), 33253 ^ _782435 : [(33254 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543) = c_Groups_Ozero__class_Ozero(_1412539)], (33256 ^ _782435) ^ [] : [_1412541 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412539), _1412545), hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543))]], 33257 ^ _782435 : [(33258 ^ _782435) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543) = c_Groups_Ozero__class_Ozero(_1412539))], (33260 ^ _782435) ^ [] : [_1412545 = c_Groups_Ozero__class_Ozero(_1412539)]]], (33234 ^ _782435) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1412539), _1412541), hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543)) = _1412545, 33237 ^ _782435 : [(33238 ^ _782435) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543) = c_Groups_Ozero__class_Ozero(_1412539)), -(_1412541 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1412539), _1412545), hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543)))], (33244 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1412539), _1412543) = c_Groups_Ozero__class_Ozero(_1412539), -(_1412545 = c_Groups_Ozero__class_Ozero(_1412539))]]]]], (33264 ^ _782435) ^ [_1413149, _1413151, _1413153, _1413155] : [class_Fields_Ofield__inverse__zero(_1413149), class_Int_Onumber(_1413149), 33271 ^ _782435 : [(33288 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413149), _1413151), _1413153) = hAPP(c_Int_Onumber__class_Onumber__of(_1413149), _1413155)), 33291 ^ _782435 : [(33292 ^ _782435) ^ [] : [_1413153 = c_Groups_Ozero__class_Ozero(_1413149)], (33294 ^ _782435) ^ [] : [_1413151 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413149), hAPP(c_Int_Onumber__class_Onumber__of(_1413149), _1413155)), _1413153)]], 33295 ^ _782435 : [(33296 ^ _782435) ^ [] : [-(_1413153 = c_Groups_Ozero__class_Ozero(_1413149))], (33298 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413149), _1413155) = c_Groups_Ozero__class_Ozero(_1413149)]]], (33272 ^ _782435) ^ [] : [hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413149), _1413151), _1413153) = hAPP(c_Int_Onumber__class_Onumber__of(_1413149), _1413155), 33275 ^ _782435 : [(33276 ^ _782435) ^ [] : [-(_1413153 = c_Groups_Ozero__class_Ozero(_1413149)), -(_1413151 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413149), hAPP(c_Int_Onumber__class_Onumber__of(_1413149), _1413155)), _1413153))], (33282 ^ _782435) ^ [] : [_1413153 = c_Groups_Ozero__class_Ozero(_1413149), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413149), _1413155) = c_Groups_Ozero__class_Ozero(_1413149))]]]]], (33302 ^ _782435) ^ [_1413744, _1413746, _1413748, _1413750] : [class_Fields_Ofield__inverse__zero(_1413744), class_Int_Onumber(_1413744), 33309 ^ _782435 : [(33326 ^ _782435) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1413744), _1413746) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413744), _1413748), _1413750)), 33329 ^ _782435 : [(33330 ^ _782435) ^ [] : [_1413750 = c_Groups_Ozero__class_Ozero(_1413744)], (33332 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413744), hAPP(c_Int_Onumber__class_Onumber__of(_1413744), _1413746)), _1413750) = _1413748]], 33333 ^ _782435 : [(33334 ^ _782435) ^ [] : [-(_1413750 = c_Groups_Ozero__class_Ozero(_1413744))], (33336 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413744), _1413746) = c_Groups_Ozero__class_Ozero(_1413744)]]], (33310 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1413744), _1413746) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1413744), _1413748), _1413750), 33313 ^ _782435 : [(33314 ^ _782435) ^ [] : [-(_1413750 = c_Groups_Ozero__class_Ozero(_1413744)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1413744), hAPP(c_Int_Onumber__class_Onumber__of(_1413744), _1413746)), _1413750) = _1413748)], (33320 ^ _782435) ^ [] : [_1413750 = c_Groups_Ozero__class_Ozero(_1413744), -(hAPP(c_Int_Onumber__class_Onumber__of(_1413744), _1413746) = c_Groups_Ozero__class_Ozero(_1413744))]]]]], (33340 ^ _782435) ^ [_1414339, _1414341, _1414343, _1414345] : [class_Fields_Ofield__inverse__zero(_1414339), class_Int_Onumber(_1414339), 33347 ^ _782435 : [(33364 ^ _782435) ^ [] : [-(_1414341 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1414339), _1414343), hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345))), 33367 ^ _782435 : [(33368 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345) = c_Groups_Ozero__class_Ozero(_1414339)], (33370 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414339), _1414341), hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345)) = _1414343]], 33371 ^ _782435 : [(33372 ^ _782435) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345) = c_Groups_Ozero__class_Ozero(_1414339))], (33374 ^ _782435) ^ [] : [_1414341 = c_Groups_Ozero__class_Ozero(_1414339)]]], (33348 ^ _782435) ^ [] : [_1414341 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1414339), _1414343), hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345)), 33351 ^ _782435 : [(33352 ^ _782435) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345) = c_Groups_Ozero__class_Ozero(_1414339)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1414339), _1414341), hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345)) = _1414343)], (33358 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1414339), _1414345) = c_Groups_Ozero__class_Ozero(_1414339), -(_1414341 = c_Groups_Ozero__class_Ozero(_1414339))]]]]], (33378 ^ _782435) ^ [_1414949, _1414951, _1414953, _1414955] : [class_Int_Onumber__ring(_1414949), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1414949), hAPP(c_Int_Onumber__class_Onumber__of(_1414949), _1414951)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414949), hAPP(c_Int_Onumber__class_Onumber__of(_1414949), _1414953)), _1414955)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1414949), hAPP(c_Int_Onumber__class_Onumber__of(_1414949), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1414951), _1414953))), _1414955))], (33384 ^ _782435) ^ [_1415118, _1415120, _1415122] : [class_Int_Onumber__ring(_1415118), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415118), hAPP(c_Groups_Ouminus__class_Ouminus(_1415118), hAPP(c_Int_Onumber__class_Onumber__of(_1415118), _1415120))), _1415122) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415118), hAPP(c_Int_Onumber__class_Onumber__of(_1415118), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1415120))), _1415122))], (33390 ^ _782435) ^ [_1415263, _1415265, _1415267] : [class_Int_Onumber__ring(_1415263), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1415263), hAPP(c_Int_Onumber__class_Onumber__of(_1415263), _1415265)), hAPP(c_Int_Onumber__class_Onumber__of(_1415263), _1415267)) = hAPP(c_Int_Onumber__class_Onumber__of(_1415263), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1415265), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1415267))))], (33396 ^ _782435) ^ [_1415404, _1415406, _1415408, _1415410] : [class_Fields_Olinordered__field__inverse__zero(_1415404), class_Int_Onumber(_1415404), 33403 ^ _782435 : [(33430 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415404), _1415406), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))), _1415410))), 33433 ^ _782435 : [(33434 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), c_Groups_Ozero__class_Ozero(_1415404)), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))))], (33436 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), _1415406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415404), _1415410), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))))]], 33437 ^ _782435 : [(33438 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), c_Groups_Ozero__class_Ozero(_1415404)), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)))], (33440 ^ _782435) ^ [] : [33441 ^ _782435 : [(33442 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)), c_Groups_Ozero__class_Ozero(_1415404))))], (33444 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415404), _1415410), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))), _1415406))]], 33445 ^ _782435 : [(33446 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)), c_Groups_Ozero__class_Ozero(_1415404)))], (33448 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), c_Groups_Ozero__class_Ozero(_1415404)), _1415410))]]]]], (33404 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1415404), _1415406), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))), _1415410)), 33407 ^ _782435 : [(33408 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), c_Groups_Ozero__class_Ozero(_1415404)), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), _1415406), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415404), _1415410), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)))))], (33414 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), c_Groups_Ozero__class_Ozero(_1415404)), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)))), 33417 ^ _782435 : [(33418 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)), c_Groups_Ozero__class_Ozero(_1415404))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1415404), _1415410), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408))), _1415406)))], (33424 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), hAPP(c_Int_Onumber__class_Onumber__of(_1415404), _1415408)), c_Groups_Ozero__class_Ozero(_1415404)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1415404), c_Groups_Ozero__class_Ozero(_1415404)), _1415410)))]]]]]]], (33452 ^ _782435) ^ [_1416518, _1416520, _1416522, _1416524] : [class_Fields_Olinordered__field__inverse__zero(_1416518), class_Int_Onumber(_1416518), 33459 ^ _782435 : [(33486 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1416518), _1416520), _1416522)), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524)))), 33489 ^ _782435 : [(33490 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), c_Groups_Ozero__class_Ozero(_1416518)), _1416522)))], (33492 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), _1416520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416518), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524)), _1416522)))]], 33493 ^ _782435 : [(33494 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), c_Groups_Ozero__class_Ozero(_1416518)), _1416522))], (33496 ^ _782435) ^ [] : [33497 ^ _782435 : [(33498 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), _1416522), c_Groups_Ozero__class_Ozero(_1416518))))], (33500 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416518), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524)), _1416522)), _1416520))]], 33501 ^ _782435 : [(33502 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), _1416522), c_Groups_Ozero__class_Ozero(_1416518)))], (33504 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), c_Groups_Ozero__class_Ozero(_1416518)), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524)))]]]]], (33460 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1416518), _1416520), _1416522)), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524))), 33463 ^ _782435 : [(33464 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), c_Groups_Ozero__class_Ozero(_1416518)), _1416522)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), _1416520), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416518), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524)), _1416522))))], (33470 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), c_Groups_Ozero__class_Ozero(_1416518)), _1416522))), 33473 ^ _782435 : [(33474 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), _1416522), c_Groups_Ozero__class_Ozero(_1416518))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1416518), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524)), _1416522)), _1416520)))], (33480 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), _1416522), c_Groups_Ozero__class_Ozero(_1416518)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1416518), c_Groups_Ozero__class_Ozero(_1416518)), hAPP(c_Int_Onumber__class_Onumber__of(_1416518), _1416524))))]]]]]]], (33508 ^ _782435) ^ [_1417587, _1417589, _1417591, _1417593] : [class_Fields_Olinordered__field__inverse__zero(_1417587), class_Int_Onumber(_1417587), 33515 ^ _782435 : [(33542 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417587), _1417591), _1417593)))), 33545 ^ _782435 : [(33546 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), c_Groups_Ozero__class_Ozero(_1417587)), _1417593)))], (33548 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), _1417593)), _1417591))]], 33549 ^ _782435 : [(33550 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), c_Groups_Ozero__class_Ozero(_1417587)), _1417593))], (33552 ^ _782435) ^ [] : [33553 ^ _782435 : [(33554 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), _1417593), c_Groups_Ozero__class_Ozero(_1417587))))], (33556 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), _1417591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), _1417593)))]], 33557 ^ _782435 : [(33558 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), _1417593), c_Groups_Ozero__class_Ozero(_1417587)))], (33560 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), c_Groups_Ozero__class_Ozero(_1417587)))]]]]], (33516 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1417587), _1417591), _1417593))), 33519 ^ _782435 : [(33520 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), c_Groups_Ozero__class_Ozero(_1417587)), _1417593)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), _1417593)), _1417591)))], (33526 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), c_Groups_Ozero__class_Ozero(_1417587)), _1417593))), 33529 ^ _782435 : [(33530 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), _1417593), c_Groups_Ozero__class_Ozero(_1417587))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), _1417591), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), _1417593))))], (33536 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), _1417593), c_Groups_Ozero__class_Ozero(_1417587)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1417587), hAPP(c_Int_Onumber__class_Onumber__of(_1417587), _1417589)), c_Groups_Ozero__class_Ozero(_1417587))))]]]]]]], (33564 ^ _782435) ^ [_1418656, _1418658, _1418660, _1418662] : [class_Fields_Olinordered__field__inverse__zero(_1418656), class_Int_Onumber(_1418656), 33571 ^ _782435 : [(33598 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), _1418658), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418656), _1418660), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662))))), 33601 ^ _782435 : [(33602 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), c_Groups_Ozero__class_Ozero(_1418656)), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662))))], (33604 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418656), _1418658), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662))), _1418660))]], 33605 ^ _782435 : [(33606 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), c_Groups_Ozero__class_Ozero(_1418656)), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)))], (33608 ^ _782435) ^ [] : [33609 ^ _782435 : [(33610 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)), c_Groups_Ozero__class_Ozero(_1418656))))], (33612 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), _1418660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418656), _1418658), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662))))]], 33613 ^ _782435 : [(33614 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)), c_Groups_Ozero__class_Ozero(_1418656)))], (33616 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), _1418658), c_Groups_Ozero__class_Ozero(_1418656)))]]]]], (33572 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), _1418658), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1418656), _1418660), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)))), 33575 ^ _782435 : [(33576 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), c_Groups_Ozero__class_Ozero(_1418656)), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418656), _1418658), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662))), _1418660)))], (33582 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), c_Groups_Ozero__class_Ozero(_1418656)), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)))), 33585 ^ _782435 : [(33586 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)), c_Groups_Ozero__class_Ozero(_1418656))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), _1418660), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1418656), _1418658), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)))))], (33592 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), hAPP(c_Int_Onumber__class_Onumber__of(_1418656), _1418662)), c_Groups_Ozero__class_Ozero(_1418656)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1418656), _1418658), c_Groups_Ozero__class_Ozero(_1418656))))]]]]]]], (33620 ^ _782435) ^ [_1419770, _1419772] : [class_Int_Onumber__ring(_1419770), class_Rings_Olinordered__idom(_1419770), 33627 ^ _782435 : [(33628 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419770), hAPP(c_Int_Onumber__class_Onumber__of(_1419770), _1419772)), c_Groups_Ozero__class_Ozero(_1419770))), -(hAPP(c_Groups_Oabs__class_Oabs(_1419770), hAPP(c_Int_Onumber__class_Onumber__of(_1419770), _1419772)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1419770), hAPP(c_Int_Onumber__class_Onumber__of(_1419770), _1419772)))], (33634 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1419770), hAPP(c_Int_Onumber__class_Onumber__of(_1419770), _1419772)), c_Groups_Ozero__class_Ozero(_1419770)))), -(hAPP(c_Groups_Oabs__class_Oabs(_1419770), hAPP(c_Int_Onumber__class_Onumber__of(_1419770), _1419772)) = hAPP(c_Int_Onumber__class_Onumber__of(_1419770), _1419772))]]], (33640 ^ _782435) ^ [_1420122, _1420124, _1420126, _1420128] : [class_Int_Onumber__ring(_1420122), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420122), hAPP(c_Int_Onumber__class_Onumber__of(_1420122), _1420124)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1420122), _1420126), hAPP(c_Int_Onumber__class_Onumber__of(_1420122), _1420128))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1420122), hAPP(c_Int_Onumber__class_Onumber__of(_1420122), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1420124), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1420128)))), _1420126))], (33646 ^ _782435) ^ [_1420297, _1420299, _1420301, _1420303] : [class_Fields_Olinordered__field__inverse__zero(_1420297), class_Int_Onumber(_1420297), 33653 ^ _782435 : [(33680 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420297), _1420299), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))), _1420303))), 33683 ^ _782435 : [(33684 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), c_Groups_Ozero__class_Ozero(_1420297)), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))))], (33686 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), _1420299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420297), _1420303), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))))]], 33687 ^ _782435 : [(33688 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), c_Groups_Ozero__class_Ozero(_1420297)), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)))], (33690 ^ _782435) ^ [] : [33691 ^ _782435 : [(33692 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)), c_Groups_Ozero__class_Ozero(_1420297))))], (33694 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420297), _1420303), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))), _1420299))]], 33695 ^ _782435 : [(33696 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)), c_Groups_Ozero__class_Ozero(_1420297)))], (33698 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), c_Groups_Ozero__class_Ozero(_1420297)), _1420303))]]]]], (33654 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1420297), _1420299), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))), _1420303)), 33657 ^ _782435 : [(33658 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), c_Groups_Ozero__class_Ozero(_1420297)), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), _1420299), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420297), _1420303), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)))))], (33664 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), c_Groups_Ozero__class_Ozero(_1420297)), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)))), 33667 ^ _782435 : [(33668 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)), c_Groups_Ozero__class_Ozero(_1420297))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1420297), _1420303), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301))), _1420299)))], (33674 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1420297), hAPP(c_Int_Onumber__class_Onumber__of(_1420297), _1420301)), c_Groups_Ozero__class_Ozero(_1420297)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1420297), c_Groups_Ozero__class_Ozero(_1420297)), _1420303)))]]]]]]], (33702 ^ _782435) ^ [_1421411, _1421413, _1421415, _1421417] : [class_Fields_Olinordered__field__inverse__zero(_1421411), class_Int_Onumber(_1421411), 33709 ^ _782435 : [(33736 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421411), _1421413), _1421415)), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417)))), 33739 ^ _782435 : [(33740 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), c_Groups_Ozero__class_Ozero(_1421411)), _1421415)))], (33742 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), _1421413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421411), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417)), _1421415)))]], 33743 ^ _782435 : [(33744 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), c_Groups_Ozero__class_Ozero(_1421411)), _1421415))], (33746 ^ _782435) ^ [] : [33747 ^ _782435 : [(33748 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), _1421415), c_Groups_Ozero__class_Ozero(_1421411))))], (33750 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421411), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417)), _1421415)), _1421413))]], 33751 ^ _782435 : [(33752 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), _1421415), c_Groups_Ozero__class_Ozero(_1421411)))], (33754 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), c_Groups_Ozero__class_Ozero(_1421411)), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417)))]]]]], (33710 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1421411), _1421413), _1421415)), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417))), 33713 ^ _782435 : [(33714 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), c_Groups_Ozero__class_Ozero(_1421411)), _1421415)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), _1421413), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421411), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417)), _1421415))))], (33720 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), c_Groups_Ozero__class_Ozero(_1421411)), _1421415))), 33723 ^ _782435 : [(33724 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), _1421415), c_Groups_Ozero__class_Ozero(_1421411))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1421411), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417)), _1421415)), _1421413)))], (33730 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1421411), _1421415), c_Groups_Ozero__class_Ozero(_1421411)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1421411), c_Groups_Ozero__class_Ozero(_1421411)), hAPP(c_Int_Onumber__class_Onumber__of(_1421411), _1421417))))]]]]]]], (33758 ^ _782435) ^ [_1422480, _1422482, _1422484, _1422486] : [class_Fields_Olinordered__field__inverse__zero(_1422480), class_Int_Onumber(_1422480), 33765 ^ _782435 : [(33792 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422480), _1422484), _1422486)))), 33795 ^ _782435 : [(33796 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), c_Groups_Ozero__class_Ozero(_1422480)), _1422486)))], (33798 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), _1422486)), _1422484))]], 33799 ^ _782435 : [(33800 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), c_Groups_Ozero__class_Ozero(_1422480)), _1422486))], (33802 ^ _782435) ^ [] : [33803 ^ _782435 : [(33804 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), _1422486), c_Groups_Ozero__class_Ozero(_1422480))))], (33806 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), _1422484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), _1422486)))]], 33807 ^ _782435 : [(33808 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), _1422486), c_Groups_Ozero__class_Ozero(_1422480)))], (33810 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), c_Groups_Ozero__class_Ozero(_1422480)))]]]]], (33766 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1422480), _1422484), _1422486))), 33769 ^ _782435 : [(33770 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), c_Groups_Ozero__class_Ozero(_1422480)), _1422486)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), _1422486)), _1422484)))], (33776 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), c_Groups_Ozero__class_Ozero(_1422480)), _1422486))), 33779 ^ _782435 : [(33780 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), _1422486), c_Groups_Ozero__class_Ozero(_1422480))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), _1422484), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), _1422486))))], (33786 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1422480), _1422486), c_Groups_Ozero__class_Ozero(_1422480)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1422480), hAPP(c_Int_Onumber__class_Onumber__of(_1422480), _1422482)), c_Groups_Ozero__class_Ozero(_1422480))))]]]]]]], (33814 ^ _782435) ^ [_1423549, _1423551, _1423553, _1423555] : [class_Fields_Olinordered__field__inverse__zero(_1423549), class_Int_Onumber(_1423549), 33821 ^ _782435 : [(33848 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), _1423551), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423549), _1423553), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555))))), 33851 ^ _782435 : [(33852 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), c_Groups_Ozero__class_Ozero(_1423549)), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555))))], (33854 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423549), _1423551), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555))), _1423553))]], 33855 ^ _782435 : [(33856 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), c_Groups_Ozero__class_Ozero(_1423549)), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)))], (33858 ^ _782435) ^ [] : [33859 ^ _782435 : [(33860 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)), c_Groups_Ozero__class_Ozero(_1423549))))], (33862 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), _1423553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423549), _1423551), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555))))]], 33863 ^ _782435 : [(33864 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)), c_Groups_Ozero__class_Ozero(_1423549)))], (33866 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), _1423551), c_Groups_Ozero__class_Ozero(_1423549)))]]]]], (33822 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), _1423551), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1423549), _1423553), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)))), 33825 ^ _782435 : [(33826 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), c_Groups_Ozero__class_Ozero(_1423549)), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423549), _1423551), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555))), _1423553)))], (33832 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), c_Groups_Ozero__class_Ozero(_1423549)), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)))), 33835 ^ _782435 : [(33836 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)), c_Groups_Ozero__class_Ozero(_1423549))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), _1423553), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1423549), _1423551), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)))))], (33842 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1423549), hAPP(c_Int_Onumber__class_Onumber__of(_1423549), _1423555)), c_Groups_Ozero__class_Ozero(_1423549)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1423549), _1423551), c_Groups_Ozero__class_Ozero(_1423549))))]]]]]]], (33870 ^ _782435) ^ [_1424669] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1424669))), -(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), _1424669)) = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (33876 ^ _782435) ^ [_1424762] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1424762)))), -(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), _1424762)) = 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), _1424762))))], (33882 ^ _782435) ^ [_1424820] : [-(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), _1424820)) = 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), _1424820))))], (33884 ^ _782435) ^ [_1424858, _1424860, _1424862] : [class_Int_Onumber__ring(_1424858), 33887 ^ _782435 : [(33888 ^ _782435) ^ [] : [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), _1424860))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424858), hAPP(c_Int_Onumber__class_Onumber__of(_1424858), _1424862)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1424860))) = hAPP(hAPP(c_HOL_OLet(_1424858, _1424858), hAPP(hAPP(c_Power_Opower__class_Opower(_1424858), hAPP(c_Int_Onumber__class_Onumber__of(_1424858), _1424862)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1424860))), hAPP(hAPP(c_COMBS(_1424858, _1424858, _1424858), hAPP(hAPP(c_COMBB(_1424858, tc_fun(_1424858, _1424858), _1424858), c_Groups_Otimes__class_Otimes(_1424858)), hAPP(c_Groups_Otimes__class_Otimes(_1424858), hAPP(c_Int_Onumber__class_Onumber__of(_1424858), _1424862)))), c_COMBI(_1424858))))], (33894 ^ _782435) ^ [] : [-(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), _1424860)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1424858), hAPP(c_Int_Onumber__class_Onumber__of(_1424858), _1424862)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1424860))) = c_Groups_Oone__class_Oone(_1424858))]]], (33900 ^ _782435) ^ [_1425265, _1425267] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425265))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425265)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425267)) = 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), _1425267)))], (33906 ^ _782435) ^ [_1425382, _1425384] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425382)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425384)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425382)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1425384))))], (33912 ^ _782435) ^ [_1425467, _1425469] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425467)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425469))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425467), _1425469)))], (33918 ^ _782435) ^ [_1425572, _1425574] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1425572), _1425574)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425572)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425574))))], (33924 ^ _782435) ^ [_1425683] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425683) = _1425683)], (33926 ^ _782435) ^ [_1425724, _1425726] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425724)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425726))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425724), _1425726)))], (33932 ^ _782435) ^ [_1425829, _1425831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1425829), _1425831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425829)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425831))))], (33938 ^ _782435) ^ [_1425940, _1425942] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425940)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425942)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1425940), _1425942)))], (33940 ^ _782435) ^ [_1425986, _1425988] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425986)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1425988)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1425986), _1425988)))], (33942 ^ _782435) ^ [_1426032] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426032)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1426032)))], (33944 ^ _782435) ^ [_1426079] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1426079)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426079))))], (33950 ^ _782435) ^ [_1426174] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1426174))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1426174)))))], (33956 ^ _782435) ^ [_1426290, _1426292] : [c_Int_OBit1(_1426290) = c_Int_OBit1(_1426292), -(_1426290 = _1426292)], (33962 ^ _782435) ^ [_1426371, _1426373] : [_1426371 = _1426373, -(c_Int_OBit1(_1426371) = c_Int_OBit1(_1426373))], (33968 ^ _782435) ^ [_1426473, _1426475] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426473)), c_Int_OBit1(_1426475))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426473), _1426475)))], (33974 ^ _782435) ^ [_1426574, _1426576] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426574), _1426576)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426574)), c_Int_OBit1(_1426576))))], (33980 ^ _782435) ^ [_1426696, _1426698] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426696)), c_Int_OBit1(_1426698))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426696), _1426698)))], (33986 ^ _782435) ^ [_1426797, _1426799] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1426797), _1426799)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1426797)), c_Int_OBit1(_1426799))))], (33992 ^ _782435) ^ [_1426919, _1426921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1426919)), c_Int_OBit1(_1426921))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1426919), _1426921)))], (33998 ^ _782435) ^ [_1427020, _1427022] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427020), _1427022)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427020)), c_Int_OBit1(_1427022))))], (34004 ^ _782435) ^ [_1427142, _1427144] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427142)), c_Int_OBit1(_1427144))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427142), _1427144)))], (34010 ^ _782435) ^ [_1427243, _1427245] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1427243), _1427245)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1427243)), c_Int_OBit1(_1427245))))], (34016 ^ _782435) ^ [_1427350] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427350) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint), _1427350))], (34018 ^ _782435) ^ [_1427391] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1427391)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427391), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34024 ^ _782435) ^ [_1427486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1427486), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1427486)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34030 ^ _782435) ^ [_1427587] : [-(c_Int_OBit1(_1427587) = 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)), _1427587)), _1427587))], (34032 ^ _782435) ^ [_1427621] : [-(hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427621)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427621))], (34034 ^ _782435) ^ [_1427653] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427653) = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427653)))], (34036 ^ _782435) ^ [_1427691] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427691))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427691)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34042 ^ _782435) ^ [_1427780] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1427780)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427780)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427780)), 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 ^ _782435) ^ [_1427835, _1427837] : [class_Int_Onumber__ring(_1427835), -(hAPP(c_Int_Onumber__class_Onumber__of(_1427835), c_Int_OBit1(_1427837)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427835), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1427835), c_Groups_Oone__class_Oone(_1427835)), hAPP(c_Int_Onumber__class_Onumber__of(_1427835), _1427837))), hAPP(c_Int_Onumber__class_Onumber__of(_1427835), _1427837)))], (34054 ^ _782435) ^ [_1427980, _1427982, _1427984] : [class_Int_Onumber__ring(_1427980), 34057 ^ _782435 : [(34058 ^ _782435) ^ [] : [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), _1427982))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427980), _1427984), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427982))) = hAPP(hAPP(c_HOL_OLet(_1427980, _1427980), hAPP(hAPP(c_Power_Opower__class_Opower(_1427980), _1427984), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1427982))), hAPP(hAPP(c_COMBS(_1427980, _1427980, _1427980), hAPP(hAPP(c_COMBB(_1427980, tc_fun(_1427980, _1427980), _1427980), c_Groups_Otimes__class_Otimes(_1427980)), hAPP(c_Groups_Otimes__class_Otimes(_1427980), _1427984))), c_COMBI(_1427980))))], (34064 ^ _782435) ^ [] : [-(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), _1427982)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1427980), _1427984), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1427982))) = c_Groups_Oone__class_Oone(_1427980))]]], (34070 ^ _782435) ^ [_1428347, _1428349] : [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), _1428347))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428349), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428347))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428349), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428347))), 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), _1428349))), c_COMBI(tc_Int_Oint))))], (34076 ^ _782435) ^ [_1428504, _1428506] : [-(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), _1428504)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1428506), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(_1428504))) = c_Groups_Oone__class_Oone(tc_Int_Oint))], (34082 ^ _782435) ^ [_1428558, _1428560] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428558)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428560)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1428558), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1428560))))], (34084 ^ _782435) ^ [_1428607] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428607))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1428607) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34090 ^ _782435) ^ [_1428713, _1428715] : [hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428713) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428715), 34093 ^ _782435 : [(34094 ^ _782435) ^ [] : [-(_1428713 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428715)))], (34096 ^ _782435) ^ [] : [-(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), _1428715))))]]], (34098 ^ _782435) ^ [_1428846, _1428848] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1428846) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428848)), _1428846 = hAPP(c_Int_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1428848)), 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), _1428848)))], (34134 ^ _782435) ^ [_1429411, _1429413] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429411) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429413)), 34137 ^ _782435 : [(34138 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429411))))], (34140 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429413)), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], 34141 ^ _782435 : [(34142 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429411)))], (34144 ^ _782435) ^ [] : [34145 ^ _782435 : [(34146 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429413))))], (34148 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429411) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], 34149 ^ _782435 : [(34150 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429413)))], (34152 ^ _782435) ^ [] : [_1429411 = _1429413]]]]], (34108 ^ _782435) ^ [_1429026, _1429028] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429026) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429028), 34111 ^ _782435 : [(34112 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429026))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429028)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (34118 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429026)))), 34121 ^ _782435 : [(34122 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429028))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429026) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34128 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429028)))), -(_1429026 = _1429028)]]]]], (34156 ^ _782435) ^ [_1429824, _1429826, _1429828] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429824))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429824)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429826)), _1429828)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429826)), _1429828))], (34162 ^ _782435) ^ [_1429962, _1429964, _1429966] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429962)))), 34165 ^ _782435 : [(34166 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429964))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429964)), _1429966)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429962)), _1429966))], (34172 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1429964)))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429962)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1429964)), _1429966)) = 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), _1429962), _1429964))), _1429966))]]], (34178 ^ _782435) ^ [_1430293] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430293))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430293)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34184 ^ _782435) ^ [_1430384] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430384)))), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430384)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430384))], (34190 ^ _782435) ^ [_1430443, _1430445] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430443))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430443), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430445)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34196 ^ _782435) ^ [_1430545, _1430547] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430545)))), 34199 ^ _782435 : [(34200 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430547))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430545), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430547)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430545))], (34206 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430547)))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430545), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430547)) = hAPP(c_Int_Onat, c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430545), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430547))))]]], (34212 ^ _782435) ^ [_1430827, _1430829] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430827))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430827)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430829)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34218 ^ _782435) ^ [_1430932, _1430934] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430932)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430932)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1430934)) = hAPP(c_Int_Onat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430932)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1430934))))], (34224 ^ _782435) ^ [_1431011, _1431013] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431011))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431011)), _1431013) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1431013))], (34230 ^ _782435) ^ [_1431116, _1431118] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431116)))), -(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431116)), _1431118) = hAPP(c_Int_Onat, hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431116)), _1431118)))], (34236 ^ _782435) ^ [_1431189, _1431191] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431189))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431189)), _1431191)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1431191))], (34242 ^ _782435) ^ [_1431300, _1431302] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1431300)))), -(hAPP(c_Nat_OSuc, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431300)), _1431302)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1431300))), _1431302))], (34248 ^ _782435) ^ [_1431375, _1431377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431375), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431377)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431375)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431377))], (34254 ^ _782435) ^ [_1431486, _1431488] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1431486), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431488)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431486)) = 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), _1431488), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1431486)))), 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 ^ _782435) ^ [_1431559, _1431561] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431559)), hAPP(c_Nat_OSuc, _1431561)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431559))), 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)), _1431561)))))], (34262 ^ _782435) ^ [_1431616, _1431618] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1431616)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1431618)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1431618))), 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), _1431616)), c_Int_Onat)))))], (34264 ^ _782435) ^ [] : [-(c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls))], (34266 ^ _782435) ^ [_1431706] : [c_Int_OPls = c_Int_OBit1(_1431706)], (34268 ^ _782435) ^ [_1431740] : [c_Int_OBit1(_1431740) = c_Int_OPls], (34270 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OPls)))], (34272 ^ _782435) ^ [_1431783] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1431783), c_Int_OPls) = _1431783)], (34274 ^ _782435) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls) = c_Int_OPls)], (34276 ^ _782435) ^ [_1431830] : [-(c_Int_Osucc(c_Int_Opred(_1431830)) = _1431830)], (34278 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OPls))], (34280 ^ _782435) ^ [] : [-(c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (34282 ^ _782435) ^ [_1431899] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OPls), _1431899) = c_Int_OPls)], (34284 ^ _782435) ^ [_1431925] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), _1431925) = _1431925)], (34286 ^ _782435) ^ [_1431951] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1431951), c_Int_OPls) = _1431951)], (34288 ^ _782435) ^ [_1431980] : [class_Int_Onumber__ring(_1431980), -(hAPP(c_Int_Onumber__class_Onumber__of(_1431980), c_Int_OPls) = c_Groups_Ozero__class_Ozero(_1431980))], (34294 ^ _782435) ^ [_1432067] : [class_Int_Onumber__ring(_1432067), -(c_Groups_Ozero__class_Ozero(_1432067) = hAPP(c_Int_Onumber__class_Onumber__of(_1432067), c_Int_OPls))], (34300 ^ _782435) ^ [_1432154, _1432156] : [class_Int_Onumber__ring(_1432154), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432154), _1432156), hAPP(c_Int_Onumber__class_Onumber__of(_1432154), c_Int_OPls)) = _1432156)], (34306 ^ _782435) ^ [_1432255, _1432257] : [class_Int_Onumber__ring(_1432255), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1432255), hAPP(c_Int_Onumber__class_Onumber__of(_1432255), c_Int_OPls)), _1432257) = _1432257)], (34312 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))], (34314 ^ _782435) ^ [] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34316 ^ _782435) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls))], (34318 ^ _782435) ^ [] : [-(c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls))], (34320 ^ _782435) ^ [_1432446] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432446))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432446)))], (34326 ^ _782435) ^ [_1432529] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1432529)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1432529))))], (34332 ^ _782435) ^ [_1432630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432630)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432630), c_Int_OPls)))], (34338 ^ _782435) ^ [_1432725] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432725), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1432725)), c_Int_OPls)))], (34344 ^ _782435) ^ [_1432826, _1432828] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1432826)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1432828)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1432826)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1432828), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1432826))))], (34350 ^ _782435) ^ [] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OPls)))], (34352 ^ _782435) ^ [_1432983] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1432983), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1432983)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34358 ^ _782435) ^ [_1433080] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433080), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433080)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1433080)))], (34364 ^ _782435) ^ [_1433141] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433141), 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), _1433141)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34370 ^ _782435) ^ [_1433232] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1433232), 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), _1433232)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1433232)))], (34376 ^ _782435) ^ [_1433299, _1433301] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433299), _1433301)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1433299)), _1433301)))], (34382 ^ _782435) ^ [_1433396, _1433398] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_Opred(_1433396)), _1433398)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433396), _1433398)))], (34388 ^ _782435) ^ [_1433499] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(_1433499)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1433499))))], (34390 ^ _782435) ^ [_1433534] : [-(c_Int_Opred(_1433534) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1433534), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34392 ^ _782435) ^ [_1433571] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433571), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433571)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34398 ^ _782435) ^ [_1433668] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1433668), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1433668)), c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Opred(_1433668)))], (34404 ^ _782435) ^ [_1433723, _1433725] : [class_Int_Onumber__ring(_1433723), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433723), hAPP(c_Int_Onumber__class_Onumber__of(_1433723), c_Int_OBit1(c_Int_OPls))), _1433725) = _1433725)], (34410 ^ _782435) ^ [_1433824, _1433826] : [class_Int_Onumber__ring(_1433824), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1433824), _1433826), hAPP(c_Int_Onumber__class_Onumber__of(_1433824), c_Int_OBit1(c_Int_OPls))) = _1433826)], (34416 ^ _782435) ^ [_1433925, _1433927] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1433925), _1433927), hAPP(c_Int_Onumber__class_Onumber__of(_1433925), c_Int_OPls)) = c_Groups_Ozero__class_Ozero(_1433925)), class_Fields_Ofield__inverse__zero(_1433925), class_Int_Onumber__ring(_1433925)], (34426 ^ _782435) ^ [_1434080] : [class_Int_Onumber__ring(_1434080), -(hAPP(c_Int_Onumber__class_Onumber__of(_1434080), c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(_1434080))], (34432 ^ _782435) ^ [_1434167] : [class_Int_Onumber__ring(_1434167), -(c_Groups_Oone__class_Oone(_1434167) = hAPP(c_Int_Onumber__class_Onumber__of(_1434167), c_Int_OBit1(c_Int_OPls)))], (34438 ^ _782435) ^ [_1434266] : [c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434266), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434266), c_Int_OPls)))], (34444 ^ _782435) ^ [_1434353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434353), c_Int_OPls)), -(c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434353))], (34450 ^ _782435) ^ [_1434458] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434458) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434458), c_Int_OPls)))], (34456 ^ _782435) ^ [_1434545] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1434545), c_Int_OPls)), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1434545) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34462 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1434668] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1434668))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1434668)))], (34470 ^ _782435) ^ [_1434751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1434751)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1434751))))], (34476 ^ _782435) ^ [_1434852] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1434852)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434852), c_Int_OPls)))], (34482 ^ _782435) ^ [_1434947] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1434947), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1434947)), c_Int_OPls)))], (34488 ^ _782435) ^ [_1435063, _1435065] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435063)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435065))), 34491 ^ _782435 : [(34498 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435063), _1435065)))], (34492 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435063), _1435065)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1435065)))]]], (34500 ^ _782435) ^ [_1435266, _1435268] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435266)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435268)))), 34503 ^ _782435 : [(34504 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435266), _1435268)))], (34506 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1435268))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1435266), _1435268))], (34512 ^ _782435) ^ [_1435476, _1435478] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435476), _1435478), hAPP(c_Int_Onumber__class_Onumber__of(_1435476), c_Int_OBit1(c_Int_OPls))) = _1435478), class_Fields_Ofield(_1435476), class_Int_Onumber__ring(_1435476)], (34522 ^ _782435) ^ [_1435627, _1435629] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1435627), _1435629), hAPP(c_Int_Onumber__class_Onumber__of(_1435627), c_Int_OBit1(c_Int_OPls))) = _1435629), class_Fields_Ofield(_1435627), class_Int_Onumber__ring(_1435627)], (34542 ^ _782435) ^ [_1435923, _1435925] : [34543 ^ _782435 : [(34544 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435923), _1435925))], (34546 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435923), 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), _1435923)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435925))))], (34532 ^ _782435) ^ [_1435793, _1435795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435793)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1435795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435793), _1435795))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1435793), c_Int_OPls)))], (34550 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1436156] : [-(c_Int_Osucc(_1436156) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1436156), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (34560 ^ _782435) ^ [_1436187, _1436189] : [class_Int_Onumber__ring(_1436187), class_Rings_Olinordered__idom(_1436187), 34567 ^ _782435 : [(34568 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436187), hAPP(c_Int_Onumber__class_Onumber__of(_1436187), _1436189)), c_Groups_Ozero__class_Ozero(_1436187))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436189), c_Int_OPls)))], (34574 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1436189), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436187), hAPP(c_Int_Onumber__class_Onumber__of(_1436187), _1436189)), c_Groups_Ozero__class_Ozero(_1436187))))]]], (34580 ^ _782435) ^ [_1436501, _1436503] : [class_Int_Onumber__ring(_1436501), class_Rings_Olinordered__idom(_1436501), 34587 ^ _782435 : [(34588 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436501), c_Groups_Ozero__class_Ozero(_1436501)), hAPP(c_Int_Onumber__class_Onumber__of(_1436501), _1436503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436503)))], (34594 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1436503)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1436501), c_Groups_Ozero__class_Ozero(_1436501)), hAPP(c_Int_Onumber__class_Onumber__of(_1436501), _1436503))))]]], (34600 ^ _782435) ^ [_1436806, _1436808] : [class_Int_Onumber__ring(_1436806), class_Rings_Olinordered__idom(_1436806), 34607 ^ _782435 : [(34608 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436806), c_Groups_Ozero__class_Ozero(_1436806)), hAPP(c_Int_Onumber__class_Onumber__of(_1436806), _1436808))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1436808)))], (34614 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1436808)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1436806), c_Groups_Ozero__class_Ozero(_1436806)), hAPP(c_Int_Onumber__class_Onumber__of(_1436806), _1436808))))]]], (34620 ^ _782435) ^ [_1437111, _1437113] : [class_Int_Onumber__ring(_1437111), class_Rings_Olinordered__idom(_1437111), 34627 ^ _782435 : [(34628 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437111), hAPP(c_Int_Onumber__class_Onumber__of(_1437111), _1437113)), c_Groups_Ozero__class_Ozero(_1437111))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437113), c_Int_OPls)))], (34634 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437113), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1437111), hAPP(c_Int_Onumber__class_Onumber__of(_1437111), _1437113)), c_Groups_Ozero__class_Ozero(_1437111))))]]], (34640 ^ _782435) ^ [_1437437] : [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), _1437437))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1437437)))], (34646 ^ _782435) ^ [_1437522] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1437522)), -(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), _1437522))))], (34652 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1437649, _1437651] : [class_Groups_Omonoid__mult(_1437649), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1437649), _1437651), 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(_1437649), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1437649), _1437651), _1437651)), _1437651))], (34662 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1437790] : [-(hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1437790))) = 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)))), _1437790))], (34666 ^ _782435) ^ [_1437834, _1437836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437834), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437834)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437836)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437836))], (34672 ^ _782435) ^ [_1437946, _1437948] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437946), c_Int_OPls))), 34675 ^ _782435 : [(34676 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437948), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437946)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437948)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437946))], (34682 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1437948), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437946)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1437948)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1437946), _1437948)))]]], (34688 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1438255, _1438257] : [class_Int_Onumber__ring(_1438255), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438255), c_Int_Osucc(_1438257)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438255), c_Groups_Oone__class_Oone(_1438255)), hAPP(c_Int_Onumber__class_Onumber__of(_1438255), _1438257)))], (34698 ^ _782435) ^ [_1438374, _1438376] : [class_Int_Onumber__ring(_1438374), -(hAPP(c_Int_Onumber__class_Onumber__of(_1438374), c_Int_Opred(_1438376)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1438374), hAPP(c_Groups_Ouminus__class_Ouminus(_1438374), c_Groups_Oone__class_Oone(_1438374))), hAPP(c_Int_Onumber__class_Onumber__of(_1438374), _1438376)))], (34704 ^ _782435) ^ [_1438503, _1438505] : [class_Int_Onumber__ring(_1438503), class_Rings_Olinordered__idom(_1438503), 34711 ^ _782435 : [(34712 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438503), hAPP(c_Int_Onumber__class_Onumber__of(_1438503), _1438505)), c_Groups_Oone__class_Oone(_1438503))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438505), c_Int_OBit1(c_Int_OPls))))], (34718 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1438505), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438503), hAPP(c_Int_Onumber__class_Onumber__of(_1438503), _1438505)), c_Groups_Oone__class_Oone(_1438503))))]]], (34724 ^ _782435) ^ [_1438817, _1438819] : [class_Int_Onumber__ring(_1438817), class_Rings_Olinordered__idom(_1438817), 34731 ^ _782435 : [(34732 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438817), c_Groups_Oone__class_Oone(_1438817)), hAPP(c_Int_Onumber__class_Onumber__of(_1438817), _1438819))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1438819)))], (34738 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1438819)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1438817), c_Groups_Oone__class_Oone(_1438817)), hAPP(c_Int_Onumber__class_Onumber__of(_1438817), _1438819))))]]], (34744 ^ _782435) ^ [_1439122, _1439124] : [class_Int_Onumber__ring(_1439122), class_Rings_Olinordered__idom(_1439122), 34751 ^ _782435 : [(34752 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439122), hAPP(c_Int_Onumber__class_Onumber__of(_1439122), _1439124)), c_Groups_Oone__class_Oone(_1439122))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439124), c_Int_OBit1(c_Int_OPls))))], (34758 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1439124), c_Int_OBit1(c_Int_OPls))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439122), hAPP(c_Int_Onumber__class_Onumber__of(_1439122), _1439124)), c_Groups_Oone__class_Oone(_1439122))))]]], (34764 ^ _782435) ^ [_1439436, _1439438] : [class_Int_Onumber__ring(_1439436), class_Rings_Olinordered__idom(_1439436), 34771 ^ _782435 : [(34772 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439436), c_Groups_Oone__class_Oone(_1439436)), hAPP(c_Int_Onumber__class_Onumber__of(_1439436), _1439438))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439438)))], (34778 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439438)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1439436), c_Groups_Oone__class_Oone(_1439436)), hAPP(c_Int_Onumber__class_Onumber__of(_1439436), _1439438))))]]], (34784 ^ _782435) ^ [_1439741, _1439743] : [class_Int_Onumber__ring(_1439741), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439741), hAPP(c_Int_Onumber__class_Onumber__of(_1439741), _1439743)), c_Groups_Oone__class_Oone(_1439741)) = hAPP(c_Int_Onumber__class_Onumber__of(_1439741), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1439743), c_Int_OBit1(c_Int_OPls))))], (34790 ^ _782435) ^ [_1439868, _1439870] : [class_Int_Onumber__ring(_1439868), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1439868), c_Groups_Oone__class_Oone(_1439868)), hAPP(c_Int_Onumber__class_Onumber__of(_1439868), _1439870)) = hAPP(c_Int_Onumber__class_Onumber__of(_1439868), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)), _1439870)))], (34796 ^ _782435) ^ [_1439989, _1439991] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OPls)), _1439989)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1439991)), _1439989) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1439991), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1439989), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit1(c_Int_OPls)))))], (34802 ^ _782435) ^ [_1440124, _1440126, _1440128] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440124), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440124)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440126)), _1440128)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34808 ^ _782435) ^ [_1440243, _1440245, _1440247] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440243), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440243)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440245)), _1440247)) = 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), _1440243), _1440245))), _1440247))], (34814 ^ _782435) ^ [_1440330, _1440332] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440330), c_Int_OPls)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440330)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440332)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34820 ^ _782435) ^ [_1440435, _1440437] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1440435), c_Int_OPls))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440435)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440437)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1440435), _1440437)))], (34826 ^ _782435) ^ [_1440511] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1440511)))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440511) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (34832 ^ _782435) ^ [_1440602] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440602) = 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(_1440602)))))], (34838 ^ _782435) ^ [_1440699, _1440701] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440699, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440701)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1440699, 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)))), _1440701)))], (34840 ^ _782435) ^ [_1440744, _1440746] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440744))), _1440746) = 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)))), _1440744), _1440746))], (34842 ^ _782435) ^ [_1440789, _1440791] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440789))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440791)) = 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)))), _1440789), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440791)))], (34844 ^ _782435) ^ [_1440840, _1440842] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440840), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440842)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1440840), 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)))), _1440842)))], (34846 ^ _782435) ^ [_1440889, _1440891] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440889)))), _1440891) = 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)))), _1440889)), _1440891))], (34848 ^ _782435) ^ [_1440938, _1440940] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1440938)))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440940)) = 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)))), _1440938)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1440940)))], (34850 ^ _782435) ^ [_1440993, _1440995] : [class_Int_Onumber__ring(_1440993), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1440993), c_Groups_Oone__class_Oone(_1440993)), hAPP(c_Int_Onumber__class_Onumber__of(_1440993), _1440995)) = hAPP(c_Int_Onumber__class_Onumber__of(_1440993), 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), _1440995))))], (34856 ^ _782435) ^ [_1441120, _1441122] : [class_Int_Onumber__ring(_1441120), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1441120), hAPP(c_Int_Onumber__class_Onumber__of(_1441120), _1441122)), c_Groups_Oone__class_Oone(_1441120)) = hAPP(c_Int_Onumber__class_Onumber__of(_1441120), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1441122), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls)))))], (34862 ^ _782435) ^ [_1441262, _1441264] : [hAPP(c_Nat_OSuc, _1441262) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441264), -(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(_1441264))), 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)), _1441262))))))], (34868 ^ _782435) ^ [_1441385, _1441387] : [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(_1441387))), 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)), _1441385))))), -(hAPP(c_Nat_OSuc, _1441385) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441387))], (34874 ^ _782435) ^ [_1441529, _1441531] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441529) = hAPP(c_Nat_OSuc, _1441531), -(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(_1441529))), 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)), _1441531))))))], (34880 ^ _782435) ^ [_1441652, _1441654] : [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(_1441652))), 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)), _1441654))))), -(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441652) = hAPP(c_Nat_OSuc, _1441654))], (34886 ^ _782435) ^ [_1441781, _1441783, _1441785, _1441787] : [-(c_Nat_Onat_Onat__case(_1441781, _1441783, _1441785, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441787)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1441781), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1441787))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1441781, _1441781), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1441781, tc_fun(_1441781, _1441781)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1441781, tc_fun(_1441781, _1441781)), tc_Int_Oint), c_If(_1441781)), c_Nat__Numeral_Oneg)), _1441783)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1441781, tc_Int_Oint), _1441785), c_Int_Onat))))], (34888 ^ _782435) ^ [_1441898, _1441900] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1441898)), hAPP(c_Nat_OSuc, _1441900))), -(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(_1441898))), 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)), _1441900)))))], (34894 ^ _782435) ^ [_1442025, _1442027] : [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(_1442025))), 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)), _1442027)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442025)), hAPP(c_Nat_OSuc, _1442027))))], (34900 ^ _782435) ^ [_1442173, _1442175] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442173)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442175))), -(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(_1442175))), 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), _1442173)), c_Int_Onat))))))], (34906 ^ _782435) ^ [_1442318, _1442320] : [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(_1442320))), 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), _1442318)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442318)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442320))))], (34912 ^ _782435) ^ [_1442484, _1442486] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442484)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442486))), -(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(_1442486))), 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), _1442484)), c_Int_Onat))))))], (34918 ^ _782435) ^ [_1442629, _1442631] : [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(_1442631))), 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), _1442629)), c_Int_Onat))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1442629)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442631))))], (34924 ^ _782435) ^ [_1442795, _1442797] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442795)), hAPP(c_Nat_OSuc, _1442797))), -(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(_1442795))), 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)), _1442797)))))], (34930 ^ _782435) ^ [_1442922, _1442924] : [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(_1442922))), 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)), _1442924)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1442922)), hAPP(c_Nat_OSuc, _1442924))))], (34936 ^ _782435) ^ [_1443061] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1443061))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443061)) = c_Groups_Oone__class_Oone(tc_Nat_Onat))], (34942 ^ _782435) ^ [_1443152] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1443152)))), -(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443152)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_Osucc(_1443152)))], (34948 ^ _782435) ^ [_1443204, _1443206] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443204)), hAPP(c_Nat_OSuc, _1443206)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443204))), 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, _1443206))), 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)), _1443206)))))], (34950 ^ _782435) ^ [_1443270, _1443272] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1443270)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443272)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443272))), 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, _1443270))), 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), _1443270)), c_Int_Onat)))))], (34952 ^ _782435) ^ [_1443342, _1443344, _1443346, _1443348, _1443350] : [-(c_Nat_Onat_Onat__case(_1443342, _1443344, _1443346, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443348)), _1443350)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1443342), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443348))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443342, _1443342), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1443342, tc_fun(_1443342, _1443342)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443342, tc_fun(_1443342, _1443342)), tc_Int_Oint), c_If(_1443342)), c_Nat__Numeral_Oneg)), c_Nat_Onat_Onat__case(_1443342, _1443344, _1443346, _1443350))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443342, tc_Int_Oint), _1443346), 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)), _1443350)))))], (34954 ^ _782435) ^ [_1443460, _1443462, _1443464, _1443466, _1443468] : [-(hAPP(c_Nat_Onat_Onat__rec(_1443460, _1443462, _1443464), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1443466)), _1443468)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1443460), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1443466))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443460, _1443460), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1443460, tc_fun(_1443460, _1443460)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1443460, tc_fun(_1443460, _1443460)), tc_Int_Oint), c_If(_1443460)), c_Nat__Numeral_Oneg)), hAPP(c_Nat_Onat_Onat__rec(_1443460, _1443462, _1443464), _1443468))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1443460, _1443460), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1443460, _1443460), tc_Int_Oint), _1443464), 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)), _1443468))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1443460, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1443460, _1443462, _1443464)), 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)), _1443468))))))], (34956 ^ _782435) ^ [_1443612, _1443614] : [class_Int_Onumber__ring(_1443612), 34959 ^ _782435 : [(34960 ^ _782435) ^ [] : [c_Groups_Oone__class_Oone(_1443612) = hAPP(c_Int_Onumber__class_Onumber__of(_1443612), _1443614), -(c_Int_Oiszero(_1443612, hAPP(c_Int_Onumber__class_Onumber__of(_1443612), 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), _1443614)))))], (34966 ^ _782435) ^ [] : [c_Int_Oiszero(_1443612, hAPP(c_Int_Onumber__class_Onumber__of(_1443612), 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), _1443614)))), -(c_Groups_Oone__class_Oone(_1443612) = hAPP(c_Int_Onumber__class_Onumber__of(_1443612), _1443614))]]], (34972 ^ _782435) ^ [_1443871, _1443873] : [class_Int_Onumber__ring(_1443871), 34975 ^ _782435 : [(34976 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1443871), _1443873) = c_Groups_Oone__class_Oone(_1443871), -(c_Int_Oiszero(_1443871, hAPP(c_Int_Onumber__class_Onumber__of(_1443871), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443873), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))))], (34982 ^ _782435) ^ [] : [c_Int_Oiszero(_1443871, hAPP(c_Int_Onumber__class_Onumber__of(_1443871), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1443873), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit1(c_Int_OPls))))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1443871), _1443873) = c_Groups_Oone__class_Oone(_1443871))]]], (34988 ^ _782435) ^ [_1444130, _1444132, _1444134, _1444136] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444130, _1444132, _1444134), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1444136)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1444130), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_Opred(_1444136))), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1444130, _1444130), hAPP(hAPP(c_COMBC(tc_Int_Oint, _1444130, tc_fun(_1444130, _1444130)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1444130, tc_fun(_1444130, _1444130)), tc_Int_Oint), c_If(_1444130)), c_Nat__Numeral_Oneg)), _1444132)), hAPP(hAPP(c_COMBS(tc_Int_Oint, _1444130, _1444130), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1444130, _1444130), tc_Int_Oint), _1444134), c_Int_Onat)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1444130, tc_Int_Oint), c_Nat_Onat_Onat__rec(_1444130, _1444132, _1444134)), c_Int_Onat)))))], (34990 ^ _782435) ^ [_1444261, _1444263] : [class_Rings_Osemiring__1(_1444261), 34993 ^ _782435 : [(34994 ^ _782435) ^ [] : [c_Int_Oiszero(_1444261, _1444263), -(_1444263 = c_Groups_Ozero__class_Ozero(_1444261))], (35000 ^ _782435) ^ [] : [_1444263 = c_Groups_Ozero__class_Ozero(_1444261), -(c_Int_Oiszero(_1444261, _1444263))]]], (35006 ^ _782435) ^ [_1444472] : [class_Rings_Osemiring__1(_1444472), -(c_Int_Oiszero(_1444472, c_Groups_Ozero__class_Ozero(_1444472)))], (35012 ^ _782435) ^ [_1444549] : [class_Rings_Osemiring__1(_1444549), c_Int_Oiszero(_1444549, c_Groups_Oone__class_Oone(_1444549))], (35018 ^ _782435) ^ [_1444627, _1444629, _1444631] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444627, _1444629, _1444631), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1444629)], (35020 ^ _782435) ^ [_1444661, _1444663, _1444665, _1444667] : [-(hAPP(c_Nat_Onat_Onat__rec(_1444661, _1444663, _1444665), hAPP(c_Nat_OSuc, _1444667)) = hAPP(hAPP(_1444665, _1444667), hAPP(c_Nat_Onat_Onat__rec(_1444661, _1444663, _1444665), _1444667)))], (35022 ^ _782435) ^ [_1444713] : [class_Int_Onumber__ring(_1444713), -(c_Int_Oiszero(_1444713, hAPP(c_Int_Onumber__class_Onumber__of(_1444713), c_Int_OPls)))], (35028 ^ _782435) ^ [_1444796, _1444798] : [c_Int_Oiszero(_1444796, hAPP(c_Int_Onumber__class_Onumber__of(_1444796), c_Int_OBit1(_1444798))), class_Int_Onumber__ring(_1444796), class_Int_Oring__char__0(_1444796)], (35038 ^ _782435) ^ [_1444936] : [class_Int_Onumber__ring(_1444936), c_Int_Oiszero(_1444936, hAPP(c_Int_Onumber__class_Onumber__of(_1444936), c_Int_OBit1(c_Int_OPls)))], (35044 ^ _782435) ^ [_1445020, _1445022, _1445024] : [class_Int_Onumber__ring(_1445020), 35047 ^ _782435 : [(35048 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1445020), _1445022) = hAPP(c_Int_Onumber__class_Onumber__of(_1445020), _1445024), -(c_Int_Oiszero(_1445020, hAPP(c_Int_Onumber__class_Onumber__of(_1445020), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445022), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445024)))))], (35054 ^ _782435) ^ [] : [c_Int_Oiszero(_1445020, hAPP(c_Int_Onumber__class_Onumber__of(_1445020), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445022), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445024)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1445020), _1445022) = hAPP(c_Int_Onumber__class_Onumber__of(_1445020), _1445024))]]], (35060 ^ _782435) ^ [_1445303, _1445305] : [class_Int_Onumber__ring(_1445303), 35063 ^ _782435 : [(35064 ^ _782435) ^ [] : [c_Groups_Ozero__class_Ozero(_1445303) = hAPP(c_Int_Onumber__class_Onumber__of(_1445303), _1445305), -(c_Int_Oiszero(_1445303, hAPP(c_Int_Onumber__class_Onumber__of(_1445303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445305)))))], (35070 ^ _782435) ^ [] : [c_Int_Oiszero(_1445303, hAPP(c_Int_Onumber__class_Onumber__of(_1445303), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OPls), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1445305)))), -(c_Groups_Ozero__class_Ozero(_1445303) = hAPP(c_Int_Onumber__class_Onumber__of(_1445303), _1445305))]]], (35076 ^ _782435) ^ [_1445562, _1445564] : [class_Int_Onumber__ring(_1445562), 35079 ^ _782435 : [(35080 ^ _782435) ^ [] : [hAPP(c_Int_Onumber__class_Onumber__of(_1445562), _1445564) = c_Groups_Ozero__class_Ozero(_1445562), -(c_Int_Oiszero(_1445562, hAPP(c_Int_Onumber__class_Onumber__of(_1445562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445564), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))))], (35086 ^ _782435) ^ [] : [c_Int_Oiszero(_1445562, hAPP(c_Int_Onumber__class_Onumber__of(_1445562), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1445564), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OPls)))), -(hAPP(c_Int_Onumber__class_Onumber__of(_1445562), _1445564) = c_Groups_Ozero__class_Ozero(_1445562))]]], (35092 ^ _782435) ^ [_1445821, _1445823] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1445821), 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)))), _1445823)), 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)))), _1445821)) = 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), _1445823), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1445821))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35098 ^ _782435) ^ [_1445981, _1445983] : [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), _1445981))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1445983)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1445981))) = 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), _1445983), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1445981)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35104 ^ _782435) ^ [_1446128, _1446130] : [-(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), _1446128)))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1446130)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1446128))) = 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), _1446130)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1446128)))), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (35110 ^ _782435) ^ [_1446210, _1446212, _1446214] : [-(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), _1446210)), 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))), _1446212))), hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1446214))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1446214)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446210), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1446210), 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), _1446214), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), _1446212)))))], (35112 ^ _782435) ^ [_1446309, _1446311] : [c_Int_OBit0(_1446309) = c_Int_OBit1(_1446311)], (35114 ^ _782435) ^ [_1446350, _1446352] : [c_Int_OBit1(_1446350) = c_Int_OBit0(_1446352)], (35116 ^ _782435) ^ [_1446394, _1446396] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446394)), c_Int_OBit0(_1446396))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446394), _1446396)))], (35122 ^ _782435) ^ [_1446495, _1446497] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446495), _1446497)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446495)), c_Int_OBit0(_1446497))))], (35128 ^ _782435) ^ [_1446617, _1446619] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446617)), c_Int_OBit0(_1446619))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446617), _1446619)))], (35134 ^ _782435) ^ [_1446718, _1446720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1446718), _1446720)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1446718)), c_Int_OBit0(_1446720))))], (35140 ^ _782435) ^ [_1446825, _1446827] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1446825)), c_Int_OBit0(_1446827)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1446825), _1446827)))], (35142 ^ _782435) ^ [_1446868, _1446870] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit0(_1446868)), _1446870) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1446868), _1446870)))], (35144 ^ _782435) ^ [_1446924, _1446926] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1446924)), c_Int_OBit0(_1446926))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1446924), _1446926)))], (35150 ^ _782435) ^ [_1447025, _1447027] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447025), _1447027)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447025)), c_Int_OBit0(_1447027))))], (35156 ^ _782435) ^ [_1447147, _1447149] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447147)), c_Int_OBit0(_1447149))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447147), _1447149)))], (35162 ^ _782435) ^ [_1447248, _1447250] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1447248), _1447250)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1447248)), c_Int_OBit0(_1447250))))], (35168 ^ _782435) ^ [_1447355] : [-(c_Int_OBit0(_1447355) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447355), _1447355))], (35170 ^ _782435) ^ [_1447386, _1447388] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1447386)), c_Int_OBit0(_1447388)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1447386), _1447388)))], (35172 ^ _782435) ^ [_1447444, _1447446] : [c_Int_OBit0(_1447444) = c_Int_OBit0(_1447446), -(_1447444 = _1447446)], (35178 ^ _782435) ^ [_1447525, _1447527] : [_1447525 = _1447527, -(c_Int_OBit0(_1447525) = c_Int_OBit0(_1447527))], (35184 ^ _782435) ^ [_1447612] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OBit0(_1447612)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1447612)))], (35186 ^ _782435) ^ [] : [-(c_Int_OBit0(c_Int_OPls) = c_Int_OPls)], (35188 ^ _782435) ^ [_1447675] : [c_Int_OPls = c_Int_OBit0(_1447675), -(c_Int_OPls = _1447675)], (35194 ^ _782435) ^ [_1447750] : [c_Int_OPls = _1447750, -(c_Int_OPls = c_Int_OBit0(_1447750))], (35200 ^ _782435) ^ [_1447843] : [c_Int_OBit0(_1447843) = c_Int_OPls, -(_1447843 = c_Int_OPls)], (35206 ^ _782435) ^ [_1447918] : [_1447918 = c_Int_OPls, -(c_Int_OBit0(_1447918) = c_Int_OPls)], (35212 ^ _782435) ^ [_1448011] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448011)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448011), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35218 ^ _782435) ^ [_1448106] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1448106), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1448106)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (35224 ^ _782435) ^ [_1448219] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448219)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448219), c_Int_OPls)))], (35230 ^ _782435) ^ [_1448314] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448314), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448314)), c_Int_OPls)))], (35236 ^ _782435) ^ [_1448427] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1448427))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1448427)))], (35242 ^ _782435) ^ [_1448510] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1448510)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1448510))))], (35248 ^ _782435) ^ [_1448614, _1448616] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448614)), c_Int_OBit1(_1448616))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448614), _1448616)))], (35254 ^ _782435) ^ [_1448715, _1448717] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448715), _1448717)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448715)), c_Int_OBit1(_1448717))))], (35260 ^ _782435) ^ [_1448837, _1448839] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448837)), c_Int_OBit1(_1448839))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448837), _1448839)))], (35266 ^ _782435) ^ [_1448938, _1448940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1448938), _1448940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1448938)), c_Int_OBit1(_1448940))))], (35272 ^ _782435) ^ [_1449057] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449057))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1449057)))], (35278 ^ _782435) ^ [_1449140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), _1449140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449140))))], (35284 ^ _782435) ^ [_1449241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1449241)), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449241), c_Int_OPls)))], (35290 ^ _782435) ^ [_1449336] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449336), c_Int_OPls)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1449336)), c_Int_OPls)))], (35296 ^ _782435) ^ [_1449452, _1449454] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449452)), c_Int_OBit0(_1449454))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449452), _1449454)))], (35302 ^ _782435) ^ [_1449553, _1449555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449553), _1449555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449553)), c_Int_OBit0(_1449555))))], (35308 ^ _782435) ^ [_1449675, _1449677] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449675)), c_Int_OBit0(_1449677))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449675), _1449677)))], (35314 ^ _782435) ^ [_1449776, _1449778] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1449776), _1449778)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1449776)), c_Int_OBit0(_1449778))))], (35320 ^ _782435) ^ [_1449883, _1449885] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(_1449883)), c_Int_OBit1(_1449885)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449883), _1449885)))], (35322 ^ _782435) ^ [_1449926, _1449928] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1449926)), c_Int_OBit0(_1449928)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1449926), _1449928)))], (35324 ^ _782435) ^ [_1449969] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit0(_1449969)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), _1449969)))], (35326 ^ _782435) ^ [_1450002, _1450004] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1450002)), c_Int_OBit1(_1450004)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450002), _1450004)))], (35328 ^ _782435) ^ [_1450045, _1450047] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit1(_1450045)), c_Int_OBit0(_1450047)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1450045), _1450047)))], (35330 ^ _782435) ^ [_1450088, _1450090] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450088))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450090))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450088)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450090)))], (35332 ^ _782435) ^ [_1450153] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450153)))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450153))))], (35338 ^ _782435) ^ [_1450248] : [hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1450248))), -(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1450248)))))], (35344 ^ _782435) ^ [_1450349] : [-(c_Int_Opred(c_Int_OBit1(_1450349)) = c_Int_OBit0(_1450349))], (35346 ^ _782435) ^ [_1450378] : [-(c_Int_Opred(c_Int_OBit0(_1450378)) = c_Int_OBit1(c_Int_Opred(_1450378)))], (35348 ^ _782435) ^ [_1450409, _1450411] : [class_Int_Onumber__ring(_1450409), class_Int_Oring__char__0(_1450409), 35355 ^ _782435 : [(35356 ^ _782435) ^ [] : [c_Int_Oiszero(_1450409, hAPP(c_Int_Onumber__class_Onumber__of(_1450409), c_Int_OBit0(_1450411))), -(c_Int_Oiszero(_1450409, hAPP(c_Int_Onumber__class_Onumber__of(_1450409), _1450411)))], (35362 ^ _782435) ^ [] : [c_Int_Oiszero(_1450409, hAPP(c_Int_Onumber__class_Onumber__of(_1450409), _1450411)), -(c_Int_Oiszero(_1450409, hAPP(c_Int_Onumber__class_Onumber__of(_1450409), c_Int_OBit0(_1450411))))]]], (35368 ^ _782435) ^ [_1450702] : [-(c_Int_Osucc(c_Int_OBit0(_1450702)) = c_Int_OBit1(_1450702))], (35370 ^ _782435) ^ [_1450731] : [-(c_Int_Osucc(c_Int_OBit1(_1450731)) = c_Int_OBit0(c_Int_Osucc(_1450731)))], (35372 ^ _782435) ^ [_1450762] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1450762)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat, tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1450762)), 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 ^ _782435) ^ [_1450799, _1450801] : [class_Int_Onumber__ring(_1450799), -(hAPP(c_Int_Onumber__class_Onumber__of(_1450799), c_Int_OBit0(_1450801)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450799), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1450799), c_Groups_Ozero__class_Ozero(_1450799)), hAPP(c_Int_Onumber__class_Onumber__of(_1450799), _1450801))), hAPP(c_Int_Onumber__class_Onumber__of(_1450799), _1450801)))], (35380 ^ _782435) ^ [_1450959, _1450961] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1450959)), c_Int_OBit1(_1450961))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1450959), _1450961)))], (35386 ^ _782435) ^ [_1451060, _1451062] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451060), _1451062)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451060)), c_Int_OBit1(_1451062))))], (35392 ^ _782435) ^ [_1451182, _1451184] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451182)), c_Int_OBit1(_1451184))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451182), _1451184)))], (35398 ^ _782435) ^ [_1451283, _1451285] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1451283), _1451285)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1451283)), c_Int_OBit1(_1451285))))], (35404 ^ _782435) ^ [_1451405, _1451407] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451405)), c_Int_OBit0(_1451407))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451405), _1451407)))], (35410 ^ _782435) ^ [_1451506, _1451508] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451506), _1451508)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451506)), c_Int_OBit0(_1451508))))], (35416 ^ _782435) ^ [_1451628, _1451630] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451628)), c_Int_OBit0(_1451630))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451628), _1451630)))], (35422 ^ _782435) ^ [_1451729, _1451731] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1451729), _1451731)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1451729)), c_Int_OBit0(_1451731))))], (35428 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1451854, _1451856] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OBit1(_1451854)), _1451856) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1451854), _1451856))), _1451856))], (35432 ^ _782435) ^ [_1451901, _1451903] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OBit0(_1451901)), c_Int_OBit1(_1451903)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_Opred(_1451901)), _1451903)))], (35434 ^ _782435) ^ [_1451946, _1451948] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OBit1(_1451946)), c_Int_OBit1(_1451948)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1451946), c_Int_Osucc(_1451948))))], (35436 ^ _782435) ^ [_1451991, _1451993, _1451995] : [class_Int_Onumber__ring(_1451991), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1451991), _1451993), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1451995))) = hAPP(hAPP(c_HOL_OLet(_1451991, _1451991), hAPP(hAPP(c_Power_Opower__class_Opower(_1451991), _1451993), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1451995))), hAPP(hAPP(c_COMBS(_1451991, _1451991, _1451991), c_Groups_Otimes__class_Otimes(_1451991)), c_COMBI(_1451991))))], (35442 ^ _782435) ^ [_1452162, _1452164] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1452162), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452164))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint), _1452162), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452164))), 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 ^ _782435) ^ [_1452213, _1452215] : [class_Int_Onumber__ring(_1452213), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452213), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452213), c_Groups_Oone__class_Oone(_1452213)), c_Groups_Oone__class_Oone(_1452213))), hAPP(c_Int_Onumber__class_Onumber__of(_1452213), _1452215)) = hAPP(c_Int_Onumber__class_Onumber__of(_1452213), c_Int_OBit0(_1452215)))], (35450 ^ _782435) ^ [_1452352] : [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), _1452352))), 35453 ^ _782435 : [(35454 ^ _782435) ^ [] : [-(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(_1452352)))))], (35456 ^ _782435) ^ [] : [-(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(_1452352)))))]]], (35458 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1452509, _1452511, _1452513] : [class_Int_Onumber__ring(_1452509), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1452509), hAPP(c_Int_Onumber__class_Onumber__of(_1452509), _1452511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(_1452513))) = hAPP(hAPP(c_HOL_OLet(_1452509, _1452509), hAPP(hAPP(c_Power_Opower__class_Opower(_1452509), hAPP(c_Int_Onumber__class_Onumber__of(_1452509), _1452511)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1452513))), hAPP(hAPP(c_COMBS(_1452509, _1452509, _1452509), c_Groups_Otimes__class_Otimes(_1452509)), c_COMBI(_1452509))))], (35466 ^ _782435) ^ [_1452700, _1452702] : [class_Int_Onumber__ring(_1452700), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452700), _1452702), hAPP(c_Int_Onumber__class_Onumber__of(_1452700), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452700), _1452702), _1452702))], (35472 ^ _782435) ^ [_1452817, _1452819] : [class_Int_Onumber__ring(_1452817), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1452817), hAPP(c_Int_Onumber__class_Onumber__of(_1452817), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1452819) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452817), _1452819), _1452819))], (35478 ^ _782435) ^ [_1452934] : [class_Int_Onumber__ring(_1452934), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1452934), c_Groups_Oone__class_Oone(_1452934)), c_Groups_Oone__class_Oone(_1452934)) = hAPP(c_Int_Onumber__class_Onumber__of(_1452934), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))], (35484 ^ _782435) ^ [_1453041] : [class_Rings_Osemiring__1(_1453041), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453041), c_Groups_Ozero__class_Ozero(_1453041)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453041))], (35490 ^ _782435) ^ [_1453138, _1453140] : [class_Rings_Oring__1__no__zero__divisors(_1453138), 35493 ^ _782435 : [(35494 ^ _782435) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1453138), _1453140), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453138), -(_1453140 = c_Groups_Ozero__class_Ozero(_1453138))], (35500 ^ _782435) ^ [] : [_1453140 = c_Groups_Ozero__class_Ozero(_1453138), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453138), _1453140), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(_1453138))]]], (35506 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1453415, _1453417] : [class_Rings_Ocomm__semiring__1(_1453415), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1453415), _1453417), _1453417) = hAPP(hAPP(c_Power_Opower__class_Opower(_1453415), _1453417), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35516 ^ _782435) ^ [_1453522, _1453524] : [class_Groups_Omonoid__mult(_1453522), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453522), _1453524), 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(_1453522), _1453524), _1453524))], (35522 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1453647] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1453647), 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, _1453647)))], (35526 ^ _782435) ^ [_1453682] : [-(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)))), _1453682) = hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1453682)))], (35528 ^ _782435) ^ [_1453714] : [class_Rings_Osemiring__1(_1453714), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453714), c_Groups_Oone__class_Oone(_1453714)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1453714))], (35534 ^ _782435) ^ [_1453811, _1453813] : [class_Rings_Oring__1(_1453811), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453811), hAPP(c_Groups_Ouminus__class_Ouminus(_1453811), _1453813)), 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(_1453811), _1453813), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35540 ^ _782435) ^ [_1453928] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1453928), 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), _1453928), _1453928))], (35542 ^ _782435) ^ [_1453963] : [-(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)))), _1453963) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1453963), _1453963))], (35544 ^ _782435) ^ [_1453995, _1453997, _1453999] : [class_Groups_Omonoid__mult(_1453995), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1453995), _1453997), 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)))), _1453999)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1453995), hAPP(hAPP(c_Power_Opower__class_Opower(_1453995), _1453997), _1453999)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35550 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1454162, _1454164] : [class_Rings_Olinordered__idom(_1454162), -(hAPP(c_Groups_Oabs__class_Oabs(_1454162), hAPP(hAPP(c_Power_Opower__class_Opower(_1454162), _1454164), 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(_1454162), _1454164), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35560 ^ _782435) ^ [_1454279, _1454281] : [class_Rings_Olinordered__idom(_1454279), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1454279), hAPP(c_Groups_Oabs__class_Oabs(_1454279), _1454281)), 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(_1454279), _1454281), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35566 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1454414] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1454414)), 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, _1454414, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))], (35570 ^ _782435) ^ [_1454451] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_OSuc, _1454451))), 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), _1454451), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35572 ^ _782435) ^ [_1454495, _1454497] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1454495)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1454497))) = 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), _1454495), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1454497))))], (35574 ^ _782435) ^ [_1454547] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1454547), _1454547)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = _1454547)], (35576 ^ _782435) ^ [_1454582, _1454584] : [class_Fields_Olinordered__field__inverse__zero(_1454582), class_Int_Onumber__ring(_1454582), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454582), c_Groups_Ozero__class_Ozero(_1454582)), _1454584)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454582), c_Groups_Ozero__class_Ozero(_1454582)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454582), _1454584), hAPP(c_Int_Onumber__class_Onumber__of(_1454582), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35590 ^ _782435) ^ [_1454823, _1454825] : [class_Fields_Olinordered__field__inverse__zero(_1454823), class_Int_Onumber__ring(_1454823), 35597 ^ _782435 : [(35598 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454823), c_Groups_Ozero__class_Ozero(_1454823)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454823), _1454825), hAPP(c_Int_Onumber__class_Onumber__of(_1454823), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454823), c_Groups_Ozero__class_Ozero(_1454823)), _1454825)))], (35604 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454823), c_Groups_Ozero__class_Ozero(_1454823)), _1454825)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1454823), c_Groups_Ozero__class_Ozero(_1454823)), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1454823), _1454825), hAPP(c_Int_Onumber__class_Onumber__of(_1454823), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (35610 ^ _782435) ^ [_1455173, _1455175, _1455177] : [class_Rings_Olinordered__semidom(_1455173), hAPP(hAPP(c_Power_Opower__class_Opower(_1455173), _1455175), 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(_1455173), _1455177), 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(_1455173), c_Groups_Ozero__class_Ozero(_1455173)), _1455175)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455173), c_Groups_Ozero__class_Ozero(_1455173)), _1455177)), -(_1455175 = _1455177)], (35628 ^ _782435) ^ [_1455480, _1455482, _1455484] : [class_Rings_Olinordered__semidom(_1455480), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455480), hAPP(hAPP(c_Power_Opower__class_Opower(_1455480), _1455482), 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(_1455480), _1455484), 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(_1455480), c_Groups_Ozero__class_Ozero(_1455480)), _1455484)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455480), _1455482), _1455484)))], (35642 ^ _782435) ^ [_1455743, _1455745] : [class_Rings_Olinordered__idom(_1455743), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1455743), c_Groups_Ozero__class_Ozero(_1455743)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455743), _1455745), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35648 ^ _782435) ^ [_1455852, _1455854] : [class_Rings_Olinordered__idom(_1455852), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455852), hAPP(hAPP(c_Power_Opower__class_Opower(_1455852), _1455854), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), c_Groups_Ozero__class_Ozero(_1455852)))], (35654 ^ _782435) ^ [_1455962, _1455964] : [class_Rings_Olinordered__idom(_1455962), 35657 ^ _782435 : [(35658 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455962), c_Groups_Ozero__class_Ozero(_1455962)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455962), _1455964), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), _1455964 = c_Groups_Ozero__class_Ozero(_1455962)], (35664 ^ _782435) ^ [] : [-(_1455964 = c_Groups_Ozero__class_Ozero(_1455962)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1455962), c_Groups_Ozero__class_Ozero(_1455962)), hAPP(hAPP(c_Power_Opower__class_Opower(_1455962), _1455964), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))]]], (35670 ^ _782435) ^ [_1456186, _1456188, _1456190] : [class_Rings_Olinordered__idom(_1456186), 35673 ^ _782435 : [(35674 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456186), hAPP(hAPP(c_Power_Opower__class_Opower(_1456186), _1456188), 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(_1456186), _1456190), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1456186), 35677 ^ _782435 : [(35678 ^ _782435) ^ [] : [-(_1456188 = c_Groups_Ozero__class_Ozero(_1456186))], (35680 ^ _782435) ^ [] : [-(_1456190 = c_Groups_Ozero__class_Ozero(_1456186))]]], (35682 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1456186), hAPP(hAPP(c_Power_Opower__class_Opower(_1456186), _1456188), 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(_1456186), _1456190), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(_1456186)), _1456188 = c_Groups_Ozero__class_Ozero(_1456186), _1456190 = c_Groups_Ozero__class_Ozero(_1456186)]]], (35692 ^ _782435) ^ [_1456561, _1456563] : [-(hAPP(hAPP(c_Power_Opower__class_Opower(_1456561), hAPP(c_Int_Onumber__class_Onumber__of(_1456561), _1456563)), 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(_1456561), hAPP(c_Int_Onumber__class_Onumber__of(_1456561), _1456563)), hAPP(c_Int_Onumber__class_Onumber__of(_1456561), _1456563))), class_Groups_Omonoid__mult(_1456561), class_Int_Onumber(_1456561)], (35702 ^ _782435) ^ [_1456748] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1456748), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))), -(_1456748 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1456748 = hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (35712 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1456864, _1456866] : [class_Rings_Oring__1__no__zero__divisors(_1456864), 35717 ^ _782435 : [(35728 ^ _782435) ^ [] : [35729 ^ _782435 : [(35730 ^ _782435) ^ [] : [_1456866 = c_Groups_Oone__class_Oone(_1456864)], (35732 ^ _782435) ^ [] : [_1456866 = hAPP(c_Groups_Ouminus__class_Ouminus(_1456864), c_Groups_Oone__class_Oone(_1456864))]], -(hAPP(hAPP(c_Power_Opower__class_Opower(_1456864), _1456866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1456864))], (35718 ^ _782435) ^ [] : [hAPP(hAPP(c_Power_Opower__class_Opower(_1456864), _1456866), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(_1456864), -(_1456866 = c_Groups_Oone__class_Oone(_1456864)), -(_1456866 = hAPP(c_Groups_Ouminus__class_Ouminus(_1456864), c_Groups_Oone__class_Oone(_1456864)))]]], (35736 ^ _782435) ^ [_1457171, _1457173, _1457175] : [class_Rings_Ocomm__semiring__1(_1457171), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1457171), _1457173), 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)))), _1457175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1457171), hAPP(hAPP(c_Power_Opower__class_Opower(_1457171), _1457173), _1457175)), hAPP(hAPP(c_Power_Opower__class_Opower(_1457171), _1457173), _1457175)))], (35742 ^ _782435) ^ [_1457318, _1457320, _1457322] : [class_Rings_Oring__1(_1457318), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1457318), hAPP(c_Groups_Ouminus__class_Ouminus(_1457318), _1457320)), 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)))), _1457322)) = hAPP(hAPP(c_Power_Opower__class_Opower(_1457318), _1457320), 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)))), _1457322)))], (35748 ^ _782435) ^ [_1457449, _1457451, _1457453] : [class_Rings_Olinordered__semidom(_1457449), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457449), hAPP(hAPP(c_Power_Opower__class_Opower(_1457449), _1457451), 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(_1457449), _1457453), 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(_1457449), c_Groups_Ozero__class_Ozero(_1457449)), _1457453)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1457449), _1457451), _1457453)))], (35762 ^ _782435) ^ [_1457712, _1457714, _1457716] : [class_Rings_Olinordered__idom(_1457712), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457712), c_Groups_Ozero__class_Ozero(_1457712)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457712), hAPP(hAPP(c_Power_Opower__class_Opower(_1457712), _1457714), 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(_1457712), _1457716), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (35768 ^ _782435) ^ [_1457855, _1457857, _1457859] : [class_Rings_Olinordered__idom(_1457855), 35771 ^ _782435 : [(35772 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457855), hAPP(hAPP(c_Power_Opower__class_Opower(_1457855), _1457857), 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(_1457855), _1457859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1457855))), 35775 ^ _782435 : [(35776 ^ _782435) ^ [] : [-(_1457857 = c_Groups_Ozero__class_Ozero(_1457855))], (35778 ^ _782435) ^ [] : [-(_1457859 = c_Groups_Ozero__class_Ozero(_1457855))]]], (35780 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1457855), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1457855), hAPP(hAPP(c_Power_Opower__class_Opower(_1457855), _1457857), 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(_1457855), _1457859), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1457855)))), _1457857 = c_Groups_Ozero__class_Ozero(_1457855), _1457859 = c_Groups_Ozero__class_Ozero(_1457855)]]], (35790 ^ _782435) ^ [_1458251, _1458253, _1458255] : [class_Rings_Olinordered__idom(_1458251), 35793 ^ _782435 : [(35804 ^ _782435) ^ [] : [35805 ^ _782435 : [(35806 ^ _782435) ^ [] : [-(_1458253 = c_Groups_Ozero__class_Ozero(_1458251))], (35808 ^ _782435) ^ [] : [-(_1458255 = c_Groups_Ozero__class_Ozero(_1458251))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458251), c_Groups_Ozero__class_Ozero(_1458251)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458251), hAPP(hAPP(c_Power_Opower__class_Opower(_1458251), _1458253), 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(_1458251), _1458255), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))))], (35794 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458251), c_Groups_Ozero__class_Ozero(_1458251)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458251), hAPP(hAPP(c_Power_Opower__class_Opower(_1458251), _1458253), 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(_1458251), _1458255), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))), _1458253 = c_Groups_Ozero__class_Ozero(_1458251), _1458255 = c_Groups_Ozero__class_Ozero(_1458251)]]], (35812 ^ _782435) ^ [_1458626, _1458628, _1458630] : [class_Rings_Olinordered__idom(_1458626), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1458626), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458626), hAPP(hAPP(c_Power_Opower__class_Opower(_1458626), _1458628), 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(_1458626), _1458630), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))), c_Groups_Ozero__class_Ozero(_1458626)))], (35818 ^ _782435) ^ [_1458770, _1458772, _1458774] : [class_Int_Onumber__ring(_1458770), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1458770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458770), _1458772), _1458774)), 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(_1458770), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1458770), hAPP(hAPP(c_Power_Opower__class_Opower(_1458770), _1458772), 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(_1458770), _1458774), 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(_1458770), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1458770), hAPP(c_Int_Onumber__class_Onumber__of(_1458770), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1458772)), _1458774)))], (35824 ^ _782435) ^ [_1458985, _1458987, _1458989] : [class_Rings_Olinordered__idom(_1458985), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1458985), c_Groups_Ozero__class_Ozero(_1458985)), hAPP(hAPP(c_Power_Opower__class_Opower(_1458985), _1458987), 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)))), _1458989)))))], (35830 ^ _782435) ^ [_1459102, _1459104, _1459106] : [class_Groups_Omonoid__mult(_1459102), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459102), _1459104), 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)))), _1459106))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459102), _1459104), hAPP(hAPP(c_Power_Opower__class_Opower(_1459102), hAPP(hAPP(c_Power_Opower__class_Opower(_1459102), _1459104), _1459106)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))], (35836 ^ _782435) ^ [_1459255, _1459257, _1459259] : [class_Rings_Ocomm__semiring__1(_1459255), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459255), _1459257), 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)))), _1459259))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459255), _1459257), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1459255), hAPP(hAPP(c_Power_Opower__class_Opower(_1459255), _1459257), _1459259)), hAPP(hAPP(c_Power_Opower__class_Opower(_1459255), _1459257), _1459259))))], (35842 ^ _782435) ^ [_1459424, _1459426] : [class_Rings_Oring__1(_1459424), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1459424), hAPP(c_Groups_Ouminus__class_Ouminus(_1459424), c_Groups_Oone__class_Oone(_1459424))), 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)))), _1459426)) = c_Groups_Oone__class_Oone(_1459424))], (35848 ^ _782435) ^ [_1459548, _1459550] : [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), _1459548))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1459550))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1459548))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459550)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459548)))], (35854 ^ _782435) ^ [_1459685, _1459687] : [-(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), _1459685)))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit1(_1459687))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(_1459685))) = 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), _1459687)), c_Groups_Oone__class_Oone(tc_Int_Oint))), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1459685)))], (35860 ^ _782435) ^ [_1459774] : [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, _1459774, 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, _1459774, 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 ^ _782435) ^ [_1459865] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1459865, 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, _1459865, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35872 ^ _782435) ^ [_1459962] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1459962)), -(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), _1459962), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35878 ^ _782435) ^ [_1460057, _1460059, _1460061] : [class_Int_Onumber__ring(_1460057), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1460057), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1460057), _1460059), _1460061)), 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(_1460057), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460057), hAPP(hAPP(c_Power_Opower__class_Opower(_1460057), _1460059), 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(_1460057), _1460061), 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(_1460057), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1460057), hAPP(c_Int_Onumber__class_Onumber__of(_1460057), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))), _1460059)), _1460061)))], (35884 ^ _782435) ^ [_1460272, _1460274, _1460276] : [class_Rings_Olinordered__idom(_1460272), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460272), c_Groups_Ozero__class_Ozero(_1460272)), hAPP(hAPP(c_Power_Opower__class_Opower(_1460272), _1460274), 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)))), _1460276))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1460272), c_Groups_Ozero__class_Ozero(_1460272)), _1460274)))], (35894 ^ _782435) ^ [_1460467, _1460469, _1460471] : [class_Rings_Olinordered__idom(_1460467), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460467), _1460469), c_Groups_Ozero__class_Ozero(_1460467))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1460467), hAPP(hAPP(c_Power_Opower__class_Opower(_1460467), _1460469), 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)))), _1460471)))), c_Groups_Ozero__class_Ozero(_1460467))))], (35904 ^ _782435) ^ [_1460662, _1460664] : [class_Rings_Oring__1(_1460662), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1460662), hAPP(c_Groups_Ouminus__class_Ouminus(_1460662), c_Groups_Oone__class_Oone(_1460662))), 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)))), _1460664))) = hAPP(c_Groups_Ouminus__class_Ouminus(_1460662), c_Groups_Oone__class_Oone(_1460662)))], (35910 ^ _782435) ^ [_1460793] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1460793)), -(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), _1460793), 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 ^ _782435) ^ [_1460900, _1460902] : [class_Rings_Osemiring__1(_1460900), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1460902)), -(hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460900), 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)))), _1460902))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1460900), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460900), hAPP(c_Int_Onat, _1460902))), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1460900), hAPP(c_Int_Onat, _1460902))))], (35926 ^ _782435) ^ [_1461101, _1461103] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461101)), -(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)))), _1461103)), 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)))), _1461101)) = 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, _1461103, _1461101))))], (35932 ^ _782435) ^ [_1461228, _1461230] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1461228)), -(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)))), _1461230))), 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)))), _1461228)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1461230), _1461228))], (35938 ^ _782435) ^ [_1461351, _1461353] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1461351), 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)))), _1461353))), 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)))), _1461351)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1461353), c_Groups_Oone__class_Oone(tc_Int_Oint))), _1461351))], (35944 ^ _782435) ^ [_1461498] : [_1461498 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Code__Numeral_Oint__of, _1461498) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (35950 ^ _782435) ^ [_1461574] : [-(_1461574 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), 35953 ^ _782435 : [(35954 ^ _782435) ^ [] : [c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1461574, 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, _1461574) = 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), _1461574), hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))], (35960 ^ _782435) ^ [] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1461574, 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, _1461574) = 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), _1461574), 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 ^ _782435) ^ [_1461834, _1461836] : [class_Rings_Oring__1(_1461834), 35969 ^ _782435 : [(35970 ^ _782435) ^ [] : [_1461836 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461834), _1461836) = c_Groups_Ozero__class_Ozero(_1461834))], (35976 ^ _782435) ^ [] : [-(_1461836 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 35979 ^ _782435 : [(35980 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461836), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461834), _1461836) = hAPP(c_Groups_Ouminus__class_Ouminus(_1461834), hAPP(c_Int_Oring__1__class_Oof__int(_1461834), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1461836))))], (35986 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1461836), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), -(hAPP(c_Int_Oring__1__class_Oof__int(_1461834), _1461836) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint, tc_Int_Oint, _1461834), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(tc_Int_Oint, tc_fun(_1461834, _1461834)), tc_fun(tc_Int_Oint, _1461834)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1461834, _1461834), _1461834), tc_fun(tc_fun(tc_Int_Oint, tc_fun(_1461834, _1461834)), tc_fun(tc_Int_Oint, _1461834)), tc_Int_Oint), c_COMBB(tc_fun(_1461834, _1461834), _1461834, tc_Int_Oint)), hAPP(hAPP(c_COMBB(_1461834, tc_fun(tc_fun(_1461834, _1461834), _1461834), tc_Int_Oint), c_HOL_OLet(_1461834, _1461834)), c_Int_Oring__1__class_Oof__int(_1461834)))), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1461834, _1461834), tc_fun(_1461834, _1461834)), hAPP(hAPP(c_COMBB(tc_fun(_1461834, tc_fun(_1461834, _1461834)), tc_fun(tc_fun(_1461834, _1461834), tc_fun(_1461834, _1461834)), tc_Int_Oint), c_COMBS(_1461834, _1461834, _1461834)), hAPP(hAPP(c_COMBC(tc_Int_Oint, tc_fun(_1461834, _1461834), tc_fun(_1461834, tc_fun(_1461834, _1461834))), hAPP(hAPP(c_COMBB(tc_fun(_1461834, tc_fun(_1461834, _1461834)), tc_fun(tc_fun(_1461834, _1461834), tc_fun(_1461834, tc_fun(_1461834, _1461834))), tc_Int_Oint), c_COMBB(_1461834, tc_fun(_1461834, _1461834), _1461834)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1461834, tc_fun(_1461834, _1461834)), tc_Int_Oint), c_If(_1461834)), 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(_1461834, _1461834, _1461834), c_Groups_Oplus__class_Oplus(_1461834)), c_COMBI(_1461834))))), hAPP(hAPP(c_COMBC(_1461834, _1461834, _1461834), hAPP(hAPP(c_COMBB(_1461834, tc_fun(_1461834, _1461834), _1461834), c_Groups_Oplus__class_Oplus(_1461834)), hAPP(hAPP(c_COMBS(_1461834, _1461834, _1461834), c_Groups_Oplus__class_Oplus(_1461834)), c_COMBI(_1461834)))), c_Groups_Oone__class_Oone(_1461834))))), c_Divides_Odivmod__int(_1461836, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))]]]]], (35992 ^ _782435) ^ [_1462747, _1462749] : [class_Int_Onumber__ring(_1462747), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1462747), hAPP(c_Int_Onumber__class_Onumber__of(_1462747), 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)))), _1462749))) = hAPP(c_Int_Onumber__class_Onumber__of(_1462747), c_Int_OMin))], (35998 ^ _782435) ^ [_1462879] : [c_Int_OBit0(_1462879) = c_Int_OMin], (36000 ^ _782435) ^ [_1462913] : [c_Int_OMin = c_Int_OBit0(_1462913)], (36002 ^ _782435) ^ [] : [c_Int_OPls = c_Int_OMin], (36004 ^ _782435) ^ [] : [c_Int_OMin = c_Int_OPls], (36006 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OMin))], (36008 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OMin)))], (36012 ^ _782435) ^ [_1463058] : [c_Int_OBit1(_1463058) = c_Int_OMin, -(_1463058 = c_Int_OMin)], (36018 ^ _782435) ^ [_1463133] : [_1463133 = c_Int_OMin, -(c_Int_OBit1(_1463133) = c_Int_OMin)], (36024 ^ _782435) ^ [_1463226] : [c_Int_OMin = c_Int_OBit1(_1463226), -(c_Int_OMin = _1463226)], (36030 ^ _782435) ^ [_1463301] : [c_Int_OMin = _1463301, -(c_Int_OMin = c_Int_OBit1(_1463301))], (36036 ^ _782435) ^ [] : [-(c_Int_OBit1(c_Int_OMin) = c_Int_OMin)], (36038 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (36040 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (36042 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (36044 ^ _782435) ^ [_1463472] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1463472))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1463472)))], (36050 ^ _782435) ^ [_1463555] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), _1463555)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1463555))))], (36056 ^ _782435) ^ [_1463656] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1463656)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1463656), c_Int_OMin)))], (36062 ^ _782435) ^ [_1463751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1463751), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit1(_1463751)), c_Int_OMin)))], (36068 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OPls), c_Int_OMin))], (36070 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OPls)))], (36072 ^ _782435) ^ [_1463906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1463906)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1463906), c_Int_OMin)))], (36078 ^ _782435) ^ [_1464001] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1464001), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit1(_1464001)), c_Int_OMin)))], (36084 ^ _782435) ^ [_1464114] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1464114))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464114)))], (36090 ^ _782435) ^ [_1464197] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464197)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1464197))))], (36096 ^ _782435) ^ [_1464298] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1464298)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464298), c_Int_OMin)))], (36102 ^ _782435) ^ [_1464393] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1464393), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OBit0(_1464393)), c_Int_OMin)))], (36108 ^ _782435) ^ [_1464506] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1464506))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464506)))], (36114 ^ _782435) ^ [_1464589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1464589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1464589))))], (36120 ^ _782435) ^ [] : [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 ^ _782435) ^ [] : [-(c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36124 ^ _782435) ^ [_1464720] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), c_Int_OMin), _1464720) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1464720))], (36126 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Nat__Numeral_Oneg, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))))], (36128 ^ _782435) ^ [] : [-(c_Int_Opred(c_Int_OPls) = c_Int_OMin)], (36130 ^ _782435) ^ [_1464785] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1464785), c_Int_OMin) = c_Int_Opred(_1464785))], (36132 ^ _782435) ^ [_1464816] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), c_Int_OMin), _1464816) = c_Int_Opred(_1464816))], (36134 ^ _782435) ^ [] : [-(c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin))], (36136 ^ _782435) ^ [_1464862] : [class_Int_Onumber__ring(_1464862), c_Int_Oiszero(_1464862, hAPP(c_Int_Onumber__class_Onumber__of(_1464862), c_Int_OMin))], (36142 ^ _782435) ^ [] : [-(c_Int_Osucc(c_Int_OMin) = c_Int_OPls)], (36144 ^ _782435) ^ [_1464964] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1464964), c_Int_OMin) = c_Int_Osucc(_1464964))], (36146 ^ _782435) ^ [_1464995, _1464997] : [class_Int_Onumber__ring(_1464995), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1464995), hAPP(c_Int_Onumber__class_Onumber__of(_1464995), c_Int_OMin)), _1464997) = hAPP(c_Groups_Ouminus__class_Ouminus(_1464995), _1464997))], (36152 ^ _782435) ^ [_1465106, _1465108] : [class_Int_Onumber__ring(_1465106), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1465106), _1465108), hAPP(c_Int_Onumber__class_Onumber__of(_1465106), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465106), _1465108))], (36158 ^ _782435) ^ [_1465217] : [class_Int_Onumber__ring(_1465217), -(hAPP(c_Int_Onumber__class_Onumber__of(_1465217), c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465217), c_Groups_Oone__class_Oone(_1465217)))], (36164 ^ _782435) ^ [_1465314] : [class_Int_Onumber__ring(_1465314), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1465314), c_Groups_Oone__class_Oone(_1465314)) = hAPP(c_Int_Onumber__class_Onumber__of(_1465314), c_Int_OMin))], (36170 ^ _782435) ^ [_1465411] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1465411), hAPP(c_Int_Onumber__class_Onumber__of(_1465411), c_Int_OMin)) = c_Groups_Oone__class_Oone(_1465411)), class_Int_Onumber__ring(_1465411), class_Rings_Olinordered__idom(_1465411)], (36180 ^ _782435) ^ [_1465556, _1465558] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1465556), _1465558), hAPP(c_Int_Onumber__class_Onumber__of(_1465556), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(_1465556), _1465558)), class_Fields_Ofield__inverse__zero(_1465556), class_Int_Onumber__ring(_1465556)], (36190 ^ _782435) ^ [_1465729] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1465729)), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1465729), c_Int_OMin)))], (36196 ^ _782435) ^ [_1465824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1465824), c_Int_OMin)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OBit0(_1465824)), c_Int_OMin)))], (36202 ^ _782435) ^ [_1465937] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1465937))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1465937)))], (36208 ^ _782435) ^ [_1466020] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Int_OMin), _1466020)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1466020))))], (36214 ^ _782435) ^ [_1466109] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1466109, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36216 ^ _782435) ^ [_1466136] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OPls), c_Int_OBit1(_1466136)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466136)))], (36218 ^ _782435) ^ [] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), c_Int_OMin) = c_Int_OBit1(c_Int_OPls))], (36220 ^ _782435) ^ [_1466187, _1466189] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466187), _1466189) = c_Groups_Oone__class_Oone(tc_Int_Oint), -(_1466187 = c_Groups_Oone__class_Oone(tc_Int_Oint)), -(_1466187 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36230 ^ _782435) ^ [_1466304, _1466306] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466304), _1466306) = c_Groups_Oone__class_Oone(tc_Int_Oint), 36235 ^ _782435 : [(36236 ^ _782435) ^ [] : [-(_1466304 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (36238 ^ _782435) ^ [] : [-(_1466306 = c_Groups_Oone__class_Oone(tc_Int_Oint))]], 36239 ^ _782435 : [(36240 ^ _782435) ^ [] : [-(_1466304 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36242 ^ _782435) ^ [] : [-(_1466306 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))]]], (36244 ^ _782435) ^ [_1466488, _1466490] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1466488), _1466490) = c_Groups_Oone__class_Oone(tc_Int_Oint)), 36245 ^ _782435 : [(36246 ^ _782435) ^ [] : [_1466488 = c_Groups_Oone__class_Oone(tc_Int_Oint), _1466490 = c_Groups_Oone__class_Oone(tc_Int_Oint)], (36252 ^ _782435) ^ [] : [_1466488 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1466490 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)]]], (36260 ^ _782435) ^ [_1466714] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit1(_1466714)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466714)))], (36262 ^ _782435) ^ [_1466747] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), c_Int_OBit0(_1466747)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), c_Int_OMin), _1466747)))], (36264 ^ _782435) ^ [_1466780] : [class_Int_Onumber__ring(_1466780), -(hAPP(c_Int_Oring__1__class_Oof__int(_1466780), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(_1466780), c_Int_OMin))], (36270 ^ _782435) ^ [_1466873] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1466873), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1466873))], (36272 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1466923, _1466925] : [-(hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1466923), hAPP(c_Int_Onumber__class_Onumber__of(_1466923), c_Int_OMin)), _1466925) = hAPP(c_Groups_Ouminus__class_Ouminus(_1466923), hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1466923), c_Groups_Oone__class_Oone(_1466923)), _1466925))), class_Fields_Ofield__inverse__zero(_1466923), class_Int_Onumber__ring(_1466923)], (36284 ^ _782435) ^ [_1467104, _1467106] : [-(hAPP(c_Groups_Oabs__class_Oabs(_1467104), hAPP(hAPP(c_Power_Opower__class_Opower(_1467104), hAPP(c_Int_Onumber__class_Onumber__of(_1467104), c_Int_OMin)), _1467106)) = c_Groups_Oone__class_Oone(_1467104)), class_Int_Onumber__ring(_1467104), class_Rings_Olinordered__idom(_1467104)], (36294 ^ _782435) ^ [_1467269] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467269)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin)), _1467269) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36300 ^ _782435) ^ [_1467354, _1467356] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467354)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1467354), _1467356)), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1467354), _1467356) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin))], (36310 ^ _782435) ^ [_1467521] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1467521)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1467521) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1467521), c_Groups_Oone__class_Oone(tc_Int_Oint)))], (36316 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1467638, _1467640] : [class_Int_Onumber__ring(_1467638), -(hAPP(hAPP(c_Power_Opower__class_Opower(_1467638), hAPP(c_Int_Onumber__class_Onumber__of(_1467638), 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)))), _1467640)) = c_Groups_Oone__class_Oone(_1467638))], (36324 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1467767] : [-(c_Int_Oint__ge__less__than2(_1467767) = 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), _1467767)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36328 ^ _782435) ^ [_1467813] : [-(c_Int_Oint__ge__less__than(_1467813) = 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), _1467813)))), c_Orderings_Oord__class_Oless(tc_Int_Oint)))))], (36330 ^ _782435) ^ [_1467859, _1467861] : [-(c_Fun_Oinj__on(tc_fun(_1467859, _1467861), tc_fun(tc_prod(_1467859, _1467861), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1467859, _1467861), tc_HOL_Obool), tc_fun(tc_prod(_1467859, _1467861), tc_HOL_Obool), tc_fun(_1467859, _1467861)), c_Set_OCollect(tc_prod(_1467859, _1467861))), hAPP(hAPP(c_COMBB(tc_fun(_1467859, tc_fun(_1467861, tc_HOL_Obool)), tc_fun(tc_prod(_1467859, _1467861), tc_HOL_Obool), tc_fun(_1467859, _1467861)), c_Product__Type_Oprod_Oprod__case(_1467859, _1467861, tc_HOL_Obool)), hAPP(c_COMBB(_1467861, tc_fun(_1467861, tc_HOL_Obool), _1467859), hAPP(c_COMBC(_1467861, _1467861, tc_HOL_Obool), c_fequal)))), c_Orderings_Otop__class_Otop(tc_fun(tc_fun(_1467859, _1467861), tc_HOL_Obool))))], (36332 ^ _782435) ^ [_1467979, _1467981, _1467983, _1467985] : [-(c_Nitpick_Oprod(_1467979, _1467981, _1467983, _1467985) = hAPP(c_Set_OCollect(tc_prod(_1467979, _1467981)), hAPP(c_Product__Type_Oprod_Oprod__case(_1467979, _1467981, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1467979, tc_fun(_1467981, tc_HOL_Obool), tc_fun(_1467981, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1467981, tc_HOL_Obool), tc_fun(_1467981, tc_HOL_Obool)), _1467979), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1467981)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1467979), c_fconj), hAPP(hAPP(c_COMBC(_1467979, tc_fun(_1467979, tc_HOL_Obool), tc_HOL_Obool), c_member(_1467979)), _1467983)))), hAPP(hAPP(c_COMBC(_1467981, tc_fun(_1467981, tc_HOL_Obool), tc_HOL_Obool), c_member(_1467981)), _1467985)))))], (36334 ^ _782435) ^ [_1468116, _1468118] : [_1468116 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(c_Code__Numeral_Onat__of__aux(_1468116, _1468118) = _1468118)], (36340 ^ _782435) ^ [_1468193, _1468195] : [-(_1468193 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(c_Code__Numeral_Onat__of__aux(_1468193, _1468195) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1468193), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), hAPP(c_Nat_OSuc, _1468195)))], (36346 ^ _782435) ^ [_1468246, _1468248] : [-(c_Divides_Odivmod__int__rel(_1468246, _1468248) = 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, _1468246))), 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), _1468248)))))), 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)), _1468248))), 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)), _1468248))))), 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)), _1468248)))), 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), _1468248))), 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 ^ _782435) ^ [_1468357, _1468359] : [-(_1468357 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468359, _1468357), c_Divides_Odivmod__int(_1468359, _1468357))))], (36354 ^ _782435) ^ [_1468401, _1468403, _1468405, _1468407, _1468409] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468401, _1468403), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1468405), _1468407))), -(_1468403 = 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)), _1468409)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1468401, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1468403), _1468409)), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1468405), _1468409)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1468403), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1468405, _1468409))), _1468407)))))], (36368 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1468725, _1468727] : [class_Int_Onumber__ring(_1468725), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Int_OPls), _1468727)), -(hBOOL(hAPP(hAPP(c_member(_1468725), hAPP(c_Int_Onumber__class_Onumber__of(_1468725), _1468727)), c_Nat_Osemiring__1__class_ONats(_1468725))))], (36380 ^ _782435) ^ [_1468905, _1468907, _1468909, _1468911] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1468905, tc_fun(_1468907, tc_HOL_Obool))), _1468909), _1468911)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1468905, _1468907)), hAPP(hAPP(c_Product__Type_OPair(_1468905, _1468907), _1468909), _1468911)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1468905, _1468907), tc_HOL_Obool)))))], (36386 ^ _782435) ^ [_1469062, _1469064, _1469066, _1469068] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1469062, _1469064)), hAPP(hAPP(c_Product__Type_OPair(_1469062, _1469064), _1469066), _1469068)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1469062, _1469064), tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1469062, tc_fun(_1469064, tc_HOL_Obool))), _1469066), _1469068)))], (36392 ^ _782435) ^ [_1469246, _1469248, _1469250, _1469252] : [hAPP(hAPP(c_COMBC(_1469246, tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_fun(_1469248, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469248, tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_fun(_1469248, tc_HOL_Obool)), _1469246), c_COMBC(_1469248, tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469248, tc_prod(_1469246, _1469248)), tc_fun(_1469248, tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool)), _1469246), hAPP(c_COMBB(tc_prod(_1469246, _1469248), tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool), _1469248), c_member(tc_prod(_1469246, _1469248)))), c_Product__Type_OPair(_1469246, _1469248)))), _1469250) = hAPP(hAPP(c_COMBC(_1469246, tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_fun(_1469248, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469248, tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_fun(_1469248, tc_HOL_Obool)), _1469246), c_COMBC(_1469248, tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469248, tc_prod(_1469246, _1469248)), tc_fun(_1469248, tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool)), _1469246), hAPP(c_COMBB(tc_prod(_1469246, _1469248), tc_fun(tc_fun(tc_prod(_1469246, _1469248), tc_HOL_Obool), tc_HOL_Obool), _1469248), c_member(tc_prod(_1469246, _1469248)))), c_Product__Type_OPair(_1469246, _1469248)))), _1469252), -(_1469250 = _1469252)], (36398 ^ _782435) ^ [_1469795, _1469797, _1469799, _1469801] : [_1469799 = _1469801, -(hAPP(hAPP(c_COMBC(_1469795, tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_fun(_1469797, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469797, tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_fun(_1469797, tc_HOL_Obool)), _1469795), c_COMBC(_1469797, tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469797, tc_prod(_1469795, _1469797)), tc_fun(_1469797, tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool)), _1469795), hAPP(c_COMBB(tc_prod(_1469795, _1469797), tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool), _1469797), c_member(tc_prod(_1469795, _1469797)))), c_Product__Type_OPair(_1469795, _1469797)))), _1469799) = hAPP(hAPP(c_COMBC(_1469795, tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_fun(_1469797, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469797, tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_fun(_1469797, tc_HOL_Obool)), _1469795), c_COMBC(_1469797, tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1469797, tc_prod(_1469795, _1469797)), tc_fun(_1469797, tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool)), _1469795), hAPP(c_COMBB(tc_prod(_1469795, _1469797), tc_fun(tc_fun(tc_prod(_1469795, _1469797), tc_HOL_Obool), tc_HOL_Obool), _1469797), c_member(tc_prod(_1469795, _1469797)))), c_Product__Type_OPair(_1469795, _1469797)))), _1469801))], (36404 ^ _782435) ^ [_1470377, _1470379, _1470381, _1470383, _1470385, _1470387] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1470377, tc_fun(_1470379, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1470377, tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_fun(_1470379, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470379, tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_fun(_1470379, tc_HOL_Obool)), _1470377), c_COMBC(_1470379, tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470379, tc_prod(_1470377, _1470379)), tc_fun(_1470379, tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool)), _1470377), hAPP(c_COMBB(tc_prod(_1470377, _1470379), tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool), _1470379), c_member(tc_prod(_1470377, _1470379)))), c_Product__Type_OPair(_1470377, _1470379)))), _1470381)), hAPP(hAPP(c_COMBC(_1470377, tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_fun(_1470379, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470379, tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_fun(_1470379, tc_HOL_Obool)), _1470377), c_COMBC(_1470379, tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1470379, tc_prod(_1470377, _1470379)), tc_fun(_1470379, tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool)), _1470377), hAPP(c_COMBB(tc_prod(_1470377, _1470379), tc_fun(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool), tc_HOL_Obool), _1470379), c_member(tc_prod(_1470377, _1470379)))), c_Product__Type_OPair(_1470377, _1470379)))), _1470383)), _1470385), _1470387)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1470377, _1470379)), hAPP(hAPP(c_Product__Type_OPair(_1470377, _1470379), _1470385), _1470387)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1470377, _1470379), tc_HOL_Obool)), _1470381), _1470383))))], (36410 ^ _782435) ^ [_1471034, _1471036, _1471038, _1471040, _1471042, _1471044] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1471034, _1471036)), hAPP(hAPP(c_Product__Type_OPair(_1471034, _1471036), _1471042), _1471044)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool)), _1471038), _1471040))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1471034, tc_fun(_1471036, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471034, tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_fun(_1471036, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471036, tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_fun(_1471036, tc_HOL_Obool)), _1471034), c_COMBC(_1471036, tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471036, tc_prod(_1471034, _1471036)), tc_fun(_1471036, tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool)), _1471034), hAPP(c_COMBB(tc_prod(_1471034, _1471036), tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool), _1471036), c_member(tc_prod(_1471034, _1471036)))), c_Product__Type_OPair(_1471034, _1471036)))), _1471038)), hAPP(hAPP(c_COMBC(_1471034, tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_fun(_1471036, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471036, tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_fun(_1471036, tc_HOL_Obool)), _1471034), c_COMBC(_1471036, tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471036, tc_prod(_1471034, _1471036)), tc_fun(_1471036, tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool)), _1471034), hAPP(c_COMBB(tc_prod(_1471034, _1471036), tc_fun(tc_fun(tc_prod(_1471034, _1471036), tc_HOL_Obool), tc_HOL_Obool), _1471036), c_member(tc_prod(_1471034, _1471036)))), c_Product__Type_OPair(_1471034, _1471036)))), _1471040)), _1471042), _1471044)))], (36416 ^ _782435) ^ [_1471718, _1471720, _1471722, _1471724] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1471718, tc_fun(_1471720, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1471718, tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_fun(_1471720, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471720, tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_fun(_1471720, tc_HOL_Obool)), _1471718), c_COMBC(_1471720, tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471720, tc_prod(_1471718, _1471720)), tc_fun(_1471720, tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool)), _1471718), hAPP(c_COMBB(tc_prod(_1471718, _1471720), tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool), _1471720), c_member(tc_prod(_1471718, _1471720)))), c_Product__Type_OPair(_1471718, _1471720)))), _1471722)), hAPP(hAPP(c_COMBC(_1471718, tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_fun(_1471720, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471720, tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_fun(_1471720, tc_HOL_Obool)), _1471718), c_COMBC(_1471720, tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1471720, tc_prod(_1471718, _1471720)), tc_fun(_1471720, tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool)), _1471718), hAPP(c_COMBB(tc_prod(_1471718, _1471720), tc_fun(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool), tc_HOL_Obool), _1471720), c_member(tc_prod(_1471718, _1471720)))), c_Product__Type_OPair(_1471718, _1471720)))), _1471724))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1471718, _1471720), tc_HOL_Obool)), _1471722), _1471724)))], (36422 ^ _782435) ^ [_1472319, _1472321, _1472323, _1472325] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool)), _1472323), _1472325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1472319, tc_fun(_1472321, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1472319, tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_fun(_1472321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472321, tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_fun(_1472321, tc_HOL_Obool)), _1472319), c_COMBC(_1472321, tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472321, tc_prod(_1472319, _1472321)), tc_fun(_1472321, tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool)), _1472319), hAPP(c_COMBB(tc_prod(_1472319, _1472321), tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool), _1472321), c_member(tc_prod(_1472319, _1472321)))), c_Product__Type_OPair(_1472319, _1472321)))), _1472323)), hAPP(hAPP(c_COMBC(_1472319, tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_fun(_1472321, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472321, tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_fun(_1472321, tc_HOL_Obool)), _1472319), c_COMBC(_1472321, tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472321, tc_prod(_1472319, _1472321)), tc_fun(_1472321, tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool)), _1472319), hAPP(c_COMBB(tc_prod(_1472319, _1472321), tc_fun(tc_fun(tc_prod(_1472319, _1472321), tc_HOL_Obool), tc_HOL_Obool), _1472321), c_member(tc_prod(_1472319, _1472321)))), c_Product__Type_OPair(_1472319, _1472321)))), _1472325))))], (36428 ^ _782435) ^ [_1472953, _1472955, _1472957, _1472959, _1472961, _1472963] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1472953, tc_fun(_1472955, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1472953, tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_fun(_1472955, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472955, tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_fun(_1472955, tc_HOL_Obool)), _1472953), c_COMBC(_1472955, tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472955, tc_prod(_1472953, _1472955)), tc_fun(_1472955, tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool)), _1472953), hAPP(c_COMBB(tc_prod(_1472953, _1472955), tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool), _1472955), c_member(tc_prod(_1472953, _1472955)))), c_Product__Type_OPair(_1472953, _1472955)))), _1472957)), hAPP(hAPP(c_COMBC(_1472953, tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_fun(_1472955, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472955, tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_fun(_1472955, tc_HOL_Obool)), _1472953), c_COMBC(_1472955, tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1472955, tc_prod(_1472953, _1472955)), tc_fun(_1472955, tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool)), _1472953), hAPP(c_COMBB(tc_prod(_1472953, _1472955), tc_fun(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool), tc_HOL_Obool), _1472955), c_member(tc_prod(_1472953, _1472955)))), c_Product__Type_OPair(_1472953, _1472955)))), _1472959)), _1472961), _1472963)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1472953, _1472955)), hAPP(hAPP(c_Product__Type_OPair(_1472953, _1472955), _1472961), _1472963)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1472953, _1472955), tc_HOL_Obool)), _1472957), _1472959))))], (36434 ^ _782435) ^ [_1473610, _1473612, _1473614, _1473616, _1473618, _1473620] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1473610, _1473612)), hAPP(hAPP(c_Product__Type_OPair(_1473610, _1473612), _1473618), _1473620)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool)), _1473614), _1473616))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1473610, tc_fun(_1473612, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1473610, tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_fun(_1473612, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473612, tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_fun(_1473612, tc_HOL_Obool)), _1473610), c_COMBC(_1473612, tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473612, tc_prod(_1473610, _1473612)), tc_fun(_1473612, tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool)), _1473610), hAPP(c_COMBB(tc_prod(_1473610, _1473612), tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool), _1473612), c_member(tc_prod(_1473610, _1473612)))), c_Product__Type_OPair(_1473610, _1473612)))), _1473614)), hAPP(hAPP(c_COMBC(_1473610, tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_fun(_1473612, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473612, tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_fun(_1473612, tc_HOL_Obool)), _1473610), c_COMBC(_1473612, tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1473612, tc_prod(_1473610, _1473612)), tc_fun(_1473612, tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool)), _1473610), hAPP(c_COMBB(tc_prod(_1473610, _1473612), tc_fun(tc_fun(tc_prod(_1473610, _1473612), tc_HOL_Obool), tc_HOL_Obool), _1473612), c_member(tc_prod(_1473610, _1473612)))), c_Product__Type_OPair(_1473610, _1473612)))), _1473616)), _1473618), _1473620)))], (36440 ^ _782435) ^ [_1474273, _1474275, _1474277] : [class_Enum_Oenum(_1474273), class_Enum_Oenum(_1474275), 36447 ^ _782435 : [(36448 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1474275, _1474273)), _1474277)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1474275), hAPP(hAPP(c_COMBB(tc_fun(_1474273, tc_HOL_Obool), tc_HOL_Obool, _1474275), c_Enum_Oenum__class_Oenum__ex(_1474273)), hAPP(hAPP(c_COMBB(tc_fun(_1474273, tc_prod(_1474275, _1474273)), tc_fun(_1474273, tc_HOL_Obool), _1474275), hAPP(c_COMBB(tc_prod(_1474275, _1474273), tc_HOL_Obool, _1474273), _1474277)), c_Product__Type_OPair(_1474275, _1474273))))))], (36454 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(_1474275), hAPP(hAPP(c_COMBB(tc_fun(_1474273, tc_HOL_Obool), tc_HOL_Obool, _1474275), c_Enum_Oenum__class_Oenum__ex(_1474273)), hAPP(hAPP(c_COMBB(tc_fun(_1474273, tc_prod(_1474275, _1474273)), tc_fun(_1474273, tc_HOL_Obool), _1474275), hAPP(c_COMBB(tc_prod(_1474275, _1474273), tc_HOL_Obool, _1474273), _1474277)), c_Product__Type_OPair(_1474275, _1474273))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(_1474275, _1474273)), _1474277)))]]], (36460 ^ _782435) ^ [_1474712, _1474714, _1474716] : [class_Enum_Oenum(_1474712), class_Enum_Oenum(_1474714), 36467 ^ _782435 : [(36468 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1474714, _1474712)), _1474716)), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1474714), hAPP(hAPP(c_COMBB(tc_fun(_1474712, tc_HOL_Obool), tc_HOL_Obool, _1474714), c_Enum_Oenum__class_Oenum__all(_1474712)), hAPP(hAPP(c_COMBB(tc_fun(_1474712, tc_prod(_1474714, _1474712)), tc_fun(_1474712, tc_HOL_Obool), _1474714), hAPP(c_COMBB(tc_prod(_1474714, _1474712), tc_HOL_Obool, _1474712), _1474716)), c_Product__Type_OPair(_1474714, _1474712))))))], (36474 ^ _782435) ^ [] : [hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(_1474714), hAPP(hAPP(c_COMBB(tc_fun(_1474712, tc_HOL_Obool), tc_HOL_Obool, _1474714), c_Enum_Oenum__class_Oenum__all(_1474712)), hAPP(hAPP(c_COMBB(tc_fun(_1474712, tc_prod(_1474714, _1474712)), tc_fun(_1474712, tc_HOL_Obool), _1474714), hAPP(c_COMBB(tc_prod(_1474714, _1474712), tc_HOL_Obool, _1474712), _1474716)), c_Product__Type_OPair(_1474714, _1474712))))), -(hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(_1474714, _1474712)), _1474716)))]]], (36480 ^ _782435) ^ [_1475175, _1475177, _1475179, _1475181, _1475183] : [hBOOL(hAPP(hAPP(c_member(_1475175), _1475177), hAPP(c_Relation_OImage(_1475179, _1475175, _1475181), _1475183))), 36484 ^ _782435 : [(36485 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1475179), 36483 ^ [_1475175, _1475177, _1475179, _1475181, _1475183]), _1475183)))], (36487 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1475179, _1475175)), hAPP(hAPP(c_Product__Type_OPair(_1475179, _1475175), 36483 ^ [_1475175, _1475177, _1475179, _1475181, _1475183]), _1475177)), _1475181)))]]], (36489 ^ _782435) ^ [_1475391, _1475393, _1475395, _1475397, _1475399] : [-(hBOOL(hAPP(hAPP(c_member(_1475391), _1475393), hAPP(c_Relation_OImage(_1475395, _1475391, _1475397), _1475399)))), 36490 ^ _782435 : [(36491 ^ _782435) ^ [_1475477] : [hBOOL(hAPP(hAPP(c_member(_1475395), _1475477), _1475399)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475395, _1475391)), hAPP(hAPP(c_Product__Type_OPair(_1475395, _1475391), _1475477), _1475393)), _1475397))]]], (36499 ^ _782435) ^ [_1475657, _1475659, _1475661, _1475663, _1475665, _1475667] : [hBOOL(hAPP(hAPP(c_member(_1475657), _1475659), _1475661)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1475657, _1475663)), hAPP(hAPP(c_Product__Type_OPair(_1475657, _1475663), _1475659), _1475665)), _1475667)), -(hBOOL(hAPP(hAPP(c_member(_1475663), _1475665), hAPP(c_Relation_OImage(_1475657, _1475663, _1475667), _1475661))))], (36509 ^ _782435) ^ [_1475882, _1475884, _1475886, _1475888, _1475890, _1475892] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475882, _1475884), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475886), _1475888))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1475882, _1475884), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1475890), _1475892))), -(_1475884 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1475888 = _1475892)], (36523 ^ _782435) ^ [_1476086, _1476088, _1476090, _1476092, _1476094, _1476096] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476086, _1476088), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476090), _1476092))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476086, _1476088), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476094), _1476096))), -(_1476088 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476090 = _1476094)], (36537 ^ _782435) ^ [_1476290, _1476292, _1476294] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1476290, _1476290), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1476292), _1476294))), -(_1476290 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1476294 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))], (36547 ^ _782435) ^ [_1476402] : [-(_1476402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1476402), 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 ^ _782435) ^ [_1476468, _1476470, _1476472, _1476474, _1476476, _1476478] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476468, tc_fun(_1476470, tc_fun(_1476472, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1476468, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_fun(_1476470, tc_fun(_1476472, tc_HOL_Obool)), _1476468), hAPP(c_COMBC(_1476470, tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_fun(_1476472, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476472, tc_fun(tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_fun(_1476472, tc_HOL_Obool)), _1476470), c_COMBC(_1476472, tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476472, tc_prod(_1476470, _1476472)), tc_fun(_1476472, tc_fun(tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_HOL_Obool)), _1476470), hAPP(c_COMBB(tc_prod(_1476470, _1476472), tc_fun(tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool), tc_HOL_Obool), _1476472), c_member(tc_prod(_1476470, _1476472)))), c_Product__Type_OPair(_1476470, _1476472))))), _1476474)), _1476476), _1476478)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1476470, _1476472)), hAPP(hAPP(c_Product__Type_OPair(_1476470, _1476472), _1476476), _1476478)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476468, tc_fun(tc_prod(_1476470, _1476472), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1476468, tc_HOL_Obool))), _1476474))))], (36559 ^ _782435) ^ [_1476951, _1476953, _1476955, _1476957, _1476959, _1476961] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1476953, _1476955)), hAPP(hAPP(c_Product__Type_OPair(_1476953, _1476955), _1476959), _1476961)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476951, tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1476951, tc_HOL_Obool))), _1476957))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1476951, tc_fun(_1476953, tc_fun(_1476955, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1476951, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_fun(_1476953, tc_fun(_1476955, tc_HOL_Obool)), _1476951), hAPP(c_COMBC(_1476953, tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_fun(_1476955, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476955, tc_fun(tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_fun(_1476955, tc_HOL_Obool)), _1476953), c_COMBC(_1476955, tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1476955, tc_prod(_1476953, _1476955)), tc_fun(_1476955, tc_fun(tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_HOL_Obool)), _1476953), hAPP(c_COMBB(tc_prod(_1476953, _1476955), tc_fun(tc_fun(tc_prod(_1476953, _1476955), tc_HOL_Obool), tc_HOL_Obool), _1476955), c_member(tc_prod(_1476953, _1476955)))), c_Product__Type_OPair(_1476953, _1476955))))), _1476957)), _1476959), _1476961)))], (36565 ^ _782435) ^ [_1477467, _1477469, _1477471, _1477473, _1477475, _1477477] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477467, tc_fun(_1477469, tc_fun(_1477471, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477467, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_fun(_1477469, tc_fun(_1477471, tc_HOL_Obool)), _1477467), hAPP(c_COMBC(_1477469, tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_fun(_1477471, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477471, tc_fun(tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_fun(_1477471, tc_HOL_Obool)), _1477469), c_COMBC(_1477471, tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477471, tc_prod(_1477469, _1477471)), tc_fun(_1477471, tc_fun(tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_HOL_Obool)), _1477469), hAPP(c_COMBB(tc_prod(_1477469, _1477471), tc_fun(tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool), tc_HOL_Obool), _1477471), c_member(tc_prod(_1477469, _1477471)))), c_Product__Type_OPair(_1477469, _1477471))))), _1477473)), _1477475), _1477477)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1477469, _1477471)), hAPP(hAPP(c_Product__Type_OPair(_1477469, _1477471), _1477475), _1477477)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477467, tc_fun(tc_prod(_1477469, _1477471), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477467, tc_HOL_Obool))), _1477473))))], (36571 ^ _782435) ^ [_1477950, _1477952, _1477954, _1477956, _1477958, _1477960] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1477952, _1477954)), hAPP(hAPP(c_Product__Type_OPair(_1477952, _1477954), _1477958), _1477960)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477950, tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1477950, tc_HOL_Obool))), _1477956))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1477950, tc_fun(_1477952, tc_fun(_1477954, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1477950, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_fun(_1477952, tc_fun(_1477954, tc_HOL_Obool)), _1477950), hAPP(c_COMBC(_1477952, tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_fun(_1477954, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477954, tc_fun(tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_fun(_1477954, tc_HOL_Obool)), _1477952), c_COMBC(_1477954, tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1477954, tc_prod(_1477952, _1477954)), tc_fun(_1477954, tc_fun(tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_HOL_Obool)), _1477952), hAPP(c_COMBB(tc_prod(_1477952, _1477954), tc_fun(tc_fun(tc_prod(_1477952, _1477954), tc_HOL_Obool), tc_HOL_Obool), _1477954), c_member(tc_prod(_1477952, _1477954)))), c_Product__Type_OPair(_1477952, _1477954))))), _1477956)), _1477958), _1477960)))], (36577 ^ _782435) ^ [_1478439, _1478441, _1478443] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478439, _1478439), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478441), _1478443))), -(_1478439 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1478441 = c_Groups_Oone__class_Oone(tc_Int_Oint))], (36587 ^ _782435) ^ [_1478555, _1478557, _1478559, _1478561] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478555, _1478557), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478559), _1478561))), -(_1478557 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1478555, _1478557) = _1478561)], (36597 ^ _782435) ^ [_1478681, _1478683, _1478685, _1478687] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1478681, _1478683), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1478685), _1478687))), -(_1478683 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1478681), _1478683) = _1478685)], (36607 ^ _782435) ^ [_1478811] : [class_Rings_Osemiring__1(_1478811), -(hBOOL(hAPP(hAPP(c_member(_1478811), c_Groups_Ozero__class_Ozero(_1478811)), c_Nat_Osemiring__1__class_ONats(_1478811))))], (36613 ^ _782435) ^ [_1478906, _1478908] : [-(c_Divides_Odivmod__int(_1478906, _1478908) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1478906), _1478908)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1478906, _1478908)))], (36615 ^ _782435) ^ [_1478950, _1478952, _1478954] : [class_Rings_Osemiring__1(_1478950), hBOOL(hAPP(hAPP(c_member(_1478950), _1478952), c_Nat_Osemiring__1__class_ONats(_1478950))), hBOOL(hAPP(hAPP(c_member(_1478950), _1478954), c_Nat_Osemiring__1__class_ONats(_1478950))), -(hBOOL(hAPP(hAPP(c_member(_1478950), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1478950), _1478952), _1478954)), c_Nat_Osemiring__1__class_ONats(_1478950))))], (36629 ^ _782435) ^ [_1479205, _1479207, _1479209] : [class_Rings_Osemiring__1(_1479205), hBOOL(hAPP(hAPP(c_member(_1479205), _1479207), c_Nat_Osemiring__1__class_ONats(_1479205))), hBOOL(hAPP(hAPP(c_member(_1479205), _1479209), c_Nat_Osemiring__1__class_ONats(_1479205))), -(hBOOL(hAPP(hAPP(c_member(_1479205), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1479205), _1479207), _1479209)), c_Nat_Osemiring__1__class_ONats(_1479205))))], (36643 ^ _782435) ^ [_1479460] : [class_Rings_Osemiring__1(_1479460), -(hBOOL(hAPP(hAPP(c_member(_1479460), c_Groups_Oone__class_Oone(_1479460)), c_Nat_Osemiring__1__class_ONats(_1479460))))], (36649 ^ _782435) ^ [_1479555, _1479557] : [class_Rings_Osemiring__1(_1479555), -(hBOOL(hAPP(hAPP(c_member(_1479555), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1479555), _1479557)), c_Nat_Osemiring__1__class_ONats(_1479555))))], (36655 ^ _782435) ^ [_1479682, _1479684, _1479686, _1479688, _1479690] : [hBOOL(hAPP(hAPP(c_member(_1479682), _1479684), hAPP(c_Relation_OImage(_1479686, _1479682, _1479688), hAPP(hAPP(c_Set_Oinsert(_1479686), _1479690), c_Orderings_Obot__class_Obot(tc_fun(_1479686, tc_HOL_Obool)))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1479686, _1479682)), hAPP(hAPP(c_Product__Type_OPair(_1479686, _1479682), _1479690), _1479684)), _1479688)))], (36661 ^ _782435) ^ [_1479853, _1479855, _1479857, _1479859, _1479861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1479857, _1479853)), hAPP(hAPP(c_Product__Type_OPair(_1479857, _1479853), _1479861), _1479855)), _1479859)), -(hBOOL(hAPP(hAPP(c_member(_1479853), _1479855), hAPP(c_Relation_OImage(_1479857, _1479853, _1479859), hAPP(hAPP(c_Set_Oinsert(_1479857), _1479861), c_Orderings_Obot__class_Obot(tc_fun(_1479857, tc_HOL_Obool)))))))], (36667 ^ _782435) ^ [_1480026, _1480028] : [-(_1480026 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480028, _1480026), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1480028), _1480026)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1480028, _1480026)))))], (36673 ^ _782435) ^ [_1480083, _1480085, _1480087, _1480089] : [-(hAPP(c_Relation_OImage(_1480083, _1480085, _1480087), hAPP(hAPP(c_Set_Oinsert(_1480083), _1480089), c_Orderings_Obot__class_Obot(tc_fun(_1480083, tc_HOL_Obool)))) = hAPP(c_Set_OCollect(_1480085), hAPP(hAPP(c_COMBC(_1480085, tc_fun(tc_prod(_1480083, _1480085), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1480083, _1480085), tc_fun(tc_fun(tc_prod(_1480083, _1480085), tc_HOL_Obool), tc_HOL_Obool), _1480085), c_member(tc_prod(_1480083, _1480085))), hAPP(c_Product__Type_OPair(_1480083, _1480085), _1480089))), _1480087)))], (36675 ^ _782435) ^ [_1480186, _1480188, _1480190, _1480192, _1480194, _1480196, _1480198] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480186, _1480188), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480190), _1480192))), hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480194, _1480188), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480196), _1480198))), -(_1480188 = 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), _1480186), _1480194), _1480188), 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), _1480190), _1480196)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480192), _1480198)), _1480188))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1480192), _1480198), _1480188)))))], (36689 ^ _782435) ^ [_1480496, _1480498, _1480500, _1480502] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480496, _1480498), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480500), _1480502))), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480496), _1480498), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1480502), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480500)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1480500)), c_Groups_Oone__class_Oone(tc_Int_Oint)))), hAPP(hAPP(hAPP(c_If(tc_Int_Oint), hAPP(hAPP(c_fequal, _1480502), 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), _1480498), _1480502))))))], (36695 ^ _782435) ^ [_1480723, _1480725, _1480727, _1480729] : [_1480723 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1480725), _1480727)), _1480729), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1480723, _1480725), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1480727), _1480729)))), 36702 ^ _782435 : [(36703 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480725)))], (36705 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480729), _1480725))]], 36710 ^ _782435 : [(36711 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1480725))], (36713 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1480725), _1480729)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1480729), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]]], (36721 ^ _782435) ^ [_1481185, _1481187, _1481189, _1481191, _1481193] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1481185, _1481187), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1481189), _1481191))), -(_1481187 = 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), _1481193), _1481185), _1481187), 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), _1481193), _1481189)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1481193), _1481191)), _1481187))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), _1481193), _1481191), _1481187)))))], (36731 ^ _782435) ^ [_1481407, _1481409, _1481411, _1481413, _1481415, _1481417, _1481419] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1481407, _1481409)), hAPP(hAPP(c_Product__Type_OPair(_1481407, _1481409), _1481411), _1481413)), _1481415)), -(hBOOL(hAPP(hAPP(c_member(_1481417), hAPP(hAPP(_1481419, _1481411), _1481413)), hAPP(c_Set_Oimage(tc_prod(_1481407, _1481409), _1481417, hAPP(c_Product__Type_Oprod_Oprod__case(_1481407, _1481409, _1481417), _1481419)), _1481415))))], (36737 ^ _782435) ^ [_1481601, _1481603] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481601), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1481603, _1481601) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481603), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1481601)))], (36743 ^ _782435) ^ [_1481707, _1481709] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1481707), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 36746 ^ _782435 : [(36747 ^ _782435) ^ [] : [36748 ^ _782435 : [(36749 ^ _782435) ^ [] : [_1481709 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (36751 ^ _782435) ^ [] : [_1481707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1481709, _1481707) = 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 ^ _782435) ^ [] : [-(c_Nitpick_Onorm__frac(_1481709, _1481707) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1481709), _1481707)), 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), _1481709))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1481707)))), -(_1481709 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1481707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]], (36765 ^ _782435) ^ [_1482005, _1482007, _1482009] : [-(hAPP(c_Divides_Oadjust(_1482005), hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1482007), _1482009)) = 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), _1482009), _1482005)), 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)))), _1482007)), 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)))), _1482007)), _1482009))))], (36767 ^ _782435) ^ [_1482085, _1482087, _1482089, _1482091, _1482093, _1482095] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482085, tc_fun(_1482087, tc_HOL_Obool))), _1482089), _1482091), _1482093), _1482095)), -(hBOOL(hAPP(hAPP(_1482089, _1482093), _1482095))), -(hBOOL(hAPP(hAPP(_1482091, _1482093), _1482095)))], (36777 ^ _782435) ^ [_1482243, _1482245, _1482247, _1482249, _1482251, _1482253] : [36778 ^ _782435 : [(36779 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1482243, _1482245), _1482247))], (36781 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1482249, _1482245), _1482247))]], -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1482251, tc_fun(_1482253, tc_HOL_Obool))), _1482249), _1482243), _1482245), _1482247)))], (36785 ^ _782435) ^ [_1482426, _1482428, _1482430, _1482432, _1482434, _1482436] : [hBOOL(hAPP(hAPP(_1482426, _1482428), _1482430)), hBOOL(hAPP(hAPP(_1482432, _1482428), _1482430)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482434, tc_fun(_1482436, tc_HOL_Obool))), _1482426), _1482432), _1482428), _1482430)))], (36795 ^ _782435) ^ [_1482629, _1482631, _1482633, _1482635, _1482637, _1482639] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1482629, tc_fun(_1482631, tc_HOL_Obool))), _1482633), _1482635), _1482637), _1482639)), 36798 ^ _782435 : [(36799 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1482633, _1482637), _1482639)))], (36801 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1482635, _1482637), _1482639)))]]], (36803 ^ _782435) ^ [_1482802, _1482804, _1482806, _1482808, _1482810, _1482812, _1482814] : [hBOOL(hAPP(hAPP(c_member(_1482802), _1482804), hAPP(hAPP(_1482806, _1482808), _1482810))), -(hBOOL(hAPP(hAPP(c_member(_1482802), _1482804), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1482812, _1482814, tc_fun(_1482802, tc_HOL_Obool)), _1482806), hAPP(hAPP(c_Product__Type_OPair(_1482812, _1482814), _1482808), _1482810)))))], (36809 ^ _782435) ^ [_1482973, _1482975, _1482977, _1482979, _1482981] : [hBOOL(hAPP(hAPP(_1482973, _1482975), _1482977)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1482979, _1482981, tc_HOL_Obool), _1482973), hAPP(hAPP(c_Product__Type_OPair(_1482979, _1482981), _1482975), _1482977))))], (36815 ^ _782435) ^ [_1483102, _1483104, _1483106, _1483108, _1483110] : [hBOOL(hAPP(hAPP(_1483102, _1483104), _1483106)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483108, _1483110, tc_HOL_Obool), _1483102), hAPP(hAPP(c_Product__Type_OPair(_1483108, _1483110), _1483104), _1483106))))], (36821 ^ _782435) ^ [_1483249, _1483251, _1483253, _1483255] : [hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(_1483249, tc_fun(_1483251, tc_HOL_Obool))), _1483253), _1483255))], (36823 ^ _782435) ^ [_1483291, _1483293, _1483295] : [-(c_Fun_Oinj__on(tc_prod(_1483291, _1483293), tc_prod(_1483293, _1483291), hAPP(c_Product__Type_Oprod_Oprod__case(_1483291, _1483293, tc_prod(_1483293, _1483291)), hAPP(c_COMBC(_1483293, _1483291, tc_prod(_1483293, _1483291)), c_Product__Type_OPair(_1483293, _1483291))), _1483295))], (36825 ^ _782435) ^ [_1483349, _1483351, _1483353, _1483355, _1483357, _1483359, _1483361] : [hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1483349, _1483351, tc_fun(_1483353, tc_HOL_Obool)), _1483355), hAPP(hAPP(c_Product__Type_OPair(_1483349, _1483351), _1483357), _1483359)), _1483361)), -(hBOOL(hAPP(hAPP(hAPP(_1483355, _1483357), _1483359), _1483361)))], (36831 ^ _782435) ^ [_1483500, _1483502, _1483504, _1483506, _1483508, _1483510] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483500, tc_fun(_1483502, tc_HOL_Obool))), _1483504), _1483506), _1483508), _1483510)), -(hBOOL(hAPP(hAPP(_1483504, _1483508), _1483510)))], (36837 ^ _782435) ^ [_1483633, _1483635, _1483637, _1483639, _1483641, _1483643] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1483633, tc_fun(_1483635, tc_HOL_Obool))), _1483637), _1483639), _1483641), _1483643)), -(hBOOL(hAPP(hAPP(_1483639, _1483641), _1483643)))], (36843 ^ _782435) ^ [_1483766, _1483768, _1483770, _1483772, _1483774, _1483776] : [hBOOL(hAPP(hAPP(_1483766, _1483768), _1483770)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483772, tc_fun(_1483774, tc_HOL_Obool))), _1483766), _1483776), _1483768), _1483770)))], (36849 ^ _782435) ^ [_1483899, _1483901, _1483903, _1483905, _1483907, _1483909] : [hBOOL(hAPP(hAPP(_1483899, _1483901), _1483903)), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1483905, tc_fun(_1483907, tc_HOL_Obool))), _1483909), _1483899), _1483901), _1483903)))], (36855 ^ _782435) ^ [_1484032, _1484034, _1484036, _1484038, _1484040, _1484042] : [hBOOL(hAPP(hAPP(_1484032, _1484034), _1484036)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484038, tc_fun(_1484040, tc_HOL_Obool))), _1484032), _1484042)), -(hBOOL(hAPP(hAPP(_1484042, _1484034), _1484036)))], (36865 ^ _782435) ^ [_1484223, _1484225, _1484227, _1484229, _1484231, _1484233] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1484223, tc_fun(_1484225, tc_HOL_Obool))), _1484227), _1484229)), hBOOL(hAPP(hAPP(_1484227, _1484231), _1484233)), -(hBOOL(hAPP(hAPP(_1484229, _1484231), _1484233)))], (36875 ^ _782435) ^ [_1484414, _1484416, _1484418, _1484420, _1484422, _1484424] : [hAPP(hAPP(c_Product__Type_OPair(_1484414, _1484416), _1484418), _1484420) = hAPP(hAPP(c_Product__Type_OPair(_1484414, _1484416), _1484422), _1484424), 36878 ^ _782435 : [(36879 ^ _782435) ^ [] : [-(_1484418 = _1484422)], (36881 ^ _782435) ^ [] : [-(_1484420 = _1484424)]]], (36883 ^ _782435) ^ [_1484592, _1484594, _1484596, _1484598, _1484600, _1484602] : [hAPP(hAPP(c_Product__Type_OPair(_1484592, _1484594), _1484596), _1484598) = hAPP(hAPP(c_Product__Type_OPair(_1484592, _1484594), _1484600), _1484602), 36886 ^ _782435 : [(36887 ^ _782435) ^ [] : [-(_1484596 = _1484600)], (36889 ^ _782435) ^ [] : [-(_1484598 = _1484602)]]], (36891 ^ _782435) ^ [_1484735, _1484737, _1484739, _1484741, _1484743, _1484745] : [-(hAPP(hAPP(c_Product__Type_OPair(_1484735, _1484737), _1484739), _1484741) = hAPP(hAPP(c_Product__Type_OPair(_1484735, _1484737), _1484743), _1484745)), _1484739 = _1484743, _1484741 = _1484745], (36901 ^ _782435) ^ [_1484936, _1484938, _1484940] : [hBOOL(hAPP(_1484936, 36902 ^ [_1484936, _1484938, _1484940])), 36905 ^ _782435 : [(36906 ^ _782435) ^ [_1485047, _1485049] : [-(hBOOL(hAPP(_1484936, hAPP(hAPP(c_Product__Type_OPair(_1484938, _1484940), _1485049), _1485047))))]]], (36908 ^ _782435) ^ [_1485083, _1485085, _1485087] : [hBOOL(hAPP(_1485083, hAPP(hAPP(c_Product__Type_OPair(_1485085, _1485087), 36909 ^ [_1485083, _1485085, _1485087]), 36910 ^ [_1485083, _1485085, _1485087]))), 36913 ^ _782435 : [(36914 ^ _782435) ^ [_1485230] : [-(hBOOL(hAPP(_1485083, _1485230)))]]], (36916 ^ _782435) ^ [_1485261, _1485263, _1485265, _1485267, _1485269, _1485271] : [_1485261 = _1485263, -(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485265, _1485267, _1485269), _1485271), _1485261) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485265, _1485267, _1485269), _1485271), _1485263))], (36922 ^ _782435) ^ [_1485386, _1485388, _1485390, _1485392, _1485394, _1485396, _1485398, _1485400] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485386, _1485388, _1485390), _1485392), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485394, _1485396, tc_prod(_1485386, _1485388)), _1485398), _1485400)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485394, _1485396, _1485390), hAPP(hAPP(c_COMBB(tc_fun(_1485396, tc_prod(_1485386, _1485388)), tc_fun(_1485396, _1485390), _1485394), hAPP(c_COMBB(tc_prod(_1485386, _1485388), _1485390, _1485396), hAPP(c_Product__Type_Oprod_Oprod__case(_1485386, _1485388, _1485390), _1485392))), _1485398)), _1485400))], (36924 ^ _782435) ^ [_1485492, _1485494, _1485496, _1485498, _1485500, _1485502] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485492, _1485494, _1485496), _1485498), hAPP(hAPP(c_Product__Type_OPair(_1485492, _1485494), _1485500), _1485502)) = hAPP(hAPP(_1485498, _1485500), _1485502))], (36926 ^ _782435) ^ [_1485550, _1485552, _1485554, _1485556, _1485558, _1485560] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485550, _1485552, _1485554), _1485556), hAPP(hAPP(c_Product__Type_OPair(_1485550, _1485552), _1485558), _1485560)) = hAPP(hAPP(_1485556, _1485558), _1485560))], (36928 ^ _782435) ^ [_1485608, _1485610, _1485612, _1485614, _1485616] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1485608, _1485610, tc_HOL_Obool), _1485612), hAPP(hAPP(c_Product__Type_OPair(_1485608, _1485610), _1485614), _1485616))), -(hBOOL(hAPP(hAPP(_1485612, _1485614), _1485616)))], (36934 ^ _782435) ^ [_1485737, _1485739, _1485741, _1485743] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1485737, _1485739, _1485741), hAPP(hAPP(c_COMBB(tc_fun(_1485739, tc_prod(_1485737, _1485739)), tc_fun(_1485739, _1485741), _1485737), hAPP(c_COMBB(tc_prod(_1485737, _1485739), _1485741, _1485739), _1485743)), c_Product__Type_OPair(_1485737, _1485739))) = _1485743)], (36936 ^ _782435) ^ [_1485805, _1485807, _1485809, _1485811] : [-(c_HOL_OThe(tc_prod(_1485805, _1485807), hAPP(c_Product__Type_Oprod_Oprod__case(_1485805, _1485807, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1485805, tc_fun(_1485807, tc_HOL_Obool), tc_fun(_1485807, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1485807, tc_HOL_Obool), tc_fun(_1485807, tc_HOL_Obool)), _1485805), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1485807)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1485805), c_fconj), hAPP(c_fequal, _1485809)))), hAPP(c_fequal, _1485811)))) = hAPP(hAPP(c_Product__Type_OPair(_1485805, _1485807), _1485809), _1485811))], (36938 ^ _782435) ^ [_1485911, _1485913, _1485915] : [-(c_HOL_OThe(tc_prod(_1485911, _1485913), _1485915) = c_HOL_OThe(tc_prod(_1485911, _1485913), hAPP(c_Product__Type_Oprod_Oprod__case(_1485911, _1485913, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1485913, tc_prod(_1485911, _1485913)), tc_fun(_1485913, tc_HOL_Obool), _1485911), hAPP(c_COMBB(tc_prod(_1485911, _1485913), tc_HOL_Obool, _1485913), _1485915)), c_Product__Type_OPair(_1485911, _1485913)))))], (36940 ^ _782435) ^ [_1485989] : [-(c_Divides_Oadjust(_1485989) = 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)), _1485989))))), 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)), _1485989))))), 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 ^ _782435) ^ [_1486074, _1486076, _1486078, _1486080, _1486082] : [hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1486074, _1486076, _1486078), _1486080), _1486082)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1486074, _1486076)), hAPP(hAPP(c_Product__Type_OPair(_1486074, _1486076), _1486080), _1486082)), _1486078)))], (36948 ^ _782435) ^ [_1486209, _1486211, _1486213, _1486215, _1486217] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1486209, _1486211)), hAPP(hAPP(c_Product__Type_OPair(_1486209, _1486211), _1486215), _1486217)), _1486213)), -(hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(_1486209, _1486211, _1486213), _1486215), _1486217)))], (36954 ^ _782435) ^ [_1486350, _1486352] : [-(c_Code__Numeral_Odiv__mod__code__numeral(_1486350, _1486352) = 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), _1486350), _1486352)), c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1486350, _1486352)))], (36956 ^ _782435) ^ [_1486394] : [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), _1486394))), 36959 ^ _782435 : [(36960 ^ _782435) ^ [] : [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), _1486394)))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486394)) = 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), _1486394))))], (36966 ^ _782435) ^ [] : [-(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), _1486394))))), -(c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486394)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1486394)), 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), _1486394)))))]]], (36972 ^ _782435) ^ [_1486684, _1486686] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1486684), 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)), _1486686)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1486684, _1486686), c_Divides_OnegDivAlg(_1486684, _1486686))))], (36982 ^ _782435) ^ [_1486843, _1486845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1486843), 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)), _1486845)), -(c_Divides_OnegDivAlg(_1486843, _1486845) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1486843), _1486845)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1486843, _1486845)))], (36992 ^ _782435) ^ [_1487024] : [-(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), c_Int_OMin), _1487024) = 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), _1487024), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (36994 ^ _782435) ^ [_1487068, _1487070] : [36995 ^ _782435 : [(36996 ^ _782435) ^ [] : [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), _1487068), _1487070)))], (36998 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1487070), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1487068, _1487070) = 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), _1487068), _1487070)))], (37002 ^ _782435) ^ [_1487227, _1487229] : [-(c_Divides_OnegDivAlg(_1487227, _1487229) = hAPP(c_Divides_Oadjust(_1487229), c_Divides_OnegDivAlg(_1487227, 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)))), _1487229)))), -(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), _1487227), _1487229)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1487229), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37012 ^ _782435) ^ [_1487299, _1487301] : [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), _1487299))), 37015 ^ _782435 : [(37016 ^ _782435) ^ [] : [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), _1487301)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487299)))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487301), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487299)) = 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), _1487301)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487299))))], (37022 ^ _782435) ^ [] : [-(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), _1487301)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487299))))), -(c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487301), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487299)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487299)), c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1487301), 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), _1487299)))))]]], (37028 ^ _782435) ^ [_1487647, _1487649] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1487647)), 37031 ^ _782435 : [(37032 ^ _782435) ^ [] : [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), _1487649), _1487647))), -(c_Divides_OnegDivAlg(_1487649, _1487647) = 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), _1487649), _1487647)))], (37038 ^ _782435) ^ [] : [-(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), _1487649), _1487647)))), -(c_Divides_OnegDivAlg(_1487649, _1487647) = hAPP(c_Divides_Oadjust(_1487647), c_Divides_OnegDivAlg(_1487649, 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)))), _1487647))))]]], (37044 ^ _782435) ^ [_1487926, _1487928] : [c_Nitpick_Orefl_H(_1487926, _1487928), 37047 ^ _782435 : [(37048 ^ _782435) ^ [_1488004] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1487926, _1487926)), hAPP(hAPP(c_Product__Type_OPair(_1487926, _1487926), _1488004), _1488004)), _1487928)))]]], (37050 ^ _782435) ^ [_1488046, _1488048] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1488046, _1488046)), hAPP(hAPP(c_Product__Type_OPair(_1488046, _1488046), 37051 ^ [_1488046, _1488048]), 37051 ^ [_1488046, _1488048])), _1488048)), -(c_Nitpick_Orefl_H(_1488046, _1488048))], (37057 ^ _782435) ^ [_1488213] : [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), _1488213))), 37060 ^ _782435 : [(37061 ^ _782435) ^ [] : [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), _1488213))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488213)) = 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 ^ _782435) ^ [] : [-(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), _1488213)))), -(c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488213)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1488213)), 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), _1488213)))))]]], (37073 ^ _782435) ^ [_1488482, _1488484] : [37074 ^ _782435 : [(37075 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488482), _1488484))], (37077 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1488484), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1488482, _1488484) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488482))], (37081 ^ _782435) ^ [_1488623, _1488625] : [-(c_Divides_OposDivAlg(_1488623, _1488625) = hAPP(c_Divides_Oadjust(_1488625), c_Divides_OposDivAlg(_1488623, 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)))), _1488625)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1488623), _1488625))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1488625), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (37091 ^ _782435) ^ [_1488692] : [-(c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint), _1488692) = 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 ^ _782435) ^ [_1488718, _1488720] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488718)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488720)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1488718, _1488720), c_Divides_OposDivAlg(_1488718, _1488720))))], (37103 ^ _782435) ^ [_1488871, _1488873] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488871)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1488873)), -(c_Divides_OposDivAlg(_1488871, _1488873) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1488871), _1488873)), c_Divides_Odiv__class_Omod(tc_Int_Oint, _1488871, _1488873)))], (37113 ^ _782435) ^ [_1489046, _1489048] : [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), _1489046))), 37116 ^ _782435 : [(37117 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489048)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489046))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489048), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489046)) = 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), _1489048)))], (37123 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489048)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489046)))), -(c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489048), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489046)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489046)), c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1489048), 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), _1489046)))))]]], (37129 ^ _782435) ^ [_1489364, _1489366] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489364)), 37132 ^ _782435 : [(37133 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489366), _1489364)), -(c_Divides_OposDivAlg(_1489366, _1489364) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489366))], (37139 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1489366), _1489364))), -(c_Divides_OposDivAlg(_1489366, _1489364) = hAPP(c_Divides_Oadjust(_1489364), c_Divides_OposDivAlg(_1489366, 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)))), _1489364))))]]], (37171 ^ _782435) ^ [_1489983, _1489985] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489983))), 37174 ^ _782435 : [(37175 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489985)), -(c_Divides_Odivmod__int(_1489983, _1489985) = c_Divides_OnegDivAlg(_1489983, _1489985))], (37181 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489985))), -(c_Divides_Odivmod__int(_1489983, _1489985) = hAPP(c_Divides_OnegateSnd, c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489983), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489985))))]]], (37145 ^ _782435) ^ [_1489613, _1489615] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489613)), 37148 ^ _782435 : [(37149 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489615)), -(c_Divides_Odivmod__int(_1489613, _1489615) = c_Divides_OposDivAlg(_1489613, _1489615))], (37155 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1489615))), 37158 ^ _782435 : [(37159 ^ _782435) ^ [] : [_1489613 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1489613, _1489615) = 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 ^ _782435) ^ [] : [-(_1489613 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1489613, _1489615) = hAPP(c_Divides_OnegateSnd, c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489613), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1489615))))]]]]], (37187 ^ _782435) ^ [_1490211, _1490213] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1490211)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1490211), _1490213)), -(c_Divides_Odivmod__nat(_1490213, _1490211) = 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), _1490213), _1490211)), _1490211))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1490213), _1490211), _1490211)))], (37197 ^ _782435) ^ [_1490431, _1490433] : [_1490431 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1490431, _1490433) = 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 ^ _782435) ^ [_1490509, _1490511] : [-(_1490509 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37206 ^ _782435 : [(37207 ^ _782435) ^ [] : [_1490511 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1490509, _1490511) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490509))], (37213 ^ _782435) ^ [] : [-(_1490511 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1490509, _1490511) = 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, _1490511))), 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)), _1490511)), hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1490509))), hAPP(hAPP(c_fconj, hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490511), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1490509), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))), c_Divides_Opdivmod(_1490509, _1490511)), 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), _1490511))))), c_Divides_Opdivmod(_1490509, _1490511)))))]]], (37219 ^ _782435) ^ [_1490869, _1490871, _1490873, _1490875, _1490877, _1490879, _1490881] : [-(hAPP(c_Product__Type_Oapsnd(_1490869, _1490871, _1490873, _1490875), hAPP(c_Product__Type_Oapsnd(_1490877, _1490869, _1490873, _1490879), _1490881)) = hAPP(c_Product__Type_Oapsnd(_1490877, _1490871, _1490873, hAPP(c_Fun_Ocomp(_1490869, _1490871, _1490877, _1490875), _1490879)), _1490881))], (37221 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1490954, _1490956, _1490958, _1490960, _1490962, _1490964] : [-(hAPP(c_Product__Type_Oapsnd(_1490954, _1490956, _1490958, _1490960), hAPP(hAPP(c_Product__Type_OPair(_1490958, _1490954), _1490962), _1490964)) = hAPP(hAPP(c_Product__Type_OPair(_1490958, _1490956), _1490962), hAPP(_1490960, _1490964)))], (37225 ^ _782435) ^ [_1491016] : [-(c_Divides_Odivmod__nat(_1491016, 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)), _1491016))], (37227 ^ _782435) ^ [_1491045, _1491047] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491045), _1491047)), -(c_Divides_Odivmod__nat(_1491045, _1491047) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491045))], (37233 ^ _782435) ^ [_1491144, _1491146] : [-(hAPP(c_Divides_OnegateSnd, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1491144), _1491146)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1491144), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491146)))], (37235 ^ _782435) ^ [_1491187, _1491189] : [-(c_Divides_Odivmod__nat(_1491187, _1491189) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1491187), _1491189)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1491187, _1491189)))], (37237 ^ _782435) ^ [_1491231, _1491233, _1491235] : [hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491231), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1491233)), _1491235)), -(hBOOL(hAPP(c_Divides_Odivmod__int__rel(_1491231, _1491233), hAPP(c_Divides_OnegateSnd, _1491235))))], (37243 ^ _782435) ^ [_1491357, _1491359] : [37244 ^ _782435 : [(37245 ^ _782435) ^ [] : [_1491357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37247 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491359), _1491357))]], -(c_Divides_Odivmod__nat(_1491359, _1491357) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1491359))], (37251 ^ _782435) ^ [_1491488, _1491490] : [-(c_Divides_Odivmod__nat(_1491490, _1491488) = 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), _1491490), _1491488), _1491488))), -(_1491488 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1491490), _1491488)))], (37261 ^ _782435) ^ [_1491553, _1491555] : [-(c_Divides_Opdivmod(_1491553, _1491555) = 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), _1491553)), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491555))), c_Divides_Odiv__class_Omod(tc_Int_Oint, hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491553), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491555))))], (37263 ^ _782435) ^ [_1491618, _1491620] : [_1491618 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Opdivmod(_1491620, _1491618) = 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), _1491620)))], (37269 ^ _782435) ^ [_1491707, _1491709] : [-(_1491707 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Opdivmod(_1491709, _1491707) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491709), hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint), _1491707)))], (37275 ^ _782435) ^ [_1491766, _1491768] : [_1491766 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1491766, _1491768) = 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 ^ _782435) ^ [_1491844, _1491846] : [-(_1491844 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 37284 ^ _782435 : [(37285 ^ _782435) ^ [] : [_1491846 = c_Groups_Ozero__class_Ozero(tc_Int_Oint), -(c_Divides_Odivmod__int(_1491844, _1491846) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1491844))], (37291 ^ _782435) ^ [] : [-(_1491846 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(c_Divides_Odivmod__int(_1491844, _1491846) = 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, _1491846))), 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, _1491844)), c_Groups_Osgn__class_Osgn(tc_Int_Oint, _1491846))), c_Divides_Opdivmod(_1491844, _1491846)), 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), _1491846))))), c_Divides_Opdivmod(_1491844, _1491846)))))]]], (37297 ^ _782435) ^ [_1492156, _1492158, _1492160, _1492162, _1492164] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492156, _1492158), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492160), _1492162))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492158)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492164), _1492156), _1492158), 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), _1492164), _1492160)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492164), _1492162)), _1492158))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492164), _1492162), _1492158)))))], (37307 ^ _782435) ^ [_1492425, _1492427, _1492429, _1492431, _1492433] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492425, _1492427), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1492429), _1492431))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492427)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1492433)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1492425, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492427), _1492433)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1492429), _1492433)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1492427), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1492429, _1492433))), _1492431)))))], (37321 ^ _782435) ^ [_1492732, _1492734] : [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), _1492732), _1492734))), 37324 ^ _782435 : [(37325 ^ _782435) ^ [] : [37326 ^ _782435 : [(37327 ^ _782435) ^ [] : [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), _1492732), _1492734)))], (37329 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1492734), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OnegDivAlg(_1492732, _1492734) = 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), _1492732), _1492734)))], (37333 ^ _782435) ^ [] : [-(c_Divides_OnegDivAlg(_1492732, _1492734) = hAPP(c_Divides_Oadjust(_1492734), c_Divides_OnegDivAlg(_1492732, 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)))), _1492734)))), -(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), _1492732), _1492734)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1492734), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37343 ^ _782435) ^ [_1493079, _1493081, _1493083, _1493085] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493079, _1493081), _1493083)), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493079, _1493081), _1493085)), -(_1493083 = _1493085)], (37353 ^ _782435) ^ [_1493236, _1493238] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493236, _1493238), c_Divides_Odivmod__nat(_1493236, _1493238))))], (37355 ^ _782435) ^ [_1493269, _1493271, _1493273] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493269, _1493271), _1493273)), -(c_Divides_Odivmod__nat(_1493269, _1493271) = _1493273)], (37361 ^ _782435) ^ [_1493364, _1493366] : [-(c_Divides_Odivmod__nat(_1493364, _1493366) = c_HOL_OThe(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat__rel(_1493364, _1493366)))], (37363 ^ _782435) ^ [_1493398, _1493400, _1493402, _1493404] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493398, _1493400), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493402), _1493404))), -(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1493398, _1493400) = _1493404)], (37369 ^ _782435) ^ [_1493509, _1493511, _1493513, _1493515] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493509, _1493511), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493513), _1493515))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1493509), _1493511) = _1493513)], (37375 ^ _782435) ^ [_1493624, _1493626] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493624, _1493626), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1493624), _1493626)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1493624, _1493626)))))], (37377 ^ _782435) ^ [_1493670, _1493672, _1493674, _1493676, _1493678, _1493680, _1493682] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493670, _1493672), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493674), _1493676))), hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1493678, _1493672), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1493680), _1493682))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1493672)), -(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493670), _1493678), _1493672), 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), _1493674), _1493680)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493676), _1493682)), _1493672))), c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1493676), _1493682), _1493672)))))], (37391 ^ _782435) ^ [_1494031, _1494033] : [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), _1494031), _1494033))), 37394 ^ _782435 : [(37395 ^ _782435) ^ [] : [37396 ^ _782435 : [(37397 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494031), _1494033))], (37399 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494033), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))]], -(c_Divides_OposDivAlg(_1494031, _1494033) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1494031))], (37403 ^ _782435) ^ [] : [-(c_Divides_OposDivAlg(_1494031, _1494033) = hAPP(c_Divides_Oadjust(_1494033), c_Divides_OposDivAlg(_1494031, 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)))), _1494033)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494031), _1494033))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1494033), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37413 ^ _782435) ^ [_1494354, _1494356] : [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), _1494354), _1494356))), 37416 ^ _782435 : [(37417 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494356), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Onorm__frac(_1494354, _1494356) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494354), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1494356)))], (37423 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1494356), c_Groups_Ozero__class_Ozero(tc_Int_Oint)))), 37426 ^ _782435 : [(37427 ^ _782435) ^ [] : [37428 ^ _782435 : [(37429 ^ _782435) ^ [] : [_1494354 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)], (37431 ^ _782435) ^ [] : [_1494356 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)]], -(c_Nitpick_Onorm__frac(_1494354, _1494356) = 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 ^ _782435) ^ [] : [-(c_Nitpick_Onorm__frac(_1494354, _1494356) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, tc_prod(tc_Int_Oint, tc_Int_Oint)), hAPP(hAPP(c_Nitpick_Oint__gcd, _1494354), _1494356)), 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), _1494354))), hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1494356)))), -(_1494354 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)), -(_1494356 = c_Groups_Ozero__class_Ozero(tc_Int_Oint))]]]]], (37445 ^ _782435) ^ [_1494846, _1494848, _1494850] : [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), _1494846), _1494848))), -(hBOOL(hAPP(hAPP(_1494850, _1494846), _1494848))), 37452 ^ _782435 : [(37453 ^ _782435) ^ [] : [-(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 ^ [_1494846, _1494848, _1494850]), 37451 ^ [_1494846, _1494848, _1494850]))))], (37465 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1494850, 37450 ^ [_1494846, _1494848, _1494850]), 37451 ^ [_1494846, _1494848, _1494850]))], (37455 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1494850, 37450 ^ [_1494846, _1494848, _1494850]), 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 ^ [_1494846, _1494848, _1494850])))), -(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 ^ [_1494846, _1494848, _1494850]), 37451 ^ [_1494846, _1494848, _1494850])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37451 ^ [_1494846, _1494848, _1494850]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37469 ^ _782435) ^ [_1495341, _1495343, _1495345] : [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), _1495341), _1495343))), -(hBOOL(hAPP(hAPP(_1495345, _1495341), _1495343))), 37476 ^ _782435 : [(37477 ^ _782435) ^ [] : [-(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 ^ [_1495341, _1495343, _1495345]), 37475 ^ [_1495341, _1495343, _1495345]))))], (37489 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1495345, 37474 ^ [_1495341, _1495343, _1495345]), 37475 ^ [_1495341, _1495343, _1495345]))], (37479 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1495345, 37474 ^ [_1495341, _1495343, _1495345]), 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 ^ [_1495341, _1495343, _1495345])))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37474 ^ [_1495341, _1495343, _1495345]), 37475 ^ [_1495341, _1495343, _1495345]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 37475 ^ [_1495341, _1495343, _1495345]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))]]], (37493 ^ _782435) ^ [_1495827, _1495829, _1495831] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495827, tc_fun(_1495827, tc_HOL_Obool))), _1495829), _1495831)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1495827, tc_HOL_Obool)), c_Wellfounded_Oaccp(_1495827, _1495831)), c_Wellfounded_Oaccp(_1495827, _1495829))))], (37499 ^ _782435) ^ [_1495964] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1495964)), 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), _1495964)) = 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), _1495964))))))], (37505 ^ _782435) ^ [_1496099, _1496101, _1496103, _1496105, _1496107] : [hAPP(c_Product__Type_Osnd(_1496099, _1496101), hAPP(hAPP(c_Product__Type_OPair(_1496099, _1496101), _1496103), _1496105)) = _1496107, -(_1496105 = _1496107)], (37511 ^ _782435) ^ [_1496212, _1496214, _1496216, _1496218] : [-(hAPP(c_Product__Type_Osnd(_1496212, _1496214), hAPP(hAPP(c_Product__Type_OPair(_1496212, _1496214), _1496216), _1496218)) = _1496218)], (37513 ^ _782435) ^ [_1496256, _1496258, _1496260] : [-(hAPP(c_Product__Type_Osnd(_1496256, _1496258), _1496260) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1496256, _1496258, _1496258), hAPP(c_COMBK(tc_fun(_1496258, _1496258), _1496256), c_COMBI(_1496258))), _1496260))], (37515 ^ _782435) ^ [_1496310, _1496312, _1496314, _1496316, _1496318] : [-(hAPP(c_Product__Type_Osnd(_1496310, _1496312), hAPP(c_Product__Type_Oapsnd(_1496314, _1496312, _1496310, _1496316), _1496318)) = hAPP(_1496316, hAPP(c_Product__Type_Osnd(_1496310, _1496314), _1496318)))], (37517 ^ _782435) ^ [_1496391, _1496393, _1496395, _1496397, _1496399, _1496401] : [hAPP(c_Product__Type_Oapsnd(_1496391, _1496393, _1496395, _1496397), _1496399) = hAPP(c_Product__Type_Oapsnd(_1496391, _1496393, _1496395, _1496401), _1496399), -(hAPP(_1496397, hAPP(c_Product__Type_Osnd(_1496395, _1496391), _1496399)) = hAPP(_1496401, hAPP(c_Product__Type_Osnd(_1496395, _1496391), _1496399)))], (37523 ^ _782435) ^ [_1496540, _1496542, _1496544, _1496546, _1496548, _1496550] : [hAPP(_1496546, hAPP(c_Product__Type_Osnd(_1496544, _1496540), _1496548)) = hAPP(_1496550, hAPP(c_Product__Type_Osnd(_1496544, _1496540), _1496548)), -(hAPP(c_Product__Type_Oapsnd(_1496540, _1496542, _1496544, _1496546), _1496548) = hAPP(c_Product__Type_Oapsnd(_1496540, _1496542, _1496544, _1496550), _1496548))], (37529 ^ _782435) ^ [_1496695, _1496697] : [-(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1496695, _1496697) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1496695, _1496697)))], (37531 ^ _782435) ^ [_1496730, _1496732, _1496734, _1496736] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496730, _1496732), _1496734)), hBOOL(hAPP(hAPP(_1496732, _1496736), _1496734)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496730, _1496732), _1496736)))], (37551 ^ _782435) ^ [_1497101, _1497103, _1497105] : [37553 ^ _782435 : [(37554 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1497103, 37552 ^ [_1497101, _1497103, _1497105]), _1497105)))], (37556 ^ _782435) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497101, _1497103), 37552 ^ [_1497101, _1497103, _1497105]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497101, _1497103), _1497105)))], (37541 ^ _782435) ^ [_1496915, _1496917, _1496919] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1496915, _1496917), _1496919)), 37544 ^ _782435 : [(37545 ^ _782435) ^ [_1497000] : [hBOOL(hAPP(hAPP(_1496917, _1497000), _1496919)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1496915, _1496917), _1497000)))]]], (37570 ^ _782435) ^ [_1497491, _1497493, _1497495] : [37572 ^ _782435 : [(37573 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1497493, 37571 ^ [_1497491, _1497493, _1497495]), _1497495)))], (37575 ^ _782435) ^ [] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497491, _1497493), 37571 ^ [_1497491, _1497493, _1497495]))]], -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497491, _1497493), _1497495)))], (37560 ^ _782435) ^ [_1497305, _1497307, _1497309] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1497305, _1497307), _1497309)), 37563 ^ _782435 : [(37564 ^ _782435) ^ [_1497390] : [hBOOL(hAPP(hAPP(_1497307, _1497390), _1497309)), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1497305, _1497307), _1497390)))]]], (37579 ^ _782435) ^ [_1497677, _1497679] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1497677), 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)), _1497679)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1497677, _1497679) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1497677, _1497679)))], (37589 ^ _782435) ^ [_1497840, _1497842] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497840)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1497842)), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1497840, _1497842) = hAPP(c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1497840, _1497842)))], (37599 ^ _782435) ^ [_1497997] : [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), _1497997))), -(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), _1497997)) = 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), _1497997))))], (37605 ^ _782435) ^ [_1498114, _1498116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1498114)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498116), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1498114, _1498116) = 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), _1498114), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498116)))))], (37615 ^ _782435) ^ [_1498295, _1498297] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1498295), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1498297), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Divides_Odiv__class_Omod(tc_Int_Oint, _1498295, _1498297) = 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), _1498295), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1498297)))))], (37625 ^ _782435) ^ [_1498482, _1498484] : [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), _1498482), _1498484))), 37628 ^ _782435 : [(37629 ^ _782435) ^ [] : [_1498484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Nitpick_Onat__gcd(_1498482, _1498484) = _1498482)], (37635 ^ _782435) ^ [] : [-(_1498484 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Nitpick_Onat__gcd(_1498482, _1498484) = c_Nitpick_Onat__gcd(_1498484, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1498482, _1498484)))]]], (37641 ^ _782435) ^ [_1498700] : [-(c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc, _1498700)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Nat_Onat_Onat__size(_1498700)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37643 ^ _782435) ^ [_1498757, _1498759, _1498761, _1498763] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1498757, _1498757)), hAPP(hAPP(c_Product__Type_OPair(_1498757, _1498757), _1498759), _1498761)), hAPP(c_Wellfounded_Omeasure(_1498757), _1498763))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1498763, _1498759)), hAPP(_1498763, _1498761))))], (37649 ^ _782435) ^ [_1498904, _1498906, _1498908, _1498910] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1498910, _1498906)), hAPP(_1498910, _1498908))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1498904, _1498904)), hAPP(hAPP(c_Product__Type_OPair(_1498904, _1498904), _1498906), _1498908)), hAPP(c_Wellfounded_Omeasure(_1498904), _1498910))))], (37655 ^ _782435) ^ [_1499057, _1499059] : [-(c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1499057, _1499059) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1499057, _1499059)))], (37657 ^ _782435) ^ [] : [-(c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37659 ^ _782435) ^ [_1499125, _1499127] : [c_Relation_Oirrefl(_1499125, _1499127), 37662 ^ _782435 : [(37663 ^ _782435) ^ [_1499207] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1499125, _1499125)), hAPP(hAPP(c_Product__Type_OPair(_1499125, _1499125), _1499207), _1499207)), _1499127))]]], (37665 ^ _782435) ^ [_1499247, _1499249] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1499247, _1499247)), hAPP(hAPP(c_Product__Type_OPair(_1499247, _1499247), 37666 ^ [_1499247, _1499249]), 37666 ^ [_1499247, _1499249])), _1499249))), -(c_Relation_Oirrefl(_1499247, _1499249))], (37672 ^ _782435) ^ [_1499318, _1499320, _1499322] : [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), _1499318), _1499320))), -(hBOOL(hAPP(hAPP(_1499322, _1499318), _1499320))), 37679 ^ _782435 : [(37680 ^ _782435) ^ [] : [-(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 ^ [_1499318, _1499320, _1499322]), 37678 ^ [_1499318, _1499320, _1499322]))))], (37688 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1499322, 37677 ^ [_1499318, _1499320, _1499322]), 37678 ^ [_1499318, _1499320, _1499322]))], (37682 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 37678 ^ [_1499318, _1499320, _1499322]), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hBOOL(hAPP(hAPP(_1499322, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37677 ^ [_1499318, _1499320, _1499322])), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), 37678 ^ [_1499318, _1499320, _1499322]))))]]], (37692 ^ _782435) ^ [_1499791] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1499791)), 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), _1499791)) = 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), _1499791))))))], (37698 ^ _782435) ^ [_1499945, _1499947, _1499949, _1499951] : [_1499945 = _1499947, 37701 ^ _782435 : [(37702 ^ _782435) ^ [] : [-(hAPP(c_Product__Type_Ofst(_1499949, _1499951), _1499945) = hAPP(c_Product__Type_Ofst(_1499949, _1499951), _1499947))], (37704 ^ _782435) ^ [] : [-(hAPP(c_Product__Type_Osnd(_1499949, _1499951), _1499945) = hAPP(c_Product__Type_Osnd(_1499949, _1499951), _1499947))]]], (37706 ^ _782435) ^ [_1500096, _1500098, _1500100, _1500102] : [-(_1500096 = _1500098), hAPP(c_Product__Type_Ofst(_1500100, _1500102), _1500096) = hAPP(c_Product__Type_Ofst(_1500100, _1500102), _1500098), hAPP(c_Product__Type_Osnd(_1500100, _1500102), _1500096) = hAPP(c_Product__Type_Osnd(_1500100, _1500102), _1500098)], (37716 ^ _782435) ^ [_1500283, _1500285, _1500287, _1500289] : [hAPP(c_Product__Type_Ofst(_1500283, _1500285), _1500287) = hAPP(c_Product__Type_Ofst(_1500283, _1500285), _1500289), hAPP(c_Product__Type_Osnd(_1500283, _1500285), _1500287) = hAPP(c_Product__Type_Osnd(_1500283, _1500285), _1500289), -(_1500287 = _1500289)], (37726 ^ _782435) ^ [_1500468, _1500470, _1500472, _1500474, _1500476] : [hAPP(c_Product__Type_Ofst(_1500468, _1500470), hAPP(hAPP(c_Product__Type_OPair(_1500468, _1500470), _1500472), _1500474)) = _1500476, -(_1500472 = _1500476)], (37732 ^ _782435) ^ [_1500581, _1500583, _1500585, _1500587] : [-(hAPP(c_Product__Type_Ofst(_1500581, _1500583), hAPP(hAPP(c_Product__Type_OPair(_1500581, _1500583), _1500585), _1500587)) = _1500585)], (37734 ^ _782435) ^ [_1500625, _1500627, _1500629] : [-(hAPP(c_Product__Type_Ofst(_1500625, _1500627), _1500629) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500625, _1500627, _1500625), c_COMBK(_1500625, _1500627)), _1500629))], (37736 ^ _782435) ^ [_1500671, _1500673, _1500675, _1500677, _1500679] : [-(hAPP(c_Product__Type_Ofst(_1500671, _1500673), hAPP(c_Product__Type_Oapsnd(_1500675, _1500673, _1500671, _1500677), _1500679)) = hAPP(c_Product__Type_Ofst(_1500671, _1500675), _1500679))], (37738 ^ _782435) ^ [_1500722, _1500724, _1500726] : [-(hAPP(hAPP(c_Product__Type_OPair(_1500722, _1500724), hAPP(c_Product__Type_Ofst(_1500722, _1500724), _1500726)), hAPP(c_Product__Type_Osnd(_1500722, _1500724), _1500726)) = _1500726)], (37740 ^ _782435) ^ [_1500770, _1500772, _1500774] : [-(_1500770 = hAPP(hAPP(c_Product__Type_OPair(_1500772, _1500774), hAPP(c_Product__Type_Ofst(_1500772, _1500774), _1500770)), hAPP(c_Product__Type_Osnd(_1500772, _1500774), _1500770)))], (37742 ^ _782435) ^ [_1500818, _1500820, _1500822, _1500824, _1500826] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500818, _1500820, _1500822), _1500824), _1500826) = hAPP(hAPP(_1500824, hAPP(c_Product__Type_Ofst(_1500818, _1500820), _1500826)), hAPP(c_Product__Type_Osnd(_1500818, _1500820), _1500826)))], (37744 ^ _782435) ^ [_1500877, _1500879] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1500877), _1500879) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_Odivmod__int(_1500877, _1500879)))], (37746 ^ _782435) ^ [_1500914, _1500916, _1500918, _1500920, _1500922] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1500914, _1500916, _1500918), _1500920), _1500922) = hAPP(hAPP(_1500920, hAPP(c_Product__Type_Ofst(_1500914, _1500916), _1500922)), hAPP(c_Product__Type_Osnd(_1500914, _1500916), _1500922)))], (37748 ^ _782435) ^ [_1500973, _1500975, _1500977, _1500979, _1500981, _1500983] : [-(hAPP(hAPP(c_COMBS(tc_prod(_1500973, _1500975), _1500975, _1500977), hAPP(hAPP(c_COMBB(_1500979, tc_fun(_1500975, _1500977), tc_prod(_1500973, _1500975)), _1500981), hAPP(hAPP(c_COMBB(_1500973, _1500979, tc_prod(_1500973, _1500975)), _1500983), c_Product__Type_Ofst(_1500973, _1500975)))), c_Product__Type_Osnd(_1500973, _1500975)) = hAPP(c_Product__Type_Oprod_Oprod__case(_1500973, _1500975, _1500977), hAPP(hAPP(c_COMBB(_1500979, tc_fun(_1500975, _1500977), _1500973), _1500981), _1500983)))], (37750 ^ _782435) ^ [_1501074, _1501076, _1501078, _1501080, _1501082] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501074, _1501076, _1501078), _1501080), _1501082) = hAPP(hAPP(_1501080, hAPP(c_Product__Type_Ofst(_1501074, _1501076), _1501082)), hAPP(c_Product__Type_Osnd(_1501074, _1501076), _1501082)))], (37752 ^ _782435) ^ [_1501133, _1501135, _1501137, _1501139, _1501141, _1501143, _1501145] : [-(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1501133, _1501135, _1501137), hAPP(c_Fun_Ocomp(_1501139, tc_fun(_1501135, _1501137), _1501133, _1501141), _1501143)), _1501145) = hAPP(hAPP(_1501141, hAPP(_1501143, hAPP(c_Product__Type_Ofst(_1501133, _1501135), _1501145))), hAPP(c_Product__Type_Osnd(_1501133, _1501135), _1501145)))], (37754 ^ _782435) ^ [_1501210, _1501212, _1501214] : [-(c_HOL_OThe(tc_prod(_1501210, _1501212), hAPP(c_Product__Type_Oprod_Oprod__case(_1501210, _1501212, tc_HOL_Obool), _1501214)) = c_HOL_OThe(tc_prod(_1501210, _1501212), hAPP(hAPP(c_COMBS(tc_prod(_1501210, _1501212), _1501212, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1501210, tc_fun(_1501212, tc_HOL_Obool), tc_prod(_1501210, _1501212)), _1501214), c_Product__Type_Ofst(_1501210, _1501212))), c_Product__Type_Osnd(_1501210, _1501212))))], (37756 ^ _782435) ^ [_1501291, _1501293] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501291), 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)), _1501293)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501291), _1501293) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OnegDivAlg(_1501291, _1501293)))], (37766 ^ _782435) ^ [_1501458, _1501460] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501458)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501460)), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501458), _1501460) = hAPP(c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint), c_Divides_OposDivAlg(_1501458, _1501460)))], (37776 ^ _782435) ^ [_1501619] : [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), _1501619))), -(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), _1501619)) = 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), _1501619))))], (37782 ^ _782435) ^ [_1501734, _1501736] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1501734)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501736), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501734), _1501736) = 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), _1501734), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501736)))))], (37792 ^ _782435) ^ [_1501919, _1501921] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1501919), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1501921), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint), _1501919), _1501921) = 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), _1501919), hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1501921)))))], (37802 ^ _782435) ^ [_1502110, _1502112, _1502114, _1502116, _1502118] : [-(c_Product__Type_Oprod_Oprod__size(_1502110, _1502112, _1502114, _1502116, _1502118) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1502114, hAPP(c_Product__Type_Ofst(_1502110, _1502112), _1502118))), hAPP(_1502116, hAPP(c_Product__Type_Osnd(_1502110, _1502112), _1502118)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (37804 ^ _782435) ^ [_1502177, _1502179, _1502181, _1502183, _1502185] : [hBOOL(hAPP(hAPP(_1502177, _1502179), _1502181)), -(hBOOL(hAPP(hAPP(_1502177, hAPP(c_Product__Type_Osnd(_1502183, _1502185), hAPP(hAPP(c_Product__Type_OPair(_1502183, _1502185), _1502181), _1502179))), hAPP(c_Product__Type_Ofst(_1502183, _1502185), hAPP(hAPP(c_Product__Type_OPair(_1502183, _1502185), _1502181), _1502179)))))], (37810 ^ _782435) ^ [_1502340, _1502342, _1502344, _1502346, _1502348, _1502350] : [hBOOL(hAPP(_1502340, _1502342)), hBOOL(hAPP(_1502344, _1502346)), 37817 ^ _782435 : [(37818 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1502340, hAPP(c_Product__Type_Ofst(_1502348, _1502350), hAPP(hAPP(c_Product__Type_OPair(_1502348, _1502350), _1502342), _1502346)))))], (37820 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1502344, hAPP(c_Product__Type_Osnd(_1502348, _1502350), hAPP(hAPP(c_Product__Type_OPair(_1502348, _1502350), _1502342), _1502346)))))]]], (37822 ^ _782435) ^ [_1502587, _1502589] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), _1502587), _1502589) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), c_Divides_Odivmod__nat(_1502587, _1502589)))], (37856 ^ _782435) ^ [_1503178, _1503180, _1503182] : [-(hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1503178, _1503180), _1503182))), _1503178 = 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), _1503182)), _1503180)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503182)), 37863 ^ _782435 : [(37864 ^ _782435) ^ [] : [-(_1503180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37866 ^ _782435) ^ [] : [hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1503182) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 37867 ^ _782435 : [(37868 ^ _782435) ^ [] : [_1503180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (37870 ^ _782435) ^ [] : [37871 ^ _782435 : [(37872 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1503180)))], (37874 ^ _782435) ^ [] : [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), _1503182))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503182)), _1503180))]], 37879 ^ _782435 : [(37880 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1503180))], (37882 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1503180), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503182))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1503182)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))]]]]], (37824 ^ _782435) ^ [_1502642, _1502644, _1502646] : [hBOOL(hAPP(c_Divides_Odivmod__nat__rel(_1502642, _1502644), _1502646)), 37827 ^ _782435 : [(37828 ^ _782435) ^ [] : [-(_1502642 = 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), _1502646)), _1502644)), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502646)))], (37830 ^ _782435) ^ [] : [_1502644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_Product__Type_Ofst(tc_Nat_Onat, tc_Nat_Onat), _1502646) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (37836 ^ _782435) ^ [] : [-(_1502644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 37839 ^ _782435 : [(37840 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1502644)), 37843 ^ _782435 : [(37844 ^ _782435) ^ [] : [-(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), _1502646))))], (37846 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502646)), _1502644)))]]], (37848 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1502644))), 37851 ^ _782435 : [(37852 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1502644), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502646))))], (37854 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Product__Type_Osnd(tc_Nat_Onat, tc_Nat_Onat), _1502646)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]]]]]], (37890 ^ _782435) ^ [_1503787] : [-(hAPP(c_Int_Onat, _1503787) = 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, _1503787)), 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 ^ _782435) ^ [_1503825, _1503827, _1503829] : [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), _1503825), _1503827))), -(hBOOL(hAPP(hAPP(_1503829, _1503825), _1503827))), 37899 ^ _782435 : [(37900 ^ _782435) ^ [] : [-(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 ^ [_1503825, _1503827, _1503829]), 37898 ^ [_1503825, _1503827, _1503829]))))], (37908 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1503829, 37897 ^ [_1503825, _1503827, _1503829]), 37898 ^ [_1503825, _1503827, _1503829]))], (37902 ^ _782435) ^ [] : [-(37898 ^ [_1503825, _1503827, _1503829] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(_1503829, 37898 ^ [_1503825, _1503827, _1503829]), c_Divides_Odiv__class_Omod(tc_Nat_Onat, 37897 ^ [_1503825, _1503827, _1503829], 37898 ^ [_1503825, _1503827, _1503829]))))]]], (37912 ^ _782435) ^ [_1504247, _1504249, _1504251, _1504253] : [-(hAPP(hAPP(c_Relation_Oinv__image(_1504247, _1504249), _1504251), _1504253) = hAPP(c_Set_OCollect(tc_prod(_1504249, _1504249)), hAPP(c_Product__Type_Oprod_Oprod__case(_1504249, _1504249, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1504249, tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_fun(_1504249, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504249, tc_fun(tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_fun(_1504249, tc_HOL_Obool)), _1504249), c_COMBC(_1504249, tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1504249, tc_prod(_1504247, _1504247)), tc_fun(_1504249, tc_fun(tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_HOL_Obool)), _1504249), hAPP(c_COMBB(tc_prod(_1504247, _1504247), tc_fun(tc_fun(tc_prod(_1504247, _1504247), tc_HOL_Obool), tc_HOL_Obool), _1504249), c_member(tc_prod(_1504247, _1504247)))), hAPP(hAPP(c_COMBC(_1504249, tc_fun(_1504249, _1504247), tc_fun(_1504249, tc_prod(_1504247, _1504247))), hAPP(hAPP(c_COMBB(tc_fun(_1504247, tc_prod(_1504247, _1504247)), tc_fun(tc_fun(_1504249, _1504247), tc_fun(_1504249, tc_prod(_1504247, _1504247))), _1504249), c_COMBB(_1504247, tc_prod(_1504247, _1504247), _1504249)), hAPP(hAPP(c_COMBB(_1504247, tc_fun(_1504247, tc_prod(_1504247, _1504247)), _1504249), c_Product__Type_OPair(_1504247, _1504247)), _1504253))), _1504253)))), _1504251))))], (37914 ^ _782435) ^ [_1504503, _1504505] : [hAPP(c_Int_ORep__Integ, _1504503) = hAPP(c_Int_ORep__Integ, _1504505), -(_1504503 = _1504505)], (37920 ^ _782435) ^ [_1504588, _1504590] : [_1504588 = _1504590, -(hAPP(c_Int_ORep__Integ, _1504588) = hAPP(c_Int_ORep__Integ, _1504590))], (37926 ^ _782435) ^ [_1504706, _1504708, _1504710, _1504712, _1504714, _1504716] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504706, _1504706)), hAPP(hAPP(c_Product__Type_OPair(_1504706, _1504706), _1504708), _1504710)), hAPP(hAPP(c_Relation_Oinv__image(_1504712, _1504706), _1504714), _1504716))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504712, _1504712)), hAPP(hAPP(c_Product__Type_OPair(_1504712, _1504712), hAPP(_1504716, _1504708)), hAPP(_1504716, _1504710))), _1504714)))], (37932 ^ _782435) ^ [_1504893, _1504895, _1504897, _1504899, _1504901, _1504903] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1504899, _1504899)), hAPP(hAPP(c_Product__Type_OPair(_1504899, _1504899), hAPP(_1504903, _1504895)), hAPP(_1504903, _1504897))), _1504901)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1504893, _1504893)), hAPP(hAPP(c_Product__Type_OPair(_1504893, _1504893), _1504895), _1504897)), hAPP(hAPP(c_Relation_Oinv__image(_1504899, _1504893), _1504901), _1504903))))], (37938 ^ _782435) ^ [_1505086, _1505088] : [-(c_FunDef_Orp__inv__image(_1505086, _1505088) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_fun(_1505088, _1505086), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_fun(_1505088, _1505086), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)), tc_fun(tc_fun(_1505088, _1505086), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool), tc_fun(tc_fun(_1505088, _1505086), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool))))), tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool)), c_COMBB(tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)), tc_fun(tc_fun(_1505088, _1505086), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool))), tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), tc_fun(tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)), tc_fun(tc_fun(_1505088, _1505086), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool)), c_COMBS(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)), tc_fun(tc_fun(_1505088, _1505086), tc_fun(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), tc_fun(tc_prod(_1505086, _1505086), tc_HOL_Obool)), hAPP(c_COMBB(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_prod(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool))), tc_fun(_1505088, _1505086)), c_Product__Type_OPair(tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool), tc_fun(tc_prod(_1505088, _1505088), tc_HOL_Obool)))), c_Relation_Oinv__image(_1505086, _1505088))))), c_Relation_Oinv__image(_1505086, _1505088))))], (37940 ^ _782435) ^ [_1505599, _1505601, _1505603, _1505605, _1505607, _1505609] : [c_Equiv__Relations_Oequiv(_1505599, _1505601, _1505603), hBOOL(hAPP(hAPP(c_member(_1505599), _1505605), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1505599, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1505599, _1505599, _1505603), hAPP(hAPP(c_Set_Oinsert(_1505599), _1505607), c_Orderings_Obot__class_Obot(tc_fun(_1505599, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1505599, _1505599, _1505603), hAPP(hAPP(c_Set_Oinsert(_1505599), _1505609), c_Orderings_Obot__class_Obot(tc_fun(_1505599, tc_HOL_Obool))))))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505599, _1505599)), hAPP(hAPP(c_Product__Type_OPair(_1505599, _1505599), _1505607), _1505609)), _1505603)))], (37950 ^ _782435) ^ [_1505900, _1505902, _1505904, _1505906, _1505908] : [c_Equiv__Relations_Oequiv(_1505900, _1505902, _1505904), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1505900, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1505900, _1505900, _1505904), hAPP(hAPP(c_Set_Oinsert(_1505900), _1505906), c_Orderings_Obot__class_Obot(tc_fun(_1505900, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1505900, _1505900, _1505904), hAPP(hAPP(c_Set_Oinsert(_1505900), _1505908), c_Orderings_Obot__class_Obot(tc_fun(_1505900, tc_HOL_Obool)))))), hBOOL(hAPP(hAPP(c_member(_1505900), _1505906), _1505902)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1505900, _1505900)), hAPP(hAPP(c_Product__Type_OPair(_1505900, _1505900), _1505908), _1505906)), _1505904)))], (37964 ^ _782435) ^ [_1506253, _1506255, _1506257] : [c_Equiv__Relations_Oequiv(_1506253, _1506255, _1506257), -(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1506253, tc_HOL_Obool), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506253), _1506255), _1506257)) = _1506255)], (37970 ^ _782435) ^ [_1506362, _1506364, _1506366, _1506368] : [c_Equiv__Relations_Oequiv(_1506362, _1506364, _1506366), hBOOL(hAPP(hAPP(c_member(_1506362), _1506368), _1506364)), -(hBOOL(hAPP(hAPP(c_member(_1506362), _1506368), hAPP(c_Relation_OImage(_1506362, _1506362, _1506366), hAPP(hAPP(c_Set_Oinsert(_1506362), _1506368), c_Orderings_Obot__class_Obot(tc_fun(_1506362, tc_HOL_Obool)))))))], (37980 ^ _782435) ^ [_1506569, _1506571, _1506573, _1506575, _1506577] : [c_Equiv__Relations_Oequiv(_1506569, _1506571, _1506573), hBOOL(hAPP(hAPP(c_member(tc_fun(_1506569, tc_HOL_Obool)), _1506575), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506569), _1506571), _1506573))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1506569, tc_HOL_Obool)), _1506577), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1506569), _1506571), _1506573))), -(_1506575 = _1506577), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1506569, tc_HOL_Obool)), _1506575), _1506577) = c_Orderings_Obot__class_Obot(tc_fun(_1506569, tc_HOL_Obool)))], (37998 ^ _782435) ^ [_1506887, _1506889, _1506891, _1506893, _1506895] : [c_Equiv__Relations_Oequiv(_1506887, _1506889, _1506891), hBOOL(hAPP(hAPP(c_member(tc_prod(_1506887, _1506887)), hAPP(hAPP(c_Product__Type_OPair(_1506887, _1506887), _1506893), _1506895)), _1506891)), -(hAPP(c_Relation_OImage(_1506887, _1506887, _1506891), hAPP(hAPP(c_Set_Oinsert(_1506887), _1506893), c_Orderings_Obot__class_Obot(tc_fun(_1506887, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1506887, _1506887, _1506891), hAPP(hAPP(c_Set_Oinsert(_1506887), _1506895), c_Orderings_Obot__class_Obot(tc_fun(_1506887, tc_HOL_Obool)))))], (38008 ^ _782435) ^ [_1507148, _1507150, _1507152, _1507154, _1507156, _1507158, _1507160] : [c_Equiv__Relations_Oequiv(_1507148, _1507150, _1507152), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507148, tc_HOL_Obool)), _1507154), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507148), _1507150), _1507152))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507148, tc_HOL_Obool)), _1507156), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507148), _1507150), _1507152))), hBOOL(hAPP(hAPP(c_member(_1507148), _1507158), _1507154)), hBOOL(hAPP(hAPP(c_member(_1507148), _1507160), _1507156)), 38027 ^ _782435 : [(38028 ^ _782435) ^ [] : [_1507154 = _1507156, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1507148, _1507148)), hAPP(hAPP(c_Product__Type_OPair(_1507148, _1507148), _1507158), _1507160)), _1507152)))], (38034 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1507148, _1507148)), hAPP(hAPP(c_Product__Type_OPair(_1507148, _1507148), _1507158), _1507160)), _1507152)), -(_1507154 = _1507156)]]], (38040 ^ _782435) ^ [_1507792, _1507794, _1507796, _1507798, _1507800, _1507802, _1507804] : [c_Equiv__Relations_Oequiv(_1507792, _1507794, _1507796), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507792, tc_HOL_Obool)), _1507798), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507792), _1507794), _1507796))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1507792, tc_HOL_Obool)), _1507800), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1507792), _1507794), _1507796))), hBOOL(hAPP(hAPP(c_member(_1507792), _1507802), _1507798)), hBOOL(hAPP(hAPP(c_member(_1507792), _1507804), _1507800)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1507792, _1507792)), hAPP(hAPP(c_Product__Type_OPair(_1507792, _1507792), _1507802), _1507804)), _1507796)), -(_1507798 = _1507800)], (38066 ^ _782435) ^ [_1508329, _1508331, _1508333, _1508335, _1508337] : [c_Equiv__Relations_Oequiv(_1508329, _1508331, _1508333), 38069 ^ _782435 : [(38070 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1508329, _1508329)), hAPP(hAPP(c_Product__Type_OPair(_1508329, _1508329), _1508335), _1508337)), _1508333)), 38073 ^ _782435 : [(38074 ^ _782435) ^ [] : [-(hAPP(c_Relation_OImage(_1508329, _1508329, _1508333), hAPP(hAPP(c_Set_Oinsert(_1508329), _1508335), c_Orderings_Obot__class_Obot(tc_fun(_1508329, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508329, _1508329, _1508333), hAPP(hAPP(c_Set_Oinsert(_1508329), _1508337), c_Orderings_Obot__class_Obot(tc_fun(_1508329, tc_HOL_Obool)))))], (38076 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508329), _1508335), _1508331)))], (38078 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1508329), _1508337), _1508331)))]]], (38080 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508329, _1508329)), hAPP(hAPP(c_Product__Type_OPair(_1508329, _1508329), _1508335), _1508337)), _1508333))), hAPP(c_Relation_OImage(_1508329, _1508329, _1508333), hAPP(hAPP(c_Set_Oinsert(_1508329), _1508335), c_Orderings_Obot__class_Obot(tc_fun(_1508329, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508329, _1508329, _1508333), hAPP(hAPP(c_Set_Oinsert(_1508329), _1508337), c_Orderings_Obot__class_Obot(tc_fun(_1508329, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(_1508329), _1508335), _1508331)), hBOOL(hAPP(hAPP(c_member(_1508329), _1508337), _1508331))]]], (38094 ^ _782435) ^ [_1508929, _1508931, _1508933, _1508935, _1508937] : [hAPP(c_Relation_OImage(_1508929, _1508929, _1508931), hAPP(hAPP(c_Set_Oinsert(_1508929), _1508933), c_Orderings_Obot__class_Obot(tc_fun(_1508929, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1508929, _1508929, _1508931), hAPP(hAPP(c_Set_Oinsert(_1508929), _1508935), c_Orderings_Obot__class_Obot(tc_fun(_1508929, tc_HOL_Obool)))), c_Equiv__Relations_Oequiv(_1508929, _1508937, _1508931), hBOOL(hAPP(hAPP(c_member(_1508929), _1508935), _1508937)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1508929, _1508929)), hAPP(hAPP(c_Product__Type_OPair(_1508929, _1508929), _1508933), _1508935)), _1508931)))], (38108 ^ _782435) ^ [_1509262, _1509264, _1509266, _1509268, _1509270] : [c_Equiv__Relations_Oequiv(_1509262, _1509264, _1509266), hBOOL(hAPP(hAPP(c_member(_1509262), _1509268), _1509264)), hBOOL(hAPP(hAPP(c_member(_1509262), _1509270), _1509264)), 38119 ^ _782435 : [(38120 ^ _782435) ^ [] : [hAPP(c_Relation_OImage(_1509262, _1509262, _1509266), hAPP(hAPP(c_Set_Oinsert(_1509262), _1509268), c_Orderings_Obot__class_Obot(tc_fun(_1509262, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509262, _1509262, _1509266), hAPP(hAPP(c_Set_Oinsert(_1509262), _1509270), c_Orderings_Obot__class_Obot(tc_fun(_1509262, tc_HOL_Obool)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1509262, _1509262)), hAPP(hAPP(c_Product__Type_OPair(_1509262, _1509262), _1509268), _1509270)), _1509266)))], (38126 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1509262, _1509262)), hAPP(hAPP(c_Product__Type_OPair(_1509262, _1509262), _1509268), _1509270)), _1509266)), -(hAPP(c_Relation_OImage(_1509262, _1509262, _1509266), hAPP(hAPP(c_Set_Oinsert(_1509262), _1509268), c_Orderings_Obot__class_Obot(tc_fun(_1509262, tc_HOL_Obool)))) = hAPP(c_Relation_OImage(_1509262, _1509262, _1509266), hAPP(hAPP(c_Set_Oinsert(_1509262), _1509270), c_Orderings_Obot__class_Obot(tc_fun(_1509262, tc_HOL_Obool)))))]]], (38132 ^ _782435) ^ [_1509810, _1509812, _1509814, _1509816, _1509818] : [c_Equiv__Relations_Oequiv(_1509810, _1509812, _1509814), hBOOL(hAPP(hAPP(c_member(tc_prod(_1509810, _1509810)), hAPP(hAPP(c_Product__Type_OPair(_1509810, _1509810), _1509816), _1509818)), _1509814)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1509810, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1509810, _1509810, _1509814), hAPP(hAPP(c_Set_Oinsert(_1509810), _1509816), c_Orderings_Obot__class_Obot(tc_fun(_1509810, tc_HOL_Obool))))), hAPP(c_Relation_OImage(_1509810, _1509810, _1509814), hAPP(hAPP(c_Set_Oinsert(_1509810), _1509818), c_Orderings_Obot__class_Obot(tc_fun(_1509810, tc_HOL_Obool)))))))], (38142 ^ _782435) ^ [_1510091, _1510093, _1510095, _1510097, _1510099] : [c_Equiv__Relations_Oequiv(_1510091, _1510093, _1510095), hBOOL(hAPP(hAPP(c_member(_1510091), _1510097), _1510093)), hBOOL(hAPP(hAPP(c_member(_1510091), _1510099), _1510093)), 38153 ^ _782435 : [(38154 ^ _782435) ^ [] : [hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510091), hAPP(hAPP(c_Set_Oinsert(_1510091), _1510097), c_Orderings_Obot__class_Obot(tc_fun(_1510091, tc_HOL_Obool)))), _1510095) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510091), hAPP(hAPP(c_Set_Oinsert(_1510091), _1510099), c_Orderings_Obot__class_Obot(tc_fun(_1510091, tc_HOL_Obool)))), _1510095), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1510091, _1510091)), hAPP(hAPP(c_Product__Type_OPair(_1510091, _1510091), _1510097), _1510099)), _1510095)))], (38160 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1510091, _1510091)), hAPP(hAPP(c_Product__Type_OPair(_1510091, _1510091), _1510097), _1510099)), _1510095)), -(hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510091), hAPP(hAPP(c_Set_Oinsert(_1510091), _1510097), c_Orderings_Obot__class_Obot(tc_fun(_1510091, tc_HOL_Obool)))), _1510095) = hAPP(hAPP(c_Equiv__Relations_Oquotient(_1510091), hAPP(hAPP(c_Set_Oinsert(_1510091), _1510099), c_Orderings_Obot__class_Obot(tc_fun(_1510091, tc_HOL_Obool)))), _1510095))]]], (38166 ^ _782435) ^ [_1510645, _1510647, _1510649, _1510651, _1510653, _1510655] : [c_Equiv__Relations_Oequiv(_1510645, _1510647, _1510649), c_Equiv__Relations_Ocongruent(_1510645, tc_fun(_1510651, tc_HOL_Obool), _1510649, _1510653), hBOOL(hAPP(hAPP(c_member(_1510645), _1510655), _1510647)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510645, tc_fun(_1510651, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510645, _1510645, _1510649), hAPP(hAPP(c_Set_Oinsert(_1510645), _1510655), c_Orderings_Obot__class_Obot(tc_fun(_1510645, tc_HOL_Obool))))), _1510653) = hAPP(_1510653, _1510655))], (38180 ^ _782435) ^ [_1510946, _1510948, _1510950, _1510952, _1510954, _1510956, _1510958, _1510960, _1510962, _1510964] : [c_Equiv__Relations_Oequiv(_1510946, _1510948, _1510950), c_Equiv__Relations_Oequiv(_1510952, _1510954, _1510956), c_Equiv__Relations_Ocongruent2(_1510946, _1510952, tc_fun(_1510958, tc_HOL_Obool), _1510950, _1510956, _1510960), hBOOL(hAPP(hAPP(c_member(_1510946), _1510962), _1510948)), hBOOL(hAPP(hAPP(c_member(_1510952), _1510964), _1510954)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510946, tc_fun(_1510958, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510946, _1510946, _1510950), hAPP(hAPP(c_Set_Oinsert(_1510946), _1510962), c_Orderings_Obot__class_Obot(tc_fun(_1510946, tc_HOL_Obool))))), hAPP(hAPP(c_COMBB(tc_fun(_1510952, tc_fun(_1510958, tc_HOL_Obool)), tc_fun(_1510958, tc_HOL_Obool), _1510946), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1510952, tc_fun(_1510958, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1510952, _1510952, _1510956), hAPP(hAPP(c_Set_Oinsert(_1510952), _1510964), c_Orderings_Obot__class_Obot(tc_fun(_1510952, tc_HOL_Obool)))))), _1510960)) = hAPP(hAPP(_1510960, _1510962), _1510964))], (38202 ^ _782435) ^ [_1511547, _1511549, _1511551] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511547, tc_HOL_Obool), tc_fun(_1511547, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511547, tc_HOL_Obool), tc_fun(_1511547, tc_HOL_Obool)), _1511549), _1511551)), c_Wellfounded_Ofinite__psubset(_1511547))), 38205 ^ _782435 : [(38206 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1511547, tc_HOL_Obool)), _1511549), _1511551)))], (38208 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1511547), _1511551)))]]], (38210 ^ _782435) ^ [_1511742, _1511744, _1511746] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1511742, tc_HOL_Obool), tc_fun(_1511742, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1511742, tc_HOL_Obool), tc_fun(_1511742, tc_HOL_Obool)), _1511744), _1511746)), c_Wellfounded_Ofinite__psubset(_1511742)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(_1511742, tc_HOL_Obool)), _1511744), _1511746)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1511742), _1511746))], (38220 ^ _782435) ^ [_1511971, _1511973, _1511975, _1511977, _1511979, _1511981, _1511983, _1511985] : [c_Equiv__Relations_Oequiv(_1511971, _1511973, _1511975), c_Equiv__Relations_Ocongruent2(_1511971, _1511977, _1511979, _1511975, _1511981, _1511983), hBOOL(hAPP(hAPP(c_member(_1511971), _1511985), _1511973)), -(c_Equiv__Relations_Ocongruent(_1511977, _1511979, _1511981, hAPP(_1511983, _1511985)))], (38234 ^ _782435) ^ [_1512222, _1512224, _1512226, _1512228, _1512230, _1512232, _1512234, _1512236, _1512238, _1512240] : [c_Equiv__Relations_Ocongruent2(_1512222, _1512224, _1512226, _1512228, _1512230, _1512232), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512222, _1512222)), hAPP(hAPP(c_Product__Type_OPair(_1512222, _1512222), _1512234), _1512236)), _1512228)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512224, _1512224)), hAPP(hAPP(c_Product__Type_OPair(_1512224, _1512224), _1512238), _1512240)), _1512230)), -(hAPP(hAPP(_1512232, _1512234), _1512238) = hAPP(hAPP(_1512232, _1512236), _1512240))], (38248 ^ _782435) ^ [_1512559, _1512561, _1512563, _1512565, _1512567, _1512569] : [c_Equiv__Relations_Ocongruent(_1512559, _1512561, _1512563, _1512565), hBOOL(hAPP(hAPP(c_member(tc_prod(_1512559, _1512559)), hAPP(hAPP(c_Product__Type_OPair(_1512559, _1512559), _1512567), _1512569)), _1512563)), -(hAPP(_1512565, _1512567) = hAPP(_1512565, _1512569))], (38258 ^ _782435) ^ [_1512758, _1512760, _1512762, _1512764, _1512766, _1512768, _1512770, _1512772, _1512774] : [c_Equiv__Relations_Oequiv(_1512758, _1512760, _1512762), c_Equiv__Relations_Oequiv(_1512764, _1512766, _1512768), c_Equiv__Relations_Ocongruent2(_1512758, _1512764, tc_fun(_1512770, tc_HOL_Obool), _1512762, _1512768, _1512772), hBOOL(hAPP(hAPP(c_member(_1512764), _1512774), _1512766)), -(c_Equiv__Relations_Ocongruent(_1512758, tc_fun(_1512770, tc_HOL_Obool), _1512762, hAPP(hAPP(c_COMBB(tc_fun(_1512764, tc_fun(_1512770, tc_HOL_Obool)), tc_fun(_1512770, tc_HOL_Obool), _1512758), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1512764, tc_fun(_1512770, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1512764, _1512764, _1512768), hAPP(hAPP(c_Set_Oinsert(_1512764), _1512774), c_Orderings_Obot__class_Obot(tc_fun(_1512764, tc_HOL_Obool)))))), _1512772)))], (38276 ^ _782435) ^ [_1513185] : [-(c_Wellfounded_Ofinite__psubset(_1513185) = hAPP(c_Set_OCollect(tc_prod(tc_fun(_1513185, tc_HOL_Obool), tc_fun(_1513185, tc_HOL_Obool))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(_1513185, tc_HOL_Obool), tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_fun(_1513185, tc_HOL_Obool), tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool)), tc_fun(_1513185, tc_HOL_Obool)), c_COMBS(tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1513185, tc_HOL_Obool), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(_1513185, tc_HOL_Obool)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1513185, tc_HOL_Obool)), c_fconj)), c_Orderings_Oord__class_Oless(tc_fun(_1513185, tc_HOL_Obool))))), c_Finite__Set_Ofinite(_1513185)))))], (38278 ^ _782435) ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357] : [c_Equiv__Relations_Oequiv(_1513345, _1513347, _1513349), c_Equiv__Relations_Ocongruent(_1513345, tc_fun(_1513351, tc_HOL_Obool), _1513349, _1513353), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513345, tc_fun(_1513351, tc_HOL_Obool)), _1513355), _1513353) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1513345, tc_fun(_1513351, tc_HOL_Obool)), _1513357), _1513353), hBOOL(hAPP(hAPP(c_member(tc_fun(_1513345, tc_HOL_Obool)), _1513355), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513345), _1513347), _1513349))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1513345, tc_HOL_Obool)), _1513357), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1513345), _1513347), _1513349))), 38300 ^ _782435 : [(38301 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513345), 38299 ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357]), _1513347)))], (38304 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1513345), 38302 ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357]), _1513347)))], (38306 ^ _782435) ^ [] : [-(hAPP(_1513353, 38299 ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357]) = hAPP(_1513353, 38302 ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357]))], (38308 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1513345, _1513345)), hAPP(hAPP(c_Product__Type_OPair(_1513345, _1513345), 38299 ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357]), 38302 ^ [_1513345, _1513347, _1513349, _1513351, _1513353, _1513355, _1513357])), _1513349))]], -(_1513355 = _1513357)], (38312 ^ _782435) ^ [_1514315, _1514317, _1514319, _1514321, _1514323, _1514325, _1514327, _1514329, _1514331, _1514333, _1514335] : [c_Equiv__Relations_Oequiv(_1514315, _1514317, _1514319), c_Equiv__Relations_Oequiv(_1514321, _1514323, _1514325), c_Equiv__Relations_Ocongruent2(_1514315, _1514321, tc_fun(_1514327, tc_HOL_Obool), _1514319, _1514325, _1514329), hBOOL(hAPP(hAPP(c_member(tc_fun(_1514315, tc_HOL_Obool)), _1514331), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1514315), _1514317), _1514319))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1514321, tc_HOL_Obool)), _1514333), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1514321), _1514323), _1514325))), 38334 ^ _782435 : [(38335 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514315), 38333 ^ [_1514315, _1514317, _1514319, _1514321, _1514323, _1514325, _1514327, _1514329, _1514331, _1514333, _1514335]), _1514317)))], (38338 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1514321), 38336 ^ [_1514315, _1514317, _1514319, _1514321, _1514323, _1514325, _1514327, _1514329, _1514331, _1514333, _1514335]), _1514323)))], (38340 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1514327, tc_HOL_Obool)), hAPP(hAPP(_1514329, 38333 ^ [_1514315, _1514317, _1514319, _1514321, _1514323, _1514325, _1514327, _1514329, _1514331, _1514333, _1514335]), 38336 ^ [_1514315, _1514317, _1514319, _1514321, _1514323, _1514325, _1514327, _1514329, _1514331, _1514333, _1514335])), _1514335))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1514327, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1514315, tc_fun(_1514327, tc_HOL_Obool)), _1514331), hAPP(hAPP(c_COMBB(tc_fun(_1514321, tc_fun(_1514327, tc_HOL_Obool)), tc_fun(_1514327, tc_HOL_Obool), _1514315), hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1514321, tc_fun(_1514327, tc_HOL_Obool)), _1514333)), _1514329))), _1514335)))], (38344 ^ _782435) ^ [_1515317, _1515319, _1515321, _1515323, _1515325, _1515327, _1515329] : [c_Equiv__Relations_Oequiv(_1515317, _1515319, _1515321), c_Equiv__Relations_Ocongruent(_1515317, tc_fun(_1515323, tc_HOL_Obool), _1515321, _1515325), hBOOL(hAPP(hAPP(c_member(tc_fun(_1515317, tc_HOL_Obool)), _1515327), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1515317), _1515319), _1515321))), 38358 ^ _782435 : [(38359 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1515317), 38357 ^ [_1515317, _1515319, _1515321, _1515323, _1515325, _1515327, _1515329]), _1515319)))], (38361 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_fun(_1515323, tc_HOL_Obool)), hAPP(_1515325, 38357 ^ [_1515317, _1515319, _1515321, _1515323, _1515325, _1515327, _1515329])), _1515329))]], -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1515323, tc_HOL_Obool)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1515317, tc_fun(_1515323, tc_HOL_Obool)), _1515327), _1515325)), _1515329)))], (38365 ^ _782435) ^ [_1515828, _1515830, _1515832, _1515834, _1515836] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1515828, _1515830)), hAPP(_1515828, _1515832))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1515834, _1515834)), hAPP(hAPP(c_Product__Type_OPair(_1515834, _1515834), _1515830), _1515832)), _1515836)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1515834, _1515834)), hAPP(hAPP(c_Product__Type_OPair(_1515834, _1515834), _1515830), _1515832)), c_Wellfounded_Omlex__prod(_1515834, _1515828, _1515836))))], (38375 ^ _782435) ^ [_1516075] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(_1516075)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(_1516075)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38377 ^ _782435) ^ [_1516110, _1516112, _1516114, _1516116, _1516118] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1516110, _1516112)), hAPP(_1516110, _1516114))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516116, _1516116)), hAPP(hAPP(c_Product__Type_OPair(_1516116, _1516116), _1516112), _1516114)), c_Wellfounded_Omlex__prod(_1516116, _1516110, _1516118))))], (38383 ^ _782435) ^ [_1516276, _1516278] : [c_Code__Numeral_OSuc__code__numeral(_1516276) = c_Code__Numeral_OSuc__code__numeral(_1516278), -(_1516276 = _1516278)], (38389 ^ _782435) ^ [_1516357, _1516359] : [_1516357 = _1516359, -(c_Code__Numeral_OSuc__code__numeral(_1516357) = c_Code__Numeral_OSuc__code__numeral(_1516359))], (38395 ^ _782435) ^ [_1516453] : [c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = c_Code__Numeral_OSuc__code__numeral(_1516453)], (38397 ^ _782435) ^ [_1516487] : [c_Code__Numeral_OSuc__code__numeral(_1516487) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)], (38399 ^ _782435) ^ [_1516512] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1516512)), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = _1516512)], (38401 ^ _782435) ^ [_1516543] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), c_Code__Numeral_OSuc__code__numeral(_1516543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral), _1516543)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38403 ^ _782435) ^ [_1516580] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1516580)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1516580)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (38405 ^ _782435) ^ [_1516618, _1516620, _1516622, _1516624, _1516626, _1516628] : [-(c_Product__Type_Oprod_Oprod__rec(_1516618, _1516620, _1516622, _1516624, hAPP(hAPP(c_Product__Type_OPair(_1516618, _1516620), _1516626), _1516628)) = hAPP(hAPP(_1516624, _1516626), _1516628))], (38407 ^ _782435) ^ [_1516672] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat), _1516672) = _1516672)], (38409 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1516734, _1516736, _1516738, _1516740, _1516742, _1516744] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1516734, _1516736)), hAPP(hAPP(c_Product__Type_OPair(_1516734, _1516736), _1516738), _1516740)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1516734, _1516736), tc_HOL_Obool), _1516742))), c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(_1516734, _1516736), tc_HOL_Obool), tc_fun(tc_prod(_1516734, _1516736), tc_HOL_Obool), _1516742), 38424 ^ _782435 : [(38425 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1516734, _1516736)), hAPP(hAPP(c_Product__Type_OPair(_1516734, _1516736), 38422 ^ [_1516734, _1516736, _1516738, _1516740, _1516742, _1516744]), 38423 ^ [_1516734, _1516736, _1516738, _1516740, _1516742, _1516744])), hAPP(_1516742, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1516734, _1516736), tc_HOL_Obool)), c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(_1516734, _1516736), tc_HOL_Obool), _1516742)), hAPP(c_Set_OCollect(tc_prod(_1516734, _1516736)), hAPP(c_Product__Type_Oprod_Oprod__case(_1516734, _1516736, tc_HOL_Obool), _1516744)))))))], (38427 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1516744, 38422 ^ [_1516734, _1516736, _1516738, _1516740, _1516742, _1516744]), 38423 ^ [_1516734, _1516736, _1516738, _1516740, _1516742, _1516744]))]], -(hBOOL(hAPP(hAPP(_1516744, _1516738), _1516740)))], (38431 ^ _782435) ^ [_1517342, _1517344, _1517346, _1517348, _1517350, _1517352, _1517354, _1517356] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1517342, _1517344), tc_prod(_1517342, _1517344))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1517342, _1517344), tc_prod(_1517342, _1517344)), hAPP(hAPP(c_Product__Type_OPair(_1517342, _1517344), _1517346), _1517348)), hAPP(hAPP(c_Product__Type_OPair(_1517342, _1517344), _1517350), _1517352))), c_Wellfounded_Olex__prod(_1517342, _1517344, _1517354, _1517356))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517342, _1517342)), hAPP(hAPP(c_Product__Type_OPair(_1517342, _1517342), _1517346), _1517350)), _1517354))), 38438 ^ _782435 : [(38439 ^ _782435) ^ [] : [-(_1517346 = _1517350)], (38441 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1517344, _1517344)), hAPP(hAPP(c_Product__Type_OPair(_1517344, _1517344), _1517348), _1517352)), _1517356)))]]], (38443 ^ _782435) ^ [_1517667, _1517669, _1517671, _1517673, _1517675, _1517677, _1517679, _1517681] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1517667, _1517669), tc_prod(_1517667, _1517669))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1517667, _1517669), tc_prod(_1517667, _1517669)), hAPP(hAPP(c_Product__Type_OPair(_1517667, _1517669), _1517671), _1517673)), hAPP(hAPP(c_Product__Type_OPair(_1517667, _1517669), _1517675), _1517677))), c_Wellfounded_Olex__prod(_1517667, _1517669, _1517679, _1517681)))), 38444 ^ _782435 : [(38445 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1517667, _1517667)), hAPP(hAPP(c_Product__Type_OPair(_1517667, _1517667), _1517671), _1517675)), _1517679))], (38447 ^ _782435) ^ [] : [_1517671 = _1517675, hBOOL(hAPP(hAPP(c_member(tc_prod(_1517669, _1517669)), hAPP(hAPP(c_Product__Type_OPair(_1517669, _1517669), _1517673), _1517677)), _1517681))]]], (38455 ^ _782435) ^ [_1518057, _1518059] : [c_Equiv__Relations_Oequiv(_1518057, c_Orderings_Otop__class_Otop(tc_fun(_1518057, tc_HOL_Obool)), _1518059), -(c_Equiv__Relations_Oequivp(_1518057, hAPP(hAPP(c_COMBC(_1518057, tc_fun(tc_prod(_1518057, _1518057), tc_HOL_Obool), tc_fun(_1518057, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518057, tc_fun(tc_fun(tc_prod(_1518057, _1518057), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518057, _1518057), tc_HOL_Obool), tc_fun(_1518057, tc_HOL_Obool)), _1518057), c_COMBC(_1518057, tc_fun(tc_prod(_1518057, _1518057), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518057, tc_prod(_1518057, _1518057)), tc_fun(_1518057, tc_fun(tc_fun(tc_prod(_1518057, _1518057), tc_HOL_Obool), tc_HOL_Obool)), _1518057), hAPP(c_COMBB(tc_prod(_1518057, _1518057), tc_fun(tc_fun(tc_prod(_1518057, _1518057), tc_HOL_Obool), tc_HOL_Obool), _1518057), c_member(tc_prod(_1518057, _1518057)))), c_Product__Type_OPair(_1518057, _1518057)))), _1518059)))], (38461 ^ _782435) ^ [_1518378, _1518380] : [c_Equiv__Relations_Oequivp(_1518378, hAPP(hAPP(c_COMBC(_1518378, tc_fun(tc_prod(_1518378, _1518378), tc_HOL_Obool), tc_fun(_1518378, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518378, tc_fun(tc_fun(tc_prod(_1518378, _1518378), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1518378, _1518378), tc_HOL_Obool), tc_fun(_1518378, tc_HOL_Obool)), _1518378), c_COMBC(_1518378, tc_fun(tc_prod(_1518378, _1518378), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1518378, tc_prod(_1518378, _1518378)), tc_fun(_1518378, tc_fun(tc_fun(tc_prod(_1518378, _1518378), tc_HOL_Obool), tc_HOL_Obool)), _1518378), hAPP(c_COMBB(tc_prod(_1518378, _1518378), tc_fun(tc_fun(tc_prod(_1518378, _1518378), tc_HOL_Obool), tc_HOL_Obool), _1518378), c_member(tc_prod(_1518378, _1518378)))), c_Product__Type_OPair(_1518378, _1518378)))), _1518380)), -(c_Equiv__Relations_Oequiv(_1518378, c_Orderings_Otop__class_Otop(tc_fun(_1518378, tc_HOL_Obool)), _1518380))], (38467 ^ _782435) ^ [_1518705] : [-(c_Equiv__Relations_Oequivp(_1518705, c_fequal))], (38485 ^ _782435) ^ [_1519041, _1519043] : [-(c_Equiv__Relations_Oequivp(_1519041, _1519043)), 38490 ^ _782435 : [(38491 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1519043, 38486 ^ [_1519041, _1519043]), 38487 ^ [_1519041, _1519043])))], (38493 ^ _782435) ^ [] : [hAPP(_1519043, 38486 ^ [_1519041, _1519043]) = hAPP(_1519043, 38487 ^ [_1519041, _1519043])]], 38494 ^ _782435 : [(38495 ^ _782435) ^ [] : [-(hAPP(_1519043, 38486 ^ [_1519041, _1519043]) = hAPP(_1519043, 38487 ^ [_1519041, _1519043]))], (38497 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1519043, 38486 ^ [_1519041, _1519043]), 38487 ^ [_1519041, _1519043]))]]], (38469 ^ _782435) ^ [_1518743, _1518745] : [c_Equiv__Relations_Oequivp(_1518743, _1518745), 38472 ^ _782435 : [(38473 ^ _782435) ^ [_1518837, _1518839] : [hBOOL(hAPP(hAPP(_1518745, _1518839), _1518837)), -(hAPP(_1518745, _1518839) = hAPP(_1518745, _1518837))], (38479 ^ _782435) ^ [_1518936, _1518938] : [hAPP(_1518745, _1518938) = hAPP(_1518745, _1518936), -(hBOOL(hAPP(hAPP(_1518745, _1518938), _1518936)))]]], (38501 ^ _782435) ^ [_1519370, _1519372, _1519374] : [c_Equiv__Relations_Oequivp(_1519370, _1519372), -(hBOOL(hAPP(hAPP(_1519372, _1519374), _1519374)))], (38507 ^ _782435) ^ [_1519459, _1519461, _1519463, _1519465] : [c_Equiv__Relations_Oequivp(_1519459, _1519461), hBOOL(hAPP(hAPP(_1519461, _1519463), _1519465)), -(hBOOL(hAPP(hAPP(_1519461, _1519465), _1519463)))], (38517 ^ _782435) ^ [_1519616, _1519618, _1519620, _1519622, _1519624] : [c_Equiv__Relations_Oequivp(_1519616, _1519618), hBOOL(hAPP(hAPP(_1519618, _1519620), _1519622)), hBOOL(hAPP(hAPP(_1519618, _1519622), _1519624)), -(hBOOL(hAPP(hAPP(_1519618, _1519620), _1519624)))], (38531 ^ _782435) ^ [_1519845, _1519847, _1519849, _1519851, _1519853, _1519855, _1519857] : [hBOOL(hAPP(_1519845, _1519847)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1519849, _1519849)), hAPP(hAPP(c_Product__Type_OPair(_1519849, _1519849), _1519851), _1519853)), hAPP(_1519855, _1519847))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1519857, _1519849), tc_prod(_1519857, _1519849))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1519857, _1519849), tc_prod(_1519857, _1519849)), hAPP(hAPP(c_Product__Type_OPair(_1519857, _1519849), _1519847), _1519851)), hAPP(hAPP(c_Product__Type_OPair(_1519857, _1519849), _1519847), _1519853))), c_Recdef_Osame__fst(_1519857, _1519849, _1519845, _1519855))))], (38541 ^ _782435) ^ [_1520150, _1520152, _1520154, _1520156, _1520158, _1520160, _1520162] : [-(hAPP(c_Product__Type_Oapfst(_1520150, _1520152, _1520154, _1520156), hAPP(c_Product__Type_Oapsnd(_1520158, _1520154, _1520150, _1520160), _1520162)) = hAPP(hAPP(c_Product__Type_OPair(_1520152, _1520154), hAPP(_1520156, hAPP(c_Product__Type_Ofst(_1520150, _1520158), _1520162))), hAPP(_1520160, hAPP(c_Product__Type_Osnd(_1520150, _1520158), _1520162))))], (38543 ^ _782435) ^ [_1520228, _1520230, _1520232, _1520234, _1520236, _1520238, _1520240] : [-(hAPP(c_Product__Type_Oapsnd(_1520228, _1520230, _1520232, _1520234), hAPP(c_Product__Type_Oapfst(_1520236, _1520232, _1520228, _1520238), _1520240)) = hAPP(hAPP(c_Product__Type_OPair(_1520232, _1520230), hAPP(_1520238, hAPP(c_Product__Type_Ofst(_1520236, _1520228), _1520240))), hAPP(_1520234, hAPP(c_Product__Type_Osnd(_1520236, _1520228), _1520240))))], (38545 ^ _782435) ^ [_1520306, _1520308, _1520310, _1520312, _1520314, _1520316] : [-(hAPP(c_Product__Type_Oapfst(_1520306, _1520308, _1520310, _1520312), hAPP(hAPP(c_Product__Type_OPair(_1520306, _1520310), _1520314), _1520316)) = hAPP(hAPP(c_Product__Type_OPair(_1520308, _1520310), hAPP(_1520312, _1520314)), _1520316))], (38547 ^ _782435) ^ [_1520368, _1520370, _1520372, _1520374, _1520376] : [-(hAPP(c_Product__Type_Ofst(_1520368, _1520370), hAPP(c_Product__Type_Oapfst(_1520372, _1520368, _1520370, _1520374), _1520376)) = hAPP(_1520374, hAPP(c_Product__Type_Ofst(_1520372, _1520370), _1520376)))], (38549 ^ _782435) ^ [_1520449, _1520451, _1520453, _1520455, _1520457, _1520459] : [hAPP(c_Product__Type_Oapfst(_1520449, _1520451, _1520453, _1520455), _1520457) = hAPP(c_Product__Type_Oapfst(_1520449, _1520451, _1520453, _1520459), _1520457), -(hAPP(_1520455, hAPP(c_Product__Type_Ofst(_1520449, _1520453), _1520457)) = hAPP(_1520459, hAPP(c_Product__Type_Ofst(_1520449, _1520453), _1520457)))], (38555 ^ _782435) ^ [_1520598, _1520600, _1520602, _1520604, _1520606, _1520608] : [hAPP(_1520604, hAPP(c_Product__Type_Ofst(_1520598, _1520602), _1520606)) = hAPP(_1520608, hAPP(c_Product__Type_Ofst(_1520598, _1520602), _1520606)), -(hAPP(c_Product__Type_Oapfst(_1520598, _1520600, _1520602, _1520604), _1520606) = hAPP(c_Product__Type_Oapfst(_1520598, _1520600, _1520602, _1520608), _1520606))], (38561 ^ _782435) ^ [_1520753, _1520755, _1520757, _1520759, _1520761] : [-(hAPP(c_Product__Type_Osnd(_1520753, _1520755), hAPP(c_Product__Type_Oapfst(_1520757, _1520753, _1520755, _1520759), _1520761)) = hAPP(c_Product__Type_Osnd(_1520757, _1520755), _1520761))], (38563 ^ _782435) ^ [_1520804, _1520806, _1520808, _1520810, _1520812, _1520814, _1520816] : [-(hAPP(c_Product__Type_Oapfst(_1520804, _1520806, _1520808, _1520810), hAPP(c_Product__Type_Oapfst(_1520812, _1520804, _1520808, _1520814), _1520816)) = hAPP(c_Product__Type_Oapfst(_1520812, _1520806, _1520808, hAPP(c_Fun_Ocomp(_1520804, _1520806, _1520812, _1520810), _1520814)), _1520816))], (38565 ^ _782435) ^ [_1520871, _1520873, _1520875, _1520877, _1520879, _1520881, _1520883] : [-(hAPP(c_Product__Type_Oapsnd(_1520871, _1520873, _1520875, _1520877), hAPP(c_Product__Type_Oapfst(_1520879, _1520875, _1520871, _1520881), _1520883)) = hAPP(c_Product__Type_Oapfst(_1520879, _1520875, _1520873, _1520881), hAPP(c_Product__Type_Oapsnd(_1520871, _1520873, _1520879, _1520877), _1520883)))], (38567 ^ _782435) ^ [_1520938, _1520940, _1520942, _1520944] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1520938), _1520940)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1520942), _1520944)), -(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), _1520938), _1520942)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1520940), _1520944))), c_FunDef_Opair__less)))], (38577 ^ _782435) ^ [_1521141, _1521143, _1521145, _1521147, _1521149] : [hBOOL(hAPP(hAPP(c_member(_1521141), _1521143), hAPP(c_Relation_OImage(_1521145, _1521141, _1521147), _1521149))), 38581 ^ _782435 : [(38582 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1521145, _1521141)), hAPP(hAPP(c_Product__Type_OPair(_1521145, _1521141), 38580 ^ [_1521141, _1521143, _1521145, _1521147, _1521149]), _1521143)), _1521147)))], (38584 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1521145), 38580 ^ [_1521141, _1521143, _1521145, _1521147, _1521149]), _1521149)))]]], (38586 ^ _782435) ^ [_1521365, _1521367, _1521369] : [-(c_Wellfounded_Omlex__prod(_1521365, _1521367, _1521369) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, _1521365), _1521365), c_Wellfounded_Olex__prod(tc_Nat_Onat, _1521365, c_Wellfounded_Oless__than, _1521369)), hAPP(hAPP(c_COMBS(_1521365, _1521365, tc_prod(tc_Nat_Onat, _1521365)), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(_1521365, tc_prod(tc_Nat_Onat, _1521365)), _1521365), c_Product__Type_OPair(tc_Nat_Onat, _1521365)), _1521367)), c_COMBI(_1521365))))], (38588 ^ _782435) ^ [] : [-(c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_Nat_Onat, c_Wellfounded_Oless__than, c_Wellfounded_Oless__than))], (38590 ^ _782435) ^ [_1521465] : [-(c_Wellfounded_Omeasure(_1521465) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat, _1521465), c_Wellfounded_Oless__than))], (38592 ^ _782435) ^ [_1521511, _1521513] : [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), _1521511), _1521513)), c_Wellfounded_Oless__than)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521511), _1521513)))], (38598 ^ _782435) ^ [_1521616, _1521618] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521616), _1521618)), -(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), _1521616), _1521618)), c_Wellfounded_Oless__than)))], (38604 ^ _782435) ^ [_1521727, _1521729, _1521731, _1521733] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1521727), _1521729)), -(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), _1521727), _1521731)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521729), _1521733))), c_FunDef_Opair__less)))], (38610 ^ _782435) ^ [_1521864, _1521866, _1521868, _1521870] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521864), _1521866)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1521868), _1521870)), -(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), _1521864), _1521868)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1521866), _1521870))), c_FunDef_Opair__leq)))], (38620 ^ _782435) ^ [_1522067, _1522069, _1522071, _1522073] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522067), _1522069)), 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)), _1522067), _1522071)), 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)), _1522069), _1522073)), 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)), _1522069), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522071), _1522073))), c_FunDef_Omin__strict)))], (38634 ^ _782435) ^ [_1522348, _1522350, _1522352, _1522354] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522348), _1522350)), 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)), _1522352), _1522348)), 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)), _1522354), _1522350)), 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)), _1522352), _1522354)), _1522350)), c_FunDef_Omax__strict)))], (38648 ^ _782435) ^ [_1522629] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522629)), -(_1522629 = 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))), _1522629)), c_FunDef_Omax__strict)))], (38658 ^ _782435) ^ [_1522735] : [-(_1522735 = 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)), _1522735), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__strict)))], (38664 ^ _782435) ^ [_1522780, _1522782, _1522784, _1522786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1522780), _1522782)), -(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), _1522780), _1522784)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1522782), _1522786))), c_FunDef_Opair__leq)))], (38670 ^ _782435) ^ [_1522917, _1522919, _1522921, _1522923] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1522917), _1522919)), 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)), _1522921), _1522917)), 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)), _1522923), _1522919)), 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)), _1522921), _1522923)), _1522919)), c_FunDef_Omax__weak)))], (38684 ^ _782435) ^ [_1523198, _1523200, _1523202, _1523204] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1523198), _1523200)), 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)), _1523198), _1523202)), 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)), _1523200), _1523204)), 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)), _1523200), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1523202), _1523204))), c_FunDef_Omin__weak)))], (38698 ^ _782435) ^ [_1523479, _1523481, _1523483, _1523485] : [-(hAPP(c_Relation_OField(_1523479), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1523479, _1523479)), hAPP(hAPP(c_Product__Type_OPair(_1523479, _1523479), _1523481), _1523483)), _1523485)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523479, tc_HOL_Obool)), hAPP(hAPP(c_Set_Oinsert(_1523479), _1523481), hAPP(hAPP(c_Set_Oinsert(_1523479), _1523483), c_Orderings_Obot__class_Obot(tc_fun(_1523479, tc_HOL_Obool))))), hAPP(c_Relation_OField(_1523479), _1523485)))], (38700 ^ _782435) ^ [_1523570, _1523572] : [-(hAPP(c_Relation_OField(_1523570), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1523570, _1523570), tc_HOL_Obool), _1523572)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1523570, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_fun(tc_prod(_1523570, _1523570), tc_HOL_Obool), tc_fun(_1523570, tc_HOL_Obool), c_Relation_OField(_1523570)), _1523572)))], (38702 ^ _782435) ^ [_1523633] : [-(hAPP(c_Relation_OField(_1523633), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1523633, _1523633), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1523633, tc_HOL_Obool)))], (38704 ^ _782435) ^ [_1523674, _1523676, _1523678] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1523674, _1523674), tc_HOL_Obool)), _1523676), _1523678)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1523674, tc_HOL_Obool)), hAPP(c_Relation_OField(_1523674), _1523676)), hAPP(c_Relation_OField(_1523674), _1523678))))], (38710 ^ _782435) ^ [_1523819, _1523821, _1523823] : [-(hAPP(c_Relation_OField(_1523819), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1523819, _1523819), tc_HOL_Obool)), _1523821), _1523823)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1523819, tc_HOL_Obool)), hAPP(c_Relation_OField(_1523819), _1523821)), hAPP(c_Relation_OField(_1523819), _1523823)))], (38712 ^ _782435) ^ [_1523886, _1523888] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1523886, _1523886)), _1523888)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1523886), hAPP(c_Relation_OField(_1523886), _1523888))))], (38718 ^ _782435) ^ [_1523995] : [-(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)), _1523995), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))), c_FunDef_Omin__weak)))], (38720 ^ _782435) ^ [_1524029] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat, tc_Nat_Onat)), _1524029)), -(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))), _1524029)), c_FunDef_Omax__weak)))], (38726 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1524160, _1524162] : [-(c_Relation_OId__on(_1524160, _1524162) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1524160, tc_fun(tc_prod(_1524160, _1524160), tc_HOL_Obool)), _1524162), hAPP(hAPP(c_COMBC(_1524160, tc_fun(tc_prod(_1524160, _1524160), tc_HOL_Obool), tc_fun(tc_prod(_1524160, _1524160), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_prod(_1524160, _1524160), tc_fun(tc_fun(tc_prod(_1524160, _1524160), tc_HOL_Obool), tc_fun(tc_prod(_1524160, _1524160), tc_HOL_Obool)), _1524160), c_Set_Oinsert(tc_prod(_1524160, _1524160))), hAPP(hAPP(c_COMBS(_1524160, _1524160, tc_prod(_1524160, _1524160)), c_Product__Type_OPair(_1524160, _1524160)), c_COMBI(_1524160)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524160, _1524160), tc_HOL_Obool)))))], (38732 ^ _782435) ^ [_1524284, _1524286] : [-(c_Relation_OId__on(_1524284, _1524286) = hAPP(c_Product__Type_Oprod_Oprod__case(_1524284, _1524284, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1524284, tc_HOL_Obool, tc_fun(_1524284, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524284, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_HOL_Obool, tc_fun(_1524284, tc_HOL_Obool)), _1524284), c_COMBC(_1524284, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1524284, tc_HOL_Obool), tc_fun(_1524284, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1524284), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1524284), c_fconj)), c_fequal))), _1524286)))], (38734 ^ _782435) ^ [_1524378] : [-(c_Relation_OId__on(_1524378, c_Orderings_Obot__class_Obot(tc_fun(_1524378, tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1524378, _1524378), tc_HOL_Obool)))], (38736 ^ _782435) ^ [_1524417, _1524419, _1524421] : [-(hAPP(c_Relation_OImage(_1524417, _1524417, c_Relation_OId__on(_1524417, _1524419)), _1524421) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1524417, tc_HOL_Obool)), _1524419), _1524421))], (38738 ^ _782435) ^ [_1524486, _1524488, _1524490, _1524492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1524486, _1524486)), hAPP(hAPP(c_Product__Type_OPair(_1524486, _1524486), _1524488), _1524490)), c_Relation_OId__on(_1524486, _1524492))), 38741 ^ _782435 : [(38742 ^ _782435) ^ [] : [-(_1524488 = _1524490)], (38744 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1524486), _1524488), _1524492)))]]], (38746 ^ _782435) ^ [_1524647, _1524649, _1524651, _1524653] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524647, _1524647)), hAPP(hAPP(c_Product__Type_OPair(_1524647, _1524647), _1524649), _1524651)), c_Relation_OId__on(_1524647, _1524653)))), _1524649 = _1524651, hBOOL(hAPP(hAPP(c_member(_1524647), _1524649), _1524653))], (38756 ^ _782435) ^ [_1524844, _1524846, _1524848, _1524850] : [_1524844 = _1524846, hBOOL(hAPP(hAPP(c_member(_1524848), _1524844), _1524850)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1524848, _1524848)), hAPP(hAPP(c_Product__Type_OPair(_1524848, _1524848), _1524844), _1524846)), c_Relation_OId__on(_1524848, _1524850))))], (38766 ^ _782435) ^ [] : [-(c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38768 ^ _782435) ^ [_1525057, _1525059, _1525061, _1525063, _1525065, _1525067] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525057, tc_HOL_Obool), tc_fun(_1525057, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525057, tc_HOL_Obool), tc_fun(_1525057, tc_HOL_Obool)), _1525059), _1525061)), c_Wellfounded_Omax__ext(_1525057, _1525063))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525057, tc_HOL_Obool), tc_fun(_1525057, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525057, tc_HOL_Obool), tc_fun(_1525057, tc_HOL_Obool)), _1525065), _1525067)), c_Wellfounded_Omax__ext(_1525057, _1525063))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525057, tc_HOL_Obool), tc_fun(_1525057, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525057, tc_HOL_Obool), tc_fun(_1525057, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525057, tc_HOL_Obool)), _1525059), _1525065)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1525057, tc_HOL_Obool)), _1525061), _1525067))), c_Wellfounded_Omax__ext(_1525057, _1525063))))], (38778 ^ _782435) ^ [] : [-(c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (38780 ^ _782435) ^ [_1525489, _1525491, _1525493, _1525495] : [c_Wellfounded_Omax__extp(_1525489, hAPP(hAPP(c_COMBC(_1525489, tc_fun(tc_prod(_1525489, _1525489), tc_HOL_Obool), tc_fun(_1525489, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525489, tc_fun(tc_fun(tc_prod(_1525489, _1525489), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525489, _1525489), tc_HOL_Obool), tc_fun(_1525489, tc_HOL_Obool)), _1525489), c_COMBC(_1525489, tc_fun(tc_prod(_1525489, _1525489), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525489, tc_prod(_1525489, _1525489)), tc_fun(_1525489, tc_fun(tc_fun(tc_prod(_1525489, _1525489), tc_HOL_Obool), tc_HOL_Obool)), _1525489), hAPP(c_COMBB(tc_prod(_1525489, _1525489), tc_fun(tc_fun(tc_prod(_1525489, _1525489), tc_HOL_Obool), tc_HOL_Obool), _1525489), c_member(tc_prod(_1525489, _1525489)))), c_Product__Type_OPair(_1525489, _1525489)))), _1525491), _1525493, _1525495), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525489, tc_HOL_Obool), tc_fun(_1525489, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525489, tc_HOL_Obool), tc_fun(_1525489, tc_HOL_Obool)), _1525493), _1525495)), c_Wellfounded_Omax__ext(_1525489, _1525491))))], (38786 ^ _782435) ^ [_1525874, _1525876, _1525878, _1525880] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1525874, tc_HOL_Obool), tc_fun(_1525874, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1525874, tc_HOL_Obool), tc_fun(_1525874, tc_HOL_Obool)), _1525878), _1525880)), c_Wellfounded_Omax__ext(_1525874, _1525876))), -(c_Wellfounded_Omax__extp(_1525874, hAPP(hAPP(c_COMBC(_1525874, tc_fun(tc_prod(_1525874, _1525874), tc_HOL_Obool), tc_fun(_1525874, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525874, tc_fun(tc_fun(tc_prod(_1525874, _1525874), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1525874, _1525874), tc_HOL_Obool), tc_fun(_1525874, tc_HOL_Obool)), _1525874), c_COMBC(_1525874, tc_fun(tc_prod(_1525874, _1525874), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1525874, tc_prod(_1525874, _1525874)), tc_fun(_1525874, tc_fun(tc_fun(tc_prod(_1525874, _1525874), tc_HOL_Obool), tc_HOL_Obool)), _1525874), hAPP(c_COMBB(tc_prod(_1525874, _1525874), tc_fun(tc_fun(tc_prod(_1525874, _1525874), tc_HOL_Obool), tc_HOL_Obool), _1525874), c_member(tc_prod(_1525874, _1525874)))), c_Product__Type_OPair(_1525874, _1525874)))), _1525876), _1525878, _1525880))], (38792 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1526301, _1526303, _1526305, _1526307] : [c_FunDef_Oreduction__pair(_1526301, _1526303), -(c_FunDef_Oreduction__pair(_1526305, hAPP(hAPP(c_FunDef_Orp__inv__image(_1526301, _1526305), _1526303), _1526307)))], (38802 ^ _782435) ^ [_1526415, _1526417] : [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)), _1526415), 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)), _1526417), 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)), _1526415), _1526417)), c_Int_Ointrel)))], (38808 ^ _782435) ^ [_1526546, _1526548] : [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)), _1526546), _1526548)), 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)), _1526546), 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)), _1526548), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)))))], (38814 ^ _782435) ^ [_1526704, _1526706, _1526708, _1526710] : [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), _1526704), _1526706)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1526708), _1526710))), c_Int_Ointrel)), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526704), _1526710) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526708), _1526706))], (38820 ^ _782435) ^ [_1526851, _1526853, _1526855, _1526857] : [hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526851), _1526857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1526855), _1526853), -(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), _1526851), _1526853)), hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat, tc_Nat_Onat), _1526855), _1526857))), c_Int_Ointrel)))], (38826 ^ _782435) ^ [_1527004, _1527006, _1527008] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1527004, _1527004)), _1527006), c_Relation_OId__on(_1527004, _1527008))), 38830 ^ _782435 : [(38831 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1527004), 38829 ^ [_1527004, _1527006, _1527008]), _1527008)))], (38833 ^ _782435) ^ [] : [-(_1527006 = hAPP(hAPP(c_Product__Type_OPair(_1527004, _1527004), 38829 ^ [_1527004, _1527006, _1527008]), 38829 ^ [_1527004, _1527006, _1527008]))]]], (38835 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1527221, _1527223, _1527225] : [class_Rings_Oring__1(_1527221), -(hAPP(c_Int_Oring__1__class_Oof__int(_1527221), 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), _1527223), _1527225)), 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(_1527221), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1527221), _1527223)), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1527221), _1527225)))], (38843 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1527398, _1527400, _1527402, _1527404] : [-(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), _1527398), _1527400)), 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), _1527402), _1527404)), 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), _1527398), _1527402)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527400), _1527404))), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527398), _1527404)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1527400), _1527402)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38847 ^ _782435) ^ [_1527523] : [-(hAPP(c_Int_OAbs__Integ, hAPP(c_Int_ORep__Integ, _1527523)) = _1527523)], (38849 ^ _782435) ^ [_1527552, _1527554] : [-(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), _1527552), _1527554)), 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), _1527554), _1527552)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38851 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1527634] : [-(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint), _1527634) = 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), _1527634), 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 ^ _782435) ^ [_1527678, _1527680, _1527682, _1527684] : [-(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), _1527678), _1527680)), 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), _1527682), _1527684)), 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), _1527678), _1527682)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1527680), _1527684))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38857 ^ _782435) ^ [_1527779, _1527781] : [-(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), _1527779), _1527781)), 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), _1527779), _1527781))], (38859 ^ _782435) ^ [_1527831] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1527831) = 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, _1527831)), 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 ^ _782435) ^ [_1527890, _1527892, _1527894, _1527896] : [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), _1527890), _1527892)), 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), _1527894), _1527896)), 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), _1527890), _1527896)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1527894), _1527892))))], (38867 ^ _782435) ^ [_1528083, _1528085, _1528087, _1528089] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528083), _1528089)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528087), _1528085))), -(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), _1528083), _1528085)), 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), _1528087), _1528089)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (38873 ^ _782435) ^ [_1528303, _1528305, _1528307, _1528309] : [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), _1528303), _1528305)), 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), _1528307), _1528309)), 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), _1528303), _1528309)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528307), _1528305))))], (38879 ^ _782435) ^ [_1528496, _1528498, _1528500, _1528502] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528496), _1528502)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1528500), _1528498))), -(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), _1528496), _1528498)), 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), _1528500), _1528502)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))))], (38887 ^ _782435) ^ [_1528695] : [-(_1528695 = 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 ^ [_1528695]), 38885 ^ [_1528695])), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool))))))], (38889 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1528764, _1528766, _1528768, _1528770] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1528764, _1528766, _1528768, c_Code__Numeral_OSuc__code__numeral(_1528770)) = hAPP(_1528768, _1528770))], (38893 ^ _782435) ^ [_1528803] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), hAPP(c_Int_ORep__Integ, _1528803)), c_Int_OInteg)))], (38895 ^ _782435) ^ [_1528834, _1528836, _1528838] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(_1528834, _1528836, _1528838, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1528836)], (38897 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1528902, _1528904, _1528906] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1528902, hAPP(hAPP(c_COMBC(_1528902, tc_fun(tc_prod(_1528902, _1528902), tc_HOL_Obool), tc_fun(_1528902, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528902, tc_fun(tc_fun(tc_prod(_1528902, _1528902), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1528902, _1528902), tc_HOL_Obool), tc_fun(_1528902, tc_HOL_Obool)), _1528902), c_COMBC(_1528902, tc_fun(tc_prod(_1528902, _1528902), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1528902, tc_prod(_1528902, _1528902)), tc_fun(_1528902, tc_fun(tc_fun(tc_prod(_1528902, _1528902), tc_HOL_Obool), tc_HOL_Obool)), _1528902), hAPP(c_COMBB(tc_prod(_1528902, _1528902), tc_fun(tc_fun(tc_prod(_1528902, _1528902), tc_HOL_Obool), tc_HOL_Obool), _1528902), c_member(tc_prod(_1528902, _1528902)))), c_Product__Type_OPair(_1528902, _1528902)))), _1528904)), _1528906)), -(hBOOL(hAPP(hAPP(c_member(_1528902), _1528906), c_Wellfounded_Oacc(_1528902, _1528904))))], (38905 ^ _782435) ^ [_1529243, _1529245, _1529247] : [hBOOL(hAPP(hAPP(c_member(_1529243), _1529247), c_Wellfounded_Oacc(_1529243, _1529245))), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1529243, hAPP(hAPP(c_COMBC(_1529243, tc_fun(tc_prod(_1529243, _1529243), tc_HOL_Obool), tc_fun(_1529243, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529243, tc_fun(tc_fun(tc_prod(_1529243, _1529243), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529243, _1529243), tc_HOL_Obool), tc_fun(_1529243, tc_HOL_Obool)), _1529243), c_COMBC(_1529243, tc_fun(tc_prod(_1529243, _1529243), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529243, tc_prod(_1529243, _1529243)), tc_fun(_1529243, tc_fun(tc_fun(tc_prod(_1529243, _1529243), tc_HOL_Obool), tc_HOL_Obool)), _1529243), hAPP(c_COMBB(tc_prod(_1529243, _1529243), tc_fun(tc_fun(tc_prod(_1529243, _1529243), tc_HOL_Obool), tc_HOL_Obool), _1529243), c_member(tc_prod(_1529243, _1529243)))), c_Product__Type_OPair(_1529243, _1529243)))), _1529245)), _1529247)))], (38911 ^ _782435) ^ [_1529590, _1529592, _1529594, _1529596, _1529598] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1529590, _1529592, _1529594), _1529596), _1529598) = hAPP(c_Set_OCollect(tc_prod(_1529590, _1529594)), hAPP(c_Product__Type_Oprod_Oprod__case(_1529590, _1529594, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1529594, tc_fun(_1529592, tc_HOL_Obool)), tc_fun(_1529594, tc_HOL_Obool), _1529590), hAPP(c_COMBB(tc_fun(_1529592, tc_HOL_Obool), tc_HOL_Obool, _1529594), c_HOL_OEx(_1529592))), hAPP(hAPP(c_COMBC(_1529590, tc_fun(_1529594, tc_fun(_1529592, tc_HOL_Obool)), tc_fun(_1529594, tc_fun(_1529592, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1529592, tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool)), tc_fun(tc_fun(_1529594, tc_fun(_1529592, tc_HOL_Obool)), tc_fun(_1529594, tc_fun(_1529592, tc_HOL_Obool))), _1529590), c_COMBB(tc_fun(_1529592, tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool), _1529594)), hAPP(hAPP(c_COMBB(tc_fun(_1529592, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1529592, tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool)), _1529590), c_COMBS(_1529592, tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529592, tc_HOL_Obool), tc_fun(_1529592, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1529590), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1529592), c_fconj)), hAPP(hAPP(c_COMBC(_1529590, tc_fun(tc_prod(_1529590, _1529592), tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529592, tc_fun(tc_fun(tc_prod(_1529590, _1529592), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529590, _1529592), tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool)), _1529590), c_COMBC(_1529592, tc_fun(tc_prod(_1529590, _1529592), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529592, tc_prod(_1529590, _1529592)), tc_fun(_1529592, tc_fun(tc_fun(tc_prod(_1529590, _1529592), tc_HOL_Obool), tc_HOL_Obool)), _1529590), hAPP(c_COMBB(tc_prod(_1529590, _1529592), tc_fun(tc_fun(tc_prod(_1529590, _1529592), tc_HOL_Obool), tc_HOL_Obool), _1529592), c_member(tc_prod(_1529590, _1529592)))), c_Product__Type_OPair(_1529590, _1529592)))), _1529596))))), hAPP(hAPP(c_COMBC(_1529594, tc_fun(tc_prod(_1529592, _1529594), tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529592, tc_fun(tc_fun(tc_prod(_1529592, _1529594), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1529592, _1529594), tc_HOL_Obool), tc_fun(_1529592, tc_HOL_Obool)), _1529594), c_COMBC(_1529592, tc_fun(tc_prod(_1529592, _1529594), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1529592, tc_prod(_1529592, _1529594)), tc_fun(_1529592, tc_fun(tc_fun(tc_prod(_1529592, _1529594), tc_HOL_Obool), tc_HOL_Obool)), _1529594), hAPP(c_COMBB(tc_prod(_1529592, _1529594), tc_fun(tc_fun(tc_prod(_1529592, _1529594), tc_HOL_Obool), tc_HOL_Obool), _1529592), c_member(tc_prod(_1529592, _1529594)))), hAPP(c_COMBC(_1529592, _1529594, tc_prod(_1529592, _1529594)), c_Product__Type_OPair(_1529592, _1529594))))), _1529598))))))], (38913 ^ _782435) ^ [_1530038, _1530040, _1530042, _1530044, _1530046, _1530048, _1530050, _1530052] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1530038, _1530040)), hAPP(hAPP(c_Product__Type_OPair(_1530038, _1530040), _1530042), _1530044)), _1530046)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1530040, _1530048)), hAPP(hAPP(c_Product__Type_OPair(_1530040, _1530048), _1530044), _1530050)), _1530052)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1530038, _1530048)), hAPP(hAPP(c_Product__Type_OPair(_1530038, _1530048), _1530042), _1530050)), hAPP(hAPP(c_Relation_Orel__comp(_1530038, _1530040, _1530048), _1530046), _1530052))))], (38923 ^ _782435) ^ [_1530325, _1530327, _1530329, _1530331, _1530333, _1530335, _1530337] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530325, _1530327, _1530329), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530331, tc_fun(tc_prod(_1530325, _1530327), tc_HOL_Obool)), _1530333), _1530335)), _1530337) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530331, tc_fun(tc_prod(_1530325, _1530329), tc_HOL_Obool)), _1530333), hAPP(hAPP(c_COMBC(_1530331, tc_fun(tc_prod(_1530327, _1530329), tc_HOL_Obool), tc_fun(tc_prod(_1530325, _1530329), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530325, _1530327), tc_HOL_Obool), tc_fun(tc_fun(tc_prod(_1530327, _1530329), tc_HOL_Obool), tc_fun(tc_prod(_1530325, _1530329), tc_HOL_Obool)), _1530331), c_Relation_Orel__comp(_1530325, _1530327, _1530329)), _1530335)), _1530337)))], (38925 ^ _782435) ^ [_1530457, _1530459, _1530461, _1530463, _1530465, _1530467, _1530469] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530457, _1530459, _1530461), _1530463), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530465, tc_fun(tc_prod(_1530459, _1530461), tc_HOL_Obool)), _1530467), _1530469)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1530465, tc_fun(tc_prod(_1530457, _1530461), tc_HOL_Obool)), _1530467), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1530459, _1530461), tc_HOL_Obool), tc_fun(tc_prod(_1530457, _1530461), tc_HOL_Obool), _1530465), hAPP(c_Relation_Orel__comp(_1530457, _1530459, _1530461), _1530463)), _1530469)))], (38927 ^ _782435) ^ [_1530561, _1530563, _1530565, _1530567] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530561, _1530563, _1530565), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530561, _1530563), tc_HOL_Obool))), _1530567) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530561, _1530565), tc_HOL_Obool)))], (38929 ^ _782435) ^ [_1530616, _1530618, _1530620, _1530622] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530616, _1530618, _1530620), _1530622), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530618, _1530620), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1530616, _1530620), tc_HOL_Obool)))], (38931 ^ _782435) ^ [_1530671, _1530673, _1530675, _1530677, _1530679, _1530681] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530671, _1530673, _1530675), _1530677), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530673, _1530675), tc_HOL_Obool)), _1530679), _1530681)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530671, _1530675), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530671, _1530673, _1530675), _1530677), _1530679)), hAPP(hAPP(c_Relation_Orel__comp(_1530671, _1530673, _1530675), _1530677), _1530681)))], (38933 ^ _782435) ^ [_1530762, _1530764, _1530766, _1530768, _1530770, _1530772] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530762, _1530764, _1530766), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530762, _1530764), tc_HOL_Obool)), _1530768), _1530770)), _1530772) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1530762, _1530766), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530762, _1530764, _1530766), _1530768), _1530772)), hAPP(hAPP(c_Relation_Orel__comp(_1530762, _1530764, _1530766), _1530770), _1530772)))], (38935 ^ _782435) ^ [_1530853, _1530855, _1530857, _1530859, _1530861, _1530863, _1530865] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1530853, _1530855, _1530857), hAPP(hAPP(c_Relation_Orel__comp(_1530853, _1530859, _1530855), _1530861), _1530863)), _1530865) = hAPP(hAPP(c_Relation_Orel__comp(_1530853, _1530859, _1530857), _1530861), hAPP(hAPP(c_Relation_Orel__comp(_1530859, _1530855, _1530857), _1530863), _1530865)))], (38937 ^ _782435) ^ [_1530928, _1530930, _1530932, _1530934, _1530936, _1530938, _1530940] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530928, _1530930), tc_HOL_Obool)), _1530932), _1530934)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530930, _1530936), tc_HOL_Obool)), _1530938), _1530940)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1530928, _1530936), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1530928, _1530930, _1530936), _1530932), _1530938)), hAPP(hAPP(c_Relation_Orel__comp(_1530928, _1530930, _1530936), _1530934), _1530940))))], (38947 ^ _782435) ^ [_1531195, _1531197, _1531199, _1531201] : [hAPP(hAPP(c_Relation_Orel__comp(_1531195, _1531195, _1531195), _1531197), _1531199) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531195, _1531195), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531195, _1531195, _1531195), _1531197), _1531201) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531195, _1531195), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531195, _1531195, _1531195), _1531197), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531195, _1531195), tc_HOL_Obool)), _1531199), _1531201)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531195, _1531195), tc_HOL_Obool)))], (38957 ^ _782435) ^ [_1531468, _1531470, _1531472, _1531474] : [hAPP(hAPP(c_Relation_Orel__comp(_1531468, _1531468, _1531468), _1531470), _1531472) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531468, _1531468), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1531468, _1531468, _1531468), _1531474), _1531472) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531468, _1531468), tc_HOL_Obool)), -(hAPP(hAPP(c_Relation_Orel__comp(_1531468, _1531468, _1531468), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1531468, _1531468), tc_HOL_Obool)), _1531470), _1531474)), _1531472) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1531468, _1531468), tc_HOL_Obool)))], (38967 ^ _782435) ^ [_1531741, _1531743, _1531745] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1531741, _1531741), tc_HOL_Obool)), _1531743), _1531745)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1531741, tc_HOL_Obool)), c_Wellfounded_Oacc(_1531741, _1531745)), c_Wellfounded_Oacc(_1531741, _1531743))))], (38973 ^ _782435) ^ [_1531878, _1531880, _1531882, _1531884] : [hBOOL(hAPP(hAPP(c_member(_1531878), _1531880), c_Wellfounded_Oacc(_1531878, _1531882))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1531878, _1531878)), hAPP(hAPP(c_Product__Type_OPair(_1531878, _1531878), _1531884), _1531880)), _1531882)), -(hBOOL(hAPP(hAPP(c_member(_1531878), _1531884), c_Wellfounded_Oacc(_1531878, _1531882))))], (38993 ^ _782435) ^ [_1532364, _1532366, _1532368] : [38995 ^ _782435 : [(38996 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1532364, _1532364)), hAPP(hAPP(c_Product__Type_OPair(_1532364, _1532364), 38994 ^ [_1532364, _1532366, _1532368]), _1532366)), _1532368)))], (38998 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1532364), 38994 ^ [_1532364, _1532366, _1532368]), c_Wellfounded_Oacc(_1532364, _1532368)))]], -(hBOOL(hAPP(hAPP(c_member(_1532364), _1532366), c_Wellfounded_Oacc(_1532364, _1532368))))], (38983 ^ _782435) ^ [_1532111, _1532113, _1532115] : [hBOOL(hAPP(hAPP(c_member(_1532111), _1532113), c_Wellfounded_Oacc(_1532111, _1532115))), 38986 ^ _782435 : [(38987 ^ _782435) ^ [_1532225] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1532111, _1532111)), hAPP(hAPP(c_Product__Type_OPair(_1532111, _1532111), _1532225), _1532113)), _1532115)), -(hBOOL(hAPP(hAPP(c_member(_1532111), _1532225), c_Wellfounded_Oacc(_1532111, _1532115))))]]], (39002 ^ _782435) ^ [_1532604, _1532606, _1532608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532604, _1532604), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532604, _1532604, _1532604), _1532606), _1532608)), _1532606)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1532604, _1532606)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omax__ext(_1532604, _1532608)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1532604, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1532604, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1532604, tc_HOL_Obool), tc_fun(_1532604, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omax__ext(_1532604, _1532606))))], (39008 ^ _782435) ^ [_1532975, _1532977, _1532979] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1532975, _1532975), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1532975, _1532975, _1532975), _1532977), _1532979)), _1532977)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool)), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1532975, _1532977)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool)), tc_HOL_Obool)), c_Wellfounded_Omin__ext(_1532975, _1532979)), hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(_1532975, tc_HOL_Obool))), c_Orderings_Obot__class_Obot(tc_fun(_1532975, tc_HOL_Obool)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(_1532975, tc_HOL_Obool), tc_fun(_1532975, tc_HOL_Obool)), tc_HOL_Obool)))))), c_Wellfounded_Omin__ext(_1532975, _1532977))))], (39014 ^ _782435) ^ [_1533346, _1533348, _1533350, _1533352, _1533354] : [c_Typedef_Otype__definition(_1533346, _1533348, _1533350, _1533352, _1533354), -(hAPP(c_Set_Oimage(_1533348, _1533346, _1533352), _1533354) = c_Orderings_Otop__class_Otop(tc_fun(_1533346, tc_HOL_Obool)))], (39020 ^ _782435) ^ [_1533459, _1533461, _1533463, _1533465, _1533467] : [c_Typedef_Otype__definition(_1533459, _1533461, _1533463, _1533465, _1533467), -(hAPP(c_Set_Oimage(_1533459, _1533461, _1533463), c_Orderings_Otop__class_Otop(tc_fun(_1533459, tc_HOL_Obool))) = _1533467)], (39026 ^ _782435) ^ [_1533572, _1533574, _1533576, _1533578, _1533580, _1533582] : [c_Typedef_Otype__definition(_1533572, _1533574, _1533576, _1533578, _1533580), -(hBOOL(hAPP(hAPP(c_member(_1533574), hAPP(_1533576, _1533582)), _1533580)))], (39032 ^ _782435) ^ [_1533683, _1533685, _1533687, _1533689, _1533691, _1533693] : [c_Typedef_Otype__definition(_1533683, _1533685, _1533687, _1533689, _1533691), -(hAPP(_1533689, hAPP(_1533687, _1533693)) = _1533693)], (39038 ^ _782435) ^ [_1533786, _1533788, _1533790, _1533792, _1533794, _1533796, _1533798] : [c_Typedef_Otype__definition(_1533786, _1533788, _1533790, _1533792, _1533794), 39041 ^ _782435 : [(39042 ^ _782435) ^ [] : [hAPP(_1533790, _1533796) = hAPP(_1533790, _1533798), -(_1533796 = _1533798)], (39048 ^ _782435) ^ [] : [_1533796 = _1533798, -(hAPP(_1533790, _1533796) = hAPP(_1533790, _1533798))]]], (39054 ^ _782435) ^ [_1534047, _1534049, _1534051, _1534053, _1534055, _1534057, _1534059] : [c_Typedef_Otype__definition(_1534047, _1534049, _1534051, _1534053, _1534055), hBOOL(hAPP(hAPP(c_member(_1534049), _1534057), _1534055)), hBOOL(hAPP(hAPP(c_member(_1534049), _1534059), _1534055)), 39065 ^ _782435 : [(39066 ^ _782435) ^ [] : [hAPP(_1534053, _1534057) = hAPP(_1534053, _1534059), -(_1534057 = _1534059)], (39072 ^ _782435) ^ [] : [_1534057 = _1534059, -(hAPP(_1534053, _1534057) = hAPP(_1534053, _1534059))]]], (39078 ^ _782435) ^ [_1534460, _1534462, _1534464, _1534466, _1534468, _1534470] : [c_Typedef_Otype__definition(_1534460, _1534462, _1534464, _1534466, _1534468), hBOOL(hAPP(hAPP(c_member(_1534462), _1534470), _1534468)), -(hAPP(_1534464, hAPP(_1534466, _1534470)) = _1534470)], (39088 ^ _782435) ^ [_1534667, _1534669, _1534671, _1534673, _1534675, _1534677, _1534679] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1534667, _1534669, _1534671, hAPP(hAPP(c_COMBC(_1534667, tc_fun(tc_prod(_1534667, _1534669), tc_HOL_Obool), tc_fun(_1534669, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534669, tc_fun(tc_fun(tc_prod(_1534667, _1534669), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534667, _1534669), tc_HOL_Obool), tc_fun(_1534669, tc_HOL_Obool)), _1534667), c_COMBC(_1534669, tc_fun(tc_prod(_1534667, _1534669), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534669, tc_prod(_1534667, _1534669)), tc_fun(_1534669, tc_fun(tc_fun(tc_prod(_1534667, _1534669), tc_HOL_Obool), tc_HOL_Obool)), _1534667), hAPP(c_COMBB(tc_prod(_1534667, _1534669), tc_fun(tc_fun(tc_prod(_1534667, _1534669), tc_HOL_Obool), tc_HOL_Obool), _1534669), c_member(tc_prod(_1534667, _1534669)))), c_Product__Type_OPair(_1534667, _1534669)))), _1534673), hAPP(hAPP(c_COMBC(_1534669, tc_fun(tc_prod(_1534669, _1534671), tc_HOL_Obool), tc_fun(_1534671, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534671, tc_fun(tc_fun(tc_prod(_1534669, _1534671), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1534669, _1534671), tc_HOL_Obool), tc_fun(_1534671, tc_HOL_Obool)), _1534669), c_COMBC(_1534671, tc_fun(tc_prod(_1534669, _1534671), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1534671, tc_prod(_1534669, _1534671)), tc_fun(_1534671, tc_fun(tc_fun(tc_prod(_1534669, _1534671), tc_HOL_Obool), tc_HOL_Obool)), _1534669), hAPP(c_COMBB(tc_prod(_1534669, _1534671), tc_fun(tc_fun(tc_prod(_1534669, _1534671), tc_HOL_Obool), tc_HOL_Obool), _1534671), c_member(tc_prod(_1534669, _1534671)))), c_Product__Type_OPair(_1534669, _1534671)))), _1534675)), _1534677), _1534679)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1534667, _1534671)), hAPP(hAPP(c_Product__Type_OPair(_1534667, _1534671), _1534677), _1534679)), hAPP(hAPP(c_Relation_Orel__comp(_1534667, _1534669, _1534671), _1534673), _1534675))))], (39094 ^ _782435) ^ [_1535302, _1535304, _1535306, _1535308, _1535310, _1535312, _1535314] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1535302, _1535306)), hAPP(hAPP(c_Product__Type_OPair(_1535302, _1535306), _1535312), _1535314)), hAPP(hAPP(c_Relation_Orel__comp(_1535302, _1535304, _1535306), _1535308), _1535310))), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1535302, _1535304, _1535306, hAPP(hAPP(c_COMBC(_1535302, tc_fun(tc_prod(_1535302, _1535304), tc_HOL_Obool), tc_fun(_1535304, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535304, tc_fun(tc_fun(tc_prod(_1535302, _1535304), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535302, _1535304), tc_HOL_Obool), tc_fun(_1535304, tc_HOL_Obool)), _1535302), c_COMBC(_1535304, tc_fun(tc_prod(_1535302, _1535304), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535304, tc_prod(_1535302, _1535304)), tc_fun(_1535304, tc_fun(tc_fun(tc_prod(_1535302, _1535304), tc_HOL_Obool), tc_HOL_Obool)), _1535302), hAPP(c_COMBB(tc_prod(_1535302, _1535304), tc_fun(tc_fun(tc_prod(_1535302, _1535304), tc_HOL_Obool), tc_HOL_Obool), _1535304), c_member(tc_prod(_1535302, _1535304)))), c_Product__Type_OPair(_1535302, _1535304)))), _1535308), hAPP(hAPP(c_COMBC(_1535304, tc_fun(tc_prod(_1535304, _1535306), tc_HOL_Obool), tc_fun(_1535306, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535306, tc_fun(tc_fun(tc_prod(_1535304, _1535306), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1535304, _1535306), tc_HOL_Obool), tc_fun(_1535306, tc_HOL_Obool)), _1535304), c_COMBC(_1535306, tc_fun(tc_prod(_1535304, _1535306), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1535306, tc_prod(_1535304, _1535306)), tc_fun(_1535306, tc_fun(tc_fun(tc_prod(_1535304, _1535306), tc_HOL_Obool), tc_HOL_Obool)), _1535304), hAPP(c_COMBB(tc_prod(_1535304, _1535306), tc_fun(tc_fun(tc_prod(_1535304, _1535306), tc_HOL_Obool), tc_HOL_Obool), _1535306), c_member(tc_prod(_1535304, _1535306)))), c_Product__Type_OPair(_1535304, _1535306)))), _1535310)), _1535312), _1535314)))], (39100 ^ _782435) ^ [_1535943, _1535945, _1535947] : [c_Wellfounded_Owf(_1535943, _1535945), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1535943, _1535943), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1535943, _1535943, _1535943), _1535945), _1535947)), _1535945)), -(c_FunDef_Oreduction__pair(_1535943, hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(_1535943, _1535943), tc_HOL_Obool), tc_fun(tc_prod(_1535943, _1535943), tc_HOL_Obool)), _1535945), _1535947)))], (39110 ^ _782435) ^ [_1536185, _1536187, _1536189, _1536191] : [c_Wellfounded_Omax__extp(_1536185, _1536187, _1536189, _1536191), 39113 ^ _782435 : [(39114 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536185), _1536189)))], (39116 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1536185), _1536191)))], (39118 ^ _782435) ^ [] : [_1536191 = c_Orderings_Obot__class_Obot(tc_fun(_1536185, tc_HOL_Obool))], (39120 ^ _782435) ^ [_1536401] : [hBOOL(hAPP(hAPP(c_member(_1536185), _1536401), _1536189)), 39124 ^ _782435 : [(39125 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536185), 39123 ^ [_1536185, _1536187, _1536189, _1536191, _1536401]), _1536191)))], (39127 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1536187, _1536401), 39123 ^ [_1536185, _1536187, _1536189, _1536191, _1536401])))]]]]], (39129 ^ _782435) ^ [_1536585, _1536587, _1536589, _1536591] : [-(c_Wellfounded_Omax__extp(_1536585, _1536587, _1536589, _1536591)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536585), _1536589)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1536585), _1536591)), -(_1536591 = c_Orderings_Obot__class_Obot(tc_fun(_1536585, tc_HOL_Obool))), 39143 ^ _782435 : [(39144 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1536585), 39142 ^ [_1536585, _1536587, _1536589, _1536591]), _1536589)))], (39146 ^ _782435) ^ [_1536930] : [hBOOL(hAPP(hAPP(c_member(_1536585), _1536930), _1536591)), hBOOL(hAPP(hAPP(_1536587, 39142 ^ [_1536585, _1536587, _1536589, _1536591]), _1536930))]]], (39154 ^ _782435) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Oless__than))], (39156 ^ _782435) ^ [_1537116, _1537118, _1537120, _1537122, _1537124, _1537126, _1537128, _1537130] : [hBOOL(hAPP(hAPP(_1537116, _1537118), _1537120)), hBOOL(hAPP(hAPP(_1537122, _1537120), _1537124)), -(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1537126, _1537128, _1537130, _1537116, _1537122), _1537118), _1537124)))], (39166 ^ _782435) ^ [_1537311] : [-(c_Wellfounded_Owf(_1537311, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1537311, _1537311), tc_HOL_Obool))))], (39168 ^ _782435) ^ [_1537342, _1537344, _1537346, _1537348] : [c_Wellfounded_Owf(_1537342, _1537344), -(c_Wellfounded_Owf(_1537346, hAPP(hAPP(c_Relation_Oinv__image(_1537342, _1537346), _1537344), _1537348)))], (39174 ^ _782435) ^ [_1537441, _1537443, _1537445, _1537447] : [c_Wellfounded_Owf(_1537441, _1537443), c_Wellfounded_Owf(_1537445, _1537447), -(c_Wellfounded_Owf(tc_prod(_1537441, _1537445), c_Wellfounded_Olex__prod(_1537441, _1537445, _1537443, _1537447)))], (39184 ^ _782435) ^ [_1537594, _1537596] : [-(c_Wellfounded_Owf(_1537594, hAPP(c_Wellfounded_Omeasure(_1537594), _1537596)))], (39186 ^ _782435) ^ [_1537639, _1537641] : [c_Wellfounded_Owf(_1537639, _1537641), -(c_Wellfounded_Owf(_1537639, hAPP(hAPP(c_Relation_Orel__comp(_1537639, _1537639, _1537639), _1537641), _1537641)))], (39192 ^ _782435) ^ [_1537732, _1537734] : [c_Wellfounded_Owf(_1537732, hAPP(hAPP(c_Relation_Orel__comp(_1537732, _1537732, _1537732), _1537734), _1537734)), -(c_Wellfounded_Owf(_1537732, _1537734))], (39198 ^ _782435) ^ [_1537831, _1537833, _1537835] : [c_Wellfounded_Owf(_1537831, _1537833), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1537831, _1537831), tc_HOL_Obool)), _1537835), _1537833)), -(c_Wellfounded_Owf(_1537831, _1537835))], (39208 ^ _782435) ^ [_1537990, _1537992] : [c_Wellfounded_Owf(_1537990, _1537992), -(c_Wellfounded_Owf(tc_fun(_1537990, tc_HOL_Obool), c_Wellfounded_Omin__ext(_1537990, _1537992)))], (39214 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1538127, _1538129, _1538131, _1538133, _1538135, _1538137, _1538139] : [hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1538127, _1538129, _1538131, _1538133, _1538135), _1538137), _1538139)), 39220 ^ _782435 : [(39221 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1538133, _1538137), 39219 ^ [_1538127, _1538129, _1538131, _1538133, _1538135, _1538137, _1538139])))], (39223 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1538135, 39219 ^ [_1538127, _1538129, _1538131, _1538133, _1538135, _1538137, _1538139]), _1538139)))]]], (39225 ^ _782435) ^ [_1538317, _1538319, _1538321, _1538323, _1538325, _1538327, _1538329] : [-(hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(_1538317, _1538319, _1538321, _1538323, _1538325), _1538327), _1538329))), 39226 ^ _782435 : [(39227 ^ _782435) ^ [_1538388] : [hBOOL(hAPP(hAPP(_1538323, _1538327), _1538388)), hBOOL(hAPP(hAPP(_1538325, _1538388), _1538329))]]], (39235 ^ _782435) ^ [_1538537, _1538539, _1538541] : [c_Wellfounded_Owf(_1538537, _1538539), -(c_Wellfounded_Owf(_1538537, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538537, _1538537), tc_HOL_Obool)), _1538541), _1538539)))], (39241 ^ _782435) ^ [_1538644, _1538646, _1538648] : [c_Wellfounded_Owf(_1538644, _1538646), -(c_Wellfounded_Owf(_1538644, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1538644, _1538644), tc_HOL_Obool)), _1538646), _1538648)))], (39247 ^ _782435) ^ [_1538751] : [-(c_Wellfounded_Owf(tc_fun(_1538751, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1538751)))], (39249 ^ _782435) ^ [_1538779, _1538781, _1538783] : [c_Wellfounded_Owf(_1538779, _1538781), -(c_Wellfounded_Owf(_1538779, c_Wellfounded_Omlex__prod(_1538779, _1538783, _1538781)))], (39255 ^ _782435) ^ [] : [-(c_Wellfounded_Owf(tc_prod(tc_Nat_Onat, tc_Nat_Onat), c_FunDef_Opair__less))], (39257 ^ _782435) ^ [_1538884, _1538886] : [c_Wellfounded_Owf(_1538884, _1538886), -(c_Wellfounded_Owf(tc_fun(_1538884, tc_HOL_Obool), c_Wellfounded_Omax__ext(_1538884, _1538886)))], (39263 ^ _782435) ^ [_1538973, _1538975, _1538977] : [c_Wellfounded_Owf(_1538973, _1538975), hBOOL(hAPP(hAPP(c_member(tc_prod(_1538973, _1538973)), hAPP(hAPP(c_Product__Type_OPair(_1538973, _1538973), _1538977), _1538977)), _1538975))], (39269 ^ _782435) ^ [_1539091, _1539093, _1539095, _1539097] : [c_Wellfounded_Owf(_1539091, _1539093), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539091, _1539091)), hAPP(hAPP(c_Product__Type_OPair(_1539091, _1539091), _1539095), _1539097)), _1539093)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539091, _1539091)), hAPP(hAPP(c_Product__Type_OPair(_1539091, _1539091), _1539097), _1539095)), _1539093))], (39279 ^ _782435) ^ [_1539305, _1539307, _1539309, _1539311] : [c_Wellfounded_Owf(_1539305, _1539307), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539305, _1539305)), hAPP(hAPP(c_Product__Type_OPair(_1539305, _1539305), _1539309), _1539311)), _1539307)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539305, _1539305)), hAPP(hAPP(c_Product__Type_OPair(_1539305, _1539305), _1539311), _1539309)), _1539307))], (39289 ^ _782435) ^ [_1539519, _1539521, _1539523] : [c_Wellfounded_Owf(_1539519, _1539521), hBOOL(hAPP(hAPP(c_member(tc_prod(_1539519, _1539519)), hAPP(hAPP(c_Product__Type_OPair(_1539519, _1539519), _1539523), _1539523)), _1539521))], (39295 ^ _782435) ^ [_1539637] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than(_1539637)))], (39297 ^ _782435) ^ [_1539662] : [-(c_Wellfounded_Owf(tc_Int_Oint, c_Int_Oint__ge__less__than2(_1539662)))], (39299 ^ _782435) ^ [_1539702, _1539704] : [c_Wellfounded_Owf(_1539702, _1539704), 39302 ^ _782435 : [(39303 ^ _782435) ^ [_1539771] : [-(hBOOL(hAPP(hAPP(c_member(_1539702), _1539771), c_Wellfounded_Oacc(_1539702, _1539704))))]]], (39305 ^ _782435) ^ [_1539804, _1539806] : [hBOOL(hAPP(hAPP(c_member(_1539804), 39306 ^ [_1539804, _1539806]), c_Wellfounded_Oacc(_1539804, _1539806))), -(c_Wellfounded_Owf(_1539804, _1539806))], (39312 ^ _782435) ^ [_1539937, _1539939, _1539941] : [c_Wellfounded_Owf(_1539937, _1539939), -(hBOOL(hAPP(hAPP(c_member(_1539937), _1539941), c_Wellfounded_Oacc(_1539937, _1539939))))], (39318 ^ _782435) ^ [_1540036, _1540038] : [hAPP(hAPP(c_Relation_Orel__comp(_1540036, _1540036, _1540036), _1540038), _1540038) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1540036, _1540036), tc_HOL_Obool)), -(c_Wellfounded_Owf(_1540036, _1540038))], (39324 ^ _782435) ^ [_1540167, _1540169, _1540171] : [c_Wellfounded_Owf(_1540167, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540167, _1540167), tc_HOL_Obool)), _1540169), _1540171)), -(c_Wellfounded_Owf(_1540167, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540167, _1540167), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540167, _1540167), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540167, _1540167, _1540167), _1540169), _1540169)), hAPP(hAPP(c_Relation_Orel__comp(_1540167, _1540167, _1540167), _1540171), _1540169))), _1540171)))], (39330 ^ _782435) ^ [_1540366, _1540368, _1540370] : [c_Wellfounded_Owf(_1540366, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540366, _1540366), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540366, _1540366), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1540366, _1540366, _1540366), _1540368), _1540368)), hAPP(hAPP(c_Relation_Orel__comp(_1540366, _1540366, _1540366), _1540370), _1540368))), _1540370)), -(c_Wellfounded_Owf(_1540366, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1540366, _1540366), tc_HOL_Obool)), _1540368), _1540370)))], (39336 ^ _782435) ^ [_1540586, _1540588] : [c_Wellfounded_Owf(_1540586, _1540588), 39340 ^ _782435 : [(39341 ^ _782435) ^ [_1540722] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1540586, _1540586)), hAPP(hAPP(c_Product__Type_OPair(_1540586, _1540586), hAPP(_1540722, hAPP(c_Nat_OSuc, 39339 ^ [_1540586, _1540588, _1540722]))), hAPP(_1540722, 39339 ^ [_1540586, _1540588, _1540722]))), _1540588))]]], (39343 ^ _782435) ^ [_1540789, _1540791] : [39345 ^ _782435 : [(39346 ^ _782435) ^ [_1540814] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1540789, _1540789)), hAPP(hAPP(c_Product__Type_OPair(_1540789, _1540789), hAPP(39344 ^ [_1540789, _1540791], hAPP(c_Nat_OSuc, _1540814))), hAPP(39344 ^ [_1540789, _1540791], _1540814))), _1540791)))]], -(c_Wellfounded_Owf(_1540789, _1540791))], (39350 ^ _782435) ^ [_1540890, _1540892, _1540894] : [c_Wellfounded_Owf(_1540890, _1540892), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1540890, tc_HOL_Obool)), _1540894), hAPP(c_Relation_OImage(_1540890, _1540890, _1540892), _1540894))), -(_1540894 = c_Orderings_Obot__class_Obot(tc_fun(_1540890, tc_HOL_Obool)))], (39360 ^ _782435) ^ [_1541067, _1541069, _1541071] : [c_Wellfounded_Owf(_1541067, _1541069), c_Wellfounded_Owf(_1541067, _1541071), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541067, _1541067), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541067, _1541067, _1541067), _1541069), _1541071)), _1541069)), -(c_Wellfounded_Owf(_1541067, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1541067, _1541067), tc_HOL_Obool)), _1541069), _1541071)))], (39374 ^ _782435) ^ [_1541328] : [class_Orderings_Owellorder(_1541328), -(c_Wellfounded_Owf(_1541328, hAPP(c_Set_OCollect(tc_prod(_1541328, _1541328)), hAPP(c_Product__Type_Oprod_Oprod__case(_1541328, _1541328, tc_HOL_Obool), c_Orderings_Oord__class_Oless(_1541328)))))], (39380 ^ _782435) ^ [_1541450, _1541452] : [c_FunDef_Oreduction__pair(_1541450, _1541452), 39383 ^ _782435 : [(39384 ^ _782435) ^ [] : [-(c_Wellfounded_Owf(_1541450, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool), tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool)), _1541452)))], (39386 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541450, _1541450, _1541450), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool), tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool)), _1541452)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool), tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool)), _1541452))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool), tc_fun(tc_prod(_1541450, _1541450), tc_HOL_Obool)), _1541452))))]]], (39388 ^ _782435) ^ [_1541739, _1541741] : [-(c_FunDef_Oreduction__pair(_1541739, _1541741)), c_Wellfounded_Owf(_1541739, hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool), tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool)), _1541741)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1541739, _1541739, _1541739), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool), tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool)), _1541741)), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool), tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool)), _1541741))), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool), tc_fun(tc_prod(_1541739, _1541739), tc_HOL_Obool)), _1541741)))], (39398 ^ _782435) ^ [_1542060, _1542062, _1542064, _1542066] : [c_FunDef_Oreduction__pair(_1542060, _1542062), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool)), _1542064), hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool), tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool)), _1542062))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool)), _1542066), hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool), tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool)), _1542062))), c_Wellfounded_Owf(_1542060, _1542066), -(c_Wellfounded_Owf(_1542060, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1542060, _1542060), tc_HOL_Obool)), _1542064), _1542066)))], (39416 ^ _782435) ^ [_1542461, _1542463] : [c_Wellfounded_Owf(_1542461, _1542463), -(c_Wellfounded_Owf(tc_List_Olist(_1542461), c_List_Olenlex(_1542461, _1542463)))], (39422 ^ _782435) ^ [_1542548, _1542550, _1542552, _1542554] : [39424 ^ _782435 : [(39425 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1542548, 39423 ^ [_1542548, _1542550, _1542552, _1542554])))], (39427 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1542550, hAPP(_1542552, 39423 ^ [_1542548, _1542550, _1542552, _1542554]))), hAPP(_1542550, 39423 ^ [_1542548, _1542550, _1542552, _1542554])))]], -(c_Wellfounded_Owf(_1542554, hAPP(c_Set_OCollect(tc_prod(_1542554, _1542554)), hAPP(c_Product__Type_Oprod_Oprod__case(_1542554, _1542554, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1542554, tc_HOL_Obool), tc_fun(_1542554, tc_HOL_Obool), _1542554), hAPP(c_COMBS(_1542554, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1542554), c_fconj), _1542548))), hAPP(hAPP(c_COMBC(_1542554, tc_fun(_1542554, _1542554), tc_fun(_1542554, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1542554, tc_HOL_Obool), tc_fun(tc_fun(_1542554, _1542554), tc_fun(_1542554, tc_HOL_Obool)), _1542554), c_COMBB(_1542554, tc_HOL_Obool, _1542554)), c_fequal)), _1542552))))))], (39431 ^ _782435) ^ [_1542941, _1542943, _1542945, _1542947] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1542941), _1542943)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1542941), _1542945)), -(_1542945 = c_Orderings_Obot__class_Obot(tc_fun(_1542941, tc_HOL_Obool))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1542941, tc_HOL_Obool), tc_fun(_1542941, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1542941, tc_HOL_Obool), tc_fun(_1542941, tc_HOL_Obool)), _1542943), _1542945)), c_Wellfounded_Omax__ext(_1542941, _1542947)))), 39445 ^ _782435 : [(39446 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1542941), 39444 ^ [_1542941, _1542943, _1542945, _1542947]), _1542943)))], (39448 ^ _782435) ^ [_1543346] : [hBOOL(hAPP(hAPP(c_member(_1542941), _1543346), _1542945)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1542941, _1542941)), hAPP(hAPP(c_Product__Type_OPair(_1542941, _1542941), 39444 ^ [_1542941, _1542943, _1542945, _1542947]), _1543346)), _1542947))]]], (39456 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1543590, _1543592] : [c_Wellfounded_Owf(_1543590, _1543592), -(c_Wellfounded_Owf(tc_List_Olist(_1543590), c_List_Olex(_1543590, _1543592)))], (39464 ^ _782435) ^ [_1543677, _1543679, _1543681] : [c_Wellfounded_Owf(_1543677, _1543679), -(c_Wellfounded_Owf(tc_List_Olist(_1543677), hAPP(c_List_Olexn(_1543677, _1543679), _1543681)))], (39470 ^ _782435) ^ [_1543772, _1543774] : [-(c_List_Olex(_1543772, _1543774) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(tc_List_Olist(_1543772), tc_List_Olist(_1543772)), tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), c_List_Olexn(_1543772, _1543774)))], (39472 ^ _782435) ^ [_1543822, _1543824] : [-(hAPP(c_List_Olexn(_1543822, _1543824), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(_1543822), tc_List_Olist(_1543822)), tc_HOL_Obool)))], (39474 ^ _782435) ^ [] : [-(c_Wellfounded_Owf(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (39476 ^ _782435) ^ [_1543883, _1543885, _1543887, _1543889] : [39478 ^ _782435 : [(39479 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1543883, 39477 ^ [_1543883, _1543885, _1543887, _1543889])))], (39481 ^ _782435) ^ [] : [c_Wellfounded_Owf(_1543885, hAPP(_1543887, 39477 ^ [_1543883, _1543885, _1543887, _1543889]))]], -(c_Wellfounded_Owf(tc_prod(_1543889, _1543885), c_Recdef_Osame__fst(_1543889, _1543885, _1543883, _1543887)))], (39485 ^ _782435) ^ [_1544068] : [-(c_Nitpick_Ozero__frac(_1544068) = c_Nitpick_OAbs__Frac(_1544068, 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 ^ _782435) ^ [_1544096, _1544098, _1544100] : [-(hAPP(c_Relation_ORange(_1544096, _1544098), hAPP(c_Set_OCollect(tc_prod(_1544096, _1544098)), hAPP(c_Product__Type_Oprod_Oprod__case(_1544096, _1544098, tc_HOL_Obool), _1544100))) = hAPP(c_Set_OCollect(_1544098), hAPP(hAPP(c_COMBB(tc_fun(_1544096, tc_HOL_Obool), tc_HOL_Obool, _1544098), c_HOL_OEx(_1544096)), hAPP(c_COMBC(_1544096, _1544098, tc_HOL_Obool), _1544100))))], (39489 ^ _782435) ^ [_1544171, _1544173, _1544175, _1544177, _1544179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1544171, _1544173)), hAPP(hAPP(c_Product__Type_OPair(_1544171, _1544173), _1544175), _1544177)), _1544179)), -(hBOOL(hAPP(hAPP(c_member(_1544173), _1544177), hAPP(c_Relation_ORange(_1544171, _1544173), _1544179))))], (39495 ^ _782435) ^ [_1544318, _1544320] : [-(hAPP(c_Relation_ORange(_1544318, _1544318), c_Relation_OId__on(_1544318, _1544320)) = _1544320)], (39497 ^ _782435) ^ [_1544352, _1544354, _1544356, _1544358] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1544352, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1544352, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544354, _1544352), _1544356)), hAPP(c_Relation_ORange(_1544354, _1544352), _1544358))), hAPP(c_Relation_ORange(_1544354, _1544352), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1544354, _1544352), tc_HOL_Obool)), _1544356), _1544358)))))], (39499 ^ _782435) ^ [_1544434, _1544436, _1544438] : [-(hAPP(c_Relation_ORange(_1544434, _1544436), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1544434, _1544436), tc_HOL_Obool), _1544438)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1544434, _1544436), tc_HOL_Obool), tc_fun(_1544436, tc_HOL_Obool)), _1544438), c_Relation_ORange(_1544434, _1544436)))], (39501 ^ _782435) ^ [_1544497, _1544499] : [-(hAPP(c_Relation_ORange(_1544497, _1544499), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544497, _1544499), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1544499, tc_HOL_Obool)))], (39503 ^ _782435) ^ [_1544559, _1544561, _1544563] : [hAPP(c_Relation_ORange(_1544559, _1544561), _1544563) = c_Orderings_Obot__class_Obot(tc_fun(_1544561, tc_HOL_Obool)), -(_1544563 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544559, _1544561), tc_HOL_Obool)))], (39509 ^ _782435) ^ [_1544672, _1544674, _1544676] : [_1544676 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1544672, _1544674), tc_HOL_Obool)), -(hAPP(c_Relation_ORange(_1544672, _1544674), _1544676) = c_Orderings_Obot__class_Obot(tc_fun(_1544674, tc_HOL_Obool)))], (39515 ^ _782435) ^ [_1544791, _1544793, _1544795, _1544797] : [-(hAPP(c_Relation_ORange(_1544791, _1544793), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1544791, _1544793), tc_HOL_Obool)), _1544795), _1544797)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1544793, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1544791, _1544793), _1544795)), hAPP(c_Relation_ORange(_1544791, _1544793), _1544797)))], (39517 ^ _782435) ^ [_1544863, _1544865, _1544867] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1544863, _1544865)), _1544867)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1544865), hAPP(c_Relation_ORange(_1544863, _1544865), _1544867))))], (39523 ^ _782435) ^ [_1544976, _1544978, _1544980] : [-(hAPP(c_Set_Oimage(tc_prod(_1544976, _1544978), _1544978, c_Product__Type_Osnd(_1544976, _1544978)), _1544980) = hAPP(c_Relation_ORange(_1544976, _1544978), _1544980))], (39525 ^ _782435) ^ [_1545043, _1545045, _1545047, _1545049] : [hBOOL(hAPP(hAPP(c_member(_1545043), _1545045), hAPP(c_Relation_ORange(_1545047, _1545043), _1545049))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1545047, _1545043)), hAPP(hAPP(c_Product__Type_OPair(_1545047, _1545043), 39528 ^ [_1545043, _1545045, _1545047, _1545049]), _1545045)), _1545049)))], (39532 ^ _782435) ^ [_1545200, _1545202, _1545204, _1545206] : [39533 ^ _782435 : [(39534 ^ _782435) ^ [_1545275] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1545204, _1545200)), hAPP(hAPP(c_Product__Type_OPair(_1545204, _1545200), _1545275), _1545202)), _1545206))]], -(hBOOL(hAPP(hAPP(c_member(_1545200), _1545202), hAPP(c_Relation_ORange(_1545204, _1545200), _1545206))))], (39538 ^ _782435) ^ [_1545360, _1545362, _1545364, _1545366, _1545368] : [-(hAPP(c_Relation_ORange(_1545360, _1545362), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1545360, _1545362)), hAPP(hAPP(c_Product__Type_OPair(_1545360, _1545362), _1545364), _1545366)), _1545368)) = hAPP(hAPP(c_Set_Oinsert(_1545362), _1545366), hAPP(c_Relation_ORange(_1545360, _1545362), _1545368)))], (39540 ^ _782435) ^ [_1545431, _1545433, _1545435, _1545437] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1545431, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545433, _1545431), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1545433, _1545431), tc_HOL_Obool)), _1545435), _1545437))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1545431, tc_HOL_Obool)), hAPP(c_Relation_ORange(_1545433, _1545431), _1545435)), hAPP(c_Relation_ORange(_1545433, _1545431), _1545437)))))], (39542 ^ _782435) ^ [_1545513] : [-(c_Nitpick_Oone__frac(_1545513) = c_Nitpick_OAbs__Frac(_1545513, 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 ^ _782435) ^ [_1545541, _1545543] : [-(c_Nitpick_Onumber__of__frac(_1545541, _1545543) = c_Nitpick_OAbs__Frac(_1545541, hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint, tc_Int_Oint), _1545543), c_Groups_Oone__class_Oone(tc_Int_Oint))))], (39546 ^ _782435) ^ [_1545599, _1545601, _1545603, _1545605] : [hBOOL(hAPP(c_Predicate_ORangeP(_1545599, _1545601, hAPP(hAPP(c_COMBC(_1545599, tc_fun(tc_prod(_1545599, _1545601), tc_HOL_Obool), tc_fun(_1545601, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545601, tc_fun(tc_fun(tc_prod(_1545599, _1545601), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545599, _1545601), tc_HOL_Obool), tc_fun(_1545601, tc_HOL_Obool)), _1545599), c_COMBC(_1545601, tc_fun(tc_prod(_1545599, _1545601), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545601, tc_prod(_1545599, _1545601)), tc_fun(_1545601, tc_fun(tc_fun(tc_prod(_1545599, _1545601), tc_HOL_Obool), tc_HOL_Obool)), _1545599), hAPP(c_COMBB(tc_prod(_1545599, _1545601), tc_fun(tc_fun(tc_prod(_1545599, _1545601), tc_HOL_Obool), tc_HOL_Obool), _1545601), c_member(tc_prod(_1545599, _1545601)))), c_Product__Type_OPair(_1545599, _1545601)))), _1545603)), _1545605)), -(hBOOL(hAPP(hAPP(c_member(_1545601), _1545605), hAPP(c_Relation_ORange(_1545599, _1545601), _1545603))))], (39552 ^ _782435) ^ [_1545950, _1545952, _1545954, _1545956] : [hBOOL(hAPP(hAPP(c_member(_1545952), _1545956), hAPP(c_Relation_ORange(_1545950, _1545952), _1545954))), -(hBOOL(hAPP(c_Predicate_ORangeP(_1545950, _1545952, hAPP(hAPP(c_COMBC(_1545950, tc_fun(tc_prod(_1545950, _1545952), tc_HOL_Obool), tc_fun(_1545952, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545952, tc_fun(tc_fun(tc_prod(_1545950, _1545952), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1545950, _1545952), tc_HOL_Obool), tc_fun(_1545952, tc_HOL_Obool)), _1545950), c_COMBC(_1545952, tc_fun(tc_prod(_1545950, _1545952), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1545952, tc_prod(_1545950, _1545952)), tc_fun(_1545952, tc_fun(tc_fun(tc_prod(_1545950, _1545952), tc_HOL_Obool), tc_HOL_Obool)), _1545950), hAPP(c_COMBB(tc_prod(_1545950, _1545952), tc_fun(tc_fun(tc_prod(_1545950, _1545952), tc_HOL_Obool), tc_HOL_Obool), _1545952), c_member(tc_prod(_1545950, _1545952)))), c_Product__Type_OPair(_1545950, _1545952)))), _1545954)), _1545956)))], (39558 ^ _782435) ^ [_1546307, _1546309, _1546311, _1546313, _1546315] : [hBOOL(hAPP(hAPP(_1546307, _1546309), _1546311)), -(hBOOL(hAPP(c_Predicate_ORangeP(_1546313, _1546315, _1546307), _1546311)))], (39564 ^ _782435) ^ [_1546433, _1546435, _1546437, _1546439] : [hBOOL(hAPP(c_Predicate_ORangeP(_1546433, _1546435, _1546437), _1546439)), -(hBOOL(hAPP(hAPP(_1546437, 39567 ^ [_1546433, _1546435, _1546437, _1546439]), _1546439)))], (39571 ^ _782435) ^ [_1546548, _1546550, _1546552, _1546554] : [39572 ^ _782435 : [(39573 ^ _782435) ^ [_1546602] : [hBOOL(hAPP(hAPP(_1546552, _1546602), _1546554))]], -(hBOOL(hAPP(c_Predicate_ORangeP(_1546548, _1546550, _1546552), _1546554)))], (39577 ^ _782435) ^ [_1546666, _1546668, _1546670] : [-(hAPP(hAPP(c_Nitpick_Ofrac(_1546666), _1546668), _1546670) = c_Nitpick_OAbs__Frac(_1546666, c_Nitpick_Onorm__frac(_1546668, _1546670)))], (39579 ^ _782435) ^ [_1546707, _1546709, _1546711, _1546713] : [hBOOL(hAPP(hAPP(c_member(_1546707), _1546709), hAPP(c_Relation_ORange(_1546711, _1546707), _1546713))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1546711, _1546707)), hAPP(hAPP(c_Product__Type_OPair(_1546711, _1546707), 39582 ^ [_1546707, _1546709, _1546711, _1546713]), _1546709)), _1546713)))], (39586 ^ _782435) ^ [_1546872, _1546874, _1546876] : [c_Wellfounded_Owf(_1546872, _1546874), c_Wellfounded_Owf(_1546872, _1546876), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1546872, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1546872, _1546872), _1546874)), hAPP(c_Relation_ORange(_1546872, _1546872), _1546876)) = c_Orderings_Obot__class_Obot(tc_fun(_1546872, tc_HOL_Obool)), -(c_Wellfounded_Owf(_1546872, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1546872, _1546872), tc_HOL_Obool)), _1546874), _1546876)))], (39600 ^ _782435) ^ [_1547143, _1547145, _1547147, _1547149, _1547151] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1547143, _1547145)), hAPP(hAPP(c_Product__Type_OPair(_1547143, _1547145), _1547147), _1547149)), _1547151)), -(hBOOL(hAPP(hAPP(c_member(_1547143), _1547147), hAPP(c_Relation_ODomain(_1547143, _1547145), _1547151))))], (39606 ^ _782435) ^ [_1547290, _1547292] : [-(hAPP(c_Relation_ODomain(_1547290, _1547290), c_Relation_OId__on(_1547290, _1547292)) = _1547292)], (39608 ^ _782435) ^ [_1547324, _1547326] : [-(hAPP(c_Relation_ODomain(_1547324, _1547326), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547324, _1547326), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(_1547324, tc_HOL_Obool)))], (39610 ^ _782435) ^ [_1547386, _1547388, _1547390] : [hAPP(c_Relation_ODomain(_1547386, _1547388), _1547390) = c_Orderings_Obot__class_Obot(tc_fun(_1547386, tc_HOL_Obool)), -(_1547390 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547386, _1547388), tc_HOL_Obool)))], (39616 ^ _782435) ^ [_1547499, _1547501, _1547503] : [_1547503 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1547499, _1547501), tc_HOL_Obool)), -(hAPP(c_Relation_ODomain(_1547499, _1547501), _1547503) = c_Orderings_Obot__class_Obot(tc_fun(_1547499, tc_HOL_Obool)))], (39622 ^ _782435) ^ [_1547618, _1547620, _1547622, _1547624] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1547618, _1547620), tc_HOL_Obool)), _1547622), _1547624)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1547618, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1547618, _1547620), _1547622)), hAPP(c_Relation_ODomain(_1547618, _1547620), _1547624))))], (39628 ^ _782435) ^ [_1547769, _1547771, _1547773, _1547775] : [-(hAPP(c_Relation_ODomain(_1547769, _1547771), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1547769, _1547771), tc_HOL_Obool)), _1547773), _1547775)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1547769, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1547769, _1547771), _1547773)), hAPP(c_Relation_ODomain(_1547769, _1547771), _1547775)))], (39630 ^ _782435) ^ [_1547841, _1547843, _1547845] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1547841, _1547843)), _1547845)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1547841), hAPP(c_Relation_ODomain(_1547841, _1547843), _1547845))))], (39636 ^ _782435) ^ [_1547954, _1547956, _1547958] : [-(hAPP(c_Set_Oimage(tc_prod(_1547954, _1547956), _1547954, c_Product__Type_Ofst(_1547954, _1547956)), _1547958) = hAPP(c_Relation_ODomain(_1547954, _1547956), _1547958))], (39638 ^ _782435) ^ [_1548021, _1548023, _1548025, _1548027] : [hBOOL(hAPP(hAPP(c_member(_1548021), _1548023), hAPP(c_Relation_ODomain(_1548021, _1548025), _1548027))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1548021, _1548025)), hAPP(hAPP(c_Product__Type_OPair(_1548021, _1548025), _1548023), 39641 ^ [_1548021, _1548023, _1548025, _1548027])), _1548027)))], (39645 ^ _782435) ^ [_1548178, _1548180, _1548182, _1548184] : [39646 ^ _782435 : [(39647 ^ _782435) ^ [_1548253] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1548178, _1548182)), hAPP(hAPP(c_Product__Type_OPair(_1548178, _1548182), _1548180), _1548253)), _1548184))]], -(hBOOL(hAPP(hAPP(c_member(_1548178), _1548180), hAPP(c_Relation_ODomain(_1548178, _1548182), _1548184))))], (39651 ^ _782435) ^ [_1548338, _1548340, _1548342, _1548344, _1548346] : [-(hAPP(c_Relation_ODomain(_1548338, _1548340), hAPP(hAPP(c_Set_Oinsert(tc_prod(_1548338, _1548340)), hAPP(hAPP(c_Product__Type_OPair(_1548338, _1548340), _1548342), _1548344)), _1548346)) = hAPP(hAPP(c_Set_Oinsert(_1548338), _1548342), hAPP(c_Relation_ODomain(_1548338, _1548340), _1548346)))], (39653 ^ _782435) ^ [_1548409, _1548411, _1548413, _1548415] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548409, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548409, _1548411), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1548409, _1548411), tc_HOL_Obool)), _1548413), _1548415))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1548409, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548409, _1548411), _1548413)), hAPP(c_Relation_ODomain(_1548409, _1548411), _1548415)))))], (39655 ^ _782435) ^ [_1548491, _1548493, _1548495, _1548497] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1548491, tc_HOL_Obool)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1548491, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548491, _1548493), _1548495)), hAPP(c_Relation_ODomain(_1548491, _1548493), _1548497))), hAPP(c_Relation_ODomain(_1548491, _1548493), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1548491, _1548493), tc_HOL_Obool)), _1548495), _1548497)))))], (39657 ^ _782435) ^ [_1548573, _1548575] : [-(hAPP(c_Relation_OField(_1548573), _1548575) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1548573, tc_HOL_Obool)), hAPP(c_Relation_ODomain(_1548573, _1548573), _1548575)), hAPP(c_Relation_ORange(_1548573, _1548573), _1548575)))], (39659 ^ _782435) ^ [_1548626, _1548628, _1548630] : [-(hAPP(c_Relation_ODomain(_1548626, _1548628), c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(_1548626, _1548628), tc_HOL_Obool), _1548630)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(_1548626, _1548628), tc_HOL_Obool), tc_fun(_1548626, tc_HOL_Obool)), _1548630), c_Relation_ODomain(_1548626, _1548628)))], (39661 ^ _782435) ^ [_1548689, _1548691, _1548693] : [-(hAPP(c_Relation_ODomain(_1548689, _1548691), hAPP(c_Set_OCollect(tc_prod(_1548689, _1548691)), hAPP(c_Product__Type_Oprod_Oprod__case(_1548689, _1548691, tc_HOL_Obool), _1548693))) = hAPP(c_Set_OCollect(_1548689), hAPP(hAPP(c_COMBB(tc_fun(_1548691, tc_HOL_Obool), tc_HOL_Obool, _1548689), c_HOL_OEx(_1548691)), _1548693)))], (39663 ^ _782435) ^ [_1548778, _1548780, _1548782, _1548784] : [hBOOL(hAPP(c_Predicate_ODomainP(_1548778, _1548780, hAPP(hAPP(c_COMBC(_1548778, tc_fun(tc_prod(_1548778, _1548780), tc_HOL_Obool), tc_fun(_1548780, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548780, tc_fun(tc_fun(tc_prod(_1548778, _1548780), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1548778, _1548780), tc_HOL_Obool), tc_fun(_1548780, tc_HOL_Obool)), _1548778), c_COMBC(_1548780, tc_fun(tc_prod(_1548778, _1548780), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1548780, tc_prod(_1548778, _1548780)), tc_fun(_1548780, tc_fun(tc_fun(tc_prod(_1548778, _1548780), tc_HOL_Obool), tc_HOL_Obool)), _1548778), hAPP(c_COMBB(tc_prod(_1548778, _1548780), tc_fun(tc_fun(tc_prod(_1548778, _1548780), tc_HOL_Obool), tc_HOL_Obool), _1548780), c_member(tc_prod(_1548778, _1548780)))), c_Product__Type_OPair(_1548778, _1548780)))), _1548782)), _1548784)), -(hBOOL(hAPP(hAPP(c_member(_1548778), _1548784), hAPP(c_Relation_ODomain(_1548778, _1548780), _1548782))))], (39669 ^ _782435) ^ [_1549129, _1549131, _1549133, _1549135] : [hBOOL(hAPP(hAPP(c_member(_1549129), _1549135), hAPP(c_Relation_ODomain(_1549129, _1549131), _1549133))), -(hBOOL(hAPP(c_Predicate_ODomainP(_1549129, _1549131, hAPP(hAPP(c_COMBC(_1549129, tc_fun(tc_prod(_1549129, _1549131), tc_HOL_Obool), tc_fun(_1549131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549131, tc_fun(tc_fun(tc_prod(_1549129, _1549131), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1549129, _1549131), tc_HOL_Obool), tc_fun(_1549131, tc_HOL_Obool)), _1549129), c_COMBC(_1549131, tc_fun(tc_prod(_1549129, _1549131), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549131, tc_prod(_1549129, _1549131)), tc_fun(_1549131, tc_fun(tc_fun(tc_prod(_1549129, _1549131), tc_HOL_Obool), tc_HOL_Obool)), _1549129), hAPP(c_COMBB(tc_prod(_1549129, _1549131), tc_fun(tc_fun(tc_prod(_1549129, _1549131), tc_HOL_Obool), tc_HOL_Obool), _1549131), c_member(tc_prod(_1549129, _1549131)))), c_Product__Type_OPair(_1549129, _1549131)))), _1549133)), _1549135)))], (39675 ^ _782435) ^ [_1549486, _1549488, _1549490, _1549492] : [hBOOL(hAPP(hAPP(c_member(_1549486), _1549488), hAPP(c_Relation_ODomain(_1549486, _1549490), _1549492))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549486, _1549490)), hAPP(hAPP(c_Product__Type_OPair(_1549486, _1549490), _1549488), 39678 ^ [_1549486, _1549488, _1549490, _1549492])), _1549492)))], (39682 ^ _782435) ^ [_1549651, _1549653, _1549655, _1549657, _1549659, _1549661] : [-(hAPP(c_Set_Oimage(_1549651, tc_prod(_1549653, _1549655), hAPP(hAPP(c_COMBS(_1549651, _1549655, tc_prod(_1549653, _1549655)), hAPP(hAPP(c_COMBB(_1549653, tc_fun(_1549655, tc_prod(_1549653, _1549655)), _1549651), c_Product__Type_OPair(_1549653, _1549655)), _1549657)), _1549659)), _1549661) = hAPP(hAPP(c_Product__Type_OSigma(_1549653, _1549655), hAPP(c_Set_Oimage(_1549651, _1549653, _1549657), _1549661)), hAPP(hAPP(c_COMBB(tc_fun(_1549651, tc_HOL_Obool), tc_fun(_1549655, tc_HOL_Obool), _1549653), c_Set_Oimage(_1549651, _1549655, _1549659)), hAPP(hAPP(c_COMBC(_1549653, tc_fun(_1549651, tc_HOL_Obool), tc_fun(_1549651, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1549651, tc_HOL_Obool), tc_fun(tc_fun(_1549651, tc_HOL_Obool), tc_fun(_1549651, tc_HOL_Obool)), _1549653), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1549651, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1549653, tc_HOL_Obool), tc_fun(_1549651, tc_HOL_Obool), _1549653), c_Set_Ovimage(_1549651, _1549653, _1549657)), hAPP(hAPP(c_COMBC(_1549653, tc_fun(_1549653, tc_HOL_Obool), tc_fun(_1549653, tc_HOL_Obool)), c_Set_Oinsert(_1549653)), c_Orderings_Obot__class_Obot(tc_fun(_1549653, tc_HOL_Obool)))))), _1549661))))], (39684 ^ _782435) ^ [_1549848, _1549850, _1549852, _1549854, _1549856] : [hBOOL(hAPP(hAPP(_1549848, _1549850), _1549852)), -(hBOOL(hAPP(c_Predicate_ODomainP(_1549854, _1549856, _1549848), _1549850)))], (39690 ^ _782435) ^ [_1549953, _1549955, _1549957, _1549959, _1549961, _1549963] : [hBOOL(hAPP(hAPP(c_member(_1549953), _1549955), _1549957)), hBOOL(hAPP(hAPP(c_member(_1549959), _1549961), hAPP(_1549963, _1549955))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1549953, _1549959)), hAPP(hAPP(c_Product__Type_OPair(_1549953, _1549959), _1549955), _1549961)), hAPP(hAPP(c_Product__Type_OSigma(_1549953, _1549959), _1549957), _1549963))))], (39700 ^ _782435) ^ [_1550188, _1550190, _1550192] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550188, _1550190), c_Orderings_Obot__class_Obot(tc_fun(_1550188, tc_HOL_Obool))), _1550192) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1550188, _1550190), tc_HOL_Obool)))], (39702 ^ _782435) ^ [_1550237, _1550239, _1550241, _1550243, _1550245, _1550247] : [hBOOL(hAPP(hAPP(c_member(_1550237), _1550239), _1550241)), 39705 ^ _782435 : [(39706 ^ _782435) ^ [] : [hAPP(hAPP(c_Product__Type_OSigma(_1550243, _1550237), _1550245), hAPP(c_COMBK(tc_fun(_1550237, tc_HOL_Obool), _1550243), _1550241)) = hAPP(hAPP(c_Product__Type_OSigma(_1550243, _1550237), _1550247), hAPP(c_COMBK(tc_fun(_1550237, tc_HOL_Obool), _1550243), _1550241)), -(_1550245 = _1550247)], (39712 ^ _782435) ^ [] : [_1550245 = _1550247, -(hAPP(hAPP(c_Product__Type_OSigma(_1550243, _1550237), _1550245), hAPP(c_COMBK(tc_fun(_1550237, tc_HOL_Obool), _1550243), _1550241)) = hAPP(hAPP(c_Product__Type_OSigma(_1550243, _1550237), _1550247), hAPP(c_COMBK(tc_fun(_1550237, tc_HOL_Obool), _1550243), _1550241)))]]], (39718 ^ _782435) ^ [_1550590, _1550592, _1550594, _1550596] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550590, _1550592), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1550590, tc_HOL_Obool), _1550594)), _1550596) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(_1550590, tc_HOL_Obool), tc_fun(tc_prod(_1550590, _1550592), tc_HOL_Obool)), _1550594), hAPP(hAPP(c_COMBC(tc_fun(_1550590, tc_HOL_Obool), tc_fun(_1550590, tc_fun(_1550592, tc_HOL_Obool)), tc_fun(tc_prod(_1550590, _1550592), tc_HOL_Obool)), c_Product__Type_OSigma(_1550590, _1550592)), _1550596)))], (39720 ^ _782435) ^ [_1550680, _1550682, _1550684, _1550686] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1550680, _1550682)), hAPP(hAPP(c_Product__Type_OSigma(_1550680, _1550682), _1550684), hAPP(c_COMBK(tc_fun(_1550682, tc_HOL_Obool), _1550680), _1550686))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1550680), _1550684)), hAPP(c_Finite__Set_Ocard(_1550682), _1550686)))], (39722 ^ _782435) ^ [_1550751, _1550753, _1550755, _1550757, _1550759, _1550761] : [class_Groups_Ocomm__monoid__add(_1550751), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550753, _1550751), hAPP(hAPP(c_COMBC(_1550753, tc_fun(_1550755, tc_HOL_Obool), _1550751), hAPP(hAPP(c_COMBB(tc_fun(_1550755, _1550751), tc_fun(tc_fun(_1550755, tc_HOL_Obool), _1550751), _1550753), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1550755, _1550751)), _1550757)), _1550759)), _1550761) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1550753, _1550755), _1550751), hAPP(c_Product__Type_Oprod_Oprod__case(_1550753, _1550755, _1550751), _1550757)), hAPP(hAPP(c_Product__Type_OSigma(_1550753, _1550755), _1550761), hAPP(c_COMBK(tc_fun(_1550755, tc_HOL_Obool), _1550753), _1550759))))], (39728 ^ _782435) ^ [_1550996, _1550998, _1551000] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1550996, _1550998), _1551000), hAPP(c_COMBK(tc_fun(_1550998, tc_HOL_Obool), _1550996), c_Orderings_Obot__class_Obot(tc_fun(_1550998, tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1550996, _1550998), tc_HOL_Obool)))], (39740 ^ _782435) ^ [_1551237, _1551239, _1551241, _1551243] : [39741 ^ _782435 : [(39742 ^ _782435) ^ [] : [_1551241 = c_Orderings_Obot__class_Obot(tc_fun(_1551237, tc_HOL_Obool))], (39744 ^ _782435) ^ [] : [_1551243 = c_Orderings_Obot__class_Obot(tc_fun(_1551239, tc_HOL_Obool))]], -(hAPP(hAPP(c_Product__Type_OSigma(_1551237, _1551239), _1551241), hAPP(c_COMBK(tc_fun(_1551239, tc_HOL_Obool), _1551237), _1551243)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551237, _1551239), tc_HOL_Obool)))], (39730 ^ _782435) ^ [_1551075, _1551077, _1551079, _1551081] : [hAPP(hAPP(c_Product__Type_OSigma(_1551075, _1551077), _1551079), hAPP(c_COMBK(tc_fun(_1551077, tc_HOL_Obool), _1551075), _1551081)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1551075, _1551077), tc_HOL_Obool)), -(_1551079 = c_Orderings_Obot__class_Obot(tc_fun(_1551075, tc_HOL_Obool))), -(_1551081 = c_Orderings_Obot__class_Obot(tc_fun(_1551077, tc_HOL_Obool)))], (39748 ^ _782435) ^ [_1551430, _1551432, _1551434] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1551430, _1551432), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551430, _1551432), _1551434), hAPP(c_COMBK(tc_fun(_1551432, tc_HOL_Obool), _1551430), c_Orderings_Otop__class_Otop(tc_fun(_1551432, tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(_1551430, _1551432), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1551430, tc_HOL_Obool)), _1551434)), hAPP(c_COMBK(tc_fun(_1551432, tc_HOL_Obool), _1551430), c_Orderings_Otop__class_Otop(tc_fun(_1551432, tc_HOL_Obool)))))], (39750 ^ _782435) ^ [_1551522, _1551524, _1551526] : [-(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(_1551522, _1551524), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551522, _1551524), c_Orderings_Otop__class_Otop(tc_fun(_1551522, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1551524, tc_HOL_Obool), _1551522), _1551526))) = hAPP(hAPP(c_Product__Type_OSigma(_1551522, _1551524), c_Orderings_Otop__class_Otop(tc_fun(_1551522, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1551524, tc_HOL_Obool), _1551522), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1551524, tc_HOL_Obool)), _1551526))))], (39752 ^ _782435) ^ [_1551614, _1551616, _1551618, _1551620, _1551622, _1551624] : [class_Groups_Ocomm__monoid__mult(_1551614), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1551616, _1551614), hAPP(hAPP(c_COMBC(_1551616, tc_fun(_1551618, tc_HOL_Obool), _1551614), hAPP(hAPP(c_COMBB(tc_fun(_1551618, _1551614), tc_fun(tc_fun(_1551618, tc_HOL_Obool), _1551614), _1551616), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1551618, _1551614)), _1551620)), _1551622)), _1551624) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1551616, _1551618), _1551614), hAPP(c_Product__Type_Oprod_Oprod__case(_1551616, _1551618, _1551614), _1551620)), hAPP(hAPP(c_Product__Type_OSigma(_1551616, _1551618), _1551624), hAPP(c_COMBK(tc_fun(_1551618, tc_HOL_Obool), _1551616), _1551622))))], (39758 ^ _782435) ^ [_1551859, _1551861, _1551863, _1551865, _1551867] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551859, _1551861), _1551863), hAPP(hAPP(c_COMBS(_1551859, tc_fun(_1551861, tc_HOL_Obool), tc_fun(_1551861, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1551861, tc_HOL_Obool), tc_fun(tc_fun(_1551861, tc_HOL_Obool), tc_fun(_1551861, tc_HOL_Obool)), _1551859), c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1551861, tc_HOL_Obool))), _1551865)), _1551867)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551859, _1551861), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551859, _1551861), _1551863), _1551865)), hAPP(hAPP(c_Product__Type_OSigma(_1551859, _1551861), _1551863), _1551867)))], (39760 ^ _782435) ^ [_1551974, _1551976, _1551978, _1551980, _1551982] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1551974, _1551976), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1551974, tc_HOL_Obool)), _1551978), _1551980)), hAPP(c_COMBK(tc_fun(_1551976, tc_HOL_Obool), _1551974), _1551982)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1551974, _1551976), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1551974, _1551976), _1551978), hAPP(c_COMBK(tc_fun(_1551976, tc_HOL_Obool), _1551974), _1551982))), hAPP(hAPP(c_Product__Type_OSigma(_1551974, _1551976), _1551980), hAPP(c_COMBK(tc_fun(_1551976, tc_HOL_Obool), _1551974), _1551982))))], (39762 ^ _782435) ^ [_1552084, _1552086, _1552088, _1552090, _1552092] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1552084, _1552086), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1552084, tc_HOL_Obool)), _1552088), _1552090)), _1552092) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1552084, _1552086), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552084, _1552086), _1552088), _1552092)), hAPP(hAPP(c_Product__Type_OSigma(_1552084, _1552086), _1552090), _1552092)))], (39764 ^ _782435) ^ [_1552167, _1552169, _1552171, _1552173, _1552175, _1552177, _1552179, _1552181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552167, _1552169), tc_HOL_Obool)), _1552171), hAPP(hAPP(c_Product__Type_OSigma(_1552167, _1552169), _1552173), hAPP(c_COMBK(tc_fun(_1552169, tc_HOL_Obool), _1552167), _1552175)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552169, _1552177), tc_HOL_Obool)), _1552179), hAPP(hAPP(c_Product__Type_OSigma(_1552169, _1552177), _1552175), hAPP(c_COMBK(tc_fun(_1552177, tc_HOL_Obool), _1552169), _1552181)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552167, _1552177), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1552167, _1552169, _1552177), _1552171), _1552179)), hAPP(hAPP(c_Product__Type_OSigma(_1552167, _1552177), _1552173), hAPP(c_COMBK(tc_fun(_1552177, tc_HOL_Obool), _1552167), _1552181)))))], (39774 ^ _782435) ^ [_1552526, _1552528, _1552530, _1552532] : [-(hAPP(c_Set_Oimage(tc_prod(_1552526, _1552528), tc_prod(_1552528, _1552526), hAPP(c_Product__Type_Oprod_Oprod__case(_1552526, _1552528, tc_prod(_1552528, _1552526)), hAPP(c_COMBC(_1552528, _1552526, tc_prod(_1552528, _1552526)), c_Product__Type_OPair(_1552528, _1552526)))), hAPP(hAPP(c_Product__Type_OSigma(_1552526, _1552528), _1552530), hAPP(c_COMBK(tc_fun(_1552528, tc_HOL_Obool), _1552526), _1552532))) = hAPP(hAPP(c_Product__Type_OSigma(_1552528, _1552526), _1552532), hAPP(c_COMBK(tc_fun(_1552526, tc_HOL_Obool), _1552528), _1552530)))], (39776 ^ _782435) ^ [_1552627, _1552629, _1552631, _1552633] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1552627), _1552629)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1552631), _1552633)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1552627, _1552631)), hAPP(hAPP(c_Product__Type_OSigma(_1552627, _1552631), _1552629), hAPP(c_COMBK(tc_fun(_1552631, tc_HOL_Obool), _1552627), _1552633)))))], (39786 ^ _782435) ^ [_1552830, _1552832, _1552834] : [c_Equiv__Relations_Oequiv(_1552830, _1552832, _1552834), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1552830, _1552830), tc_HOL_Obool)), _1552834), hAPP(hAPP(c_Product__Type_OSigma(_1552830, _1552830), _1552832), hAPP(c_COMBK(tc_fun(_1552830, tc_HOL_Obool), _1552830), _1552832)))))], (39792 ^ _782435) ^ [_1552973, _1552975, _1552977, _1552979, _1552981] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1552973, _1552975), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1552973, tc_HOL_Obool)), _1552977), _1552979)), _1552981) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1552973, _1552975), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1552973, _1552975), _1552977), _1552981)), hAPP(hAPP(c_Product__Type_OSigma(_1552973, _1552975), _1552979), _1552981)))], (39794 ^ _782435) ^ [_1553056, _1553058, _1553060, _1553062, _1553064] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553056, _1553058), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553056, tc_HOL_Obool)), _1553060), _1553062)), hAPP(c_COMBK(tc_fun(_1553058, tc_HOL_Obool), _1553056), _1553064)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553056, _1553058), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553056, _1553058), _1553060), hAPP(c_COMBK(tc_fun(_1553058, tc_HOL_Obool), _1553056), _1553064))), hAPP(hAPP(c_Product__Type_OSigma(_1553056, _1553058), _1553062), hAPP(c_COMBK(tc_fun(_1553058, tc_HOL_Obool), _1553056), _1553064))))], (39796 ^ _782435) ^ [_1553166, _1553168, _1553170, _1553172, _1553174] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553166, _1553168), _1553170), hAPP(hAPP(c_COMBS(_1553166, tc_fun(_1553168, tc_HOL_Obool), tc_fun(_1553168, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553168, tc_HOL_Obool), tc_fun(tc_fun(_1553168, tc_HOL_Obool), tc_fun(_1553168, tc_HOL_Obool)), _1553166), c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1553168, tc_HOL_Obool))), _1553172)), _1553174)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1553166, _1553168), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553166, _1553168), _1553170), _1553172)), hAPP(hAPP(c_Product__Type_OSigma(_1553166, _1553168), _1553170), _1553174)))], (39798 ^ _782435) ^ [_1553281, _1553283] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1553281, _1553281), tc_HOL_Obool)), c_Relation_OId__on(_1553281, _1553283)), hAPP(hAPP(c_Product__Type_OSigma(_1553281, _1553281), _1553283), hAPP(c_COMBK(tc_fun(_1553281, tc_HOL_Obool), _1553281), _1553283)))))], (39800 ^ _782435) ^ [_1553340, _1553342, _1553344, _1553346, _1553348] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553340, _1553342), _1553344), hAPP(hAPP(c_COMBS(_1553340, tc_fun(_1553342, tc_HOL_Obool), tc_fun(_1553342, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1553342, tc_HOL_Obool), tc_fun(tc_fun(_1553342, tc_HOL_Obool), tc_fun(_1553342, tc_HOL_Obool)), _1553340), c_Groups_Ominus__class_Ominus(tc_fun(_1553342, tc_HOL_Obool))), _1553346)), _1553348)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553340, _1553342), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553340, _1553342), _1553344), _1553346)), hAPP(hAPP(c_Product__Type_OSigma(_1553340, _1553342), _1553344), _1553348)))], (39802 ^ _782435) ^ [_1553455, _1553457, _1553459, _1553461, _1553463] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553455, _1553457), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553455, tc_HOL_Obool)), _1553459), _1553461)), hAPP(c_COMBK(tc_fun(_1553457, tc_HOL_Obool), _1553455), _1553463)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553455, _1553457), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553455, _1553457), _1553459), hAPP(c_COMBK(tc_fun(_1553457, tc_HOL_Obool), _1553455), _1553463))), hAPP(hAPP(c_Product__Type_OSigma(_1553455, _1553457), _1553461), hAPP(c_COMBK(tc_fun(_1553457, tc_HOL_Obool), _1553455), _1553463))))], (39804 ^ _782435) ^ [_1553565, _1553567, _1553569, _1553571, _1553573] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553565, _1553567), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1553565, tc_HOL_Obool)), _1553569), _1553571)), _1553573) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1553565, _1553567), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1553565, _1553567), _1553569), _1553573)), hAPP(hAPP(c_Product__Type_OSigma(_1553565, _1553567), _1553571), _1553573)))], (39806 ^ _782435) ^ [_1553669, _1553671, _1553673, _1553675] : [hBOOL(hAPP(c_Predicate_ODomainP(_1553669, _1553671, _1553673), _1553675)), -(hBOOL(hAPP(hAPP(_1553673, _1553675), 39809 ^ [_1553669, _1553671, _1553673, _1553675])))], (39813 ^ _782435) ^ [_1553784, _1553786, _1553788, _1553790] : [39814 ^ _782435 : [(39815 ^ _782435) ^ [_1553838] : [hBOOL(hAPP(hAPP(_1553788, _1553790), _1553838))]], -(hBOOL(hAPP(c_Predicate_ODomainP(_1553784, _1553786, _1553788), _1553790)))], (39819 ^ _782435) ^ [_1553902, _1553904] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1553902, _1553904), c_Orderings_Otop__class_Otop(tc_fun(_1553902, tc_HOL_Obool))), hAPP(c_COMBK(tc_fun(_1553904, tc_HOL_Obool), _1553902), c_Orderings_Otop__class_Otop(tc_fun(_1553904, tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1553902, _1553904), tc_HOL_Obool)))], (39821 ^ _782435) ^ [_1553963, _1553965, _1553967, _1553969, _1553971, _1553973] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1553963, _1553965)), hAPP(hAPP(c_Product__Type_OPair(_1553963, _1553965), _1553967), _1553969)), hAPP(hAPP(c_Product__Type_OSigma(_1553963, _1553965), _1553971), _1553973))), 39824 ^ _782435 : [(39825 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553963), _1553967), _1553971)))], (39827 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1553965), _1553969), hAPP(_1553973, _1553967))))]]], (39829 ^ _782435) ^ [_1554168, _1554170, _1554172, _1554174, _1554176, _1554178] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554168, _1554170)), hAPP(hAPP(c_Product__Type_OPair(_1554168, _1554170), _1554172), _1554174)), hAPP(hAPP(c_Product__Type_OSigma(_1554168, _1554170), _1554176), _1554178))), -(hBOOL(hAPP(hAPP(c_member(_1554170), _1554174), hAPP(_1554178, _1554172))))], (39835 ^ _782435) ^ [_1554329, _1554331, _1554333, _1554335, _1554337, _1554339] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554329, _1554331)), hAPP(hAPP(c_Product__Type_OPair(_1554329, _1554331), _1554333), _1554335)), hAPP(hAPP(c_Product__Type_OSigma(_1554329, _1554331), _1554337), _1554339))), -(hBOOL(hAPP(hAPP(c_member(_1554329), _1554333), _1554337)))], (39841 ^ _782435) ^ [_1554511, _1554513, _1554515, _1554517, _1554519, _1554521] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1554511, _1554513)), hAPP(hAPP(c_Product__Type_OPair(_1554511, _1554513), _1554515), _1554517)), hAPP(hAPP(c_Product__Type_OSigma(_1554511, _1554513), _1554519), _1554521))), 39844 ^ _782435 : [(39845 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554511), _1554515), _1554519)))], (39847 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1554513), _1554517), hAPP(_1554521, _1554515))))]]], (39849 ^ _782435) ^ [_1554708, _1554710, _1554712, _1554714, _1554716, _1554718] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1554708, _1554710)), hAPP(hAPP(c_Product__Type_OPair(_1554708, _1554710), _1554712), _1554714)), hAPP(hAPP(c_Product__Type_OSigma(_1554708, _1554710), _1554716), _1554718)))), hBOOL(hAPP(hAPP(c_member(_1554708), _1554712), _1554716)), hBOOL(hAPP(hAPP(c_member(_1554710), _1554714), hAPP(_1554718, _1554712)))], (39859 ^ _782435) ^ [_1554945, _1554947, _1554949, _1554951] : [-(hAPP(c_Finite__Set_Ocard(tc_prod(_1554945, _1554947)), hAPP(hAPP(c_Product__Type_OSigma(_1554945, _1554947), hAPP(hAPP(c_Set_Oinsert(_1554945), _1554949), c_Orderings_Obot__class_Obot(tc_fun(_1554945, tc_HOL_Obool)))), hAPP(c_COMBK(tc_fun(_1554947, tc_HOL_Obool), _1554945), _1554951))) = hAPP(c_Finite__Set_Ocard(_1554947), _1554951))], (39861 ^ _782435) ^ [_1555018, _1555020, _1555022, _1555024, _1555026, _1555028] : [hBOOL(hAPP(hAPP(c_member(_1555018), _1555020), _1555022)), 39864 ^ _782435 : [(39865 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555024, _1555018), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555024, _1555018), _1555026), hAPP(c_COMBK(tc_fun(_1555018, tc_HOL_Obool), _1555024), _1555022))), hAPP(hAPP(c_Product__Type_OSigma(_1555024, _1555018), _1555028), hAPP(c_COMBK(tc_fun(_1555018, tc_HOL_Obool), _1555024), _1555022)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555024, tc_HOL_Obool)), _1555026), _1555028)))], (39871 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555024, tc_HOL_Obool)), _1555026), _1555028)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555024, _1555018), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1555024, _1555018), _1555026), hAPP(c_COMBK(tc_fun(_1555018, tc_HOL_Obool), _1555024), _1555022))), hAPP(hAPP(c_Product__Type_OSigma(_1555024, _1555018), _1555028), hAPP(c_COMBK(tc_fun(_1555018, tc_HOL_Obool), _1555024), _1555022)))))]]], (39877 ^ _782435) ^ [_1555440, _1555442, _1555444, _1555446, _1555448, _1555450] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1555440, _1555442), tc_HOL_Obool)), _1555444), hAPP(hAPP(c_Product__Type_OSigma(_1555440, _1555442), _1555446), hAPP(c_COMBK(tc_fun(_1555442, tc_HOL_Obool), _1555440), _1555448)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1555442, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1555440, _1555442, _1555444), _1555450)), _1555448)))], (39883 ^ _782435) ^ [_1555621, _1555623, _1555625, _1555627] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555621, _1555623)), hAPP(hAPP(c_Product__Type_OSigma(_1555621, _1555623), _1555625), hAPP(c_COMBK(tc_fun(_1555623, tc_HOL_Obool), _1555621), _1555627)))), -(_1555625 = c_Orderings_Obot__class_Obot(tc_fun(_1555621, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555623), _1555627)))], (39893 ^ _782435) ^ [_1555785, _1555787, _1555789, _1555791] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1555785, _1555787)), hAPP(hAPP(c_Product__Type_OSigma(_1555785, _1555787), _1555789), hAPP(c_COMBK(tc_fun(_1555787, tc_HOL_Obool), _1555785), _1555791)))), -(_1555791 = c_Orderings_Obot__class_Obot(tc_fun(_1555787, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1555785), _1555789)))], (39903 ^ _782435) ^ [_1555949, _1555951, _1555953, _1555955] : [-(hAPP(c_Set_OCollect(tc_prod(_1555949, _1555951)), hAPP(c_Product__Type_Oprod_Oprod__case(_1555949, _1555951, tc_HOL_Obool), hAPP(hAPP(c_COMBS(_1555949, tc_fun(_1555951, tc_HOL_Obool), tc_fun(_1555951, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1555951, tc_HOL_Obool), tc_fun(_1555951, tc_HOL_Obool)), _1555949), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1555951)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1555949), c_fconj), _1555953))), _1555955))) = hAPP(hAPP(c_Product__Type_OSigma(_1555949, _1555951), hAPP(c_Set_OCollect(_1555949), _1555953)), hAPP(hAPP(c_COMBB(tc_fun(_1555951, tc_HOL_Obool), tc_fun(_1555951, tc_HOL_Obool), _1555949), c_Set_OCollect(_1555951)), _1555955)))], (39905 ^ _782435) ^ [_1556074, _1556076, _1556078, _1556080] : [-(hAPP(c_Set_OCollect(tc_prod(_1556074, _1556076)), hAPP(c_Product__Type_Oprod_Oprod__case(_1556074, _1556076, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1556074, tc_fun(_1556076, tc_HOL_Obool), tc_fun(_1556076, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1556076, tc_HOL_Obool), tc_fun(_1556076, tc_HOL_Obool)), _1556074), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1556076)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1556074), c_fconj), _1556078))), _1556080))) = hAPP(hAPP(c_Product__Type_OSigma(_1556074, _1556076), hAPP(c_Set_OCollect(_1556074), _1556078)), hAPP(c_COMBK(tc_fun(_1556076, tc_HOL_Obool), _1556074), hAPP(c_Set_OCollect(_1556076), _1556080))))], (39907 ^ _782435) ^ [_1556210, _1556212, _1556214, _1556216] : [_1556210 = c_Orderings_Obot__class_Obot(tc_fun(_1556212, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1556214, _1556212), _1556214, c_Product__Type_Ofst(_1556214, _1556212)), hAPP(hAPP(c_Product__Type_OSigma(_1556214, _1556212), _1556216), hAPP(c_COMBK(tc_fun(_1556212, tc_HOL_Obool), _1556214), _1556210))) = c_Orderings_Obot__class_Obot(tc_fun(_1556214, tc_HOL_Obool)))], (39913 ^ _782435) ^ [_1556367, _1556369, _1556371, _1556373] : [-(_1556367 = c_Orderings_Obot__class_Obot(tc_fun(_1556369, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1556371, _1556369), _1556371, c_Product__Type_Ofst(_1556371, _1556369)), hAPP(hAPP(c_Product__Type_OSigma(_1556371, _1556369), _1556373), hAPP(c_COMBK(tc_fun(_1556369, tc_HOL_Obool), _1556371), _1556367))) = _1556373)], (39919 ^ _782435) ^ [_1556460, _1556462, _1556464, _1556466] : [_1556460 = c_Orderings_Obot__class_Obot(tc_fun(_1556462, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1556462, _1556464), _1556464, c_Product__Type_Osnd(_1556462, _1556464)), hAPP(hAPP(c_Product__Type_OSigma(_1556462, _1556464), _1556460), hAPP(c_COMBK(tc_fun(_1556464, tc_HOL_Obool), _1556462), _1556466))) = c_Orderings_Obot__class_Obot(tc_fun(_1556464, tc_HOL_Obool)))], (39925 ^ _782435) ^ [_1556617, _1556619, _1556621, _1556623] : [-(_1556617 = c_Orderings_Obot__class_Obot(tc_fun(_1556619, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(tc_prod(_1556619, _1556621), _1556621, c_Product__Type_Osnd(_1556619, _1556621)), hAPP(hAPP(c_Product__Type_OSigma(_1556619, _1556621), _1556617), hAPP(c_COMBK(tc_fun(_1556621, tc_HOL_Obool), _1556619), _1556623))) = _1556623)], (39931 ^ _782435) ^ [_1556695, _1556697, _1556699, _1556701, _1556703, _1556705] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1556695, _1556697), hAPP(hAPP(c_Set_Oinsert(_1556695), _1556699), _1556701)), hAPP(c_COMBK(tc_fun(_1556697, tc_HOL_Obool), _1556695), hAPP(hAPP(c_Set_Oinsert(_1556697), _1556703), _1556705))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(_1556695, _1556697)), hAPP(hAPP(c_Product__Type_OPair(_1556695, _1556697), _1556699), _1556703)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1556695, _1556697), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1556695, _1556697), _1556701), hAPP(c_COMBK(tc_fun(_1556697, tc_HOL_Obool), _1556695), hAPP(hAPP(c_Set_Oinsert(_1556697), _1556703), _1556705)))), hAPP(hAPP(c_Product__Type_OSigma(_1556695, _1556697), hAPP(hAPP(c_Set_Oinsert(_1556695), _1556699), _1556701)), hAPP(c_COMBK(tc_fun(_1556697, tc_HOL_Obool), _1556695), _1556705)))))], (39933 ^ _782435) ^ [_1556848, _1556850, _1556852, _1556854] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1556848), _1556850)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1556848, _1556848), tc_HOL_Obool)), _1556852), hAPP(hAPP(c_Product__Type_OSigma(_1556848, _1556848), _1556850), hAPP(c_COMBK(tc_fun(_1556848, tc_HOL_Obool), _1556848), _1556850)))), hBOOL(hAPP(hAPP(c_member(tc_fun(_1556848, tc_HOL_Obool)), _1556854), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1556848), _1556850), _1556852))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1556848), _1556854)))], (39947 ^ _782435) ^ [_1557155, _1557157, _1557159, _1557161, _1557163, _1557165] : [-(hAPP(c_Set_Ovimage(_1557155, tc_prod(_1557157, _1557159), _1557161), hAPP(hAPP(c_Product__Type_OSigma(_1557157, _1557159), _1557163), hAPP(c_COMBK(tc_fun(_1557159, tc_HOL_Obool), _1557157), _1557165))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1557155, tc_HOL_Obool)), hAPP(c_Set_Ovimage(_1557155, _1557157, hAPP(c_Fun_Ocomp(tc_prod(_1557157, _1557159), _1557157, _1557155, c_Product__Type_Ofst(_1557157, _1557159)), _1557161)), _1557163)), hAPP(c_Set_Ovimage(_1557155, _1557159, hAPP(c_Fun_Ocomp(tc_prod(_1557157, _1557159), _1557159, _1557155, c_Product__Type_Osnd(_1557157, _1557159)), _1557161)), _1557165)))], (39949 ^ _782435) ^ [_1557269, _1557271, _1557273, _1557275, _1557277, _1557279, _1557281, _1557283] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(_1557269, _1557271), tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1557269, _1557271), _1557277), hAPP(c_COMBK(tc_fun(_1557271, tc_HOL_Obool), _1557269), _1557279))), hAPP(c_Product__Type_Oprod_Oprod__case(_1557269, _1557271, tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1557269, tc_fun(_1557271, tc_fun(_1557273, tc_fun(_1557275, tc_HOL_Obool))), tc_fun(_1557271, tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1557273, tc_fun(_1557275, tc_HOL_Obool)), tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool)), tc_fun(tc_fun(_1557271, tc_fun(_1557273, tc_fun(_1557275, tc_HOL_Obool))), tc_fun(_1557271, tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool))), _1557269), c_COMBB(tc_fun(_1557273, tc_fun(_1557275, tc_HOL_Obool)), tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool), _1557271)), hAPP(hAPP(c_COMBB(tc_fun(_1557273, tc_HOL_Obool), tc_fun(tc_fun(_1557273, tc_fun(_1557275, tc_HOL_Obool)), tc_fun(tc_prod(_1557273, _1557275), tc_HOL_Obool)), _1557269), c_Product__Type_OSigma(_1557273, _1557275)), _1557281))), hAPP(hAPP(c_COMBB(tc_fun(_1557275, tc_HOL_Obool), tc_fun(_1557273, tc_fun(_1557275, tc_HOL_Obool)), _1557271), c_COMBK(tc_fun(_1557275, tc_HOL_Obool), _1557273)), _1557283)))) = hAPP(hAPP(c_Product__Type_OSigma(_1557273, _1557275), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557269, tc_fun(_1557273, tc_HOL_Obool)), _1557277), _1557281)), hAPP(c_COMBK(tc_fun(_1557275, tc_HOL_Obool), _1557273), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557271, tc_fun(_1557275, tc_HOL_Obool)), _1557279), _1557283))))], (39951 ^ _782435) ^ [_1557543, _1557545, _1557547, _1557549] : [-(hAPP(hAPP(c_Product__Type_OSigma(_1557543, _1557545), _1557547), _1557549) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557543, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool)), _1557547), hAPP(hAPP(c_COMBS(_1557543, tc_fun(_1557545, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool)), tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1557545, tc_HOL_Obool), tc_fun(tc_fun(_1557545, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool)), tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool)), _1557543), c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1557545, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))), _1557549)), hAPP(hAPP(c_COMBC(_1557543, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool), tc_fun(_1557545, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557545, tc_fun(tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool), tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))), tc_fun(tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool), tc_fun(_1557545, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))), _1557543), c_COMBC(_1557545, tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool), tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1557545, tc_prod(_1557543, _1557545)), tc_fun(_1557545, tc_fun(tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool), tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))), _1557543), hAPP(c_COMBB(tc_prod(_1557543, _1557545), tc_fun(tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool), tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool)), _1557545), c_Set_Oinsert(tc_prod(_1557543, _1557545)))), c_Product__Type_OPair(_1557543, _1557545)))), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1557543, _1557545), tc_HOL_Obool))))))], (39953 ^ _782435) ^ [_1557823, _1557825, _1557827] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1557823), _1557825)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1557823, _1557823), tc_HOL_Obool)), _1557827), hAPP(hAPP(c_Product__Type_OSigma(_1557823, _1557823), _1557825), hAPP(c_COMBK(tc_fun(_1557823, tc_HOL_Obool), _1557823), _1557825)))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1557823, tc_HOL_Obool)), hAPP(hAPP(c_Equiv__Relations_Oquotient(_1557823), _1557825), _1557827))))], (39963 ^ _782435) ^ [_1558056, _1558058, _1558060, _1558062, _1558064, _1558066, _1558068] : [class_Rings_Osemiring__0(_1558056), c_Fun_Oinj__on(tc_prod(_1558058, _1558060), _1558056, hAPP(c_Product__Type_Oprod_Oprod__case(_1558058, _1558060, _1558056), hAPP(hAPP(c_COMBC(_1558058, tc_fun(_1558060, _1558056), tc_fun(_1558060, _1558056)), hAPP(hAPP(c_COMBB(tc_fun(_1558056, _1558056), tc_fun(tc_fun(_1558060, _1558056), tc_fun(_1558060, _1558056)), _1558058), c_COMBB(_1558056, _1558056, _1558060)), hAPP(hAPP(c_COMBB(_1558056, tc_fun(_1558056, _1558056), _1558058), c_Groups_Otimes__class_Otimes(_1558056)), _1558062))), _1558064)), hAPP(hAPP(c_Product__Type_OSigma(_1558058, _1558060), _1558066), hAPP(c_COMBK(tc_fun(_1558060, tc_HOL_Obool), _1558058), _1558068))), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1558056), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558058, _1558056), _1558062), _1558066)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558060, _1558056), _1558064), _1558068)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1558056, _1558056), c_Fun_Oid(_1558056)), hAPP(c_Set_OCollect(_1558056), hAPP(hAPP(c_COMBB(tc_fun(_1558058, tc_HOL_Obool), tc_HOL_Obool, _1558056), c_HOL_OEx(_1558058)), hAPP(hAPP(c_COMBB(tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool)), tc_fun(_1558058, tc_HOL_Obool), _1558056), hAPP(c_COMBB(tc_fun(_1558060, tc_HOL_Obool), tc_HOL_Obool, _1558058), c_HOL_OEx(_1558060))), hAPP(hAPP(c_COMBC(_1558056, tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool)), tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558058, tc_fun(tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_HOL_Obool))), tc_fun(tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool)), tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool))), _1558056), c_COMBS(_1558058, tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558058, tc_fun(_1558060, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1558058, tc_fun(tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_HOL_Obool))), _1558056), hAPP(c_COMBB(tc_fun(_1558060, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_HOL_Obool)), _1558058), c_COMBS(_1558060, tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool)), tc_fun(_1558058, tc_fun(_1558060, tc_fun(tc_HOL_Obool, tc_HOL_Obool))), _1558056), hAPP(c_COMBB(tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1558058), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558060), c_fconj))), hAPP(hAPP(c_COMBC(_1558056, tc_fun(_1558058, tc_fun(_1558060, _1558056)), tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1558060, _1558056), tc_fun(_1558060, tc_HOL_Obool)), tc_fun(tc_fun(_1558058, tc_fun(_1558060, _1558056)), tc_fun(_1558058, tc_fun(_1558060, tc_HOL_Obool))), _1558056), c_COMBB(tc_fun(_1558060, _1558056), tc_fun(_1558060, tc_HOL_Obool), _1558058)), hAPP(hAPP(c_COMBB(tc_fun(_1558056, tc_HOL_Obool), tc_fun(tc_fun(_1558060, _1558056), tc_fun(_1558060, tc_HOL_Obool)), _1558056), c_COMBB(_1558056, tc_HOL_Obool, _1558060)), c_fequal))), hAPP(hAPP(c_COMBC(_1558058, tc_fun(_1558060, _1558056), tc_fun(_1558060, _1558056)), hAPP(hAPP(c_COMBB(tc_fun(_1558056, _1558056), tc_fun(tc_fun(_1558060, _1558056), tc_fun(_1558060, _1558056)), _1558058), c_COMBB(_1558056, _1558056, _1558060)), hAPP(hAPP(c_COMBB(_1558056, tc_fun(_1558056, _1558056), _1558058), c_Groups_Otimes__class_Otimes(_1558056)), _1558062))), _1558064)))))), hAPP(hAPP(c_COMBC(_1558058, tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1558060, tc_HOL_Obool), tc_fun(_1558060, tc_HOL_Obool)), _1558058), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1558060)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1558058), c_fconj), hAPP(hAPP(c_COMBC(_1558058, tc_fun(_1558058, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558058)), _1558066)))), hAPP(hAPP(c_COMBC(_1558060, tc_fun(_1558060, tc_HOL_Obool), tc_HOL_Obool), c_member(_1558060)), _1558068))))))))], (39974 ^ _782435) ^ [_1559331, _1559333, _1559335, _1559337] : [-(c_Fun_Oinj__on(_1559331, tc_prod(_1559333, _1559331), 39972 ^ [_1559331, _1559333, _1559335, _1559337], hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559333, tc_fun(_1559331, tc_HOL_Obool)), _1559335), _1559337)))], (39976 ^ _782435) ^ [_1559385, _1559387, _1559389, _1559391] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1559387, _1559385), tc_HOL_Obool)), hAPP(c_Set_Oimage(_1559385, tc_prod(_1559387, _1559385), 39972 ^ [_1559385, _1559387, _1559389, _1559391]), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1559387, tc_fun(_1559385, tc_HOL_Obool)), _1559389), _1559391))), hAPP(hAPP(c_Product__Type_OSigma(_1559387, _1559385), _1559389), _1559391))))], (39978 ^ _782435) ^ [_1559471, _1559473, _1559475, _1559477, _1559479, _1559481] : [class_Groups_Ocomm__monoid__mult(_1559471), hBOOL(hAPP(c_Finite__Set_Ofinite(_1559473), _1559475)), 39988 ^ _782435 : [(39989 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1559473), 39987 ^ [_1559471, _1559473, _1559475, _1559477, _1559479, _1559481]), _1559475)))], (39991 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1559477), hAPP(_1559479, 39987 ^ [_1559471, _1559473, _1559475, _1559477, _1559479, _1559481])))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559471, _1559473, c_Groups_Otimes__class_Otimes(_1559471)), hAPP(hAPP(c_COMBS(_1559473, tc_fun(_1559477, tc_HOL_Obool), _1559471), hAPP(hAPP(c_COMBC(_1559473, _1559471, tc_fun(tc_fun(_1559477, tc_HOL_Obool), _1559471)), hAPP(hAPP(c_COMBB(tc_fun(_1559477, _1559471), tc_fun(_1559471, tc_fun(tc_fun(_1559477, tc_HOL_Obool), _1559471)), _1559473), c_Finite__Set_Ofold__image(_1559471, _1559477, c_Groups_Otimes__class_Otimes(_1559471))), _1559481)), c_Groups_Oone__class_Oone(_1559471))), _1559479)), c_Groups_Oone__class_Oone(_1559471)), _1559475) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1559471, tc_prod(_1559473, _1559477), c_Groups_Otimes__class_Otimes(_1559471)), hAPP(c_Product__Type_Oprod_Oprod__case(_1559473, _1559477, _1559471), _1559481)), c_Groups_Oone__class_Oone(_1559471)), hAPP(hAPP(c_Product__Type_OSigma(_1559473, _1559477), _1559475), _1559479)))], (39995 ^ _782435) ^ [_1560028, _1560030] : [-(c_Fun_Obij__betw(_1560028, _1560028, c_Fun_Oid(_1560028), _1560030, _1560030))], (39997 ^ _782435) ^ [_1560058, _1560060] : [-(hAPP(c_Set_Oimage(_1560058, _1560058, c_Fun_Oid(_1560058)), _1560060) = _1560060)], (39999 ^ _782435) ^ [_1560092, _1560094] : [-(c_Product__Type_Oapsnd(_1560092, _1560092, _1560094, c_Fun_Oid(_1560092)) = c_Fun_Oid(tc_prod(_1560094, _1560092)))], (40001 ^ _782435) ^ [_1560129, _1560131] : [-(hAPP(c_Fun_Oid(_1560129), _1560131) = _1560131)], (40003 ^ _782435) ^ [_1560159, _1560161] : [-(hAPP(c_Fun_Oid(_1560159), _1560161) = _1560161)], (40005 ^ _782435) ^ [_1560189, _1560191] : [-(hAPP(c_Set_Ovimage(_1560189, _1560189, c_Fun_Oid(_1560189)), _1560191) = _1560191)], (40007 ^ _782435) ^ [_1560241, _1560243, _1560245] : [c_Fun_Obij__betw(_1560241, _1560241, c_Fun_Oid(_1560241), _1560243, _1560245), -(_1560243 = _1560245)], (40013 ^ _782435) ^ [_1560326, _1560328, _1560330] : [_1560328 = _1560330, -(c_Fun_Obij__betw(_1560326, _1560326, c_Fun_Oid(_1560326), _1560328, _1560330))], (40019 ^ _782435) ^ [_1560417, _1560419] : [-(c_Fun_Oinj__on(_1560417, _1560417, c_Fun_Oid(_1560417), _1560419))], (40021 ^ _782435) ^ [_1560446, _1560448, _1560450] : [-(hAPP(c_Fun_Ocomp(_1560446, _1560448, _1560446, _1560450), c_Fun_Oid(_1560446)) = _1560450)], (40023 ^ _782435) ^ [_1560483, _1560485, _1560487] : [-(hAPP(c_Fun_Ocomp(_1560483, _1560483, _1560485, c_Fun_Oid(_1560483)), _1560487) = _1560487)], (40025 ^ _782435) ^ [_1560520, _1560522, _1560524, _1560526, _1560528, _1560530, _1560532] : [hAPP(c_Fun_Ocomp(_1560520, _1560522, _1560524, _1560526), _1560528) = hAPP(c_Fun_Ocomp(_1560522, _1560522, _1560524, c_Fun_Oid(_1560522)), _1560530), -(hAPP(_1560526, hAPP(_1560528, _1560532)) = hAPP(_1560530, _1560532))], (40031 ^ _782435) ^ [_1560661, _1560663] : [-(c_Product__Type_Oapfst(_1560661, _1560661, _1560663, c_Fun_Oid(_1560661)) = c_Fun_Oid(tc_prod(_1560661, _1560663)))], (40033 ^ _782435) ^ [] : [-(c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint))], (40035 ^ _782435) ^ [_1560716] : [-(hAPP(c_Set_Oimage(_1560716, _1560716, c_Fun_Oid(_1560716)), c_Orderings_Otop__class_Otop(tc_fun(_1560716, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1560716, tc_HOL_Obool)))], (40037 ^ _782435) ^ [_1560758] : [-(c_Fun_Obij__betw(_1560758, _1560758, c_Fun_Oid(_1560758), c_Orderings_Otop__class_Otop(tc_fun(_1560758, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1560758, tc_HOL_Obool))))], (40039 ^ _782435) ^ [_1560796, _1560798, _1560800, _1560802] : [c_Finite__Set_Ofolding(_1560796, _1560798, _1560800, _1560802), -(hAPP(_1560802, c_Orderings_Obot__class_Obot(tc_fun(_1560796, tc_HOL_Obool))) = c_Fun_Oid(_1560798))], (40045 ^ _782435) ^ [_1560901, _1560903] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1560901, _1560903, tc_prod(_1560901, _1560903)), c_Product__Type_OPair(_1560901, _1560903)) = c_Fun_Oid(tc_prod(_1560901, _1560903)))], (40047 ^ _782435) ^ [_1560944, _1560946, _1560948, _1560950] : [class_Groups_Ocomm__monoid__add(_1560944), c_Fun_Oinj__on(_1560946, _1560944, _1560948, _1560950), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560946, _1560944), _1560948), _1560950) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1560944, _1560944), c_Fun_Oid(_1560944)), hAPP(c_Set_Oimage(_1560946, _1560944, _1560948), _1560950)))], (40057 ^ _782435) ^ [_1561137, _1561139, _1561141, _1561143] : [class_Groups_Ocomm__monoid__mult(_1561137), c_Fun_Oinj__on(_1561139, _1561137, _1561141, _1561143), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561139, _1561137), _1561141), _1561143) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561137, _1561137), c_Fun_Oid(_1561137)), hAPP(c_Set_Oimage(_1561139, _1561137, _1561141), _1561143)))], (40067 ^ _782435) ^ [_1561330, _1561332, _1561334, _1561336, _1561338, _1561340] : [class_Groups_Ocomm__monoid__mult(_1561330), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561332), _1561334)), 40077 ^ _782435 : [(40078 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561332), 40076 ^ [_1561330, _1561332, _1561334, _1561336, _1561338, _1561340]), _1561334)))], (40080 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1561336), hAPP(_1561338, 40076 ^ [_1561330, _1561332, _1561334, _1561336, _1561338, _1561340])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561332, _1561330), hAPP(hAPP(c_COMBS(_1561332, tc_fun(_1561336, tc_HOL_Obool), _1561330), hAPP(hAPP(c_COMBB(tc_fun(_1561336, _1561330), tc_fun(tc_fun(_1561336, tc_HOL_Obool), _1561330), _1561332), c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1561336, _1561330)), _1561340)), _1561338)), _1561334) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(_1561332, _1561336), _1561330), hAPP(c_Product__Type_Oprod_Oprod__case(_1561332, _1561336, _1561330), _1561340)), hAPP(hAPP(c_Product__Type_OSigma(_1561332, _1561336), _1561334), _1561338)))], (40084 ^ _782435) ^ [_1561807, _1561809, _1561811, _1561813, _1561815, _1561817] : [class_Groups_Ocomm__monoid__add(_1561807), hBOOL(hAPP(c_Finite__Set_Ofinite(_1561809), _1561811)), 40094 ^ _782435 : [(40095 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1561809), 40093 ^ [_1561807, _1561809, _1561811, _1561813, _1561815, _1561817]), _1561811)))], (40097 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1561813), hAPP(_1561815, 40093 ^ [_1561807, _1561809, _1561811, _1561813, _1561815, _1561817])))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561809, _1561807), hAPP(hAPP(c_COMBS(_1561809, tc_fun(_1561813, tc_HOL_Obool), _1561807), hAPP(hAPP(c_COMBB(tc_fun(_1561813, _1561807), tc_fun(tc_fun(_1561813, tc_HOL_Obool), _1561807), _1561809), c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1561813, _1561807)), _1561817)), _1561815)), _1561811) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(_1561809, _1561813), _1561807), hAPP(c_Product__Type_Oprod_Oprod__case(_1561809, _1561813, _1561807), _1561817)), hAPP(hAPP(c_Product__Type_OSigma(_1561809, _1561813), _1561811), _1561815)))], (40101 ^ _782435) ^ [_1562284, _1562286, _1562288, _1562290] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562284), _1562286)), 40107 ^ _782435 : [(40108 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562284), 40106 ^ [_1562284, _1562286, _1562288, _1562290]), _1562286)))], (40110 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562288), hAPP(_1562290, 40106 ^ [_1562284, _1562286, _1562288, _1562290])))]], -(hAPP(c_Finite__Set_Ocard(tc_prod(_1562284, _1562288)), hAPP(hAPP(c_Product__Type_OSigma(_1562284, _1562288), _1562286), _1562290)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1562284, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_fun(_1562288, tc_HOL_Obool), tc_Nat_Onat, _1562284), c_Finite__Set_Ocard(_1562288)), _1562290)), _1562286))], (40114 ^ _782435) ^ [_1562621, _1562623, _1562625, _1562627] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562621), _1562623)), 40120 ^ _782435 : [(40121 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562621), 40119 ^ [_1562621, _1562623, _1562625, _1562627]), _1562623)))], (40123 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1562625), hAPP(_1562627, 40119 ^ [_1562621, _1562623, _1562625, _1562627])))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1562621, _1562625)), hAPP(hAPP(c_Product__Type_OSigma(_1562621, _1562625), _1562623), _1562627))))], (40127 ^ _782435) ^ [_1562908, _1562910, _1562912, _1562914, _1562916] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1562908, _1562910)), _1562912), hAPP(hAPP(c_Product__Type_OSigma(_1562908, _1562910), _1562914), _1562916))), 40131 ^ _782435 : [(40132 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562908), 40130 ^ [_1562908, _1562910, _1562912, _1562914, _1562916]), _1562914)))], (40135 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1562910), 40133 ^ [_1562908, _1562910, _1562912, _1562914, _1562916]), hAPP(_1562916, 40130 ^ [_1562908, _1562910, _1562912, _1562914, _1562916]))))], (40137 ^ _782435) ^ [] : [-(_1562912 = hAPP(hAPP(c_Product__Type_OPair(_1562908, _1562910), 40130 ^ [_1562908, _1562910, _1562912, _1562914, _1562916]), 40133 ^ [_1562908, _1562910, _1562912, _1562914, _1562916]))]]], (40139 ^ _782435) ^ [_1563210, _1563212, _1563214, _1563216, _1563218, _1563220] : [hAPP(c_Set_Oimage(_1563210, _1563212, _1563214), c_Orderings_Otop__class_Otop(tc_fun(_1563210, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1563212, tc_HOL_Obool)), hAPP(c_Set_Oimage(_1563216, _1563218, _1563220), c_Orderings_Otop__class_Otop(tc_fun(_1563216, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1563218, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(tc_prod(_1563210, _1563216), tc_prod(_1563212, _1563218), c_Product__Type_Omap__pair(_1563210, _1563212, _1563216, _1563218, _1563214, _1563220)), c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1563210, _1563216), tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(_1563212, _1563218), tc_HOL_Obool)))], (40149 ^ _782435) ^ [_1563495, _1563497, _1563499, _1563501, _1563503, _1563505, _1563507, _1563509, _1563511] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1563495, _1563497)), hAPP(hAPP(c_Product__Type_OPair(_1563495, _1563497), _1563499), _1563501)), _1563503)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1563505, _1563507)), hAPP(hAPP(c_Product__Type_OPair(_1563505, _1563507), hAPP(_1563509, _1563499)), hAPP(_1563511, _1563501))), hAPP(c_Set_Oimage(tc_prod(_1563495, _1563497), tc_prod(_1563505, _1563507), c_Product__Type_Omap__pair(_1563495, _1563505, _1563497, _1563507, _1563509, _1563511)), _1563503))))], (40155 ^ _782435) ^ [_1563714, _1563716, _1563718, _1563720, _1563722, _1563724, _1563726, _1563728] : [-(hAPP(c_Product__Type_Omap__pair(_1563714, _1563716, _1563718, _1563720, _1563722, _1563724), hAPP(hAPP(c_Product__Type_OPair(_1563714, _1563718), _1563726), _1563728)) = hAPP(hAPP(c_Product__Type_OPair(_1563716, _1563720), hAPP(_1563722, _1563726)), hAPP(_1563724, _1563728)))], (40157 ^ _782435) ^ [_1563785, _1563787, _1563789] : [-(hAPP(c_Product__Type_Omap__pair(_1563785, _1563785, _1563787, _1563787, c_COMBI(_1563785), c_COMBI(_1563787)), _1563789) = _1563789)], (40159 ^ _782435) ^ [_1563826, _1563828, _1563830, _1563832, _1563834, _1563836, _1563838] : [-(hAPP(c_Product__Type_Osnd(_1563826, _1563828), hAPP(c_Product__Type_Omap__pair(_1563830, _1563826, _1563832, _1563828, _1563834, _1563836), _1563838)) = hAPP(_1563836, hAPP(c_Product__Type_Osnd(_1563830, _1563832), _1563838)))], (40161 ^ _782435) ^ [_1563886, _1563888, _1563890, _1563892, _1563894, _1563896, _1563898] : [-(hAPP(c_Product__Type_Ofst(_1563886, _1563888), hAPP(c_Product__Type_Omap__pair(_1563890, _1563886, _1563892, _1563888, _1563894, _1563896), _1563898)) = hAPP(_1563894, hAPP(c_Product__Type_Ofst(_1563890, _1563892), _1563898)))], (40163 ^ _782435) ^ [_1563946, _1563948, _1563950, _1563952, _1563954, _1563956] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1563946, _1563948), _1563946, tc_prod(_1563950, _1563952), c_Product__Type_Ofst(_1563946, _1563948)), c_Product__Type_Omap__pair(_1563950, _1563946, _1563952, _1563948, _1563954, _1563956)) = hAPP(c_Fun_Ocomp(_1563950, _1563946, tc_prod(_1563950, _1563952), _1563954), c_Product__Type_Ofst(_1563950, _1563952)))], (40165 ^ _782435) ^ [_1564017, _1564019, _1564021, _1564023, _1564025, _1564027] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1564017, _1564019), _1564019, tc_prod(_1564021, _1564023), c_Product__Type_Osnd(_1564017, _1564019)), c_Product__Type_Omap__pair(_1564021, _1564017, _1564023, _1564019, _1564025, _1564027)) = hAPP(c_Fun_Ocomp(_1564023, _1564019, tc_prod(_1564021, _1564023), _1564027), c_Product__Type_Osnd(_1564021, _1564023)))], (40167 ^ _782435) ^ [_1564088, _1564090, _1564092, _1564094, _1564096, _1564098, _1564100, _1564102, _1564104, _1564106] : [-(hAPP(c_Fun_Ocomp(tc_prod(_1564088, _1564090), tc_prod(_1564092, _1564094), tc_prod(_1564096, _1564098), c_Product__Type_Omap__pair(_1564088, _1564092, _1564090, _1564094, _1564100, _1564102)), c_Product__Type_Omap__pair(_1564096, _1564088, _1564098, _1564090, _1564104, _1564106)) = c_Product__Type_Omap__pair(_1564096, _1564092, _1564098, _1564094, hAPP(c_Fun_Ocomp(_1564088, _1564092, _1564096, _1564100), _1564104), hAPP(c_Fun_Ocomp(_1564090, _1564094, _1564098, _1564102), _1564106)))], (40169 ^ _782435) ^ [_1564183, _1564185, _1564187, _1564189, _1564191, _1564193, _1564195, _1564197, _1564199, _1564201] : [-(c_Product__Type_Omap__pair(_1564183, _1564185, _1564187, _1564189, hAPP(c_Fun_Ocomp(_1564191, _1564185, _1564183, _1564193), _1564195), hAPP(c_Fun_Ocomp(_1564197, _1564189, _1564187, _1564199), _1564201)) = hAPP(c_Fun_Ocomp(tc_prod(_1564191, _1564197), tc_prod(_1564185, _1564189), tc_prod(_1564183, _1564187), c_Product__Type_Omap__pair(_1564191, _1564185, _1564197, _1564189, _1564193, _1564199)), c_Product__Type_Omap__pair(_1564183, _1564191, _1564187, _1564197, _1564195, _1564201)))], (40171 ^ _782435) ^ [_1564278, _1564280, _1564282, _1564284, _1564286, _1564288, _1564290, _1564292, _1564294, _1564296, _1564298] : [-(hAPP(c_Product__Type_Omap__pair(_1564278, _1564280, _1564282, _1564284, _1564286, _1564288), hAPP(c_Product__Type_Omap__pair(_1564290, _1564278, _1564292, _1564282, _1564294, _1564296), _1564298)) = hAPP(c_Product__Type_Omap__pair(_1564290, _1564280, _1564292, _1564284, hAPP(c_Fun_Ocomp(_1564278, _1564280, _1564290, _1564286), _1564294), hAPP(c_Fun_Ocomp(_1564282, _1564284, _1564292, _1564288), _1564296)), _1564298))], (40173 ^ _782435) ^ [_1564367, _1564369] : [-(c_Product__Type_Omap__pair(_1564367, _1564367, _1564369, _1564369, c_COMBI(_1564367), c_COMBI(_1564369)) = c_Fun_Oid(tc_prod(_1564367, _1564369)))], (40175 ^ _782435) ^ [_1564408, _1564410, _1564412, _1564414] : [-(c_Product__Type_Oapsnd(_1564408, _1564410, _1564412, _1564414) = c_Product__Type_Omap__pair(_1564412, _1564412, _1564408, _1564410, c_Fun_Oid(_1564412), _1564414))], (40177 ^ _782435) ^ [_1564451, _1564453, _1564455, _1564457] : [-(c_Product__Type_Oapfst(_1564451, _1564453, _1564455, _1564457) = c_Product__Type_Omap__pair(_1564451, _1564453, _1564455, _1564455, _1564457, c_Fun_Oid(_1564455)))], (40179 ^ _782435) ^ [_1564494, _1564496] : [-(c_Product__Type_Omap__pair(_1564494, _1564494, _1564496, _1564496, c_Fun_Oid(_1564494), c_Fun_Oid(_1564496)) = c_Fun_Oid(tc_prod(_1564494, _1564496)))], (40181 ^ _782435) ^ [_1564535, _1564537, _1564539, _1564541, _1564543, _1564545] : [-(c_Product__Type_Omap__pair(_1564535, _1564537, _1564539, _1564541, _1564543, _1564545) = hAPP(c_Product__Type_Oprod_Oprod__case(_1564535, _1564539, tc_prod(_1564537, _1564541)), hAPP(hAPP(c_COMBC(_1564535, tc_fun(_1564539, _1564541), tc_fun(_1564539, tc_prod(_1564537, _1564541))), hAPP(hAPP(c_COMBB(tc_fun(_1564541, tc_prod(_1564537, _1564541)), tc_fun(tc_fun(_1564539, _1564541), tc_fun(_1564539, tc_prod(_1564537, _1564541))), _1564535), c_COMBB(_1564541, tc_prod(_1564537, _1564541), _1564539)), hAPP(hAPP(c_COMBB(_1564537, tc_fun(_1564541, tc_prod(_1564537, _1564541)), _1564535), c_Product__Type_OPair(_1564537, _1564541)), _1564543))), _1564545)))], (40183 ^ _782435) ^ [_1564658, _1564660, _1564662, _1564664, _1564666, _1564668, _1564670, _1564672, _1564674, _1564676] : [hAPP(c_Set_Oimage(_1564658, _1564660, _1564662), _1564664) = _1564666, hAPP(c_Set_Oimage(_1564668, _1564670, _1564672), _1564674) = _1564676, -(hAPP(c_Set_Oimage(tc_prod(_1564658, _1564668), tc_prod(_1564660, _1564670), c_Product__Type_Omap__pair(_1564658, _1564660, _1564668, _1564670, _1564662, _1564672)), hAPP(hAPP(c_Product__Type_OSigma(_1564658, _1564668), _1564664), hAPP(c_COMBK(tc_fun(_1564668, tc_HOL_Obool), _1564658), _1564674))) = hAPP(hAPP(c_Product__Type_OSigma(_1564660, _1564670), _1564666), hAPP(c_COMBK(tc_fun(_1564670, tc_HOL_Obool), _1564660), _1564676)))], (40193 ^ _782435) ^ [_1564959, _1564961, _1564963, _1564965] : [c_Wellfounded_Owf(_1564959, _1564961), c_Fun_Oinj__on(_1564959, _1564963, _1564965, c_Orderings_Otop__class_Otop(tc_fun(_1564959, tc_HOL_Obool))), -(c_Wellfounded_Owf(_1564963, hAPP(c_Set_Oimage(tc_prod(_1564959, _1564959), tc_prod(_1564963, _1564963), c_Product__Type_Omap__pair(_1564959, _1564963, _1564959, _1564963, _1564965, _1564965)), _1564961)))], (40203 ^ _782435) ^ [_1565150, _1565152, _1565154, _1565156, _1565158, _1565160, _1565162, _1565164] : [c_Fun_Oinj__on(_1565150, _1565152, _1565154, _1565156), c_Fun_Oinj__on(_1565158, _1565160, _1565162, _1565164), -(c_Fun_Oinj__on(tc_prod(_1565150, _1565158), tc_prod(_1565152, _1565160), c_Product__Type_Omap__pair(_1565150, _1565152, _1565158, _1565160, _1565154, _1565162), hAPP(hAPP(c_Product__Type_OSigma(_1565150, _1565158), _1565156), hAPP(c_COMBK(tc_fun(_1565158, tc_HOL_Obool), _1565150), _1565164))))], (40213 ^ _782435) ^ [_1565377, _1565379, _1565381, _1565383, _1565385, _1565387, _1565389, _1565391] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1565377, _1565379)), _1565381), hAPP(c_Set_Oimage(tc_prod(_1565383, _1565385), tc_prod(_1565377, _1565379), c_Product__Type_Omap__pair(_1565383, _1565377, _1565385, _1565379, _1565387, _1565389)), _1565391))), 40218 ^ _782435 : [(40219 ^ _782435) ^ [] : [-(_1565381 = hAPP(hAPP(c_Product__Type_OPair(_1565377, _1565379), hAPP(_1565387, 40216 ^ [_1565377, _1565379, _1565381, _1565383, _1565385, _1565387, _1565389, _1565391])), hAPP(_1565389, 40217 ^ [_1565377, _1565379, _1565381, _1565383, _1565385, _1565387, _1565389, _1565391])))], (40221 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565383, _1565385)), hAPP(hAPP(c_Product__Type_OPair(_1565383, _1565385), 40216 ^ [_1565377, _1565379, _1565381, _1565383, _1565385, _1565387, _1565389, _1565391]), 40217 ^ [_1565377, _1565379, _1565381, _1565383, _1565385, _1565387, _1565389, _1565391])), _1565391)))]]], (40223 ^ _782435) ^ [_1565728, _1565730, _1565732] : [c_Relation_Orefl__on(_1565728, _1565730, _1565732), 40226 ^ _782435 : [(40227 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1565728, _1565728), tc_HOL_Obool)), _1565732), hAPP(hAPP(c_Product__Type_OSigma(_1565728, _1565728), _1565730), hAPP(c_COMBK(tc_fun(_1565728, tc_HOL_Obool), _1565728), _1565730)))))], (40229 ^ _782435) ^ [_1565910] : [hBOOL(hAPP(hAPP(c_member(_1565728), _1565910), _1565730)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1565728, _1565728)), hAPP(hAPP(c_Product__Type_OPair(_1565728, _1565728), _1565910), _1565910)), _1565732)))]]], (40235 ^ _782435) ^ [_1566045, _1566047, _1566049] : [-(c_Relation_Orefl__on(_1566045, _1566047, _1566049)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1566045, _1566045), tc_HOL_Obool)), _1566049), hAPP(hAPP(c_Product__Type_OSigma(_1566045, _1566045), _1566047), hAPP(c_COMBK(tc_fun(_1566045, tc_HOL_Obool), _1566045), _1566047)))), 40241 ^ _782435 : [(40242 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1566045), 40240 ^ [_1566045, _1566047, _1566049]), _1566047)))], (40244 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1566045, _1566045)), hAPP(hAPP(c_Product__Type_OPair(_1566045, _1566045), 40240 ^ [_1566045, _1566047, _1566049]), 40240 ^ [_1566045, _1566047, _1566049])), _1566049))]]], (40248 ^ _782435) ^ [_1566409, _1566411] : [c_Wellfounded_OwfP(_1566409, _1566411), -(c_Wellfounded_Owf(_1566409, hAPP(c_Set_OCollect(tc_prod(_1566409, _1566409)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566409, _1566409, tc_HOL_Obool), _1566411))))], (40254 ^ _782435) ^ [_1566512, _1566514] : [c_Wellfounded_Owf(_1566512, hAPP(c_Set_OCollect(tc_prod(_1566512, _1566512)), hAPP(c_Product__Type_Oprod_Oprod__case(_1566512, _1566512, tc_HOL_Obool), _1566514))), -(c_Wellfounded_OwfP(_1566512, _1566514))], (40260 ^ _782435) ^ [_1566621] : [-(c_Wellfounded_OwfP(_1566621, hAPP(c_COMBK(tc_fun(_1566621, tc_HOL_Obool), _1566621), hAPP(c_COMBK(tc_HOL_Obool, _1566621), c_fFalse))))], (40262 ^ _782435) ^ [_1566659, _1566661] : [-(c_Relation_Orefl__on(_1566659, _1566661, c_Relation_OId__on(_1566659, _1566661)))], (40264 ^ _782435) ^ [_1566688, _1566690, _1566692] : [c_Wellfounded_OwfP(_1566688, _1566690), -(hBOOL(hAPP(c_Wellfounded_Oaccp(_1566688, _1566690), _1566692)))], (40270 ^ _782435) ^ [_1566792, _1566794] : [c_Wellfounded_OwfP(_1566792, _1566794), 40273 ^ _782435 : [(40274 ^ _782435) ^ [_1566856] : [-(hBOOL(hAPP(c_Wellfounded_Oaccp(_1566792, _1566794), _1566856)))]]], (40276 ^ _782435) ^ [_1566884, _1566886] : [hBOOL(hAPP(c_Wellfounded_Oaccp(_1566884, _1566886), 40277 ^ [_1566884, _1566886])), -(c_Wellfounded_OwfP(_1566884, _1566886))], (40283 ^ _782435) ^ [_1567002, _1567004, _1567006] : [c_Wellfounded_OwfP(_1567002, _1567004), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1567002, tc_fun(_1567002, tc_HOL_Obool))), _1567006), _1567004)), -(c_Wellfounded_OwfP(_1567002, _1567006))], (40293 ^ _782435) ^ [_1567161] : [-(c_Relation_Orefl__on(_1567161, c_Orderings_Obot__class_Obot(tc_fun(_1567161, tc_HOL_Obool)), c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1567161, _1567161), tc_HOL_Obool))))], (40295 ^ _782435) ^ [_1567198, _1567200, _1567202, _1567204, _1567206] : [c_Relation_Orefl__on(_1567198, _1567200, _1567202), c_Relation_Orefl__on(_1567198, _1567204, _1567206), -(c_Relation_Orefl__on(_1567198, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1567198, tc_HOL_Obool)), _1567200), _1567204), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1567198, _1567198), tc_HOL_Obool)), _1567202), _1567206)))], (40305 ^ _782435) ^ [_1567395, _1567397, _1567399, _1567401, _1567403] : [c_Relation_Orefl__on(_1567395, _1567397, _1567399), c_Relation_Orefl__on(_1567395, _1567401, _1567403), -(c_Relation_Orefl__on(_1567395, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1567395, tc_HOL_Obool)), _1567397), _1567401), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1567395, _1567395), tc_HOL_Obool)), _1567399), _1567403)))], (40315 ^ _782435) ^ [_1567592, _1567594, _1567596, _1567598, _1567600] : [c_Relation_Orefl__on(_1567592, _1567594, _1567596), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567592, _1567592)), hAPP(hAPP(c_Product__Type_OPair(_1567592, _1567592), _1567598), _1567600)), _1567596)), -(hBOOL(hAPP(hAPP(c_member(_1567592), _1567600), _1567594)))], (40325 ^ _782435) ^ [_1567787, _1567789, _1567791, _1567793, _1567795] : [c_Relation_Orefl__on(_1567787, _1567789, _1567791), hBOOL(hAPP(hAPP(c_member(tc_prod(_1567787, _1567787)), hAPP(hAPP(c_Product__Type_OPair(_1567787, _1567787), _1567793), _1567795)), _1567791)), -(hBOOL(hAPP(hAPP(c_member(_1567787), _1567793), _1567789)))], (40335 ^ _782435) ^ [_1567982, _1567984, _1567986, _1567988] : [c_Relation_Orefl__on(_1567982, _1567984, _1567986), hBOOL(hAPP(hAPP(c_member(_1567982), _1567988), _1567984)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1567982, _1567982)), hAPP(hAPP(c_Product__Type_OPair(_1567982, _1567982), _1567988), _1567988)), _1567986)))], (40345 ^ _782435) ^ [_1568173, _1568175] : [c_Wellfounded_Owf(_1568173, _1568175), -(c_Wellfounded_OwfP(_1568173, c_FunDef_Oin__rel(_1568173, _1568173, _1568175)))], (40351 ^ _782435) ^ [_1568273, _1568275] : [c_Wellfounded_OwfP(_1568273, hAPP(hAPP(c_COMBC(_1568273, tc_fun(tc_prod(_1568273, _1568273), tc_HOL_Obool), tc_fun(_1568273, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568273, tc_fun(tc_fun(tc_prod(_1568273, _1568273), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568273, _1568273), tc_HOL_Obool), tc_fun(_1568273, tc_HOL_Obool)), _1568273), c_COMBC(_1568273, tc_fun(tc_prod(_1568273, _1568273), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568273, tc_prod(_1568273, _1568273)), tc_fun(_1568273, tc_fun(tc_fun(tc_prod(_1568273, _1568273), tc_HOL_Obool), tc_HOL_Obool)), _1568273), hAPP(c_COMBB(tc_prod(_1568273, _1568273), tc_fun(tc_fun(tc_prod(_1568273, _1568273), tc_HOL_Obool), tc_HOL_Obool), _1568273), c_member(tc_prod(_1568273, _1568273)))), c_Product__Type_OPair(_1568273, _1568273)))), _1568275)), -(c_Wellfounded_Owf(_1568273, _1568275))], (40357 ^ _782435) ^ [_1568582, _1568584] : [c_Wellfounded_Owf(_1568582, _1568584), -(c_Wellfounded_OwfP(_1568582, hAPP(hAPP(c_COMBC(_1568582, tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool), tc_fun(_1568582, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568582, tc_fun(tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool), tc_fun(_1568582, tc_HOL_Obool)), _1568582), c_COMBC(_1568582, tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1568582, tc_prod(_1568582, _1568582)), tc_fun(_1568582, tc_fun(tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool), tc_HOL_Obool)), _1568582), hAPP(c_COMBB(tc_prod(_1568582, _1568582), tc_fun(tc_fun(tc_prod(_1568582, _1568582), tc_HOL_Obool), tc_HOL_Obool), _1568582), c_member(tc_prod(_1568582, _1568582)))), c_Product__Type_OPair(_1568582, _1568582)))), _1568584)))], (40363 ^ _782435) ^ [_1568912, _1568914] : [c_Predicate_Oreflp(_1568912, _1568914), -(c_Relation_Orefl__on(_1568912, c_Orderings_Otop__class_Otop(tc_fun(_1568912, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1568912, _1568912)), hAPP(c_Product__Type_Oprod_Oprod__case(_1568912, _1568912, tc_HOL_Obool), _1568914))))], (40369 ^ _782435) ^ [_1569027, _1569029] : [c_Relation_Orefl__on(_1569027, c_Orderings_Otop__class_Otop(tc_fun(_1569027, tc_HOL_Obool)), hAPP(c_Set_OCollect(tc_prod(_1569027, _1569027)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569027, _1569027, tc_HOL_Obool), _1569029))), -(c_Predicate_Oreflp(_1569027, _1569029))], (40375 ^ _782435) ^ [_1569148, _1569150, _1569152] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569148, _1569148), tc_HOL_Obool)), _1569150), hAPP(hAPP(c_Product__Type_OSigma(_1569148, _1569148), _1569152), hAPP(c_COMBK(tc_fun(_1569148, tc_HOL_Obool), _1569148), _1569152)))), 40381 ^ _782435 : [(40382 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1569148), 40380 ^ [_1569148, _1569150, _1569152]), _1569152)))], (40384 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1569148, _1569148)), hAPP(hAPP(c_Product__Type_OPair(_1569148, _1569148), 40380 ^ [_1569148, _1569150, _1569152]), 40380 ^ [_1569148, _1569150, _1569152])), _1569150))]], -(c_Relation_Orefl__on(_1569148, _1569152, _1569150))], (40388 ^ _782435) ^ [_1569495, _1569497] : [c_Wellfounded_OwfP(_1569495, _1569497), -(c_Wellfounded_Oacyclic(_1569495, hAPP(c_Set_OCollect(tc_prod(_1569495, _1569495)), hAPP(c_Product__Type_Oprod_Oprod__case(_1569495, _1569495, tc_HOL_Obool), _1569497))))], (40394 ^ _782435) ^ [_1569602, _1569604, _1569606] : [c_Predicate_Oreflp(_1569602, _1569604), -(hBOOL(hAPP(hAPP(_1569604, _1569606), _1569606)))], (40400 ^ _782435) ^ [_1569691, _1569693, _1569695] : [c_Wellfounded_Oacyclic(_1569691, _1569693), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1569691, _1569691), tc_HOL_Obool)), _1569695), _1569693)), -(c_Wellfounded_Oacyclic(_1569691, _1569695))], (40410 ^ _782435) ^ [_1569850, _1569852] : [c_Wellfounded_Owf(_1569850, _1569852), -(c_Wellfounded_Oacyclic(_1569850, _1569852))], (40416 ^ _782435) ^ [_1569927, _1569929] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1569927, _1569927)), _1569929)), 40419 ^ _782435 : [(40420 ^ _782435) ^ [] : [c_Wellfounded_Owf(_1569927, _1569929), -(c_Wellfounded_Oacyclic(_1569927, _1569929))], (40426 ^ _782435) ^ [] : [c_Wellfounded_Oacyclic(_1569927, _1569929), -(c_Wellfounded_Owf(_1569927, _1569929))]]], (40432 ^ _782435) ^ [_1570148, _1570150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570148, _1570148)), _1570150)), c_Wellfounded_Oacyclic(_1570148, _1570150), -(c_Wellfounded_Owf(_1570148, _1570150))], (40442 ^ _782435) ^ [_1570306, _1570308] : [c_Nitpick_Owf_H(_1570306, _1570308), 40445 ^ _782435 : [(40446 ^ _782435) ^ [] : [-(c_Wellfounded_Oacyclic(_1570306, _1570308))], (40448 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570306, _1570306)), _1570308))), -(c_Nitpick_Ounknown(tc_HOL_Obool))]]], (40454 ^ _782435) ^ [_1570426, _1570428] : [-(c_Nitpick_Owf_H(_1570426, _1570428)), c_Wellfounded_Oacyclic(_1570426, _1570428), 40459 ^ _782435 : [(40460 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1570426, _1570426)), _1570428))], (40462 ^ _782435) ^ [] : [c_Nitpick_Ounknown(tc_HOL_Obool)]]], (40466 ^ _782435) ^ [_1570603, _1570605] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1570603), c_Int_OInteg)), hBOOL(hAPP(_1570605, hAPP(c_Int_ORep__Integ, 40471 ^ [_1570603, _1570605]))), -(hBOOL(hAPP(_1570605, _1570603)))], (40477 ^ _782435) ^ [_1570785] : [hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), _1570785), c_Int_OInteg)), -(_1570785 = hAPP(c_Int_ORep__Integ, 40480 ^ [_1570785]))], (40500 ^ _782435) ^ [_1571527, _1571529, _1571531] : [-(c_Relation_Orefl__on(_1571527, _1571529, _1571531)), 40504 ^ _782435 : [(40505 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1571527, _1571527)), 40503 ^ [_1571527, _1571529, _1571531]), _1571531)))], (40507 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1571527, _1571527, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1571527, tc_fun(_1571527, tc_HOL_Obool), tc_fun(_1571527, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1571527, tc_HOL_Obool), tc_fun(_1571527, tc_HOL_Obool)), _1571527), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1571527)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1571527), c_fconj), hAPP(hAPP(c_COMBC(_1571527, tc_fun(_1571527, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571527)), _1571529)))), hAPP(hAPP(c_COMBC(_1571527, tc_fun(_1571527, tc_HOL_Obool), tc_HOL_Obool), c_member(_1571527)), _1571529))), 40503 ^ [_1571527, _1571529, _1571531]))]], 40509 ^ _782435 : [(40510 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1571527), 40508 ^ [_1571527, _1571529, _1571531]), _1571529)))], (40512 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1571527, _1571527)), hAPP(hAPP(c_Product__Type_OPair(_1571527, _1571527), 40508 ^ [_1571527, _1571529, _1571531]), 40508 ^ [_1571527, _1571529, _1571531])), _1571531))]]], (40484 ^ _782435) ^ [_1570908, _1570910, _1570912] : [c_Relation_Orefl__on(_1570908, _1570910, _1570912), 40487 ^ _782435 : [(40488 ^ _782435) ^ [_1571119] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1570908, _1570908)), _1571119), _1570912)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1570908, _1570908, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1570908, tc_fun(_1570908, tc_HOL_Obool), tc_fun(_1570908, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1570908, tc_HOL_Obool), tc_fun(_1570908, tc_HOL_Obool)), _1570908), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1570908)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1570908), c_fconj), hAPP(hAPP(c_COMBC(_1570908, tc_fun(_1570908, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570908)), _1570910)))), hAPP(hAPP(c_COMBC(_1570908, tc_fun(_1570908, tc_HOL_Obool), tc_HOL_Obool), c_member(_1570908)), _1570910))), _1571119)))], (40494 ^ _782435) ^ [_1571392] : [hBOOL(hAPP(hAPP(c_member(_1570908), _1571392), _1570910)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1570908, _1570908)), hAPP(hAPP(c_Product__Type_OPair(_1570908, _1570908), _1571392), _1571392)), _1570912)))]]], (40516 ^ _782435) ^ [_1572168, _1572170] : [40518 ^ _782435 : [(40519 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40517 ^ [_1572168, _1572170]), c_Int_OInteg)))], (40521 ^ _782435) ^ [] : [hBOOL(hAPP(_1572168, hAPP(c_Int_OAbs__Integ, 40517 ^ [_1572168, _1572170])))]], -(hBOOL(hAPP(_1572168, _1572170)))], (40526 ^ _782435) ^ [_1572335] : [-(_1572335 = hAPP(c_Int_OAbs__Integ, 40524 ^ [_1572335]))], (40528 ^ _782435) ^ [_1572363] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat, tc_Nat_Onat), tc_HOL_Obool)), 40524 ^ [_1572363]), c_Int_OInteg)))], (40540 ^ _782435) ^ [_1572599, _1572601, _1572603] : [40542 ^ _782435 : [(40543 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1572599), 40541 ^ [_1572599, _1572601, _1572603]), _1572603)))], (40545 ^ _782435) ^ [] : [hBOOL(hAPP(_1572601, 40541 ^ [_1572599, _1572601, _1572603]))]], -(hBOOL(hAPP(c_Predicate_OPowp(_1572599, _1572601), _1572603)))], (40530 ^ _782435) ^ [_1572416, _1572418, _1572420] : [hBOOL(hAPP(c_Predicate_OPowp(_1572416, _1572418), _1572420)), 40533 ^ _782435 : [(40534 ^ _782435) ^ [_1572500] : [hBOOL(hAPP(hAPP(c_member(_1572416), _1572500), _1572420)), -(hBOOL(hAPP(_1572418, _1572500)))]]], (40549 ^ _782435) ^ [_1572779] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1572779, tc_HOL_Obool) = c_Set_OBall(_1572779))], (40551 ^ _782435) ^ [_1572807, _1572809, _1572811] : [hBOOL(hAPP(hAPP(c_member(_1572809), _1572807), c_Orderings_Obot__class_Obot(tc_fun(_1572809, tc_HOL_Obool)))), -(hBOOL(hAPP(_1572811, _1572807)))], (40557 ^ _782435) ^ [_1572914, _1572916, _1572918, _1572920] : [-(hAPP(c_Set_OCollect(_1572914), hAPP(hAPP(c_COMBB(tc_fun(_1572916, tc_HOL_Obool), tc_HOL_Obool, _1572914), c_HOL_OAll(_1572916)), hAPP(hAPP(c_COMBB(tc_fun(_1572916, tc_HOL_Obool), tc_fun(_1572916, tc_HOL_Obool), _1572914), hAPP(c_COMBS(_1572916, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1572916), c_fimplies), hAPP(hAPP(c_COMBC(_1572916, tc_fun(_1572916, tc_HOL_Obool), tc_HOL_Obool), c_member(_1572916)), _1572918)))), _1572920))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1572916, tc_fun(_1572914, tc_HOL_Obool)), _1572918), hAPP(hAPP(c_COMBB(tc_fun(_1572914, tc_HOL_Obool), tc_fun(_1572914, tc_HOL_Obool), _1572916), c_Set_OCollect(_1572914)), hAPP(c_COMBC(_1572914, _1572916, tc_HOL_Obool), _1572920))))], (40569 ^ _782435) ^ [_1573445, _1573447, _1573449, _1573451] : [40571 ^ _782435 : [(40572 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1573445, _1573445)), 40570 ^ [_1573445, _1573447, _1573449, _1573451]), _1573449)))], (40574 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1573445, _1573445, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1573445, tc_fun(_1573445, _1573447), tc_fun(_1573445, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573447, tc_HOL_Obool), tc_fun(tc_fun(_1573445, _1573447), tc_fun(_1573445, tc_HOL_Obool)), _1573445), c_COMBB(_1573447, tc_HOL_Obool, _1573445)), hAPP(hAPP(c_COMBB(_1573447, tc_fun(_1573447, tc_HOL_Obool), _1573445), c_fequal), _1573451))), _1573451)), 40570 ^ [_1573445, _1573447, _1573449, _1573451]))]], -(c_Equiv__Relations_Ocongruent(_1573445, _1573447, _1573449, _1573451))], (40559 ^ _782435) ^ [_1573069, _1573071, _1573073, _1573075] : [c_Equiv__Relations_Ocongruent(_1573069, _1573071, _1573073, _1573075), 40562 ^ _782435 : [(40563 ^ _782435) ^ [_1573214] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1573069, _1573069)), _1573214), _1573073)), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1573069, _1573069, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1573069, tc_fun(_1573069, _1573071), tc_fun(_1573069, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1573071, tc_HOL_Obool), tc_fun(tc_fun(_1573069, _1573071), tc_fun(_1573069, tc_HOL_Obool)), _1573069), c_COMBB(_1573071, tc_HOL_Obool, _1573069)), hAPP(hAPP(c_COMBB(_1573071, tc_fun(_1573071, tc_HOL_Obool), _1573069), c_fequal), _1573075))), _1573075)), _1573214)))]]], (40578 ^ _782435) ^ [_1573820, _1573822, _1573824, _1573826] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1573820, tc_fun(_1573822, tc_HOL_Obool)), _1573824), _1573826) = hAPP(c_Set_OCollect(_1573822), hAPP(hAPP(c_COMBB(tc_fun(_1573820, tc_HOL_Obool), tc_HOL_Obool, _1573822), c_HOL_OAll(_1573820)), hAPP(hAPP(c_COMBB(tc_fun(_1573820, tc_HOL_Obool), tc_fun(_1573820, tc_HOL_Obool), _1573822), hAPP(c_COMBS(_1573820, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573820), c_fimplies), hAPP(hAPP(c_COMBC(_1573820, tc_fun(_1573820, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573820)), _1573824)))), hAPP(hAPP(c_COMBC(_1573822, tc_fun(_1573820, tc_fun(_1573822, tc_HOL_Obool)), tc_fun(_1573820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1573822, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1573820, tc_fun(_1573822, tc_HOL_Obool)), tc_fun(_1573820, tc_HOL_Obool)), _1573822), c_COMBB(tc_fun(_1573822, tc_HOL_Obool), tc_HOL_Obool, _1573820)), c_member(_1573822))), _1573826)))))], (40580 ^ _782435) ^ [_1573985, _1573987] : [class_Complete__Lattice_Ocomplete__lattice(_1573985), -(c_Complete__Lattice_OInf__class_OInf(_1573985, _1573987) = c_Complete__Lattice_OSup__class_OSup(_1573985, hAPP(c_Set_OCollect(_1573985), hAPP(hAPP(c_COMBB(tc_fun(_1573985, tc_HOL_Obool), tc_HOL_Obool, _1573985), c_HOL_OAll(_1573985)), hAPP(hAPP(c_COMBB(tc_fun(_1573985, tc_HOL_Obool), tc_fun(_1573985, tc_HOL_Obool), _1573985), hAPP(c_COMBS(_1573985, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1573985), c_fimplies), hAPP(hAPP(c_COMBC(_1573985, tc_fun(_1573985, tc_HOL_Obool), tc_HOL_Obool), c_member(_1573985)), _1573987)))), c_Orderings_Oord__class_Oless__eq(_1573985))))))], (40586 ^ _782435) ^ [_1574212, _1574214] : [class_Complete__Lattice_Ocomplete__lattice(_1574212), -(c_Complete__Lattice_OSup__class_OSup(_1574212, _1574214) = c_Complete__Lattice_OInf__class_OInf(_1574212, hAPP(c_Set_OCollect(_1574212), hAPP(hAPP(c_COMBB(tc_fun(_1574212, tc_HOL_Obool), tc_HOL_Obool, _1574212), c_HOL_OAll(_1574212)), hAPP(hAPP(c_COMBB(tc_fun(_1574212, tc_HOL_Obool), tc_fun(_1574212, tc_HOL_Obool), _1574212), hAPP(c_COMBS(_1574212, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1574212), c_fimplies), hAPP(hAPP(c_COMBC(_1574212, tc_fun(_1574212, tc_HOL_Obool), tc_HOL_Obool), c_member(_1574212)), _1574214)))), hAPP(c_COMBC(_1574212, _1574212, tc_HOL_Obool), c_Orderings_Oord__class_Oless__eq(_1574212)))))))], (40592 ^ _782435) ^ [_1574453, _1574455, _1574457] : [c_Wellfounded_OwfP(_1574453, hAPP(_1574455, 40593 ^ [_1574453, _1574455, _1574457])), 40600 ^ _782435 : [(40601 ^ _782435) ^ [] : [hAPP(_1574455, 40598 ^ [_1574453, _1574455, _1574457]) = hAPP(_1574455, 40599 ^ [_1574453, _1574455, _1574457])], (40603 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1574453, tc_HOL_Obool)), c_Predicate_ODomainP(_1574453, _1574453, hAPP(_1574455, 40598 ^ [_1574453, _1574455, _1574457]))), c_Predicate_ORangeP(_1574453, _1574453, hAPP(_1574455, 40599 ^ [_1574453, _1574455, _1574457]))) = c_Orderings_Obot__class_Obot(tc_fun(_1574453, tc_HOL_Obool))]], -(c_Wellfounded_OwfP(_1574453, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1574457, tc_fun(_1574453, tc_fun(_1574453, tc_HOL_Obool))), c_Orderings_Otop__class_Otop(tc_fun(_1574457, tc_HOL_Obool))), _1574455)))], (40607 ^ _782435) ^ [_1574893, _1574895, _1574897, _1574899, _1574901, _1574903] : [hBOOL(hAPP(hAPP(c_member(_1574893), _1574895), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1574897, _1574899, tc_fun(_1574893, tc_HOL_Obool)), _1574901), _1574903))), 40612 ^ _782435 : [(40613 ^ _782435) ^ [] : [-(_1574903 = hAPP(hAPP(c_Product__Type_OPair(_1574897, _1574899), 40610 ^ [_1574893, _1574895, _1574897, _1574899, _1574901, _1574903]), 40611 ^ [_1574893, _1574895, _1574897, _1574899, _1574901, _1574903]))], (40615 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1574893), _1574895), hAPP(hAPP(_1574901, 40610 ^ [_1574893, _1574895, _1574897, _1574899, _1574901, _1574903]), 40611 ^ [_1574893, _1574895, _1574897, _1574899, _1574901, _1574903]))))]]], (40617 ^ _782435) ^ [_1575162, _1575164, _1575166, _1575168, _1575170, _1575172] : [40620 ^ _782435 : [(40621 ^ _782435) ^ [] : [-(_1575162 = hAPP(hAPP(c_Product__Type_OPair(_1575164, _1575166), 40618 ^ [_1575162, _1575164, _1575166, _1575168, _1575170, _1575172]), 40619 ^ [_1575162, _1575164, _1575166, _1575168, _1575170, _1575172]))], (40623 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1575168), _1575170), hAPP(hAPP(_1575172, 40618 ^ [_1575162, _1575164, _1575166, _1575168, _1575170, _1575172]), 40619 ^ [_1575162, _1575164, _1575166, _1575168, _1575170, _1575172])))]], -(hBOOL(hAPP(hAPP(c_member(_1575168), _1575170), hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1575164, _1575166, tc_fun(_1575168, tc_HOL_Obool)), _1575172), _1575162))))], (40627 ^ _782435) ^ [_1575487, _1575489] : [-(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1575487, tc_HOL_Obool), _1575489) = hAPP(c_Set_OCollect(_1575487), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575487, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1575487), c_HOL_OAll(tc_fun(_1575487, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1575487, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1575487, tc_HOL_Obool), tc_HOL_Obool), _1575487), hAPP(c_COMBS(tc_fun(_1575487, 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(_1575487, tc_HOL_Obool)), c_fimplies), hAPP(hAPP(c_COMBC(tc_fun(_1575487, tc_HOL_Obool), tc_fun(tc_fun(_1575487, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1575487, tc_HOL_Obool))), _1575489)))), c_member(_1575487)))))], (40629 ^ _782435) ^ [_1575615, _1575617, _1575619] : [-(c_Hilbert__Choice_OEps(tc_prod(_1575615, _1575617), hAPP(c_Product__Type_Oprod_Oprod__case(_1575615, _1575617, tc_HOL_Obool), _1575619)) = c_Hilbert__Choice_OEps(tc_prod(_1575615, _1575617), hAPP(hAPP(c_COMBS(tc_prod(_1575615, _1575617), _1575617, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1575615, tc_fun(_1575617, tc_HOL_Obool), tc_prod(_1575615, _1575617)), _1575619), c_Product__Type_Ofst(_1575615, _1575617))), c_Product__Type_Osnd(_1575615, _1575617))))], (40631 ^ _782435) ^ [_1575696, _1575698] : [40633 ^ _782435 : [(40634 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575696, tc_HOL_Obool)), 40632 ^ [_1575696, _1575698]), hAPP(c_Relation_OImage(_1575696, _1575696, _1575698), 40632 ^ [_1575696, _1575698]))))], (40636 ^ _782435) ^ [] : [40632 ^ [_1575696, _1575698] = c_Orderings_Obot__class_Obot(tc_fun(_1575696, tc_HOL_Obool))]], -(c_Wellfounded_Owf(_1575696, _1575698))], (40640 ^ _782435) ^ [_1575893, _1575895, _1575897, _1575899, _1575901, _1575903] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575893, tc_HOL_Obool)), _1575895), _1575897)), 40646 ^ _782435 : [(40647 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1575893), 40645 ^ [_1575893, _1575895, _1575897, _1575899, _1575901, _1575903]), _1575895)))], (40649 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1575899, tc_HOL_Obool)), hAPP(_1575901, 40645 ^ [_1575893, _1575895, _1575897, _1575899, _1575901, _1575903])), hAPP(_1575903, 40645 ^ [_1575893, _1575895, _1575897, _1575899, _1575901, _1575903])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1575893, _1575899), tc_HOL_Obool)), hAPP(hAPP(c_Product__Type_OSigma(_1575893, _1575899), _1575895), _1575901)), hAPP(hAPP(c_Product__Type_OSigma(_1575893, _1575899), _1575897), _1575903))))], (40653 ^ _782435) ^ [_1576284, _1576286] : [-(c_Hilbert__Choice_OEps(_1576284, hAPP(c_fequal, _1576286)) = _1576286)], (40655 ^ _782435) ^ [_1576315, _1576317] : [-(c_Hilbert__Choice_OEps(_1576315, hAPP(hAPP(c_COMBC(_1576315, _1576315, tc_HOL_Obool), c_fequal), _1576317)) = _1576317)], (40657 ^ _782435) ^ [_1576368, _1576370] : [hBOOL(hAPP(_1576368, c_Hilbert__Choice_OEps(_1576370, _1576368))), -(hBOOL(hAPP(_1576368, 40660 ^ [_1576368, _1576370])))], (40664 ^ _782435) ^ [_1576467, _1576469] : [40665 ^ _782435 : [(40666 ^ _782435) ^ [_1576513] : [hBOOL(hAPP(_1576467, _1576513))]], -(hBOOL(hAPP(_1576467, c_Hilbert__Choice_OEps(_1576469, _1576467))))], (40670 ^ _782435) ^ [_1576573, _1576575] : [40671 ^ _782435 : [(40672 ^ _782435) ^ [_1576619] : [hBOOL(hAPP(_1576573, _1576619))]], -(hBOOL(hAPP(_1576573, c_Hilbert__Choice_OEps(_1576575, _1576573))))], (40676 ^ _782435) ^ [_1576677, _1576679, _1576681] : [hBOOL(hAPP(_1576677, _1576679)), -(hBOOL(hAPP(_1576677, c_Hilbert__Choice_OEps(_1576681, _1576677))))], (40682 ^ _782435) ^ [_1576770, _1576772] : [40683 ^ _782435 : [(40684 ^ _782435) ^ [_1576816] : [hBOOL(hAPP(_1576770, _1576816))]], -(hBOOL(hAPP(_1576770, c_Hilbert__Choice_OEps(_1576772, _1576770))))], (40688 ^ _782435) ^ [_1576874, _1576876, _1576878] : [40689 ^ _782435 : [(40690 ^ _782435) ^ [_1576928] : [hBOOL(hAPP(_1576874, _1576928))]], _1576876 = c_Hilbert__Choice_OEps(_1576878, _1576874), -(hBOOL(hAPP(_1576874, _1576876)))], (40698 ^ _782435) ^ [_1577034, _1577036, _1577038] : [-(c_Hilbert__Choice_OEps(tc_prod(_1577034, _1577036), _1577038) = c_Hilbert__Choice_OEps(tc_prod(_1577034, _1577036), hAPP(c_Product__Type_Oprod_Oprod__case(_1577034, _1577036, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1577036, tc_prod(_1577034, _1577036)), tc_fun(_1577036, tc_HOL_Obool), _1577034), hAPP(c_COMBB(tc_prod(_1577034, _1577036), tc_HOL_Obool, _1577036), _1577038)), c_Product__Type_OPair(_1577034, _1577036)))))], (40700 ^ _782435) ^ [_1577112, _1577114, _1577116, _1577118] : [-(c_Hilbert__Choice_OEps(tc_prod(_1577112, _1577114), hAPP(c_Product__Type_Oprod_Oprod__case(_1577112, _1577114, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1577112, tc_fun(_1577114, tc_HOL_Obool), tc_fun(_1577114, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1577114, tc_HOL_Obool), tc_fun(_1577114, tc_HOL_Obool)), _1577112), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1577114)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1577112), c_fconj), hAPP(c_fequal, _1577116)))), hAPP(c_fequal, _1577118)))) = hAPP(hAPP(c_Product__Type_OPair(_1577112, _1577114), _1577116), _1577118))], (40702 ^ _782435) ^ [_1577218, _1577220, _1577222] : [40704 ^ _782435 : [(40705 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577218, _1577218)), hAPP(hAPP(c_Product__Type_OPair(_1577218, _1577218), 40703 ^ [_1577218, _1577220, _1577222]), _1577220)), _1577222)))], (40707 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1577218), 40703 ^ [_1577218, _1577220, _1577222]), c_Wellfounded_Oacc(_1577218, _1577222)))]], -(hBOOL(hAPP(hAPP(c_member(_1577218), _1577220), c_Wellfounded_Oacc(_1577218, _1577222))))], (40711 ^ _782435) ^ [_1577455, _1577457, _1577459] : [-(hBOOL(hAPP(hAPP(c_member(_1577455), _1577457), c_Wellfounded_Oacc(_1577455, _1577459)))), 40715 ^ _782435 : [(40716 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577455, _1577455)), hAPP(hAPP(c_Product__Type_OPair(_1577455, _1577455), 40714 ^ [_1577455, _1577457, _1577459]), _1577457)), _1577459)))], (40718 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1577455), 40714 ^ [_1577455, _1577457, _1577459]), c_Wellfounded_Oacc(_1577455, _1577459)))]]], (40720 ^ _782435) ^ [_1577703, _1577705, _1577707, _1577709] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1577703, tc_HOL_Obool), tc_fun(_1577703, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1577703, tc_HOL_Obool), tc_fun(_1577703, tc_HOL_Obool)), _1577705), _1577707)), c_Wellfounded_Omax__ext(_1577703, _1577709))), 40723 ^ _782435 : [(40724 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577703), _1577705)))], (40726 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1577703), _1577707)))], (40728 ^ _782435) ^ [] : [_1577707 = c_Orderings_Obot__class_Obot(tc_fun(_1577703, tc_HOL_Obool))], (40730 ^ _782435) ^ [_1577997] : [hBOOL(hAPP(hAPP(c_member(_1577703), _1577997), _1577705)), 40734 ^ _782435 : [(40735 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1577703), 40733 ^ [_1577703, _1577705, _1577707, _1577709, _1577997]), _1577707)))], (40737 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1577703, _1577703)), hAPP(hAPP(c_Product__Type_OPair(_1577703, _1577703), _1577997), 40733 ^ [_1577703, _1577705, _1577707, _1577709, _1577997])), _1577709)))]]]]], (40739 ^ _782435) ^ [_1578209, _1578211, _1578213, _1578215] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(_1578209, tc_HOL_Obool), tc_fun(_1578209, tc_HOL_Obool))), hAPP(hAPP(c_Product__Type_OPair(tc_fun(_1578209, tc_HOL_Obool), tc_fun(_1578209, tc_HOL_Obool)), _1578211), _1578213)), c_Wellfounded_Omax__ext(_1578209, _1578215)))), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578209), _1578211)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1578209), _1578213)), -(_1578213 = c_Orderings_Obot__class_Obot(tc_fun(_1578209, tc_HOL_Obool))), 40753 ^ _782435 : [(40754 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1578209), 40752 ^ [_1578209, _1578211, _1578213, _1578215]), _1578211)))], (40756 ^ _782435) ^ [_1578614] : [hBOOL(hAPP(hAPP(c_member(_1578209), _1578614), _1578213)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578209, _1578209)), hAPP(hAPP(c_Product__Type_OPair(_1578209, _1578209), 40752 ^ [_1578209, _1578211, _1578213, _1578215]), _1578614)), _1578215))]]], (40764 ^ _782435) ^ [_1578842, _1578844, _1578846] : [c_Wellfounded_Owf(_1578842, _1578844), hBOOL(hAPP(hAPP(c_member(tc_prod(_1578842, _1578842)), hAPP(hAPP(c_Product__Type_OPair(_1578842, _1578842), hAPP(_1578846, hAPP(c_Nat_OSuc, 40767 ^ [_1578842, _1578844, _1578846]))), hAPP(_1578846, 40767 ^ [_1578842, _1578844, _1578846]))), _1578844))], (40771 ^ _782435) ^ [_1579043, _1579045, _1579047, _1579049, _1579051, _1579053, _1579055, _1579057] : [class_Groups_Ocomm__monoid__add(_1579043), c_Fun_Oinj__on(_1579045, _1579047, _1579049, _1579051), _1579053 = hAPP(c_Set_Oimage(_1579045, _1579047, _1579049), _1579051), 40785 ^ _782435 : [(40786 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1579045), 40784 ^ [_1579043, _1579045, _1579047, _1579049, _1579051, _1579053, _1579055, _1579057]), _1579051)))], (40788 ^ _782435) ^ [] : [hAPP(_1579055, 40784 ^ [_1579043, _1579045, _1579047, _1579049, _1579051, _1579053, _1579055, _1579057]) = hAPP(_1579057, hAPP(_1579049, 40784 ^ [_1579043, _1579045, _1579047, _1579049, _1579051, _1579053, _1579055, _1579057]))]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579047, _1579043), _1579057), _1579053) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1579045, _1579043), _1579055), _1579051))], (40792 ^ _782435) ^ [_1579535, _1579537, _1579539, _1579541, _1579543, _1579545, _1579547] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579535, _1579537, _1579539, _1579541), _1579543), _1579545), _1579547) = hAPP(hAPP(_1579545, hAPP(c_Product__Type_Ofst(_1579537, _1579539), hAPP(_1579543, _1579547))), hAPP(c_Product__Type_Osnd(_1579537, _1579539), hAPP(_1579543, _1579547))))], (40794 ^ _782435) ^ [_1579608, _1579610, _1579612, _1579614] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579608, _1579610, _1579612, tc_prod(_1579610, _1579612)), _1579614), c_Product__Type_OPair(_1579610, _1579612)) = _1579614)], (40796 ^ _782435) ^ [_1579654, _1579656, _1579658, _1579660, _1579662] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579654, _1579656, _1579654, _1579658), hAPP(c_Product__Type_OPair(_1579656, _1579654), _1579660)), _1579662) = hAPP(_1579662, _1579660))], (40798 ^ _782435) ^ [_1579705, _1579707, _1579709, _1579711, _1579713, _1579715, _1579717, _1579719, _1579721] : [-(hAPP(hAPP(c_Product__Type_Oscomp(_1579705, _1579707, _1579709, _1579711), hAPP(hAPP(c_Product__Type_Oscomp(_1579705, _1579713, _1579715, tc_prod(_1579707, _1579709)), _1579717), _1579719)), _1579721) = hAPP(hAPP(c_Product__Type_Oscomp(_1579705, _1579713, _1579715, _1579711), _1579717), hAPP(hAPP(c_COMBC(_1579713, tc_fun(_1579707, tc_fun(_1579709, _1579711)), tc_fun(_1579715, _1579711)), hAPP(hAPP(c_COMBB(tc_fun(_1579715, tc_prod(_1579707, _1579709)), tc_fun(tc_fun(_1579707, tc_fun(_1579709, _1579711)), tc_fun(_1579715, _1579711)), _1579713), c_Product__Type_Oscomp(_1579715, _1579707, _1579709, _1579711)), _1579719)), _1579721)))], (40800 ^ _782435) ^ [_1579832, _1579834, _1579836, _1579838, _1579840, _1579842, _1579844] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579832, _1579834, _1579836, _1579838), _1579840), _1579842), _1579844) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579834, _1579836, _1579838), _1579842), hAPP(_1579840, _1579844)))], (40802 ^ _782435) ^ [_1579894, _1579896, _1579898, _1579900, _1579902, _1579904, _1579906] : [-(hAPP(hAPP(hAPP(c_Product__Type_Oscomp(_1579894, _1579896, _1579898, _1579900), _1579902), _1579904), _1579906) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1579896, _1579898, _1579900), _1579904), hAPP(_1579902, _1579906)))], (40804 ^ _782435) ^ [_1579974, _1579976, _1579978, _1579980, _1579982] : [_1579974 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_Random_Oiterate(_1579976, _1579978, _1579974, _1579980), _1579982) = hAPP(c_Product__Type_OPair(_1579976, _1579978), _1579982))], (40810 ^ _782435) ^ [_1580079, _1580081, _1580083, _1580085, _1580087] : [-(_1580079 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_Random_Oiterate(_1580081, _1580083, _1580079, _1580085), _1580087) = hAPP(hAPP(c_Product__Type_Oscomp(_1580083, _1580081, _1580083, tc_prod(_1580081, _1580083)), hAPP(_1580085, _1580087)), c_Random_Oiterate(_1580081, _1580083, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1580079), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1580085)))], (40816 ^ _782435) ^ [_1580159, _1580161, _1580163, _1580165, _1580167, _1580169, _1580171, _1580173] : [class_Groups_Ocomm__monoid__add(_1580159), class_Orderings_Oord(_1580161), _1580163 = _1580165, _1580167 = _1580169, 40834 ^ _782435 : [(40835 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1580161), _1580165), 40833 ^ [_1580159, _1580161, _1580163, _1580165, _1580167, _1580169, _1580171, _1580173])))], (40837 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1580161), 40833 ^ [_1580159, _1580161, _1580163, _1580165, _1580167, _1580169, _1580171, _1580173]), _1580169)))], (40839 ^ _782435) ^ [] : [hAPP(_1580171, 40833 ^ [_1580159, _1580161, _1580163, _1580165, _1580167, _1580169, _1580171, _1580173]) = hAPP(_1580173, 40833 ^ [_1580159, _1580161, _1580163, _1580165, _1580167, _1580169, _1580171, _1580173])]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580161, _1580159), _1580171), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1580161, _1580163), _1580167)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1580161, _1580159), _1580173), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(_1580161, _1580165), _1580169)))], (40843 ^ _782435) ^ [_1580797, _1580799] : [40844 ^ _782435 : [(40845 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1580797), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40847 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1580799), _1580797))]], -(c_Random_Olog(_1580797, _1580799) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40851 ^ _782435) ^ [_1580932, _1580934] : [-(c_Random_Olog(_1580932, _1580934) = 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(_1580932, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1580934), _1580932)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1580932), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1580934), _1580932)))], (40861 ^ _782435) ^ [_1581014, _1581016, _1581018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1581014), _1581016)), -(c_Random_Ominus__shift(_1581018, _1581014, _1581016) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1581018), _1581014)), _1581016))], (40867 ^ _782435) ^ [_1581129, _1581131, _1581133] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1581129), _1581131))), -(c_Random_Ominus__shift(_1581133, _1581129, _1581131) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1581129), _1581131))], (40873 ^ _782435) ^ [_1581193, _1581195] : [_1581193 = _1581195, -(c_Random_Oinc__shift(_1581193, _1581195) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))], (40879 ^ _782435) ^ [_1581270, _1581272] : [-(_1581270 = _1581272), -(c_Random_Oinc__shift(_1581270, _1581272) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1581272), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))], (40885 ^ _782435) ^ [_1581317, _1581319] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1581317)), -(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(_1581317), _1581319))), _1581317)))], (40891 ^ _782435) ^ [_1581439, _1581441] : [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), _1581439), _1581441)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581439), _1581441)))], (40897 ^ _782435) ^ [_1581544, _1581546] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581544), _1581546)), -(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), _1581544), _1581546)), c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (40903 ^ _782435) ^ [_1581655, _1581657, _1581659, _1581661] : [40905 ^ _782435 : [(40906 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1581655), 40904 ^ [_1581655, _1581657, _1581659, _1581661])))], (40908 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 40904 ^ [_1581655, _1581657, _1581659, _1581661]), _1581657)))], (40910 ^ _782435) ^ [] : [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(_1581659, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 40904 ^ [_1581655, _1581657, _1581659, _1581661]), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(_1581659, 40904 ^ [_1581655, _1581657, _1581659, _1581661])))), c_Groups_Oone__class_Oone(tc_Int_Oint)))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1581655), _1581657)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(_1581659, _1581655)), _1581661)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1581661), hAPP(_1581659, _1581657))), 40924 ^ _782435 : [(40925 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1581655), 40923 ^ [_1581655, _1581657, _1581659, _1581661])))], (40927 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 40923 ^ [_1581655, _1581657, _1581659, _1581661]), _1581657)))], (40929 ^ _782435) ^ [] : [-(hAPP(_1581659, 40923 ^ [_1581655, _1581657, _1581659, _1581661]) = _1581661)]]], (40931 ^ _782435) ^ [_1582281, _1582283] : [c_Wellfounded_Owf(_1582281, _1582283), -(c_Wellfounded_Owf(_1582281, c_Transitive__Closure_Otrancl(_1582281, _1582283)))], (40937 ^ _782435) ^ [] : [-(c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))], (40939 ^ _782435) ^ [_1582397, _1582399] : [c_Wellfounded_Oacyclic(_1582397, _1582399), 40942 ^ _782435 : [(40943 ^ _782435) ^ [_1582482] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582397, _1582397)), hAPP(hAPP(c_Product__Type_OPair(_1582397, _1582397), _1582482), _1582482)), c_Transitive__Closure_Otrancl(_1582397, _1582399)))]]], (40945 ^ _782435) ^ [_1582525, _1582527] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582525, _1582525)), hAPP(hAPP(c_Product__Type_OPair(_1582525, _1582525), 40946 ^ [_1582525, _1582527]), 40946 ^ [_1582525, _1582527])), c_Transitive__Closure_Otrancl(_1582525, _1582527)))), -(c_Wellfounded_Oacyclic(_1582525, _1582527))], (40952 ^ _782435) ^ [_1582599, _1582601, _1582603, _1582605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582599, _1582599)), hAPP(hAPP(c_Product__Type_OPair(_1582599, _1582599), _1582601), _1582603)), _1582605)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582599, _1582599)), hAPP(hAPP(c_Product__Type_OPair(_1582599, _1582599), _1582601), _1582603)), c_Transitive__Closure_Otrancl(_1582599, _1582605))))], (40958 ^ _782435) ^ [_1582762, _1582764] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1582762, _1582762), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1582762, _1582764)), hAPP(hAPP(c_Product__Type_OSigma(_1582762, _1582762), hAPP(c_Relation_OField(_1582762), _1582764)), hAPP(c_COMBK(tc_fun(_1582762, tc_HOL_Obool), _1582762), hAPP(c_Relation_OField(_1582762), _1582764))))))], (40960 ^ _782435) ^ [_1582831, _1582833, _1582835] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1582831, _1582831)), _1582833), _1582835)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1582831, _1582831)), _1582833), c_Transitive__Closure_Otrancl(_1582831, _1582835))))], (40966 ^ _782435) ^ [_1582956] : [-(c_Transitive__Closure_Otrancl(_1582956, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582956, _1582956), tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1582956, _1582956), tc_HOL_Obool)))], (40968 ^ _782435) ^ [_1582998, _1583000] : [-(hAPP(c_Relation_ODomain(_1582998, _1582998), c_Transitive__Closure_Otrancl(_1582998, _1583000)) = hAPP(c_Relation_ODomain(_1582998, _1582998), _1583000))], (40970 ^ _782435) ^ [_1583038, _1583040] : [-(hAPP(c_Relation_ORange(_1583038, _1583038), c_Transitive__Closure_Otrancl(_1583038, _1583040)) = hAPP(c_Relation_ORange(_1583038, _1583038), _1583040))], (40972 ^ _782435) ^ [_1583093, _1583095] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583093, _1583093)), c_Transitive__Closure_Otrancl(_1583093, _1583095))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583093, _1583093)), _1583095)))], (40978 ^ _782435) ^ [_1583200, _1583202] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583200, _1583200)), _1583202)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1583200, _1583200)), c_Transitive__Closure_Otrancl(_1583200, _1583202))))], (40984 ^ _782435) ^ [_1583313, _1583315, _1583317, _1583319, _1583321] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583313, _1583313)), hAPP(hAPP(c_Product__Type_OPair(_1583313, _1583313), _1583315), _1583317)), c_Transitive__Closure_Otrancl(_1583313, _1583319))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583313, _1583313)), hAPP(hAPP(c_Product__Type_OPair(_1583313, _1583313), _1583317), _1583321)), c_Transitive__Closure_Otrancl(_1583313, _1583319))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583313, _1583313)), hAPP(hAPP(c_Product__Type_OPair(_1583313, _1583313), _1583315), _1583321)), c_Transitive__Closure_Otrancl(_1583313, _1583319))))], (40994 ^ _782435) ^ [_1583586, _1583588, _1583590, _1583592, _1583594] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583586, _1583586)), hAPP(hAPP(c_Product__Type_OPair(_1583586, _1583586), _1583588), _1583590)), c_Transitive__Closure_Otrancl(_1583586, _1583592))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583586, _1583586)), hAPP(hAPP(c_Product__Type_OPair(_1583586, _1583586), _1583590), _1583594)), _1583592)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583586, _1583586)), hAPP(hAPP(c_Product__Type_OPair(_1583586, _1583586), _1583588), _1583594)), c_Transitive__Closure_Otrancl(_1583586, _1583592))))], (41004 ^ _782435) ^ [_1583853, _1583855, _1583857, _1583859, _1583861] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1583853, _1583853)), hAPP(hAPP(c_Product__Type_OPair(_1583853, _1583853), _1583855), _1583857)), _1583859)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1583853, _1583853)), hAPP(hAPP(c_Product__Type_OPair(_1583853, _1583853), _1583857), _1583861)), c_Transitive__Closure_Otrancl(_1583853, _1583859))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1583853, _1583853)), hAPP(hAPP(c_Product__Type_OPair(_1583853, _1583853), _1583855), _1583861)), c_Transitive__Closure_Otrancl(_1583853, _1583859))))], (41014 ^ _782435) ^ [_1584120, _1584122, _1584124, _1584126, _1584128] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584120, _1584120)), hAPP(hAPP(c_Product__Type_OPair(_1584120, _1584120), _1584122), _1584124)), _1584126)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1584120, _1584120)), hAPP(hAPP(c_Product__Type_OPair(_1584120, _1584120), _1584124), _1584128)), _1584126)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584120, _1584120)), hAPP(hAPP(c_Product__Type_OPair(_1584120, _1584120), _1584122), _1584128)), c_Transitive__Closure_Otrancl(_1584120, _1584126))))], (41024 ^ _782435) ^ [_1584381, _1584383, _1584385, _1584387] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1584381, _1584381)), _1584383), c_Transitive__Closure_Otrancl(_1584381, _1584385))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584381, _1584381), tc_HOL_Obool)), _1584385), _1584387)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1584381, _1584381)), _1584383), c_Transitive__Closure_Otrancl(_1584381, _1584387))))], (41034 ^ _782435) ^ [_1584596, _1584598] : [-(c_Transitive__Closure_Otrancl(_1584596, _1584598) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1584596, _1584596), tc_HOL_Obool)), _1584598), hAPP(hAPP(c_Relation_Orel__comp(_1584596, _1584596, _1584596), c_Transitive__Closure_Otrancl(_1584596, _1584598)), _1584598)))], (41036 ^ _782435) ^ [_1584651, _1584653, _1584655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584651, _1584651), tc_HOL_Obool)), _1584653), hAPP(hAPP(c_Product__Type_OSigma(_1584651, _1584651), _1584655), hAPP(c_COMBK(tc_fun(_1584651, tc_HOL_Obool), _1584651), _1584655)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584651, _1584651), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584651, _1584653)), hAPP(hAPP(c_Product__Type_OSigma(_1584651, _1584651), _1584655), hAPP(c_COMBK(tc_fun(_1584651, tc_HOL_Obool), _1584651), _1584655)))))], (41042 ^ _782435) ^ [_1584860, _1584862, _1584864] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584860, _1584860), tc_HOL_Obool)), _1584862), _1584864)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584860, _1584860), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1584860, _1584860, _1584860), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1584860, _1584860), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584860, _1584862)), _1584864)), _1584862)), _1584864)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1584860, _1584860), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1584860, _1584862)), _1584864)))], (41052 ^ _782435) ^ [_1585131, _1585133, _1585135, _1585137] : [-(c_Transitive__Closure_Otrancl(_1585131, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1585131, _1585131)), hAPP(hAPP(c_Product__Type_OPair(_1585131, _1585131), _1585133), _1585135)), _1585137)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585131, _1585131), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1585131, _1585137)), hAPP(c_Set_OCollect(tc_prod(_1585131, _1585131)), hAPP(c_Product__Type_Oprod_Oprod__case(_1585131, _1585131, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1585131, tc_fun(_1585131, tc_HOL_Obool), tc_fun(_1585131, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(_1585131, tc_HOL_Obool), tc_fun(_1585131, tc_HOL_Obool)), _1585131), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1585131)), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1585131), c_fconj), hAPP(hAPP(c_COMBC(_1585131, tc_fun(tc_prod(_1585131, _1585131), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585131, _1585131), tc_fun(tc_fun(tc_prod(_1585131, _1585131), tc_HOL_Obool), tc_HOL_Obool), _1585131), c_member(tc_prod(_1585131, _1585131))), hAPP(hAPP(c_COMBC(_1585131, _1585131, tc_prod(_1585131, _1585131)), c_Product__Type_OPair(_1585131, _1585131)), _1585133))), c_Transitive__Closure_Ortrancl(_1585131, _1585137))))), hAPP(hAPP(c_COMBC(_1585131, tc_fun(tc_prod(_1585131, _1585131), tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_prod(_1585131, _1585131), tc_fun(tc_fun(tc_prod(_1585131, _1585131), tc_HOL_Obool), tc_HOL_Obool), _1585131), c_member(tc_prod(_1585131, _1585131))), hAPP(c_Product__Type_OPair(_1585131, _1585131), _1585135))), c_Transitive__Closure_Ortrancl(_1585131, _1585137)))))))], (41054 ^ _782435) ^ [_1585399, _1585401, _1585403, _1585405] : [hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585399, tc_fun(_1585399, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585399, tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool), tc_fun(_1585399, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585399, tc_fun(tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool), tc_fun(_1585399, tc_HOL_Obool)), _1585399), c_COMBC(_1585399, tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585399, tc_prod(_1585399, _1585399)), tc_fun(_1585399, tc_fun(tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool), tc_HOL_Obool)), _1585399), hAPP(c_COMBB(tc_prod(_1585399, _1585399), tc_fun(tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool), tc_HOL_Obool), _1585399), c_member(tc_prod(_1585399, _1585399)))), c_Product__Type_OPair(_1585399, _1585399)))), _1585401)), c_fequal), _1585403), _1585405)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1585399, _1585399)), hAPP(hAPP(c_Product__Type_OPair(_1585399, _1585399), _1585403), _1585405)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585399, _1585399), tc_HOL_Obool)), _1585401), c_Relation_OId(_1585399)))))], (41060 ^ _782435) ^ [_1585820, _1585822, _1585824, _1585826] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1585820, _1585820)), hAPP(hAPP(c_Product__Type_OPair(_1585820, _1585820), _1585824), _1585826)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool)), _1585822), c_Relation_OId(_1585820)))), -(hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1585820, tc_fun(_1585820, tc_HOL_Obool))), hAPP(hAPP(c_COMBC(_1585820, tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool), tc_fun(_1585820, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585820, tc_fun(tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool), tc_fun(_1585820, tc_HOL_Obool)), _1585820), c_COMBC(_1585820, tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1585820, tc_prod(_1585820, _1585820)), tc_fun(_1585820, tc_fun(tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool), tc_HOL_Obool)), _1585820), hAPP(c_COMBB(tc_prod(_1585820, _1585820), tc_fun(tc_fun(tc_prod(_1585820, _1585820), tc_HOL_Obool), tc_HOL_Obool), _1585820), c_member(tc_prod(_1585820, _1585820)))), c_Product__Type_OPair(_1585820, _1585820)))), _1585822)), c_fequal), _1585824), _1585826)))], (41066 ^ _782435) ^ [_1586247, _1586249, _1586251] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586247, _1586247)), _1586249), _1586251)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586247, _1586247)), _1586249), c_Transitive__Closure_Ortrancl(_1586247, _1586251))))], (41072 ^ _782435) ^ [_1586372, _1586374, _1586376] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586372, _1586372)), hAPP(hAPP(c_Product__Type_OPair(_1586372, _1586372), _1586374), _1586374)), c_Transitive__Closure_Ortrancl(_1586372, _1586376))))], (41074 ^ _782435) ^ [_1586421, _1586423] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586421, _1586421)), hAPP(hAPP(c_Product__Type_OPair(_1586421, _1586421), _1586423), _1586423)), c_Relation_OId(_1586421))))], (41076 ^ _782435) ^ [_1586467, _1586469, _1586471, _1586473] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1586467, _1586467)), hAPP(hAPP(c_Product__Type_OPair(_1586467, _1586467), _1586469), _1586471)), c_Transitive__Closure_Otrancl(_1586467, _1586473))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1586467, _1586467)), hAPP(hAPP(c_Product__Type_OPair(_1586467, _1586467), _1586469), _1586471)), c_Transitive__Closure_Ortrancl(_1586467, _1586473))))], (41082 ^ _782435) ^ [_1586636, _1586638] : [-(c_Transitive__Closure_Otrancl(_1586636, c_Transitive__Closure_Ortrancl(_1586636, _1586638)) = c_Transitive__Closure_Ortrancl(_1586636, _1586638))], (41084 ^ _782435) ^ [_1586670, _1586672] : [-(c_Transitive__Closure_Ortrancl(_1586670, c_Transitive__Closure_Otrancl(_1586670, _1586672)) = c_Transitive__Closure_Ortrancl(_1586670, _1586672))], (41086 ^ _782435) ^ [_1586704, _1586706] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586704, _1586704), tc_HOL_Obool)), c_Transitive__Closure_Otrancl(_1586704, _1586706)), c_Relation_OId(_1586704)) = c_Transitive__Closure_Ortrancl(_1586704, _1586706))], (41088 ^ _782435) ^ [_1586751, _1586753] : [-(c_Transitive__Closure_Otrancl(_1586751, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1586751, _1586751), tc_HOL_Obool)), _1586753), c_Relation_OId(_1586751))) = c_Transitive__Closure_Ortrancl(_1586751, _1586753))], (41090 ^ _782435) ^ [_1586798, _1586800] : [-(c_Transitive__Closure_Otrancl(_1586798, _1586800) = hAPP(hAPP(c_Relation_Orel__comp(_1586798, _1586798, _1586798), _1586800), c_Transitive__Closure_Ortrancl(_1586798, _1586800)))], (41092 ^ _782435) ^ [_1586839, _1586841] : [-(c_Transitive__Closure_Otrancl(_1586839, _1586841) = hAPP(hAPP(c_Relation_Orel__comp(_1586839, _1586839, _1586839), c_Transitive__Closure_Ortrancl(_1586839, _1586841)), _1586841))], (41094 ^ _782435) ^ [_1586880, _1586882, _1586884] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1586880, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1586880, _1586880, _1586882), _1586884)), _1586884)), -(hAPP(c_Relation_OImage(_1586880, _1586880, c_Transitive__Closure_Ortrancl(_1586880, _1586882)), _1586884) = _1586884)], (41100 ^ _782435) ^ [_1587013, _1587015, _1587017] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587013, _1587013), tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587013, _1587013), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587013, _1587015)), c_Transitive__Closure_Ortrancl(_1587013, _1587017))), c_Transitive__Closure_Ortrancl(_1587013, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587013, _1587013), tc_HOL_Obool)), _1587015), _1587017)))))], (41102 ^ _782435) ^ [_1587090, _1587092, _1587094] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587090, _1587090), tc_HOL_Obool)), _1587092), _1587094)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587090, _1587090), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587090, _1587092)), c_Transitive__Closure_Ortrancl(_1587090, _1587094))))], (41108 ^ _782435) ^ [_1587233, _1587235, _1587237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587233, _1587233), tc_HOL_Obool)), _1587235), _1587237)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587233, _1587233), tc_HOL_Obool)), _1587237), c_Transitive__Closure_Ortrancl(_1587233, _1587235))), -(c_Transitive__Closure_Ortrancl(_1587233, _1587237) = c_Transitive__Closure_Ortrancl(_1587233, _1587235))], (41118 ^ _782435) ^ [_1587436, _1587438, _1587440] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587436, _1587436), tc_HOL_Obool)), _1587438), c_Transitive__Closure_Ortrancl(_1587436, _1587440))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587436, _1587436), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587436, _1587438)), c_Transitive__Closure_Ortrancl(_1587436, _1587440))))], (41124 ^ _782435) ^ [_1587585, _1587587, _1587589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587585, _1587585), tc_HOL_Obool)), c_Relation_OId(_1587585)), _1587587)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587585, _1587585), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1587585, _1587585, _1587585), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1587585, _1587585), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587585, _1587589)), _1587587)), _1587589)), _1587587)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1587585, _1587585), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1587585, _1587589)), _1587587)))], (41134 ^ _782435) ^ [_1587860, _1587862] : [-(hAPP(c_Relation_ODomain(_1587860, _1587860), c_Transitive__Closure_Ortrancl(_1587860, _1587862)) = c_Orderings_Otop__class_Otop(tc_fun(_1587860, tc_HOL_Obool)))], (41136 ^ _782435) ^ [_1587899, _1587901] : [-(hAPP(c_Relation_ORange(_1587899, _1587899), c_Transitive__Closure_Ortrancl(_1587899, _1587901)) = c_Orderings_Otop__class_Otop(tc_fun(_1587899, tc_HOL_Obool)))], (41138 ^ _782435) ^ [_1587938] : [-(c_Transitive__Closure_Ortrancl(_1587938, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1587938, _1587938), tc_HOL_Obool))) = c_Relation_OId(_1587938))], (41140 ^ _782435) ^ [_1587974, _1587976] : [-(c_Transitive__Closure_Ortrancl(_1587974, _1587976) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1587974, _1587974), tc_HOL_Obool)), c_Relation_OId(_1587974)), hAPP(hAPP(c_Relation_Orel__comp(_1587974, _1587974, _1587974), c_Transitive__Closure_Ortrancl(_1587974, _1587976)), _1587976)))], (41142 ^ _782435) ^ [_1588031, _1588033, _1588035, _1588037] : [41143 ^ _782435 : [(41144 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588031, _1588031)), _1588033), c_Transitive__Closure_Ortrancl(_1588031, _1588035)))], (41146 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588031, _1588031)), _1588033), c_Transitive__Closure_Ortrancl(_1588031, _1588037)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588031, _1588031)), _1588033), c_Transitive__Closure_Ortrancl(_1588031, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588031, _1588031), tc_HOL_Obool)), _1588035), _1588037)))))], (41150 ^ _782435) ^ [_1588256, _1588258] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588256, _1588256, _1588256), c_Transitive__Closure_Ortrancl(_1588256, _1588258)), c_Transitive__Closure_Ortrancl(_1588256, _1588258)) = c_Transitive__Closure_Ortrancl(_1588256, _1588258))], (41152 ^ _782435) ^ [_1588300, _1588302] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1588300, _1588300, _1588300), _1588302), c_Transitive__Closure_Ortrancl(_1588300, _1588302)) = hAPP(hAPP(c_Relation_Orel__comp(_1588300, _1588300, _1588300), c_Transitive__Closure_Ortrancl(_1588300, _1588302)), _1588302))], (41154 ^ _782435) ^ [_1588351, _1588353] : [-(c_Transitive__Closure_Ortrancl(_1588351, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588351, _1588351), tc_HOL_Obool)), _1588353), c_Relation_OId(_1588351))) = c_Transitive__Closure_Ortrancl(_1588351, _1588353))], (41156 ^ _782435) ^ [_1588398, _1588400, _1588402] : [-(c_Transitive__Closure_Ortrancl(_1588398, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588398, _1588398), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588398, _1588400)), c_Transitive__Closure_Ortrancl(_1588398, _1588402))) = c_Transitive__Closure_Ortrancl(_1588398, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588398, _1588398), tc_HOL_Obool)), _1588400), _1588402)))], (41158 ^ _782435) ^ [_1588465, _1588467] : [-(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1588465, _1588465), tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1588465, _1588467)), c_Relation_OId(_1588465)) = c_Transitive__Closure_Ortrancl(_1588465, _1588467))], (41160 ^ _782435) ^ [_1588512, _1588514] : [-(c_Transitive__Closure_Ortrancl(_1588512, c_Transitive__Closure_Ortrancl(_1588512, _1588514)) = c_Transitive__Closure_Ortrancl(_1588512, _1588514))], (41162 ^ _782435) ^ [_1588546, _1588548, _1588550, _1588552, _1588554] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588546, _1588546)), hAPP(hAPP(c_Product__Type_OPair(_1588546, _1588546), _1588548), _1588550)), c_Transitive__Closure_Ortrancl(_1588546, _1588552))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588546, _1588546)), hAPP(hAPP(c_Product__Type_OPair(_1588546, _1588546), _1588550), _1588554)), c_Transitive__Closure_Ortrancl(_1588546, _1588552))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588546, _1588546)), hAPP(hAPP(c_Product__Type_OPair(_1588546, _1588546), _1588548), _1588554)), c_Transitive__Closure_Ortrancl(_1588546, _1588552))))], (41172 ^ _782435) ^ [_1588819, _1588821, _1588823, _1588825, _1588827] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1588819, _1588819)), hAPP(hAPP(c_Product__Type_OPair(_1588819, _1588819), _1588821), _1588823)), c_Transitive__Closure_Ortrancl(_1588819, _1588825))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1588819, _1588819)), hAPP(hAPP(c_Product__Type_OPair(_1588819, _1588819), _1588823), _1588827)), _1588825)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1588819, _1588819)), hAPP(hAPP(c_Product__Type_OPair(_1588819, _1588819), _1588821), _1588827)), c_Transitive__Closure_Ortrancl(_1588819, _1588825))))], (41182 ^ _782435) ^ [_1589086, _1589088, _1589090, _1589092, _1589094] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589086, _1589086)), hAPP(hAPP(c_Product__Type_OPair(_1589086, _1589086), _1589088), _1589090)), _1589092)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589086, _1589086)), hAPP(hAPP(c_Product__Type_OPair(_1589086, _1589086), _1589090), _1589094)), c_Transitive__Closure_Ortrancl(_1589086, _1589092))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589086, _1589086)), hAPP(hAPP(c_Product__Type_OPair(_1589086, _1589086), _1589088), _1589094)), c_Transitive__Closure_Ortrancl(_1589086, _1589092))))], (41192 ^ _782435) ^ [_1589353, _1589355] : [-(c_Transitive__Closure_Ortrancl(_1589353, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1589353, _1589353), tc_HOL_Obool)), _1589355), c_Relation_OId(_1589353))) = c_Transitive__Closure_Ortrancl(_1589353, _1589355))], (41194 ^ _782435) ^ [_1589400, _1589402] : [-(c_Relation_Orefl__on(_1589400, c_Orderings_Otop__class_Otop(tc_fun(_1589400, tc_HOL_Obool)), c_Transitive__Closure_Ortrancl(_1589400, _1589402)))], (41196 ^ _782435) ^ [_1589434, _1589436] : [-(hAPP(c_Relation_OImage(_1589434, _1589434, c_Relation_OId(_1589434)), _1589436) = _1589436)], (41198 ^ _782435) ^ [_1589468, _1589470, _1589472] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589468, _1589470, _1589470), _1589472), c_Relation_OId(_1589470)) = _1589472)], (41200 ^ _782435) ^ [_1589507, _1589509, _1589511] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1589507, _1589507, _1589509), c_Relation_OId(_1589507)), _1589511) = _1589511)], (41202 ^ _782435) ^ [_1589564, _1589566, _1589568] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589564, _1589564)), hAPP(hAPP(c_Product__Type_OPair(_1589564, _1589564), _1589566), _1589568)), c_Relation_OId(_1589564))), -(_1589566 = _1589568)], (41208 ^ _782435) ^ [_1589681, _1589683, _1589685] : [_1589683 = _1589685, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589681, _1589681)), hAPP(hAPP(c_Product__Type_OPair(_1589681, _1589681), _1589683), _1589685)), c_Relation_OId(_1589681))))], (41214 ^ _782435) ^ [_1589804, _1589806, _1589808, _1589810, _1589812] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1589804, _1589804)), hAPP(hAPP(c_Product__Type_OPair(_1589804, _1589804), _1589806), _1589808)), c_Transitive__Closure_Ortrancl(_1589804, _1589810))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1589804, _1589804)), hAPP(hAPP(c_Product__Type_OPair(_1589804, _1589804), _1589808), _1589812)), c_Transitive__Closure_Otrancl(_1589804, _1589810))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1589804, _1589804)), hAPP(hAPP(c_Product__Type_OPair(_1589804, _1589804), _1589806), _1589812)), c_Transitive__Closure_Otrancl(_1589804, _1589810))))], (41224 ^ _782435) ^ [_1590077, _1590079, _1590081, _1590083, _1590085] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590077, _1590077)), hAPP(hAPP(c_Product__Type_OPair(_1590077, _1590077), _1590079), _1590081)), c_Transitive__Closure_Otrancl(_1590077, _1590083))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590077, _1590077)), hAPP(hAPP(c_Product__Type_OPair(_1590077, _1590077), _1590081), _1590085)), c_Transitive__Closure_Ortrancl(_1590077, _1590083))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590077, _1590077)), hAPP(hAPP(c_Product__Type_OPair(_1590077, _1590077), _1590079), _1590085)), c_Transitive__Closure_Otrancl(_1590077, _1590083))))], (41234 ^ _782435) ^ [_1590350, _1590352, _1590354, _1590356, _1590358] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590350, _1590350)), hAPP(hAPP(c_Product__Type_OPair(_1590350, _1590350), _1590352), _1590354)), c_Transitive__Closure_Ortrancl(_1590350, _1590356))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590350, _1590350)), hAPP(hAPP(c_Product__Type_OPair(_1590350, _1590350), _1590354), _1590358)), _1590356)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590350, _1590350)), hAPP(hAPP(c_Product__Type_OPair(_1590350, _1590350), _1590352), _1590358)), c_Transitive__Closure_Otrancl(_1590350, _1590356))))], (41244 ^ _782435) ^ [_1590617, _1590619, _1590621, _1590623] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590617, _1590617)), hAPP(hAPP(c_Product__Type_OPair(_1590617, _1590617), _1590619), _1590621)), c_Transitive__Closure_Ortrancl(_1590617, _1590623))), -(_1590619 = _1590621), 41251 ^ _782435 : [(41252 ^ _782435) ^ [] : [_1590619 = _1590621], (41254 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590617, _1590617)), hAPP(hAPP(c_Product__Type_OPair(_1590617, _1590617), _1590619), _1590621)), c_Transitive__Closure_Otrancl(_1590617, _1590623))))]]], (41256 ^ _782435) ^ [_1590879, _1590881, _1590883, _1590885, _1590887] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1590879, _1590879)), hAPP(hAPP(c_Product__Type_OPair(_1590879, _1590879), _1590881), _1590883)), _1590885)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1590879, _1590879)), hAPP(hAPP(c_Product__Type_OPair(_1590879, _1590879), _1590883), _1590887)), c_Transitive__Closure_Ortrancl(_1590879, _1590885))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1590879, _1590879)), hAPP(hAPP(c_Product__Type_OPair(_1590879, _1590879), _1590881), _1590887)), c_Transitive__Closure_Otrancl(_1590879, _1590885))))], (41266 ^ _782435) ^ [_1591167, _1591169, _1591171, _1591173] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591167, _1591167)), hAPP(hAPP(c_Product__Type_OPair(_1591167, _1591167), _1591169), _1591171)), c_Transitive__Closure_Ortrancl(_1591167, _1591173))), -(_1591169 = _1591171), 41273 ^ _782435 : [(41274 ^ _782435) ^ [] : [_1591169 = _1591171], (41276 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591167, _1591167)), hAPP(hAPP(c_Product__Type_OPair(_1591167, _1591167), _1591169), _1591171)), c_Transitive__Closure_Otrancl(_1591167, _1591173))))]]], (41278 ^ _782435) ^ [_1591425, _1591427, _1591429, _1591431] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591425, _1591425)), hAPP(hAPP(c_Product__Type_OPair(_1591425, _1591425), _1591427), _1591429)), c_Transitive__Closure_Ortrancl(_1591425, _1591431)))), 41279 ^ _782435 : [(41280 ^ _782435) ^ [] : [_1591427 = _1591429], (41282 ^ _782435) ^ [] : [-(_1591427 = _1591429), hBOOL(hAPP(hAPP(c_member(tc_prod(_1591425, _1591425)), hAPP(hAPP(c_Product__Type_OPair(_1591425, _1591425), _1591427), _1591429)), c_Transitive__Closure_Otrancl(_1591425, _1591431)))]]], (41290 ^ _782435) ^ [_1591691] : [-(hAPP(c_Relation_ODomain(_1591691, _1591691), c_Relation_OId(_1591691)) = c_Orderings_Otop__class_Otop(tc_fun(_1591691, tc_HOL_Obool)))], (41292 ^ _782435) ^ [_1591727] : [-(hAPP(c_Relation_ORange(_1591727, _1591727), c_Relation_OId(_1591727)) = c_Orderings_Otop__class_Otop(tc_fun(_1591727, tc_HOL_Obool)))], (41294 ^ _782435) ^ [_1591763] : [-(c_Relation_Orefl__on(_1591763, c_Orderings_Otop__class_Otop(tc_fun(_1591763, tc_HOL_Obool)), c_Relation_OId(_1591763)))], (41296 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1591811, _1591813, _1591815, _1591817] : [-(hBOOL(hAPP(hAPP(c_member(_1591811), _1591813), hAPP(c_Relation_ODomain(_1591811, _1591811), _1591815)))), 41301 ^ _782435 : [(41302 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1591811, _1591811)), hAPP(hAPP(c_Product__Type_OPair(_1591811, _1591811), _1591813), _1591817)), c_Transitive__Closure_Ortrancl(_1591811, _1591815))), -(_1591813 = _1591817)], (41308 ^ _782435) ^ [] : [_1591813 = _1591817, -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1591811, _1591811)), hAPP(hAPP(c_Product__Type_OPair(_1591811, _1591811), _1591813), _1591817)), c_Transitive__Closure_Ortrancl(_1591811, _1591815))))]]], (41314 ^ _782435) ^ [_1592107, _1592109, _1592111, _1592113] : [hBOOL(hAPP(hAPP(c_member(_1592107), _1592109), c_Wellfounded_Oacc(_1592107, _1592111))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1592107, _1592107)), hAPP(hAPP(c_Product__Type_OPair(_1592107, _1592107), _1592113), _1592109)), c_Transitive__Closure_Ortrancl(_1592107, _1592111))), -(hBOOL(hAPP(hAPP(c_member(_1592107), _1592113), c_Wellfounded_Oacc(_1592107, _1592111))))], (41324 ^ _782435) ^ [_1592328, _1592330, _1592332, _1592334] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592328, _1592328)), hAPP(hAPP(c_Product__Type_OPair(_1592328, _1592328), _1592330), _1592332)), c_Transitive__Closure_Ortrancl(_1592328, _1592334))), hBOOL(hAPP(hAPP(c_member(_1592328), _1592332), c_Wellfounded_Oacc(_1592328, _1592334))), -(hBOOL(hAPP(hAPP(c_member(_1592328), _1592330), c_Wellfounded_Oacc(_1592328, _1592334))))], (41334 ^ _782435) ^ [_1592570, _1592572, _1592574, _1592576] : [c_Wellfounded_Owf(_1592570, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1592570, _1592570)), hAPP(hAPP(c_Product__Type_OPair(_1592570, _1592570), _1592572), _1592574)), _1592576)), 41337 ^ _782435 : [(41338 ^ _782435) ^ [] : [-(c_Wellfounded_Owf(_1592570, _1592576))], (41340 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1592570, _1592570)), hAPP(hAPP(c_Product__Type_OPair(_1592570, _1592570), _1592574), _1592572)), c_Transitive__Closure_Ortrancl(_1592570, _1592576)))]]], (41342 ^ _782435) ^ [_1592765, _1592767, _1592769, _1592771] : [-(c_Wellfounded_Owf(_1592765, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1592765, _1592765)), hAPP(hAPP(c_Product__Type_OPair(_1592765, _1592765), _1592767), _1592769)), _1592771))), c_Wellfounded_Owf(_1592765, _1592771), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1592765, _1592765)), hAPP(hAPP(c_Product__Type_OPair(_1592765, _1592765), _1592769), _1592767)), c_Transitive__Closure_Ortrancl(_1592765, _1592771))))], (41352 ^ _782435) ^ [_1593012, _1593014, _1593016, _1593018] : [c_Wellfounded_Oacyclic(_1593012, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593012, _1593012)), hAPP(hAPP(c_Product__Type_OPair(_1593012, _1593012), _1593014), _1593016)), _1593018)), 41355 ^ _782435 : [(41356 ^ _782435) ^ [] : [-(c_Wellfounded_Oacyclic(_1593012, _1593018))], (41358 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593012, _1593012)), hAPP(hAPP(c_Product__Type_OPair(_1593012, _1593012), _1593016), _1593014)), c_Transitive__Closure_Ortrancl(_1593012, _1593018)))]]], (41360 ^ _782435) ^ [_1593207, _1593209, _1593211, _1593213] : [-(c_Wellfounded_Oacyclic(_1593207, hAPP(hAPP(c_Set_Oinsert(tc_prod(_1593207, _1593207)), hAPP(hAPP(c_Product__Type_OPair(_1593207, _1593207), _1593209), _1593211)), _1593213))), c_Wellfounded_Oacyclic(_1593207, _1593213), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1593207, _1593207)), hAPP(hAPP(c_Product__Type_OPair(_1593207, _1593207), _1593211), _1593209)), c_Transitive__Closure_Ortrancl(_1593207, _1593213))))], (41370 ^ _782435) ^ [_1593433, _1593435] : [-(c_Relation_Orefl__on(_1593433, c_Orderings_Otop__class_Otop(tc_fun(_1593433, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1593433, _1593433), tc_HOL_Obool)), _1593435), c_Relation_OId(_1593433))))], (41372 ^ _782435) ^ [_1593480] : [-(c_Relation_OId(_1593480) = hAPP(c_Set_OCollect(tc_prod(_1593480, _1593480)), hAPP(hAPP(c_COMBB(tc_fun(_1593480, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1593480, _1593480)), c_HOL_OEx(_1593480)), hAPP(hAPP(c_COMBC(tc_prod(_1593480, _1593480), tc_fun(_1593480, tc_prod(_1593480, _1593480)), tc_fun(_1593480, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1593480, _1593480), tc_HOL_Obool), tc_fun(tc_fun(_1593480, tc_prod(_1593480, _1593480)), tc_fun(_1593480, tc_HOL_Obool)), tc_prod(_1593480, _1593480)), c_COMBB(tc_prod(_1593480, _1593480), tc_HOL_Obool, _1593480)), c_fequal)), hAPP(hAPP(c_COMBS(_1593480, _1593480, tc_prod(_1593480, _1593480)), c_Product__Type_OPair(_1593480, _1593480)), c_COMBI(_1593480))))))], (41374 ^ _782435) ^ [_1593609, _1593611] : [-(c_Relation_Oirrefl(_1593609, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1593609, _1593609), tc_HOL_Obool)), _1593611), c_Relation_OId(_1593609))))], (41376 ^ _782435) ^ [_1593665, _1593667] : [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), _1593665), _1593667)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1593665), _1593667)))], (41382 ^ _782435) ^ [_1593770, _1593772] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1593770), _1593772)), -(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), _1593770), _1593772)), c_Transitive__Closure_Ortrancl(tc_Nat_Onat, c_Wellfounded_Opred__nat))))], (41388 ^ _782435) ^ [_1593881, _1593883, _1593885, _1593887, _1593889] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1593881, _1593881)), hAPP(hAPP(c_Product__Type_OPair(_1593881, _1593881), _1593883), _1593885)), c_Transitive__Closure_Ortrancl(_1593881, _1593887))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1593881, _1593881), tc_HOL_Obool)), _1593887), hAPP(hAPP(c_Product__Type_OSigma(_1593881, _1593881), _1593889), hAPP(c_COMBK(tc_fun(_1593881, tc_HOL_Obool), _1593881), _1593889)))), -(_1593883 = _1593885), -(hBOOL(hAPP(hAPP(c_member(_1593881), _1593883), _1593889)))], (41402 ^ _782435) ^ [_1594155, _1594157, _1594159] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1594155, _1594155), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1594155, _1594155), _1594157)), c_Transitive__Closure_Ortrancl(_1594155, _1594157)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1594155, _1594155), tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1594155, _1594155)), hAPP(hAPP(c_Product__Type_OPair(_1594155, _1594155), _1594159), _1594159)), c_Transitive__Closure_Otrancl(_1594155, _1594157)))], (41408 ^ _782435) ^ [_1594341, _1594343, _1594345, _1594347, _1594349] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594341, _1594341)), hAPP(hAPP(c_Product__Type_OPair(_1594341, _1594341), hAPP(_1594343, hAPP(c_Nat_OSuc, 41409 ^ [_1594341, _1594343, _1594345, _1594347, _1594349]))), hAPP(_1594343, 41409 ^ [_1594341, _1594343, _1594345, _1594347, _1594349]))), c_Transitive__Closure_Ortrancl(_1594341, _1594345))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594341, _1594341)), hAPP(hAPP(c_Product__Type_OPair(_1594341, _1594341), hAPP(_1594343, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1594347), _1594349))), hAPP(_1594343, _1594347))), c_Transitive__Closure_Ortrancl(_1594341, _1594345))))], (41415 ^ _782435) ^ [_1594634, _1594636] : [-(c_Transitive__Closure_Ortrancl(_1594634, hAPP(c_Relation_Oconverse(_1594634, _1594634), _1594636)) = hAPP(c_Relation_Oconverse(_1594634, _1594634), c_Transitive__Closure_Ortrancl(_1594634, _1594636)))], (41417 ^ _782435) ^ [_1594677] : [-(hAPP(c_Relation_Oconverse(_1594677, _1594677), c_Relation_OId(_1594677)) = c_Relation_OId(_1594677))], (41419 ^ _782435) ^ [_1594725, _1594727] : [c_Wellfounded_Oacyclic(_1594725, hAPP(c_Relation_Oconverse(_1594725, _1594725), _1594727)), -(c_Wellfounded_Oacyclic(_1594725, _1594727))], (41425 ^ _782435) ^ [_1594810, _1594812] : [c_Wellfounded_Oacyclic(_1594810, _1594812), -(c_Wellfounded_Oacyclic(_1594810, hAPP(c_Relation_Oconverse(_1594810, _1594810), _1594812)))], (41431 ^ _782435) ^ [_1594901, _1594903, _1594905, _1594907, _1594909] : [-(hAPP(c_Relation_Oconverse(_1594901, _1594903), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594905, tc_fun(tc_prod(_1594901, _1594903), tc_HOL_Obool)), _1594907), _1594909)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1594905, tc_fun(tc_prod(_1594903, _1594901), tc_HOL_Obool)), _1594907), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1594901, _1594903), tc_HOL_Obool), tc_fun(tc_prod(_1594903, _1594901), tc_HOL_Obool), _1594905), c_Relation_Oconverse(_1594901, _1594903)), _1594909)))], (41433 ^ _782435) ^ [_1594993, _1594995, _1594997, _1594999, _1595001] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1594993, _1594995)), hAPP(hAPP(c_Product__Type_OPair(_1594993, _1594995), _1594997), _1594999)), hAPP(c_Relation_Oconverse(_1594995, _1594993), _1595001))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1594995, _1594993)), hAPP(hAPP(c_Product__Type_OPair(_1594995, _1594993), _1594999), _1594997)), _1595001)))], (41439 ^ _782435) ^ [_1595164, _1595166, _1595168, _1595170, _1595172] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595164, _1595166)), hAPP(hAPP(c_Product__Type_OPair(_1595164, _1595166), _1595168), _1595170)), _1595172)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595166, _1595164)), hAPP(hAPP(c_Product__Type_OPair(_1595166, _1595164), _1595170), _1595168)), hAPP(c_Relation_Oconverse(_1595164, _1595166), _1595172))))], (41445 ^ _782435) ^ [_1595359, _1595361, _1595363, _1595365, _1595367] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595359, _1595361)), hAPP(hAPP(c_Product__Type_OPair(_1595359, _1595361), _1595363), _1595365)), hAPP(c_Relation_Oconverse(_1595361, _1595359), _1595367))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595361, _1595359)), hAPP(hAPP(c_Product__Type_OPair(_1595361, _1595359), _1595365), _1595363)), _1595367)))], (41451 ^ _782435) ^ [_1595526, _1595528, _1595530, _1595532, _1595534] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1595528, _1595526)), hAPP(hAPP(c_Product__Type_OPair(_1595528, _1595526), _1595532), _1595530)), _1595534)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1595526, _1595528)), hAPP(hAPP(c_Product__Type_OPair(_1595526, _1595528), _1595530), _1595532)), hAPP(c_Relation_Oconverse(_1595528, _1595526), _1595534))))], (41457 ^ _782435) ^ [_1595699, _1595701, _1595703, _1595705, _1595707] : [-(hAPP(c_Relation_Oconverse(_1595699, _1595701), hAPP(hAPP(c_Relation_Orel__comp(_1595699, _1595703, _1595701), _1595705), _1595707)) = hAPP(hAPP(c_Relation_Orel__comp(_1595701, _1595703, _1595699), hAPP(c_Relation_Oconverse(_1595703, _1595701), _1595707)), hAPP(c_Relation_Oconverse(_1595699, _1595703), _1595705)))], (41459 ^ _782435) ^ [_1595768, _1595770, _1595772, _1595774] : [-(hAPP(c_Relation_Oconverse(_1595768, _1595770), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595768, _1595770), tc_HOL_Obool)), _1595772), _1595774)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1595770, _1595768), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1595768, _1595770), _1595772)), hAPP(c_Relation_Oconverse(_1595768, _1595770), _1595774)))], (41461 ^ _782435) ^ [_1595843, _1595845] : [-(hAPP(c_Relation_Oconverse(_1595843, _1595843), c_Relation_OId__on(_1595843, _1595845)) = c_Relation_OId__on(_1595843, _1595845))], (41463 ^ _782435) ^ [_1595880, _1595882, _1595884, _1595886] : [-(hAPP(c_Relation_Oconverse(_1595880, _1595880), hAPP(hAPP(c_Relation_Oinv__image(_1595882, _1595880), _1595884), _1595886)) = hAPP(hAPP(c_Relation_Oinv__image(_1595882, _1595880), hAPP(c_Relation_Oconverse(_1595882, _1595882), _1595884)), _1595886))], (41465 ^ _782435) ^ [_1595939, _1595941, _1595943] : [-(hAPP(c_Relation_Oconverse(_1595939, _1595941), hAPP(c_Relation_Oconverse(_1595941, _1595939), _1595943)) = _1595943)], (41467 ^ _782435) ^ [_1595978, _1595980, _1595982, _1595984] : [-(hAPP(c_Relation_Oconverse(_1595978, _1595980), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1595978, _1595980), tc_HOL_Obool)), _1595982), _1595984)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1595980, _1595978), tc_HOL_Obool)), hAPP(c_Relation_Oconverse(_1595978, _1595980), _1595982)), hAPP(c_Relation_Oconverse(_1595978, _1595980), _1595984)))], (41469 ^ _782435) ^ [_1596071, _1596073, _1596075] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596071, _1596073)), hAPP(c_Relation_Oconverse(_1596073, _1596071), _1596075))), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596073, _1596071)), _1596075)))], (41475 ^ _782435) ^ [_1596186, _1596188, _1596190] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596188, _1596186)), _1596190)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1596186, _1596188)), hAPP(c_Relation_Oconverse(_1596188, _1596186), _1596190))))], (41481 ^ _782435) ^ [_1596307, _1596309] : [-(hAPP(c_Relation_OField(_1596307), hAPP(c_Relation_Oconverse(_1596307, _1596307), _1596309)) = hAPP(c_Relation_OField(_1596307), _1596309))], (41483 ^ _782435) ^ [_1596366, _1596368, _1596370] : [c_Relation_Orefl__on(_1596366, _1596368, hAPP(c_Relation_Oconverse(_1596366, _1596366), _1596370)), -(c_Relation_Orefl__on(_1596366, _1596368, _1596370))], (41489 ^ _782435) ^ [_1596457, _1596459, _1596461] : [c_Relation_Orefl__on(_1596457, _1596459, _1596461), -(c_Relation_Orefl__on(_1596457, _1596459, hAPP(c_Relation_Oconverse(_1596457, _1596457), _1596461)))], (41495 ^ _782435) ^ [_1596554, _1596556, _1596558, _1596560, _1596562] : [-(hAPP(c_Relation_Oconverse(_1596554, _1596556), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596558, tc_fun(tc_prod(_1596554, _1596556), tc_HOL_Obool)), _1596560), _1596562)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1596558, tc_fun(tc_prod(_1596556, _1596554), tc_HOL_Obool)), _1596560), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1596554, _1596556), tc_HOL_Obool), tc_fun(tc_prod(_1596556, _1596554), tc_HOL_Obool), _1596558), c_Relation_Oconverse(_1596554, _1596556)), _1596562)))], (41497 ^ _782435) ^ [_1596646, _1596648] : [-(c_Transitive__Closure_Otrancl(_1596646, hAPP(c_Relation_Oconverse(_1596646, _1596646), _1596648)) = hAPP(c_Relation_Oconverse(_1596646, _1596646), c_Transitive__Closure_Otrancl(_1596646, _1596648)))], (41499 ^ _782435) ^ [_1596689, _1596691] : [c_Wellfounded_Owf(_1596689, hAPP(c_Relation_Oconverse(_1596689, _1596689), _1596691)), -(c_Wellfounded_Owf(_1596689, hAPP(c_Relation_Oconverse(_1596689, _1596689), c_Transitive__Closure_Otrancl(_1596689, _1596691))))], (41505 ^ _782435) ^ [_1596796, _1596798, _1596800] : [c_Equiv__Relations_Oequiv(_1596796, _1596798, _1596800), -(hAPP(hAPP(c_Relation_Orel__comp(_1596796, _1596796, _1596796), hAPP(c_Relation_Oconverse(_1596796, _1596796), _1596800)), _1596800) = _1596800)], (41511 ^ _782435) ^ [_1596909, _1596911, _1596913] : [-(hAPP(c_Relation_ORange(_1596909, _1596911), _1596913) = hAPP(c_Relation_ODomain(_1596911, _1596909), hAPP(c_Relation_Oconverse(_1596909, _1596911), _1596913)))], (41513 ^ _782435) ^ [_1596954, _1596956, _1596958] : [-(hAPP(c_Relation_ODomain(_1596954, _1596956), hAPP(c_Relation_Oconverse(_1596956, _1596954), _1596958)) = hAPP(c_Relation_ORange(_1596956, _1596954), _1596958))], (41515 ^ _782435) ^ [_1596999, _1597001, _1597003] : [-(hAPP(c_Relation_ORange(_1596999, _1597001), hAPP(c_Relation_Oconverse(_1597001, _1596999), _1597003)) = hAPP(c_Relation_ODomain(_1597001, _1596999), _1597003))], (41517 ^ _782435) ^ [_1597044, _1597046, _1597048, _1597050] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597044, _1597044)), hAPP(hAPP(c_Product__Type_OPair(_1597044, _1597044), _1597046), _1597048)), c_Transitive__Closure_Ortrancl(_1597044, _1597050))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597044, _1597044)), hAPP(hAPP(c_Product__Type_OPair(_1597044, _1597044), _1597048), _1597046)), c_Transitive__Closure_Ortrancl(_1597044, hAPP(c_Relation_Oconverse(_1597044, _1597044), _1597050)))))], (41523 ^ _782435) ^ [_1597225, _1597227, _1597229, _1597231] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597225, _1597225)), hAPP(hAPP(c_Product__Type_OPair(_1597225, _1597225), _1597227), _1597229)), c_Transitive__Closure_Ortrancl(_1597225, hAPP(c_Relation_Oconverse(_1597225, _1597225), _1597231)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597225, _1597225)), hAPP(hAPP(c_Product__Type_OPair(_1597225, _1597225), _1597229), _1597227)), c_Transitive__Closure_Ortrancl(_1597225, _1597231))))], (41529 ^ _782435) ^ [_1597406, _1597408, _1597410, _1597412] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597406, _1597406)), hAPP(hAPP(c_Product__Type_OPair(_1597406, _1597406), _1597408), _1597410)), hAPP(c_Relation_Oconverse(_1597406, _1597406), c_Transitive__Closure_Otrancl(_1597406, _1597412)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597406, _1597406)), hAPP(hAPP(c_Product__Type_OPair(_1597406, _1597406), _1597408), _1597410)), c_Transitive__Closure_Otrancl(_1597406, hAPP(c_Relation_Oconverse(_1597406, _1597406), _1597412)))))], (41535 ^ _782435) ^ [_1597599, _1597601, _1597603, _1597605] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1597599, _1597599)), hAPP(hAPP(c_Product__Type_OPair(_1597599, _1597599), _1597601), _1597603)), c_Transitive__Closure_Otrancl(_1597599, hAPP(c_Relation_Oconverse(_1597599, _1597599), _1597605)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1597599, _1597599)), hAPP(hAPP(c_Product__Type_OPair(_1597599, _1597599), _1597601), _1597603)), hAPP(c_Relation_Oconverse(_1597599, _1597599), c_Transitive__Closure_Otrancl(_1597599, _1597605)))))], (41541 ^ _782435) ^ [_1597816, _1597818, _1597820, _1597822, _1597824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597816, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1597818, _1597816, _1597820), _1597822)), _1597824)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1597818, tc_HOL_Obool)), _1597822), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1597818, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1597816, _1597818, hAPP(c_Relation_Oconverse(_1597818, _1597816), _1597820)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1597816, tc_HOL_Obool)), _1597824))))))], (41547 ^ _782435) ^ [_1598007, _1598009, _1598011, _1598013, _1598015] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598009, tc_HOL_Obool)), _1598013), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598009, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598007, _1598009, hAPP(c_Relation_Oconverse(_1598009, _1598007), _1598011)), hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(_1598007, tc_HOL_Obool)), _1598015))))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1598007, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1598009, _1598007, _1598011), _1598013)), _1598015)))], (41553 ^ _782435) ^ [_1598204, _1598206, _1598208] : [c_Relation_Orefl__on(_1598204, _1598206, _1598208), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1598204, _1598204), tc_HOL_Obool)), _1598208), hAPP(hAPP(c_Relation_Orel__comp(_1598204, _1598204, _1598204), hAPP(c_Relation_Oconverse(_1598204, _1598204), _1598208)), _1598208))))], (41559 ^ _782435) ^ [_1598343, _1598345, _1598347] : [hAPP(hAPP(c_Relation_Orel__comp(_1598343, _1598343, _1598343), hAPP(c_Relation_Oconverse(_1598343, _1598343), _1598345)), _1598345) = _1598345, hAPP(c_Relation_ODomain(_1598343, _1598343), _1598345) = _1598347, -(c_Equiv__Relations_Oequiv(_1598343, _1598347, _1598345))], (41569 ^ _782435) ^ [_1598522, _1598524] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(_1598522, _1598522)), _1598524)), c_Wellfounded_Oacyclic(_1598522, _1598524), -(c_Wellfounded_Owf(_1598522, hAPP(c_Relation_Oconverse(_1598522, _1598522), _1598524)))], (41579 ^ _782435) ^ [_1598677, _1598679, _1598681] : [-(hAPP(c_Relation_Oconverse(_1598677, _1598679), _1598681) = hAPP(c_Set_OCollect(tc_prod(_1598679, _1598677)), hAPP(c_Product__Type_Oprod_Oprod__case(_1598679, _1598677, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1598679, tc_fun(tc_prod(_1598677, _1598679), tc_HOL_Obool), tc_fun(_1598677, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598677, tc_fun(tc_fun(tc_prod(_1598677, _1598679), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1598677, _1598679), tc_HOL_Obool), tc_fun(_1598677, tc_HOL_Obool)), _1598679), c_COMBC(_1598677, tc_fun(tc_prod(_1598677, _1598679), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1598677, tc_prod(_1598677, _1598679)), tc_fun(_1598677, tc_fun(tc_fun(tc_prod(_1598677, _1598679), tc_HOL_Obool), tc_HOL_Obool)), _1598679), hAPP(c_COMBB(tc_prod(_1598677, _1598679), tc_fun(tc_fun(tc_prod(_1598677, _1598679), tc_HOL_Obool), tc_HOL_Obool), _1598677), c_member(tc_prod(_1598677, _1598679)))), hAPP(c_COMBC(_1598677, _1598679, tc_prod(_1598677, _1598679)), c_Product__Type_OPair(_1598677, _1598679))))), _1598681))))], (41581 ^ _782435) ^ [_1598853, _1598855, _1598857, _1598859, _1598861, _1598863] : [c_Relation_Osingle__valued(_1598853, _1598855, hAPP(c_Relation_Oconverse(_1598855, _1598853), _1598857)), -(_1598859 = c_Orderings_Obot__class_Obot(tc_fun(_1598861, tc_HOL_Obool))), -(hAPP(c_Relation_OImage(_1598855, _1598853, _1598857), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598861, tc_fun(_1598855, tc_HOL_Obool)), _1598859), _1598863)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1598861, tc_fun(_1598853, tc_HOL_Obool)), _1598859), hAPP(hAPP(c_COMBB(tc_fun(_1598855, tc_HOL_Obool), tc_fun(_1598853, tc_HOL_Obool), _1598861), c_Relation_OImage(_1598855, _1598853, _1598857)), _1598863)))], (41591 ^ _782435) ^ [_1599097, _1599099, _1599101] : [c_Relation_Ototal__on(_1599097, _1599099, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599097, _1599097), tc_HOL_Obool)), _1599101), c_Relation_OId(_1599097))), -(c_Relation_Ototal__on(_1599097, _1599099, _1599101))], (41597 ^ _782435) ^ [_1599208, _1599210, _1599212] : [c_Relation_Ototal__on(_1599208, _1599210, _1599212), -(c_Relation_Ototal__on(_1599208, _1599210, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1599208, _1599208), tc_HOL_Obool)), _1599212), c_Relation_OId(_1599208))))], (41603 ^ _782435) ^ [_1599325] : [-(c_Relation_Osingle__valued(_1599325, _1599325, c_Relation_OId(_1599325)))], (41605 ^ _782435) ^ [_1599351, _1599353, _1599355, _1599357, _1599359] : [c_Relation_Osingle__valued(_1599351, _1599353, _1599355), c_Relation_Osingle__valued(_1599353, _1599357, _1599359), -(c_Relation_Osingle__valued(_1599351, _1599357, hAPP(hAPP(c_Relation_Orel__comp(_1599351, _1599353, _1599357), _1599355), _1599359)))], (41615 ^ _782435) ^ [_1599518, _1599520, _1599522, _1599524] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1599518, _1599520), tc_HOL_Obool)), _1599522), _1599524)), c_Relation_Osingle__valued(_1599518, _1599520, _1599524), -(c_Relation_Osingle__valued(_1599518, _1599520, _1599522))], (41625 ^ _782435) ^ [_1599685, _1599687] : [-(c_Relation_Osingle__valued(_1599685, _1599685, c_Relation_OId__on(_1599685, _1599687)))], (41627 ^ _782435) ^ [_1599714, _1599716] : [-(c_Relation_Ototal__on(_1599714, c_Orderings_Obot__class_Obot(tc_fun(_1599714, tc_HOL_Obool)), _1599716))], (41629 ^ _782435) ^ [_1599763, _1599765, _1599767] : [c_Relation_Ototal__on(_1599763, _1599765, hAPP(c_Relation_Oconverse(_1599763, _1599763), _1599767)), -(c_Relation_Ototal__on(_1599763, _1599765, _1599767))], (41635 ^ _782435) ^ [_1599854, _1599856, _1599858] : [c_Relation_Ototal__on(_1599854, _1599856, _1599858), -(c_Relation_Ototal__on(_1599854, _1599856, hAPP(c_Relation_Oconverse(_1599854, _1599854), _1599858)))], (41655 ^ _782435) ^ [_1600343, _1600345, _1600347] : [41658 ^ _782435 : [(41659 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600343, _1600345)), hAPP(hAPP(c_Product__Type_OPair(_1600343, _1600345), 41656 ^ [_1600343, _1600345, _1600347]), 41657 ^ [_1600343, _1600345, _1600347])), _1600347)))], (41662 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1600343, _1600345)), hAPP(hAPP(c_Product__Type_OPair(_1600343, _1600345), 41656 ^ [_1600343, _1600345, _1600347]), 41660 ^ [_1600343, _1600345, _1600347])), _1600347)))], (41664 ^ _782435) ^ [] : [41657 ^ [_1600343, _1600345, _1600347] = 41660 ^ [_1600343, _1600345, _1600347]]], -(c_Relation_Osingle__valued(_1600343, _1600345, _1600347))], (41641 ^ _782435) ^ [_1599969, _1599971, _1599973] : [c_Relation_Osingle__valued(_1599969, _1599971, _1599973), 41644 ^ _782435 : [(41645 ^ _782435) ^ [_1600090, _1600092] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599969, _1599971)), hAPP(hAPP(c_Product__Type_OPair(_1599969, _1599971), _1600092), _1600090)), _1599973)), 41648 ^ _782435 : [(41649 ^ _782435) ^ [_1600216] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1599969, _1599971)), hAPP(hAPP(c_Product__Type_OPair(_1599969, _1599971), _1600092), _1600216)), _1599973)), -(_1600090 = _1600216)]]]]], (41668 ^ _782435) ^ [_1600713, _1600715, _1600717, _1600719, _1600721, _1600723] : [c_Relation_Osingle__valued(_1600713, _1600715, _1600717), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600713, _1600715)), hAPP(hAPP(c_Product__Type_OPair(_1600713, _1600715), _1600719), _1600721)), _1600717)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1600713, _1600715)), hAPP(hAPP(c_Product__Type_OPair(_1600713, _1600715), _1600719), _1600723)), _1600717)), -(_1600721 = _1600723)], (41704 ^ _782435) ^ [_1601503, _1601505, _1601507] : [41706 ^ _782435 : [(41707 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601503), 41705 ^ [_1601503, _1601505, _1601507]), _1601505)))], (41710 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1601503), 41708 ^ [_1601503, _1601505, _1601507]), _1601505)))], (41712 ^ _782435) ^ [] : [41705 ^ [_1601503, _1601505, _1601507] = 41708 ^ [_1601503, _1601505, _1601507]], (41714 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601503, _1601503)), hAPP(hAPP(c_Product__Type_OPair(_1601503, _1601503), 41705 ^ [_1601503, _1601505, _1601507]), 41708 ^ [_1601503, _1601505, _1601507])), _1601507))], (41716 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1601503, _1601503)), hAPP(hAPP(c_Product__Type_OPair(_1601503, _1601503), 41708 ^ [_1601503, _1601505, _1601507]), 41705 ^ [_1601503, _1601505, _1601507])), _1601507))]], -(c_Relation_Ototal__on(_1601503, _1601505, _1601507))], (41682 ^ _782435) ^ [_1601014, _1601016, _1601018] : [c_Relation_Ototal__on(_1601014, _1601016, _1601018), 41685 ^ _782435 : [(41686 ^ _782435) ^ [_1601158] : [hBOOL(hAPP(hAPP(c_member(_1601014), _1601158), _1601016)), 41689 ^ _782435 : [(41690 ^ _782435) ^ [_1601298] : [hBOOL(hAPP(hAPP(c_member(_1601014), _1601298), _1601016)), -(_1601158 = _1601298), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601014, _1601014)), hAPP(hAPP(c_Product__Type_OPair(_1601014, _1601014), _1601158), _1601298)), _1601018))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1601014, _1601014)), hAPP(hAPP(c_Product__Type_OPair(_1601014, _1601014), _1601298), _1601158)), _1601018)))]]]]], (41720 ^ _782435) ^ [_1602085, _1602087, _1602089, _1602091, _1602093] : [c_Relation_Osingle__valued(_1602085, _1602085, _1602087), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602085, _1602085)), hAPP(hAPP(c_Product__Type_OPair(_1602085, _1602085), _1602089), _1602091)), c_Transitive__Closure_Ortrancl(_1602085, _1602087))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1602085, _1602085)), hAPP(hAPP(c_Product__Type_OPair(_1602085, _1602085), _1602089), _1602093)), c_Transitive__Closure_Ortrancl(_1602085, _1602087))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602085, _1602085)), hAPP(hAPP(c_Product__Type_OPair(_1602085, _1602085), _1602091), _1602093)), c_Transitive__Closure_Ortrancl(_1602085, _1602087)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602085, _1602085)), hAPP(hAPP(c_Product__Type_OPair(_1602085, _1602085), _1602093), _1602091)), c_Transitive__Closure_Ortrancl(_1602085, _1602087))))], (41738 ^ _782435) ^ [_1602475, _1602477, _1602479, _1602481, _1602483] : [c_Relation_Osingle__valued(_1602475, _1602477, hAPP(c_Relation_Oconverse(_1602477, _1602475), _1602479)), -(hAPP(c_Relation_OImage(_1602477, _1602475, _1602479), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602477, tc_HOL_Obool)), _1602481), _1602483)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1602475, tc_HOL_Obool)), hAPP(c_Relation_OImage(_1602477, _1602475, _1602479), _1602481)), hAPP(c_Relation_OImage(_1602477, _1602475, _1602479), _1602483)))], (41744 ^ _782435) ^ [_1602658, _1602660, _1602662] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1602658, _1602658)), _1602660), c_Transitive__Closure_Ortrancl(_1602658, _1602662))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602658, _1602658)), _1602660), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1602658, _1602658), 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(_1602658, _1602658), tc_HOL_Obool), tc_fun(tc_prod(_1602658, _1602658), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1602658, _1602658), tc_HOL_Obool)), _1602662)))))], (41750 ^ _782435) ^ [_1602865, _1602867] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1602865, _1602865)), hAPP(hAPP(c_Product__Type_OPair(_1602865, _1602865), 41751 ^ [_1602865, _1602867]), 41751 ^ [_1602865, _1602867])), c_Transitive__Closure_Otrancl(_1602865, _1602867)))), -(c_Wellfounded_Oacyclic(_1602865, _1602867))], (41757 ^ _782435) ^ [_1602937, _1602939, _1602941] : [c_Relation_Osingle__valued(_1602937, _1602937, _1602939), -(c_Relation_Osingle__valued(_1602937, _1602937, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1602937, _1602937), tc_HOL_Obool), _1602941), _1602939)))], (41763 ^ _782435) ^ [_1603044, _1603046, _1603048] : [c_Wellfounded_Owf(_1603044, hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603044, _1603044), tc_HOL_Obool), _1603046), _1603048)), -(c_Wellfounded_Owf(_1603044, _1603048))], (41769 ^ _782435) ^ [_1603147, _1603149, _1603151, _1603153] : [-(hAPP(hAPP(c_Nat_Ocompow(_1603147, _1603147), _1603149), hAPP(hAPP(c_Nat_Ocompow(_1603147, _1603147), _1603151), _1603153)) = hAPP(hAPP(c_Nat_Ocompow(_1603147, _1603147), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1603151), _1603149)), _1603153))], (41771 ^ _782435) ^ [_1603209, _1603211, _1603213, _1603215] : [-(hAPP(_1603209, hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603211, _1603211), _1603213), _1603209), _1603215)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(_1603211, _1603211), _1603213), _1603209), hAPP(_1603209, _1603215)))], (41773 ^ _782435) ^ [_1603268, _1603270, _1603272, _1603274] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_fun(_1603268, _1603270), tc_fun(_1603268, _1603270)), _1603272), c_Fun_Ocomp(_1603270, _1603270, _1603268, _1603274)) = c_Fun_Ocomp(_1603270, _1603270, _1603268, hAPP(hAPP(c_Nat_Ocompow(_1603270, _1603270), _1603272), _1603274)))], (41775 ^ _782435) ^ [_1603331, _1603333] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603331, _1603331), tc_HOL_Obool), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1603333) = _1603333)], (41777 ^ _782435) ^ [_1603368, _1603370, _1603372] : [-(hAPP(hAPP(c_Relation_Orel__comp(_1603368, _1603368, _1603368), _1603370), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603368, _1603368), tc_HOL_Obool), _1603372), _1603370)) = hAPP(hAPP(c_Relation_Orel__comp(_1603368, _1603368, _1603368), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603368, _1603368), tc_HOL_Obool), _1603372), _1603370)), _1603370))], (41779 ^ _782435) ^ [_1603439, _1603441, _1603443, _1603445] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603439, _1603439)), _1603441), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603439, _1603439), tc_HOL_Obool), _1603443), _1603445))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603439, _1603439)), _1603441), c_Transitive__Closure_Ortrancl(_1603439, _1603445))))], (41785 ^ _782435) ^ [_1603608, _1603610, _1603612] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603608, _1603608)), _1603610), c_Transitive__Closure_Ortrancl(_1603608, _1603612))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603608, _1603608)), _1603610), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603608, _1603608), tc_HOL_Obool), 41788 ^ [_1603608, _1603610, _1603612]), _1603612))))], (41792 ^ _782435) ^ [_1603767, _1603769, _1603771] : [41793 ^ _782435 : [(41794 ^ _782435) ^ [_1603843] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1603767, _1603767)), _1603769), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603767, _1603767), tc_HOL_Obool), _1603843), _1603771)))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1603767, _1603767)), _1603769), c_Transitive__Closure_Ortrancl(_1603767, _1603771))))], (41798 ^ _782435) ^ [_1603931, _1603933, _1603935] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603931, _1603931), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1603933)), _1603935) = hAPP(hAPP(c_Relation_Orel__comp(_1603931, _1603931, _1603931), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603931, _1603931), tc_HOL_Obool), _1603933), _1603935)), _1603935))], (41800 ^ _782435) ^ [_1603995, _1603997, _1603999, _1604001] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603995, _1603995), tc_HOL_Obool), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1603997), _1603999)), _1604001) = hAPP(hAPP(c_Relation_Orel__comp(_1603995, _1603995, _1603995), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603995, _1603995), tc_HOL_Obool), _1603997), _1604001)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1603995, _1603995), tc_HOL_Obool), _1603999), _1604001)))], (41802 ^ _782435) ^ [_1604076, _1604078] : [-(hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604076, _1604076), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604078) = c_Relation_OId(_1604076))], (41804 ^ _782435) ^ [_1604115, _1604117, _1604119] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604115, _1604115)), hAPP(hAPP(c_Product__Type_OPair(_1604115, _1604115), _1604117), _1604117)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604115, _1604115), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604119))))], (41806 ^ _782435) ^ [_1604173, _1604175, _1604177, _1604179] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604173, _1604173)), hAPP(hAPP(c_Product__Type_OPair(_1604173, _1604173), _1604175), _1604177)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604173, _1604173), tc_HOL_Obool), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1604179))), -(_1604175 = _1604177)], (41812 ^ _782435) ^ [_1604316, _1604318, _1604320, _1604322, _1604324, _1604326] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604316, _1604316)), hAPP(hAPP(c_Product__Type_OPair(_1604316, _1604316), _1604318), _1604320)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604316, _1604316), tc_HOL_Obool), _1604322), _1604324))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604316, _1604316)), hAPP(hAPP(c_Product__Type_OPair(_1604316, _1604316), _1604320), _1604326)), _1604324)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604316, _1604316)), hAPP(hAPP(c_Product__Type_OPair(_1604316, _1604316), _1604318), _1604326)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604316, _1604316), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604322)), _1604324))))], (41822 ^ _782435) ^ [_1604629, _1604631, _1604633, _1604635, _1604637, _1604639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1604629, _1604629)), hAPP(hAPP(c_Product__Type_OPair(_1604629, _1604629), _1604631), _1604633)), _1604635)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1604629, _1604629)), hAPP(hAPP(c_Product__Type_OPair(_1604629, _1604629), _1604633), _1604637)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604629, _1604629), tc_HOL_Obool), _1604639), _1604635))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1604629, _1604629)), hAPP(hAPP(c_Product__Type_OPair(_1604629, _1604629), _1604631), _1604637)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1604629, _1604629), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1604639)), _1604635))))], (41832 ^ _782435) ^ [_1604942, _1604944, _1604946] : [-(hAPP(hAPP(c_Nat_Ocompow(_1604942, _1604942), hAPP(c_Nat_OSuc, _1604944)), _1604946) = hAPP(c_Fun_Ocomp(_1604942, _1604942, _1604942, _1604946), hAPP(hAPP(c_Nat_Ocompow(_1604942, _1604942), _1604944), _1604946)))], (41834 ^ _782435) ^ [_1604998, _1605000, _1605002, _1605004] : [-(hAPP(hAPP(c_Nat_Ocompow(_1604998, _1604998), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1605000), _1605002)), _1605004) = hAPP(c_Fun_Ocomp(_1604998, _1604998, _1604998, hAPP(hAPP(c_Nat_Ocompow(_1604998, _1604998), _1605000), _1605004)), hAPP(hAPP(c_Nat_Ocompow(_1604998, _1604998), _1605002), _1605004)))], (41836 ^ _782435) ^ [_1605068, _1605070] : [-(hAPP(hAPP(c_Nat_Ocompow(_1605068, _1605068), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605070) = c_Fun_Oid(_1605068))], (41838 ^ _782435) ^ [_1605122, _1605124, _1605126] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605122, _1605122)), _1605124), c_Transitive__Closure_Otrancl(_1605122, _1605126))), 41842 ^ _782435 : [(41843 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), 41841 ^ [_1605122, _1605124, _1605126])))], (41845 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605122, _1605122)), _1605124), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605122, _1605122), tc_HOL_Obool), 41841 ^ [_1605122, _1605124, _1605126]), _1605126))))]]], (41847 ^ _782435) ^ [_1605320, _1605322, _1605324] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605320, _1605320)), _1605322), c_Transitive__Closure_Otrancl(_1605320, _1605324)))), 41848 ^ _782435 : [(41849 ^ _782435) ^ [_1605399] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1605399)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1605320, _1605320)), _1605322), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605320, _1605320), tc_HOL_Obool), _1605399), _1605324)))]]], (41857 ^ _782435) ^ [_1605570, _1605572] : [-(c_Transitive__Closure_Ortrancl(_1605570, _1605572) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat, tc_fun(tc_prod(_1605570, _1605570), 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(_1605570, _1605570), tc_HOL_Obool), tc_fun(tc_prod(_1605570, _1605570), tc_HOL_Obool)), c_Nat_Ocompow(tc_prod(_1605570, _1605570), tc_HOL_Obool)), _1605572)))], (41859 ^ _782435) ^ [_1605641] : [-(c_Nat_Ofunpow(_1605641) = c_Nat_Ocompow(_1605641, _1605641))], (41861 ^ _782435) ^ [_1605669, _1605671, _1605673, _1605675, _1605677] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1605669, _1605669)), hAPP(hAPP(c_Product__Type_OPair(_1605669, _1605669), _1605671), _1605673)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605669, _1605669), tc_HOL_Obool), _1605675), _1605677))), 41866 ^ _782435 : [(41867 ^ _782435) ^ [] : [-(_1605675 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41869 ^ _782435) ^ [] : [-(_1605671 = _1605673)]], 41872 ^ _782435 : [(41873 ^ _782435) ^ [] : [-(_1605675 = hAPP(c_Nat_OSuc, 41871 ^ [_1605669, _1605671, _1605673, _1605675, _1605677]))], (41875 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605669, _1605669)), hAPP(hAPP(c_Product__Type_OPair(_1605669, _1605669), _1605671), 41870 ^ [_1605669, _1605671, _1605673, _1605675, _1605677])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1605669, _1605669), tc_HOL_Obool), 41871 ^ [_1605669, _1605671, _1605673, _1605675, _1605677]), _1605677))))], (41877 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1605669, _1605669)), hAPP(hAPP(c_Product__Type_OPair(_1605669, _1605669), 41870 ^ [_1605669, _1605671, _1605673, _1605675, _1605677]), _1605673)), _1605677)))]]], (41879 ^ _782435) ^ [_1606111, _1606113, _1606115, _1606117, _1606119] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606111, _1606111)), hAPP(hAPP(c_Product__Type_OPair(_1606111, _1606111), _1606113), _1606115)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606111, _1606111), tc_HOL_Obool), _1606117), _1606119))), 41884 ^ _782435 : [(41885 ^ _782435) ^ [] : [-(_1606117 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (41887 ^ _782435) ^ [] : [-(_1606113 = _1606115)]], 41890 ^ _782435 : [(41891 ^ _782435) ^ [] : [-(_1606117 = hAPP(c_Nat_OSuc, 41889 ^ [_1606111, _1606113, _1606115, _1606117, _1606119]))], (41893 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606111, _1606111)), hAPP(hAPP(c_Product__Type_OPair(_1606111, _1606111), _1606113), 41888 ^ [_1606111, _1606113, _1606115, _1606117, _1606119])), _1606119)))], (41895 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606111, _1606111)), hAPP(hAPP(c_Product__Type_OPair(_1606111, _1606111), 41888 ^ [_1606111, _1606113, _1606115, _1606117, _1606119]), _1606115)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1606111, _1606111), tc_HOL_Obool), 41889 ^ [_1606111, _1606113, _1606115, _1606117, _1606119]), _1606119))))]]], (41897 ^ _782435) ^ [_1606553, _1606555, _1606557, _1606559, _1606561] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1606553, _1606553)), hAPP(hAPP(c_Product__Type_OPair(_1606553, _1606553), _1606555), _1606557)), c_Transitive__Closure_Ortrancl(_1606553, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1606553, _1606553), tc_HOL_Obool)), _1606559), _1606561)))), 41903 ^ _782435 : [(41904 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606553, _1606553)), hAPP(hAPP(c_Product__Type_OPair(_1606553, _1606553), 41902 ^ [_1606553, _1606555, _1606557, _1606559, _1606561]), _1606557)), c_Transitive__Closure_Ortrancl(_1606553, _1606559))))], (41907 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606553, _1606553)), hAPP(hAPP(c_Product__Type_OPair(_1606553, _1606553), 41905 ^ [_1606553, _1606555, _1606557, _1606559, _1606561]), 41902 ^ [_1606553, _1606555, _1606557, _1606559, _1606561])), _1606561)))], (41909 ^ _782435) ^ [] : [41905 ^ [_1606553, _1606555, _1606557, _1606559, _1606561] = 41902 ^ [_1606553, _1606555, _1606557, _1606559, _1606561]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1606553, _1606553)), hAPP(hAPP(c_Product__Type_OPair(_1606553, _1606553), _1606555), _1606557)), c_Transitive__Closure_Ortrancl(_1606553, _1606559))))], (41913 ^ _782435) ^ [_1607112, _1607114, _1607116, _1607118, _1607120] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), _1607114), _1607116)), c_Transitive__Closure_Ortrancl(_1607112, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1607112, _1607112), tc_HOL_Obool)), _1607118), _1607120)))), 41919 ^ _782435 : [(41920 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), _1607114), 41918 ^ [_1607112, _1607114, _1607116, _1607118, _1607120])), c_Transitive__Closure_Ortrancl(_1607112, _1607118))))], (41923 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), 41918 ^ [_1607112, _1607114, _1607116, _1607118, _1607120]), 41921 ^ [_1607112, _1607114, _1607116, _1607118, _1607120])), _1607120)))], (41925 ^ _782435) ^ [] : [41918 ^ [_1607112, _1607114, _1607116, _1607118, _1607120] = 41921 ^ [_1607112, _1607114, _1607116, _1607118, _1607120]]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607112, _1607112)), hAPP(hAPP(c_Product__Type_OPair(_1607112, _1607112), _1607114), _1607116)), c_Transitive__Closure_Ortrancl(_1607112, _1607118))))], (41929 ^ _782435) ^ [_1607671, _1607673, _1607675, _1607677, _1607679] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), _1607673), _1607675)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607671, _1607671), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1607677)), _1607679))), 41933 ^ _782435 : [(41934 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), _1607673), 41932 ^ [_1607671, _1607673, _1607675, _1607677, _1607679])), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607671, _1607671), tc_HOL_Obool), _1607677), _1607679))))], (41936 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607671, _1607671)), hAPP(hAPP(c_Product__Type_OPair(_1607671, _1607671), 41932 ^ [_1607671, _1607673, _1607675, _1607677, _1607679]), _1607675)), _1607679)))]]], (41938 ^ _782435) ^ [_1607983, _1607985, _1607987, _1607989, _1607991] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1607983, _1607983)), hAPP(hAPP(c_Product__Type_OPair(_1607983, _1607983), _1607985), _1607987)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607983, _1607983), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1607989)), _1607991))), 41942 ^ _782435 : [(41943 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607983, _1607983)), hAPP(hAPP(c_Product__Type_OPair(_1607983, _1607983), _1607985), 41941 ^ [_1607983, _1607985, _1607987, _1607989, _1607991])), _1607991)))], (41945 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1607983, _1607983)), hAPP(hAPP(c_Product__Type_OPair(_1607983, _1607983), 41941 ^ [_1607983, _1607985, _1607987, _1607989, _1607991]), _1607987)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1607983, _1607983), tc_HOL_Obool), _1607989), _1607991))))]]], (41947 ^ _782435) ^ [_1608291, _1608293, _1608295, _1608297, _1608299] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608291, _1608291)), hAPP(hAPP(c_Product__Type_OPair(_1608291, _1608291), _1608293), _1608295)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608291, _1608291), tc_HOL_Obool), hAPP(c_Nat_OSuc, _1608297)), _1608299))), 41951 ^ _782435 : [(41952 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608291, _1608291)), hAPP(hAPP(c_Product__Type_OPair(_1608291, _1608291), _1608293), 41950 ^ [_1608291, _1608293, _1608295, _1608297, _1608299])), _1608299)))], (41954 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608291, _1608291)), hAPP(hAPP(c_Product__Type_OPair(_1608291, _1608291), 41950 ^ [_1608291, _1608293, _1608295, _1608297, _1608299]), _1608295)), hAPP(hAPP(c_Nat_Ocompow(tc_prod(_1608291, _1608291), tc_HOL_Obool), _1608297), _1608299))))]]], (41956 ^ _782435) ^ [_1608603, _1608605, _1608607, _1608609] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608603, _1608603)), hAPP(hAPP(c_Product__Type_OPair(_1608603, _1608603), _1608605), _1608607)), c_Transitive__Closure_Otrancl(_1608603, _1608609))), 41960 ^ _782435 : [(41961 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608603, _1608603)), hAPP(hAPP(c_Product__Type_OPair(_1608603, _1608603), _1608605), 41959 ^ [_1608603, _1608605, _1608607, _1608609])), c_Transitive__Closure_Ortrancl(_1608603, _1608609))))], (41963 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608603, _1608603)), hAPP(hAPP(c_Product__Type_OPair(_1608603, _1608603), 41959 ^ [_1608603, _1608605, _1608607, _1608609]), _1608607)), _1608609)))]]], (41965 ^ _782435) ^ [_1608863, _1608865, _1608867, _1608869] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1608863, _1608863)), hAPP(hAPP(c_Product__Type_OPair(_1608863, _1608863), _1608865), _1608867)), c_Transitive__Closure_Otrancl(_1608863, _1608869))), 41969 ^ _782435 : [(41970 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608863, _1608863)), hAPP(hAPP(c_Product__Type_OPair(_1608863, _1608863), _1608865), 41968 ^ [_1608863, _1608865, _1608867, _1608869])), _1608869)))], (41972 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1608863, _1608863)), hAPP(hAPP(c_Product__Type_OPair(_1608863, _1608863), 41968 ^ [_1608863, _1608865, _1608867, _1608869]), _1608867)), c_Transitive__Closure_Ortrancl(_1608863, _1608869))))]]], (41974 ^ _782435) ^ [_1609123, _1609125] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1609123, _1609123)), _1609125), c_Relation_OId(_1609123))), -(_1609125 = hAPP(hAPP(c_Product__Type_OPair(_1609123, _1609123), 41977 ^ [_1609123, _1609125]), 41977 ^ [_1609123, _1609125]))], (41981 ^ _782435) ^ [_1609265, _1609267, _1609269] : [class_Orderings_Olinorder(_1609265), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609265), _1609267)), -(hBOOL(hAPP(hAPP(c_member(_1609265), _1609269), _1609267))), -(c_Big__Operators_Olattice_OSup__fin(_1609265, c_Orderings_Oord__class_Omax(_1609265), hAPP(hAPP(c_Set_Oinsert(_1609265), _1609269), _1609267)) = hAPP(hAPP(c_Finite__Set_Ofold(_1609265, _1609265, c_Orderings_Oord__class_Omax(_1609265)), _1609269), _1609267))], (41995 ^ _782435) ^ [_1609485, _1609487, _1609489, _1609491, _1609493, _1609495] : [c_Finite__Set_Ofolding(_1609485, _1609487, _1609489, _1609491), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609485), _1609493)), -(hAPP(hAPP(_1609491, _1609493), _1609495) = hAPP(hAPP(c_Finite__Set_Ofold(_1609485, _1609487, _1609489), _1609495), _1609493))], (42005 ^ _782435) ^ [_1609674, _1609676, _1609678, _1609680] : [-(hAPP(c_Finite__Set_Ofold__image(_1609674, _1609676, _1609678), _1609680) = c_Finite__Set_Ofold(_1609676, _1609674, hAPP(hAPP(c_COMBB(_1609674, tc_fun(_1609674, _1609674), _1609676), _1609678), _1609680)))], (42007 ^ _782435) ^ [_1609727, _1609729, _1609731, _1609733] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1609727, _1609729, _1609731), _1609733), c_Orderings_Obot__class_Obot(tc_fun(_1609727, tc_HOL_Obool))) = _1609733)], (42009 ^ _782435) ^ [_1609771, _1609773, _1609775, _1609777, _1609779] : [-(hAPP(hAPP(c_Finite__Set_Ofold(_1609771, _1609773, _1609775), _1609777), _1609779) = c_HOL_OThe(_1609773, c_Finite__Set_Ofold__graph(_1609771, _1609773, _1609775, _1609777, _1609779)))], (42011 ^ _782435) ^ [_1609821, _1609823, _1609825] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1609821), _1609823)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1609821, tc_HOL_Obool)), _1609823), _1609825) = hAPP(hAPP(c_Finite__Set_Ofold(_1609821, tc_fun(_1609821, tc_HOL_Obool), c_Set_Oinsert(_1609821)), _1609825), _1609823))], (42017 ^ _782435) ^ [_1609960, _1609962, _1609964, _1609966] : [class_Lattices_Osemilattice__sup(_1609960), hBOOL(hAPP(c_Finite__Set_Ofinite(_1609960), _1609962)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1609960, _1609960, c_Lattices_Osemilattice__sup__class_Osup(_1609960)), _1609964), hAPP(hAPP(c_Set_Oinsert(_1609960), _1609966), _1609962)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1609960), _1609966), hAPP(hAPP(c_Finite__Set_Ofold(_1609960, _1609960, c_Lattices_Osemilattice__sup__class_Osup(_1609960)), _1609964), _1609962)))], (42027 ^ _782435) ^ [_1610183, _1610185, _1610187, _1610189] : [class_Lattices_Osemilattice__inf(_1610183), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610183), _1610185)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610183, _1610183, c_Lattices_Osemilattice__inf__class_Oinf(_1610183)), _1610187), hAPP(hAPP(c_Set_Oinsert(_1610183), _1610189), _1610185)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1610183), _1610189), hAPP(hAPP(c_Finite__Set_Ofold(_1610183, _1610183, c_Lattices_Osemilattice__inf__class_Oinf(_1610183)), _1610187), _1610185)))], (42037 ^ _782435) ^ [_1610406, _1610408, _1610410, _1610412] : [class_Orderings_Olinorder(_1610406), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610406), _1610408)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610406, _1610406, c_Orderings_Oord__class_Omin(_1610406)), _1610410), hAPP(hAPP(c_Set_Oinsert(_1610406), _1610412), _1610408)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(_1610406), _1610412), hAPP(hAPP(c_Finite__Set_Ofold(_1610406, _1610406, c_Orderings_Oord__class_Omin(_1610406)), _1610410), _1610408)))], (42047 ^ _782435) ^ [_1610629, _1610631, _1610633, _1610635] : [class_Orderings_Olinorder(_1610629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610629), _1610631)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1610629, _1610629, c_Orderings_Oord__class_Omax(_1610629)), _1610633), hAPP(hAPP(c_Set_Oinsert(_1610629), _1610635), _1610631)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1610629), _1610635), hAPP(hAPP(c_Finite__Set_Ofold(_1610629, _1610629, c_Orderings_Oord__class_Omax(_1610629)), _1610633), _1610631)))], (42057 ^ _782435) ^ [_1610852, _1610854, _1610856] : [class_Complete__Lattice_Ocomplete__lattice(_1610852), hBOOL(hAPP(c_Finite__Set_Ofinite(_1610852), _1610854)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1610852), _1610856), c_Complete__Lattice_OSup__class_OSup(_1610852, _1610854)) = hAPP(hAPP(c_Finite__Set_Ofold(_1610852, _1610852, c_Lattices_Osemilattice__sup__class_Osup(_1610852)), _1610856), _1610854))], (42067 ^ _782435) ^ [_1611037, _1611039, _1611041] : [class_Complete__Lattice_Ocomplete__lattice(_1611037), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611037), _1611039)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1611037), _1611041), c_Complete__Lattice_OInf__class_OInf(_1611037, _1611039)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611037, _1611037, c_Lattices_Osemilattice__inf__class_Oinf(_1611037)), _1611041), _1611039))], (42077 ^ _782435) ^ [_1611222, _1611224, _1611226, _1611228, _1611230, _1611232] : [c_Finite__Set_Ofun__left__comm__idem(_1611222, _1611224, _1611226), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611222), _1611228)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1611222, _1611224, _1611226), _1611230), hAPP(hAPP(c_Set_Oinsert(_1611222), _1611232), _1611228)) = hAPP(hAPP(_1611226, _1611232), hAPP(hAPP(c_Finite__Set_Ofold(_1611222, _1611224, _1611226), _1611230), _1611228)))], (42087 ^ _782435) ^ [_1611445, _1611447, _1611449, _1611451, _1611453, _1611455] : [c_Finite__Set_Ofun__left__comm__idem(_1611445, _1611447, _1611449), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611445), _1611451)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1611445, _1611447, _1611449), _1611453), hAPP(hAPP(c_Set_Oinsert(_1611445), _1611455), _1611451)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611445, _1611447, _1611449), hAPP(hAPP(_1611449, _1611455), _1611453)), _1611451))], (42097 ^ _782435) ^ [_1611668, _1611670, _1611672, _1611674, _1611676] : [class_Complete__Lattice_Ocomplete__lattice(_1611668), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611670), _1611672)), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1611668), _1611674), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1611670, _1611668), _1611672), _1611676)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611670, _1611668, hAPP(hAPP(c_COMBB(_1611668, tc_fun(_1611668, _1611668), _1611670), c_Lattices_Osemilattice__sup__class_Osup(_1611668)), _1611676)), _1611674), _1611672))], (42107 ^ _782435) ^ [_1611899, _1611901, _1611903, _1611905, _1611907] : [class_Complete__Lattice_Ocomplete__lattice(_1611899), hBOOL(hAPP(c_Finite__Set_Ofinite(_1611901), _1611903)), -(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1611899), _1611905), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1611901, _1611899), _1611903), _1611907)) = hAPP(hAPP(c_Finite__Set_Ofold(_1611901, _1611899, hAPP(hAPP(c_COMBB(_1611899, tc_fun(_1611899, _1611899), _1611901), c_Lattices_Osemilattice__inf__class_Oinf(_1611899)), _1611907)), _1611905), _1611903))], (42117 ^ _782435) ^ [_1612130, _1612132, _1612134, _1612136, _1612138] : [c_Finite__Set_Ofolding__one__idem(_1612130, _1612132, _1612134), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612130), _1612136)), -(hAPP(_1612134, hAPP(hAPP(c_Set_Oinsert(_1612130), _1612138), _1612136)) = hAPP(hAPP(c_Finite__Set_Ofold(_1612130, _1612130, _1612132), _1612138), _1612136))], (42127 ^ _782435) ^ [_1612323, _1612325, _1612327, _1612329] : [class_Lattices_Osemilattice__sup(_1612323), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612323), _1612325)), hBOOL(hAPP(hAPP(c_member(_1612323), _1612327), _1612325)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612323), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1612323), _1612327), _1612329)), hAPP(hAPP(c_Finite__Set_Ofold(_1612323, _1612323, c_Lattices_Osemilattice__sup__class_Osup(_1612323)), _1612329), _1612325))))], (42141 ^ _782435) ^ [_1612590, _1612592, _1612594, _1612596] : [class_Lattices_Osemilattice__inf(_1612590), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612590), _1612592)), hBOOL(hAPP(hAPP(c_member(_1612590), _1612594), _1612592)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612590), hAPP(hAPP(c_Finite__Set_Ofold(_1612590, _1612590, c_Lattices_Osemilattice__inf__class_Oinf(_1612590)), _1612596), _1612592)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1612590), _1612594), _1612596))))], (42155 ^ _782435) ^ [_1612857, _1612859, _1612861, _1612863] : [class_Orderings_Olinorder(_1612857), hBOOL(hAPP(c_Finite__Set_Ofinite(_1612857), _1612859)), hBOOL(hAPP(hAPP(c_member(_1612857), _1612861), _1612859)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1612857), hAPP(hAPP(c_Finite__Set_Ofold(_1612857, _1612857, c_Orderings_Oord__class_Omin(_1612857)), _1612863), _1612859)), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1612857), _1612861), _1612863))))], (42169 ^ _782435) ^ [_1613124, _1613126, _1613128, _1613130] : [class_Orderings_Olinorder(_1613124), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613124), _1613126)), hBOOL(hAPP(hAPP(c_member(_1613124), _1613128), _1613126)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1613124), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1613124), _1613128), _1613130)), hAPP(hAPP(c_Finite__Set_Ofold(_1613124, _1613124, c_Orderings_Oord__class_Omax(_1613124)), _1613130), _1613126))))], (42183 ^ _782435) ^ [_1613391, _1613393] : [class_Complete__Lattice_Ocomplete__lattice(_1613391), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613391), _1613393)), -(c_Complete__Lattice_OSup__class_OSup(_1613391, _1613393) = hAPP(hAPP(c_Finite__Set_Ofold(_1613391, _1613391, c_Lattices_Osemilattice__sup__class_Osup(_1613391)), c_Orderings_Obot__class_Obot(_1613391)), _1613393))], (42193 ^ _782435) ^ [_1613560, _1613562] : [class_Complete__Lattice_Ocomplete__lattice(_1613560), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613560), _1613562)), -(c_Complete__Lattice_OInf__class_OInf(_1613560, _1613562) = hAPP(hAPP(c_Finite__Set_Ofold(_1613560, _1613560, c_Lattices_Osemilattice__inf__class_Oinf(_1613560)), c_Orderings_Otop__class_Otop(_1613560)), _1613562))], (42203 ^ _782435) ^ [_1613729, _1613731, _1613733] : [class_Lattices_Oab__semigroup__idem__mult(_1613729), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613729), _1613731)), -(hAPP(c_Finite__Set_Ofold1(_1613729, c_Groups_Otimes__class_Otimes(_1613729)), hAPP(hAPP(c_Set_Oinsert(_1613729), _1613733), _1613731)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613729, _1613729, c_Groups_Otimes__class_Otimes(_1613729)), _1613733), _1613731))], (42213 ^ _782435) ^ [_1613924, _1613926, _1613928] : [class_Lattices_Olattice(_1613924), hBOOL(hAPP(c_Finite__Set_Ofinite(_1613924), _1613926)), -(c_Big__Operators_Olattice__class_OSup__fin(_1613924, hAPP(hAPP(c_Set_Oinsert(_1613924), _1613928), _1613926)) = hAPP(hAPP(c_Finite__Set_Ofold(_1613924, _1613924, c_Lattices_Osemilattice__sup__class_Osup(_1613924)), _1613928), _1613926))], (42223 ^ _782435) ^ [_1614109, _1614111, _1614113] : [class_Lattices_Olattice(_1614109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614109), _1614111)), -(c_Big__Operators_Olattice__class_OInf__fin(_1614109, hAPP(hAPP(c_Set_Oinsert(_1614109), _1614113), _1614111)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614109, _1614109, c_Lattices_Osemilattice__inf__class_Oinf(_1614109)), _1614113), _1614111))], (42233 ^ _782435) ^ [_1614294, _1614296, _1614298] : [class_Orderings_Olinorder(_1614294), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614294), _1614296)), -(c_Big__Operators_Olinorder__class_OMin(_1614294, hAPP(hAPP(c_Set_Oinsert(_1614294), _1614298), _1614296)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614294, _1614294, c_Orderings_Oord__class_Omin(_1614294)), _1614298), _1614296))], (42243 ^ _782435) ^ [_1614479, _1614481, _1614483] : [class_Orderings_Olinorder(_1614479), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614479), _1614481)), -(c_Big__Operators_Olinorder__class_OMax(_1614479, hAPP(hAPP(c_Set_Oinsert(_1614479), _1614483), _1614481)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614479, _1614479, c_Orderings_Oord__class_Omax(_1614479)), _1614483), _1614481))], (42253 ^ _782435) ^ [_1614664, _1614666, _1614668] : [class_Orderings_Olinorder(_1614664), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614664), _1614666)), -(c_Big__Operators_Olattice_OInf__fin(_1614664, c_Orderings_Oord__class_Omin(_1614664), hAPP(hAPP(c_Set_Oinsert(_1614664), _1614668), _1614666)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614664, _1614664, c_Orderings_Oord__class_Omin(_1614664)), _1614668), _1614666))], (42263 ^ _782435) ^ [_1614855, _1614857, _1614859] : [class_Orderings_Olinorder(_1614855), hBOOL(hAPP(c_Finite__Set_Ofinite(_1614855), _1614857)), -(c_Big__Operators_Olattice_OSup__fin(_1614855, c_Orderings_Oord__class_Omax(_1614855), hAPP(hAPP(c_Set_Oinsert(_1614855), _1614859), _1614857)) = hAPP(hAPP(c_Finite__Set_Ofold(_1614855, _1614855, c_Orderings_Oord__class_Omax(_1614855)), _1614859), _1614857))], (42273 ^ _782435) ^ [_1615046, _1615048, _1615050] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1615046), _1615048)), -(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1615046, tc_HOL_Obool)), _1615050), _1615048) = hAPP(hAPP(c_Finite__Set_Ofold(_1615046, tc_fun(_1615046, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1615046, tc_HOL_Obool), tc_fun(tc_fun(_1615046, tc_HOL_Obool), tc_fun(_1615046, tc_HOL_Obool)), _1615046), hAPP(c_COMBC(tc_fun(_1615046, tc_HOL_Obool), tc_fun(_1615046, tc_HOL_Obool), tc_fun(_1615046, tc_HOL_Obool)), c_Groups_Ominus__class_Ominus(tc_fun(_1615046, tc_HOL_Obool)))), hAPP(hAPP(c_COMBC(_1615046, tc_fun(_1615046, tc_HOL_Obool), tc_fun(_1615046, tc_HOL_Obool)), c_Set_Oinsert(_1615046)), c_Orderings_Obot__class_Obot(tc_fun(_1615046, tc_HOL_Obool))))), _1615050), _1615048))], (42279 ^ _782435) ^ [_1615313, _1615315, _1615317, _1615319, _1615321] : [c_Finite__Set_Ofolding__one(_1615313, _1615315, _1615317), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615313), _1615319)), -(hBOOL(hAPP(hAPP(c_member(_1615313), _1615321), _1615319))), -(hAPP(_1615317, hAPP(hAPP(c_Set_Oinsert(_1615313), _1615321), _1615319)) = hAPP(hAPP(c_Finite__Set_Ofold(_1615313, _1615313, _1615315), _1615321), _1615319))], (42293 ^ _782435) ^ [_1615535, _1615537, _1615539, _1615541] : [class_Complete__Lattice_Ocomplete__lattice(_1615535), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615537), _1615539)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1615537, _1615535), _1615539), _1615541) = hAPP(hAPP(c_Finite__Set_Ofold(_1615537, _1615535, hAPP(hAPP(c_COMBB(_1615535, tc_fun(_1615535, _1615535), _1615537), c_Lattices_Osemilattice__sup__class_Osup(_1615535)), _1615541)), c_Orderings_Obot__class_Obot(_1615535)), _1615539))], (42303 ^ _782435) ^ [_1615750, _1615752, _1615754, _1615756] : [class_Complete__Lattice_Ocomplete__lattice(_1615750), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615752), _1615754)), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1615752, _1615750), _1615754), _1615756) = hAPP(hAPP(c_Finite__Set_Ofold(_1615752, _1615750, hAPP(hAPP(c_COMBB(_1615750, tc_fun(_1615750, _1615750), _1615752), c_Lattices_Osemilattice__inf__class_Oinf(_1615750)), _1615756)), c_Orderings_Otop__class_Otop(_1615750)), _1615754))], (42313 ^ _782435) ^ [_1615965, _1615967, _1615969] : [class_Groups_Oab__semigroup__mult(_1615965), hBOOL(hAPP(c_Finite__Set_Ofinite(_1615965), _1615967)), -(hBOOL(hAPP(hAPP(c_member(_1615965), _1615969), _1615967))), -(hAPP(c_Finite__Set_Ofold1(_1615965, c_Groups_Otimes__class_Otimes(_1615965)), hAPP(hAPP(c_Set_Oinsert(_1615965), _1615969), _1615967)) = hAPP(hAPP(c_Finite__Set_Ofold(_1615965, _1615965, c_Groups_Otimes__class_Otimes(_1615965)), _1615969), _1615967))], (42327 ^ _782435) ^ [_1616189, _1616191, _1616193] : [class_Lattices_Olattice(_1616189), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616189), _1616191)), -(hBOOL(hAPP(hAPP(c_member(_1616189), _1616193), _1616191))), -(c_Big__Operators_Olattice__class_OSup__fin(_1616189, hAPP(hAPP(c_Set_Oinsert(_1616189), _1616193), _1616191)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616189, _1616189, c_Lattices_Osemilattice__sup__class_Osup(_1616189)), _1616193), _1616191))], (42341 ^ _782435) ^ [_1616403, _1616405, _1616407] : [class_Lattices_Olattice(_1616403), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616403), _1616405)), -(hBOOL(hAPP(hAPP(c_member(_1616403), _1616407), _1616405))), -(c_Big__Operators_Olattice__class_OInf__fin(_1616403, hAPP(hAPP(c_Set_Oinsert(_1616403), _1616407), _1616405)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616403, _1616403, c_Lattices_Osemilattice__inf__class_Oinf(_1616403)), _1616407), _1616405))], (42355 ^ _782435) ^ [_1616617, _1616619, _1616621] : [class_Orderings_Olinorder(_1616617), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616617), _1616619)), -(hBOOL(hAPP(hAPP(c_member(_1616617), _1616621), _1616619))), -(c_Big__Operators_Olinorder__class_OMin(_1616617, hAPP(hAPP(c_Set_Oinsert(_1616617), _1616621), _1616619)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616617, _1616617, c_Orderings_Oord__class_Omin(_1616617)), _1616621), _1616619))], (42369 ^ _782435) ^ [_1616831, _1616833, _1616835] : [class_Orderings_Olinorder(_1616831), hBOOL(hAPP(c_Finite__Set_Ofinite(_1616831), _1616833)), -(hBOOL(hAPP(hAPP(c_member(_1616831), _1616835), _1616833))), -(c_Big__Operators_Olinorder__class_OMax(_1616831, hAPP(hAPP(c_Set_Oinsert(_1616831), _1616835), _1616833)) = hAPP(hAPP(c_Finite__Set_Ofold(_1616831, _1616831, c_Orderings_Oord__class_Omax(_1616831)), _1616835), _1616833))], (42383 ^ _782435) ^ [_1617045, _1617047, _1617049] : [class_Orderings_Olinorder(_1617045), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617045), _1617047)), -(hBOOL(hAPP(hAPP(c_member(_1617045), _1617049), _1617047))), -(c_Big__Operators_Olattice_OInf__fin(_1617045, c_Orderings_Oord__class_Omin(_1617045), hAPP(hAPP(c_Set_Oinsert(_1617045), _1617049), _1617047)) = hAPP(hAPP(c_Finite__Set_Ofold(_1617045, _1617045, c_Orderings_Oord__class_Omin(_1617045)), _1617049), _1617047))], (42397 ^ _782435) ^ [_1617265, _1617267, _1617269, _1617271, _1617273, _1617275] : [c_Finite__Set_Ofun__left__comm(_1617265, _1617267, _1617269), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617265), _1617271)), hBOOL(hAPP(hAPP(c_member(_1617265), _1617273), _1617271)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617265, _1617267, _1617269), _1617275), _1617271) = hAPP(hAPP(_1617269, _1617273), hAPP(hAPP(c_Finite__Set_Ofold(_1617265, _1617267, _1617269), _1617275), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1617265, tc_HOL_Obool)), _1617271), hAPP(hAPP(c_Set_Oinsert(_1617265), _1617273), c_Orderings_Obot__class_Obot(tc_fun(_1617265, tc_HOL_Obool)))))))], (42411 ^ _782435) ^ [_1617594, _1617596, _1617598, _1617600, _1617602, _1617604] : [c_Finite__Set_Ofun__left__comm(_1617594, _1617596, _1617598), hBOOL(hAPP(c_Finite__Set_Ofinite(_1617594), _1617600)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1617594, _1617596, _1617598), _1617602), hAPP(hAPP(c_Set_Oinsert(_1617594), _1617604), _1617600)) = hAPP(hAPP(_1617598, _1617604), hAPP(hAPP(c_Finite__Set_Ofold(_1617594, _1617596, _1617598), _1617602), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1617594, tc_HOL_Obool)), _1617600), hAPP(hAPP(c_Set_Oinsert(_1617594), _1617604), c_Orderings_Obot__class_Obot(tc_fun(_1617594, tc_HOL_Obool)))))))], (42421 ^ _782435) ^ [_1617865, _1617867, _1617869, _1617871, _1617873] : [c_Finite__Set_Ofun__left__comm(_1617865, _1617867, _1617869), -(hAPP(c_Fun_Ocomp(_1617867, _1617867, _1617867, hAPP(_1617869, _1617871)), hAPP(_1617869, _1617873)) = hAPP(c_Fun_Ocomp(_1617867, _1617867, _1617867, hAPP(_1617869, _1617873)), hAPP(_1617869, _1617871)))], (42427 ^ _782435) ^ [_1618006, _1618008, _1618010, _1618012, _1618014] : [c_Finite__Set_Ofun__left__comm(_1618006, _1618008, _1618010), -(c_Finite__Set_Ofun__left__comm(_1618012, _1618008, hAPP(hAPP(c_COMBB(_1618006, tc_fun(_1618008, _1618008), _1618012), _1618010), _1618014)))], (42433 ^ _782435) ^ [_1618119] : [class_Groups_Oab__semigroup__mult(_1618119), -(c_Finite__Set_Ofun__left__comm(_1618119, _1618119, c_Groups_Otimes__class_Otimes(_1618119)))], (42439 ^ _782435) ^ [_1618198, _1618200, _1618202, _1618204, _1618206, _1618208] : [c_Finite__Set_Ofun__left__comm(_1618198, _1618200, _1618202), -(hAPP(hAPP(_1618202, _1618204), hAPP(hAPP(_1618202, _1618206), _1618208)) = hAPP(hAPP(_1618202, _1618206), hAPP(hAPP(_1618202, _1618204), _1618208)))], (42445 ^ _782435) ^ [_1618333, _1618335, _1618337, _1618339, _1618341, _1618343, _1618345] : [c_Finite__Set_Ofun__left__comm(_1618333, _1618335, _1618337), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618333, _1618335, _1618337, _1618339, _1618341), _1618343)), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618333, _1618335, _1618337, _1618339, _1618341), _1618345)), -(_1618345 = _1618343)], (42459 ^ _782435) ^ [_1618578, _1618580, _1618582, _1618584, _1618586, _1618588] : [c_Finite__Set_Ofun__left__comm(_1618578, _1618580, _1618582), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618578), _1618584)), -(hAPP(hAPP(_1618582, _1618586), hAPP(hAPP(c_Finite__Set_Ofold(_1618578, _1618580, _1618582), _1618588), _1618584)) = hAPP(hAPP(c_Finite__Set_Ofold(_1618578, _1618580, _1618582), hAPP(hAPP(_1618582, _1618586), _1618588)), _1618584))], (42469 ^ _782435) ^ [_1618797, _1618799, _1618801, _1618803, _1618805, _1618807] : [c_Finite__Set_Ofun__left__comm(_1618797, _1618799, _1618801), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618797, _1618799, _1618801, _1618803, _1618805), _1618807)), -(hAPP(hAPP(c_Finite__Set_Ofold(_1618797, _1618799, _1618801), _1618803), _1618805) = _1618807)], (42479 ^ _782435) ^ [_1618980, _1618982, _1618984, _1618986, _1618988] : [c_Finite__Set_Ofun__left__comm(_1618980, _1618982, _1618984), hBOOL(hAPP(c_Finite__Set_Ofinite(_1618980), _1618986)), -(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1618980, _1618982, _1618984, _1618988, _1618986), hAPP(hAPP(c_Finite__Set_Ofold(_1618980, _1618982, _1618984), _1618988), _1618986))))], (42489 ^ _782435) ^ [_1619167, _1619169, _1619171, _1619173, _1619175, _1619177] : [c_Finite__Set_Ofun__left__comm(_1619167, _1619169, _1619171), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619167), _1619173)), -(hBOOL(hAPP(hAPP(c_member(_1619167), _1619175), _1619173))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619167, _1619169, _1619171), _1619177), hAPP(hAPP(c_Set_Oinsert(_1619167), _1619175), _1619173)) = hAPP(hAPP(c_Finite__Set_Ofold(_1619167, _1619169, _1619171), hAPP(hAPP(_1619171, _1619175), _1619177)), _1619173))], (42503 ^ _782435) ^ [_1619419, _1619421, _1619423, _1619425, _1619427, _1619429] : [c_Finite__Set_Ofun__left__comm(_1619419, _1619421, _1619423), hBOOL(hAPP(c_Finite__Set_Ofinite(_1619419), _1619425)), -(hBOOL(hAPP(hAPP(c_member(_1619419), _1619427), _1619425))), -(hAPP(hAPP(c_Finite__Set_Ofold(_1619419, _1619421, _1619423), _1619429), hAPP(hAPP(c_Set_Oinsert(_1619419), _1619427), _1619425)) = hAPP(hAPP(_1619423, _1619427), hAPP(hAPP(c_Finite__Set_Ofold(_1619419, _1619421, _1619423), _1619429), _1619425)))], (42517 ^ _782435) ^ [_1619671, _1619673, _1619675, _1619677, _1619679, _1619681, _1619683] : [c_Finite__Set_Ofun__left__comm(_1619671, _1619673, _1619675), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619671, _1619673, _1619675, _1619677, _1619679), _1619681)), hBOOL(hAPP(hAPP(c_member(_1619671), _1619683), _1619679)), 42529 ^ _782435 : [(42530 ^ _782435) ^ [] : [-(_1619681 = hAPP(hAPP(_1619675, _1619683), 42528 ^ [_1619671, _1619673, _1619675, _1619677, _1619679, _1619681, _1619683]))], (42532 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1619671, _1619673, _1619675, _1619677, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1619671, tc_HOL_Obool)), _1619679), hAPP(hAPP(c_Set_Oinsert(_1619671), _1619683), c_Orderings_Obot__class_Obot(tc_fun(_1619671, tc_HOL_Obool))))), 42528 ^ [_1619671, _1619673, _1619675, _1619677, _1619679, _1619681, _1619683])))]]], (42534 ^ _782435) ^ [_1620055, _1620057, _1620059, _1620061, _1620063, _1620065, _1620067] : [c_Finite__Set_Ofun__left__comm(_1620055, _1620057, _1620059), hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1620055, _1620057, _1620059, _1620061, hAPP(hAPP(c_Set_Oinsert(_1620055), _1620063), _1620065)), _1620067)), -(hBOOL(hAPP(hAPP(c_member(_1620055), _1620063), _1620065))), 42546 ^ _782435 : [(42547 ^ _782435) ^ [] : [-(_1620067 = hAPP(hAPP(_1620059, _1620063), 42545 ^ [_1620055, _1620057, _1620059, _1620061, _1620063, _1620065, _1620067]))], (42549 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofold__graph(_1620055, _1620057, _1620059, _1620061, _1620065), 42545 ^ [_1620055, _1620057, _1620059, _1620061, _1620063, _1620065, _1620067])))]]], (42551 ^ _782435) ^ [_1620381, _1620383, _1620385, _1620387] : [class_Orderings_Olinorder(_1620381), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620381), _1620383)), 42561 ^ _782435 : [(42562 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620381), 42560 ^ [_1620381, _1620383, _1620385, _1620387]), _1620383)))], (42564 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620381), 42560 ^ [_1620381, _1620383, _1620385, _1620387]), _1620385))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620381), hAPP(hAPP(c_Finite__Set_Ofold(_1620381, _1620381, c_Orderings_Oord__class_Omax(_1620381)), _1620387), _1620383)), hAPP(hAPP(c_Orderings_Oord__class_Omax(_1620381), _1620385), _1620387))))], (42568 ^ _782435) ^ [_1620745, _1620747, _1620749, _1620751] : [class_Orderings_Olinorder(_1620745), hBOOL(hAPP(c_Finite__Set_Ofinite(_1620745), _1620747)), 42578 ^ _782435 : [(42579 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1620745), 42577 ^ [_1620745, _1620747, _1620749, _1620751]), _1620747)))], (42581 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620745), _1620749), 42577 ^ [_1620745, _1620747, _1620749, _1620751]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1620745), hAPP(hAPP(c_Orderings_Oord__class_Omin(_1620745), _1620749), _1620751)), hAPP(hAPP(c_Finite__Set_Ofold(_1620745, _1620745, c_Orderings_Oord__class_Omin(_1620745)), _1620751), _1620747))))], (42585 ^ _782435) ^ [_1621109, _1621111, _1621113, _1621115] : [class_Lattices_Osemilattice__inf(_1621109), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621109), _1621111)), 42595 ^ _782435 : [(42596 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621109), 42594 ^ [_1621109, _1621111, _1621113, _1621115]), _1621111)))], (42598 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621109), _1621113), 42594 ^ [_1621109, _1621111, _1621113, _1621115]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621109), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(_1621109), _1621113), _1621115)), hAPP(hAPP(c_Finite__Set_Ofold(_1621109, _1621109, c_Lattices_Osemilattice__inf__class_Oinf(_1621109)), _1621115), _1621111))))], (42602 ^ _782435) ^ [_1621473, _1621475, _1621477, _1621479] : [class_Lattices_Osemilattice__sup(_1621473), hBOOL(hAPP(c_Finite__Set_Ofinite(_1621473), _1621475)), 42612 ^ _782435 : [(42613 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621473), 42611 ^ [_1621473, _1621475, _1621477, _1621479]), _1621475)))], (42615 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621473), 42611 ^ [_1621473, _1621475, _1621477, _1621479]), _1621477))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1621473), hAPP(hAPP(c_Finite__Set_Ofold(_1621473, _1621473, c_Lattices_Osemilattice__sup__class_Osup(_1621473)), _1621479), _1621475)), hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(_1621473), _1621477), _1621479))))], (42619 ^ _782435) ^ [_1621837, _1621839, _1621841] : [class_Divides_Osemiring__div(_1621837), -(_1621839 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1621837), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1621837), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1621837), _1621839), _1621841)), _1621841)), c_Divides_Odiv__class_Omod(_1621837, _1621839, _1621841)))], (42642 ^ _782435) ^ [_1622504, _1622506] : [-(c_Wellfounded_Owf(_1622504, _1622506)), 42645 ^ _782435 : [(42646 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622504), 42644 ^ [_1622504, _1622506]), 42643 ^ [_1622504, _1622506])))], (42648 ^ _782435) ^ [_1622724] : [hBOOL(hAPP(hAPP(c_member(_1622504), _1622724), 42643 ^ [_1622504, _1622506])), 42652 ^ _782435 : [(42653 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1622504, _1622504)), hAPP(hAPP(c_Product__Type_OPair(_1622504, _1622504), 42651 ^ [_1622504, _1622506, _1622724]), _1622724)), _1622506)))], (42655 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1622504), 42651 ^ [_1622504, _1622506, _1622724]), 42643 ^ [_1622504, _1622506])))]]]]], (42625 ^ _782435) ^ [_1621985, _1621987] : [c_Wellfounded_Owf(_1621985, _1621987), 42628 ^ _782435 : [(42629 ^ _782435) ^ [_1622117] : [42630 ^ _782435 : [(42631 ^ _782435) ^ [_1622222] : [hBOOL(hAPP(hAPP(c_member(_1621985), _1622222), _1622117))]], 42633 ^ _782435 : [(42634 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1621985), 42632 ^ [_1621985, _1621987, _1622117]), _1622117)))], (42636 ^ _782435) ^ [_1622344] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1621985, _1621985)), hAPP(hAPP(c_Product__Type_OPair(_1621985, _1621985), _1622344), 42632 ^ [_1621985, _1621987, _1622117])), _1621987)), hBOOL(hAPP(hAPP(c_member(_1621985), _1622344), _1622117))]]]]], (42659 ^ _782435) ^ [_1622980, _1622982, _1622984, _1622986, _1622988, _1622990, _1622992, _1622994] : [c_Finite__Set_Ofolding__image__simple__idem(_1622980, _1622982, _1622984, _1622986, _1622988, _1622990), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622982), _1622992)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1622982), _1622994)), -(hAPP(_1622990, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1622982, tc_HOL_Obool)), _1622992), _1622994)) = hAPP(hAPP(_1622984, hAPP(_1622990, _1622992)), hAPP(_1622990, _1622994)))], (42673 ^ _782435) ^ [_1623273, _1623275] : [-(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)))), _1623273)) = 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)))), _1623275))), 42675 ^ _782435 : [(42676 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), 42674 ^ [_1623273, _1623275])))], (42678 ^ _782435) ^ [] : [42679 ^ _782435 : [(42680 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1623273, 42674 ^ [_1623273, _1623275])))], (42682 ^ _782435) ^ [] : [hBOOL(hAPP(_1623275, 42674 ^ [_1623273, _1623275]))]], 42683 ^ _782435 : [(42684 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1623275, 42674 ^ [_1623273, _1623275])))], (42686 ^ _782435) ^ [] : [hBOOL(hAPP(_1623273, 42674 ^ [_1623273, _1623275]))]]]]], (42690 ^ _782435) ^ [_1623594, _1623596, _1623598, _1623600, _1623602, _1623604, _1623606] : [c_Finite__Set_Ofolding__image__simple__idem(_1623594, _1623596, _1623598, _1623600, _1623602, _1623604), -(hAPP(hAPP(_1623598, _1623606), _1623606) = _1623606)], (42696 ^ _782435) ^ [_1623701, _1623703, _1623705, _1623707, _1623709, _1623711, _1623713, _1623715] : [c_Finite__Set_Ofolding__image__simple__idem(_1623701, _1623703, _1623705, _1623707, _1623709, _1623711), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623703), _1623713)), hBOOL(hAPP(hAPP(c_member(_1623703), _1623715), _1623713)), -(hAPP(hAPP(_1623705, hAPP(_1623709, _1623715)), hAPP(_1623711, _1623713)) = hAPP(_1623711, _1623713))], (42710 ^ _782435) ^ [_1623978, _1623980, _1623982, _1623984, _1623986, _1623988, _1623990, _1623992] : [c_Finite__Set_Ofolding__image__simple__idem(_1623978, _1623980, _1623982, _1623984, _1623986, _1623988), hBOOL(hAPP(c_Finite__Set_Ofinite(_1623980), _1623990)), -(hAPP(_1623988, hAPP(hAPP(c_Set_Oinsert(_1623980), _1623992), _1623990)) = hAPP(hAPP(_1623982, hAPP(_1623986, _1623992)), hAPP(_1623988, _1623990)))], (42720 ^ _782435) ^ [_1624193, _1624195, _1624197, _1624199, _1624201, _1624203, _1624205, _1624207] : [c_Finite__Set_Ofolding__image__simple__idem(_1624193, _1624195, _1624197, _1624199, _1624201, _1624203), hBOOL(hAPP(c_Finite__Set_Ofinite(_1624195), _1624205)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624195, tc_HOL_Obool)), _1624207), _1624205)), -(hAPP(hAPP(_1624197, hAPP(_1624203, _1624207)), hAPP(_1624203, _1624205)) = hAPP(_1624203, _1624205))], (42734 ^ _782435) ^ [_1624476, _1624478, _1624480, _1624482, _1624484] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624476, tc_HOL_Obool)), _1624478), _1624480)), 42740 ^ _782435 : [(42741 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1624476), 42739 ^ [_1624476, _1624478, _1624480, _1624482, _1624484]), _1624478)))], (42743 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1624482, 42739 ^ [_1624476, _1624478, _1624480, _1624482, _1624484])))], (42745 ^ _782435) ^ [] : [hBOOL(hAPP(_1624484, 42739 ^ [_1624476, _1624478, _1624480, _1624482, _1624484]))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1624476, tc_HOL_Obool)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624476, tc_HOL_Obool)), _1624478), hAPP(c_Set_OCollect(_1624476), _1624482))), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1624476, tc_HOL_Obool)), _1624480), hAPP(c_Set_OCollect(_1624476), _1624484)))))], (42749 ^ _782435) ^ [_1624876, _1624878, _1624880, _1624882] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1624876, _1624878)), _1624880), hAPP(c_Relation_Oconverse(_1624878, _1624876), _1624882))), 42754 ^ _782435 : [(42755 ^ _782435) ^ [] : [-(_1624880 = hAPP(hAPP(c_Product__Type_OPair(_1624876, _1624878), 42753 ^ [_1624876, _1624878, _1624880, _1624882]), 42752 ^ [_1624876, _1624878, _1624880, _1624882]))], (42757 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1624878, _1624876)), hAPP(hAPP(c_Product__Type_OPair(_1624878, _1624876), 42752 ^ [_1624876, _1624878, _1624880, _1624882]), 42753 ^ [_1624876, _1624878, _1624880, _1624882])), _1624882)))]]], (42759 ^ _782435) ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1625129, _1625131)), _1625133), hAPP(hAPP(c_Relation_Orel__comp(_1625129, _1625135, _1625131), _1625137), _1625139))), 42765 ^ _782435 : [(42766 ^ _782435) ^ [] : [-(_1625133 = hAPP(hAPP(c_Product__Type_OPair(_1625129, _1625131), 42762 ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139]), 42764 ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139]))], (42768 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625129, _1625135)), hAPP(hAPP(c_Product__Type_OPair(_1625129, _1625135), 42762 ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139]), 42763 ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139])), _1625137)))], (42770 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1625135, _1625131)), hAPP(hAPP(c_Product__Type_OPair(_1625135, _1625131), 42763 ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139]), 42764 ^ [_1625129, _1625131, _1625133, _1625135, _1625137, _1625139])), _1625139)))]]], (42772 ^ _782435) ^ [_1625507, _1625509, _1625511] : [-(c_Nitpick_Oplus__frac(_1625507, _1625509, _1625511) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint, _1625507), c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(_1625507), _1625509), hAPP(c_Nitpick_Odenom(_1625507), _1625511))), hAPP(hAPP(c_COMBS(tc_Int_Oint, tc_Int_Oint, _1625507), hAPP(hAPP(c_COMBB(tc_Int_Oint, tc_fun(tc_Int_Oint, _1625507), tc_Int_Oint), c_Nitpick_Ofrac(_1625507)), 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(_1625507), _1625509))), 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(_1625507), _1625509))))), 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(_1625507), _1625511))), 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(_1625507), _1625511)))))), c_COMBI(tc_Int_Oint))))], (42774 ^ _782435) ^ [_1625638, _1625640, _1625642] : [-(c_Nitpick_Otimes__frac(_1625638, _1625640, _1625642) = hAPP(hAPP(c_Nitpick_Ofrac(_1625638), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1625638), _1625640)), hAPP(c_Nitpick_Onum(_1625638), _1625642))), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint), hAPP(c_Nitpick_Odenom(_1625638), _1625640)), hAPP(c_Nitpick_Odenom(_1625638), _1625642))))], (42776 ^ _782435) ^ [_1625709, _1625711, _1625713] : [-(c_Nitpick_Oof__frac(_1625711, _1625709, _1625713) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(_1625709), hAPP(c_Int_Oring__1__class_Oof__int(_1625709), hAPP(c_Nitpick_Onum(_1625711), _1625713))), hAPP(c_Int_Oring__1__class_Oof__int(_1625709), hAPP(c_Nitpick_Odenom(_1625711), _1625713)))), class_Rings_Oinverse(_1625709), class_Rings_Oring__1(_1625709)], (42786 ^ _782435) ^ [_1625902, _1625904] : [-(c_Nitpick_Oinverse__frac(_1625902, _1625904) = hAPP(hAPP(c_Nitpick_Ofrac(_1625902), hAPP(c_Nitpick_Odenom(_1625902), _1625904)), hAPP(c_Nitpick_Onum(_1625902), _1625904)))], (42788 ^ _782435) ^ [_1625948, _1625950] : [-(c_Nitpick_Ouminus__frac(_1625948, _1625950) = c_Nitpick_OAbs__Frac(_1625948, 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(_1625948), _1625950))), hAPP(c_Nitpick_Odenom(_1625948), _1625950))))], (42790 ^ _782435) ^ [_1626016, _1626018, _1626020] : [c_Nitpick_Oless__frac(_1626016, _1626018, _1626020), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626016), c_Nitpick_Oplus__frac(_1626016, _1626018, c_Nitpick_Ouminus__frac(_1626016, _1626020)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42796 ^ _782435) ^ [_1626127, _1626129, _1626131] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626127), c_Nitpick_Oplus__frac(_1626127, _1626129, c_Nitpick_Ouminus__frac(_1626127, _1626131)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__frac(_1626127, _1626129, _1626131))], (42802 ^ _782435) ^ [_1626262, _1626264, _1626266] : [c_Nitpick_Oless__eq__frac(_1626262, _1626264, _1626266), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626262), c_Nitpick_Oplus__frac(_1626262, _1626264, c_Nitpick_Ouminus__frac(_1626262, _1626266)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))))], (42808 ^ _782435) ^ [_1626373, _1626375, _1626377] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Nitpick_Onum(_1626373), c_Nitpick_Oplus__frac(_1626373, _1626375, c_Nitpick_Ouminus__frac(_1626373, _1626377)))), c_Groups_Ozero__class_Ozero(tc_Int_Oint))), -(c_Nitpick_Oless__eq__frac(_1626373, _1626375, _1626377))], (42814 ^ _782435) ^ [_1626490] : [-(c_Nitpick_Onum(_1626490) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1626490, c_Product__Type_Ofst(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1626490)))], (42816 ^ _782435) ^ [_1626525] : [-(c_Nitpick_Odenom(_1626525) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint, tc_Int_Oint), tc_Int_Oint, _1626525, c_Product__Type_Osnd(tc_Int_Oint, tc_Int_Oint)), c_Nitpick_ORep__Frac(_1626525)))], (42818 ^ _782435) ^ [_1626560, _1626562, _1626564, _1626566] : [class_Rings_Olinordered__semidom(_1626560), 42824 ^ _782435 : [(42825 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626562), 42823 ^ [_1626560, _1626562, _1626564, _1626566]), _1626564)))], (42827 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1626560), c_Groups_Ozero__class_Ozero(_1626560)), hAPP(_1626566, 42823 ^ [_1626560, _1626562, _1626564, _1626566])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1626560), c_Groups_Ozero__class_Ozero(_1626560)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1626562, _1626560), _1626566), _1626564))))], (42831 ^ _782435) ^ [_1626856, _1626858, _1626860] : [-(c_Product__Type_Ointernal__split(_1626856, _1626858, _1626860) = c_Product__Type_Oprod_Oprod__case(_1626856, _1626858, _1626860))], (42833 ^ _782435) ^ [_1626891, _1626893, _1626895, _1626897, _1626899, _1626901] : [-(hAPP(hAPP(c_Product__Type_Ointernal__split(_1626891, _1626893, _1626895), _1626897), hAPP(hAPP(c_Product__Type_OPair(_1626891, _1626893), _1626899), _1626901)) = hAPP(hAPP(_1626897, _1626899), _1626901))], (42835 ^ _782435) ^ [_1626949, _1626951, _1626953, _1626955] : [class_Rings_Olinordered__semidom(_1626949), 42841 ^ _782435 : [(42842 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1626951), 42840 ^ [_1626949, _1626951, _1626953, _1626955]), _1626953)))], (42844 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626949), c_Groups_Ozero__class_Ozero(_1626949)), hAPP(_1626955, 42840 ^ [_1626949, _1626951, _1626953, _1626955])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1626949), c_Groups_Ozero__class_Ozero(_1626949)), hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(_1626951, _1626949), _1626955), _1626953))))], (42848 ^ _782435) ^ [] : [-(c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42850 ^ _782435) ^ [] : [-(c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (42852 ^ _782435) ^ [_1627281, _1627283] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 42853 ^ [_1627281, _1627283]), hAPP(_1627281, 42853 ^ [_1627281, _1627283]))), -(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)), _1627281)), _1627283)))))], (42859 ^ _782435) ^ [_1627441, _1627443] : [-(c_List_Olenlex(_1627441, _1627443) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat, tc_List_Olist(_1627441)), tc_List_Olist(_1627441)), c_Wellfounded_Olex__prod(tc_Nat_Onat, tc_List_Olist(_1627441), c_Wellfounded_Oless__than, c_List_Olex(_1627441, _1627443))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627441), tc_List_Olist(_1627441), tc_prod(tc_Nat_Onat, tc_List_Olist(_1627441))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_List_Olist(_1627441), tc_prod(tc_Nat_Onat, tc_List_Olist(_1627441))), tc_List_Olist(_1627441)), c_Product__Type_OPair(tc_Nat_Onat, tc_List_Olist(_1627441))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627441)))), c_COMBI(tc_List_Olist(_1627441)))))], (42861 ^ _782435) ^ [_1627549, _1627551, _1627553, _1627555, _1627557] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1627549), tc_List_Olist(_1627549))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1627549), tc_List_Olist(_1627549)), _1627551), _1627553)), hAPP(c_List_Olexn(_1627549, _1627555), _1627557))), 42864 ^ _782435 : [(42865 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627549)), _1627551) = _1627557)], (42867 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627549)), _1627553) = _1627557)]]], (42869 ^ _782435) ^ [_1627751, _1627753, _1627755] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627751)), _1627753) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1627751)), _1627755)), _1627753 = _1627755], (42875 ^ _782435) ^ [_1627843, _1627845] : [-(c_List_Olenlex(_1627843, _1627845) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1627843), tc_List_Olist(_1627843), tc_HOL_Obool), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627843), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627843), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), tc_List_Olist(_1627843)), c_COMBS(tc_List_Olist(_1627843), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1627843)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627843)), c_fdisj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627843), tc_fun(tc_List_Olist(_1627843), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1627843), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), tc_List_Olist(_1627843)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1627843))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1627843)), c_Orderings_Oord__class_Oless(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1627843))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627843)))))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1627843), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627843), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), tc_List_Olist(_1627843)), c_COMBS(tc_List_Olist(_1627843), tc_HOL_Obool, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_List_Olist(_1627843)), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1627843)), c_fconj)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627843), tc_fun(tc_List_Olist(_1627843), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1627843), tc_Nat_Onat), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), tc_List_Olist(_1627843)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1627843))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1627843)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1627843))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1627843)))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1627843), tc_fun(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627843), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_HOL_Obool), tc_fun(tc_List_Olist(_1627843), tc_HOL_Obool)), tc_List_Olist(_1627843)), c_COMBC(tc_List_Olist(_1627843), tc_fun(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1627843), tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843))), tc_fun(tc_List_Olist(_1627843), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_HOL_Obool), tc_HOL_Obool)), tc_List_Olist(_1627843)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_fun(tc_fun(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843)), tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1627843)), c_member(tc_prod(tc_List_Olist(_1627843), tc_List_Olist(_1627843))))), c_Product__Type_OPair(tc_List_Olist(_1627843), tc_List_Olist(_1627843))))), c_List_Olex(_1627843, _1627845)))))))], (42877 ^ _782435) ^ [_1628399, _1628401] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1628399))), c_Enum_Osublists(_1628399, _1628401)) = 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(_1628399)), _1628401)))], (42879 ^ _782435) ^ [_1628446, _1628448, _1628450] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628446)), c_List_Osublist(_1628446, _1628448, _1628450)) = 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(_1628446)), _1628448)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1628450)))))], (42881 ^ _782435) ^ [_1628512, _1628514, _1628516] : [-(hAPP(c_List_Olexn(_1628512, _1628514), hAPP(c_Nat_OSuc, _1628516)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(_1628512), tc_List_Olist(_1628512)), tc_HOL_Obool)), hAPP(c_Set_Oimage(tc_prod(tc_prod(_1628512, tc_List_Olist(_1628512)), tc_prod(_1628512, tc_List_Olist(_1628512))), tc_prod(tc_List_Olist(_1628512), tc_List_Olist(_1628512)), c_Product__Type_Omap__pair(tc_prod(_1628512, tc_List_Olist(_1628512)), tc_List_Olist(_1628512), tc_prod(_1628512, tc_List_Olist(_1628512)), tc_List_Olist(_1628512), hAPP(c_Product__Type_Oprod_Oprod__case(_1628512, tc_List_Olist(_1628512), tc_List_Olist(_1628512)), c_List_Olist_OCons(_1628512)), hAPP(c_Product__Type_Oprod_Oprod__case(_1628512, tc_List_Olist(_1628512), tc_List_Olist(_1628512)), c_List_Olist_OCons(_1628512)))), c_Wellfounded_Olex__prod(_1628512, tc_List_Olist(_1628512), _1628514, hAPP(c_List_Olexn(_1628512, _1628514), _1628516)))), hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(_1628512), tc_List_Olist(_1628512))), hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1628512), tc_List_Olist(_1628512), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628512), tc_fun(tc_List_Olist(_1628512), tc_HOL_Obool), tc_fun(tc_List_Olist(_1628512), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1628512), tc_HOL_Obool), tc_fun(tc_List_Olist(_1628512), tc_HOL_Obool)), tc_List_Olist(_1628512)), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1628512))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1628512)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628512), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1628512)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1628512)))), hAPP(c_Nat_OSuc, _1628516))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1628512), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1628512)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1628512)))), hAPP(c_Nat_OSuc, _1628516)))))))], (42883 ^ _782435) ^ [_1628824, _1628826, _1628828, _1628830] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628824), tc_List_Olist(_1628824))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628824), tc_List_Olist(_1628824)), _1628826), _1628828)), c_List_Olex(_1628824, _1628830))), 42886 ^ _782435 : [(42887 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1628824), tc_List_Olist(_1628824))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1628824), tc_List_Olist(_1628824)), _1628826), _1628828)), c_List_Olexord(_1628824, _1628830))))], (42889 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628824)), _1628826) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1628824)), _1628828))]]], (42891 ^ _782435) ^ [_1629075, _1629077, _1629079, _1629081] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629075), tc_List_Olist(_1629075))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629075), tc_List_Olist(_1629075)), _1629077), _1629079)), c_List_Olex(_1629075, _1629081)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629075), tc_List_Olist(_1629075))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629075), tc_List_Olist(_1629075)), _1629077), _1629079)), c_List_Olexord(_1629075, _1629081))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629075)), _1629077) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1629075)), _1629079)], (42901 ^ _782435) ^ [_1629389, _1629391, _1629393, _1629395, _1629397, _1629399] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629389), tc_List_Olist(_1629389))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629389), tc_List_Olist(_1629389)), hAPP(hAPP(c_List_Olist_OCons(_1629389), _1629391), _1629393)), hAPP(hAPP(c_List_Olist_OCons(_1629389), _1629395), _1629397))), c_List_Olexord(_1629389, _1629399))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1629389, _1629389)), hAPP(hAPP(c_Product__Type_OPair(_1629389, _1629389), _1629391), _1629395)), _1629399))), 42908 ^ _782435 : [(42909 ^ _782435) ^ [] : [-(_1629391 = _1629395)], (42911 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629389), tc_List_Olist(_1629389))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629389), tc_List_Olist(_1629389)), _1629393), _1629397)), c_List_Olexord(_1629389, _1629399))))]]], (42913 ^ _782435) ^ [_1629716, _1629718, _1629720, _1629722, _1629724, _1629726] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629716), tc_List_Olist(_1629716))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629716), tc_List_Olist(_1629716)), hAPP(hAPP(c_List_Olist_OCons(_1629716), _1629718), _1629720)), hAPP(hAPP(c_List_Olist_OCons(_1629716), _1629722), _1629724))), c_List_Olexord(_1629716, _1629726)))), 42914 ^ _782435 : [(42915 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1629716, _1629716)), hAPP(hAPP(c_Product__Type_OPair(_1629716, _1629716), _1629718), _1629722)), _1629726))], (42917 ^ _782435) ^ [] : [_1629718 = _1629722, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1629716), tc_List_Olist(_1629716))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1629716), tc_List_Olist(_1629716)), _1629720), _1629724)), c_List_Olexord(_1629716, _1629726)))]]], (42925 ^ _782435) ^ [_1630089, _1630091, _1630093, _1630095] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630089)), _1630091)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630089)), _1630093))), _1630091 = hAPP(hAPP(c_List_Olist_OCons(_1630089), _1630095), _1630093)], (42931 ^ _782435) ^ [_1630249, _1630251, _1630253, _1630255, _1630257] : [hAPP(hAPP(c_List_Olist_OCons(_1630249), _1630251), _1630253) = hAPP(hAPP(c_List_Olist_OCons(_1630249), _1630255), _1630257), 42934 ^ _782435 : [(42935 ^ _782435) ^ [] : [-(_1630251 = _1630255)], (42937 ^ _782435) ^ [] : [-(_1630253 = _1630257)]]], (42939 ^ _782435) ^ [_1630386, _1630388, _1630390, _1630392, _1630394] : [-(hAPP(hAPP(c_List_Olist_OCons(_1630386), _1630388), _1630390) = hAPP(hAPP(c_List_Olist_OCons(_1630386), _1630392), _1630394)), _1630388 = _1630392, _1630390 = _1630394], (42949 ^ _782435) ^ [_1630576, _1630578, _1630580] : [hAPP(hAPP(c_List_Olist_OCons(_1630576), _1630578), _1630580) = _1630580], (42951 ^ _782435) ^ [_1630626, _1630628, _1630630] : [_1630626 = hAPP(hAPP(c_List_Olist_OCons(_1630628), _1630630), _1630626)], (42953 ^ _782435) ^ [_1630661, _1630663, _1630665] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630661)), hAPP(hAPP(c_List_Olist_OCons(_1630661), _1630663), _1630665)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630661)), _1630665)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (42955 ^ _782435) ^ [_1630743, _1630745, _1630747, _1630749, _1630751, _1630753] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630743), tc_List_Olist(_1630743))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630743), tc_List_Olist(_1630743)), hAPP(hAPP(c_List_Olist_OCons(_1630743), _1630745), _1630747)), hAPP(hAPP(c_List_Olist_OCons(_1630743), _1630749), _1630751))), c_List_Olex(_1630743, _1630753))), 42960 ^ _782435 : [(42961 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1630743, _1630743)), hAPP(hAPP(c_Product__Type_OPair(_1630743, _1630743), _1630745), _1630749)), _1630753)))], (42963 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630743)), _1630747) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1630743)), _1630751))]], 42964 ^ _782435 : [(42965 ^ _782435) ^ [] : [-(_1630745 = _1630749)], (42967 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1630743), tc_List_Olist(_1630743))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1630743), tc_List_Olist(_1630743)), _1630747), _1630751)), c_List_Olex(_1630743, _1630753))))]]], (42969 ^ _782435) ^ [_1631141, _1631143, _1631145, _1631147, _1631149, _1631151] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631141), tc_List_Olist(_1631141))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631141), tc_List_Olist(_1631141)), hAPP(hAPP(c_List_Olist_OCons(_1631141), _1631143), _1631145)), hAPP(hAPP(c_List_Olist_OCons(_1631141), _1631147), _1631149))), c_List_Olex(_1631141, _1631151)))), 42970 ^ _782435 : [(42971 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1631141, _1631141)), hAPP(hAPP(c_Product__Type_OPair(_1631141, _1631141), _1631143), _1631147)), _1631151)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631141)), _1631145) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1631141)), _1631149)], (42977 ^ _782435) ^ [] : [_1631143 = _1631147, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1631141), tc_List_Olist(_1631141))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1631141), tc_List_Olist(_1631141)), _1631145), _1631149)), c_List_Olex(_1631141, _1631151)))]]], (42985 ^ _782435) ^ [_1631597, _1631599, _1631601] : [-(c_List_Oset__Cons(_1631597, _1631599, _1631601) = hAPP(c_Set_OCollect(tc_List_Olist(_1631597)), hAPP(hAPP(c_COMBB(tc_fun(_1631597, tc_HOL_Obool), tc_HOL_Obool, tc_List_Olist(_1631597)), c_HOL_OEx(_1631597)), hAPP(hAPP(c_COMBB(tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), tc_fun(_1631597, tc_HOL_Obool), tc_List_Olist(_1631597)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_HOL_Obool, _1631597), c_HOL_OEx(tc_List_Olist(_1631597)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631597), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631597, tc_fun(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), tc_fun(tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), tc_List_Olist(_1631597)), c_COMBS(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_fun(_1631597, tc_fun(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), tc_List_Olist(_1631597)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631597), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), tc_fun(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), _1631597), c_COMBS(tc_List_Olist(_1631597), tc_HOL_Obool, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_fun(tc_HOL_Obool, tc_HOL_Obool))), tc_List_Olist(_1631597)), hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_fun(tc_HOL_Obool, tc_HOL_Obool)), _1631597), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1631597)), c_fconj))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631597), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_List_Olist(_1631597))), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(_1631597), tc_List_Olist(_1631597)), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), tc_fun(tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_List_Olist(_1631597))), tc_fun(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool))), tc_List_Olist(_1631597)), c_COMBB(tc_fun(tc_List_Olist(_1631597), tc_List_Olist(_1631597)), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), _1631597)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631597), tc_List_Olist(_1631597)), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), tc_List_Olist(_1631597)), c_COMBB(tc_List_Olist(_1631597), tc_HOL_Obool, tc_List_Olist(_1631597))), c_fequal))), c_List_Olist_OCons(_1631597)))))), hAPP(hAPP(c_COMBC(_1631597, tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool)), _1631597), c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1631597))), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1631597), c_fconj), hAPP(hAPP(c_COMBC(_1631597, tc_fun(_1631597, tc_HOL_Obool), tc_HOL_Obool), c_member(_1631597)), _1631599)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1631597), tc_fun(tc_List_Olist(_1631597), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1631597))), _1631601)))))))], (42987 ^ _782435) ^ [_1632147, _1632149, _1632151, _1632153] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1632147), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632149), _1632151))), -(hAPP(c_Random_Opick(_1632149, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632149)), _1632151), _1632153)), _1632147) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1632149), _1632151))], (42993 ^ _782435) ^ [_1632290, _1632292, _1632294, _1632296] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1632290), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632292), _1632294)))), -(hAPP(c_Random_Opick(_1632292, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632292)), _1632294), _1632296)), _1632290) = hAPP(c_Random_Opick(_1632292, _1632296), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1632290), hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1632292), _1632294))))], (42999 ^ _782435) ^ [_1632378, _1632380, _1632382] : [-(c_Random_Oselect__weight(_1632378, hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral, _1632378)), hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1632378), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), _1632380)), _1632382)) = c_Random_Oselect__weight(_1632378, _1632382))], (43001 ^ _782435) ^ [_1632431, _1632433, _1632435, _1632437, _1632439, _1632441] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1632431, _1632431)), hAPP(hAPP(c_Product__Type_OPair(_1632431, _1632431), _1632433), _1632435)), c_Transitive__Closure_Ortrancl(_1632431, _1632437))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632431), tc_List_Olist(_1632431))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632431), tc_List_Olist(_1632431)), _1632439), _1632441)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1632431), c_List_Olistrel1(_1632431, _1632437)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1632431), tc_List_Olist(_1632431))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1632431), tc_List_Olist(_1632431)), hAPP(hAPP(c_List_Olist_OCons(_1632431), _1632433), _1632439)), hAPP(hAPP(c_List_Olist_OCons(_1632431), _1632435), _1632441))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1632431), c_List_Olistrel1(_1632431, _1632437)))))], (43011 ^ _782435) ^ [_1632792, _1632794, _1632796, _1632798] : [hBOOL(hAPP(hAPP(c_member(_1632792), _1632794), c_Wellfounded_Oacc(_1632792, _1632796))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632792)), _1632798), c_Wellfounded_Oacc(tc_List_Olist(_1632792), c_List_Olistrel1(_1632792, _1632796)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1632792)), hAPP(hAPP(c_List_Olist_OCons(_1632792), _1632794), _1632798)), c_Wellfounded_Oacc(tc_List_Olist(_1632792), c_List_Olistrel1(_1632792, _1632796)))))], (43021 ^ _782435) ^ [_1633033, _1633035] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1633033), tc_List_Olist(_1633033)), tc_HOL_Obool)), c_List_Olistrel1(_1633033, c_Transitive__Closure_Ortrancl(_1633033, _1633035))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633033), c_List_Olistrel1(_1633033, _1633035)))))], (43023 ^ _782435) ^ [_1633089, _1633091] : [-(c_List_Olistrel1(_1633089, hAPP(c_Relation_Oconverse(_1633089, _1633089), _1633091)) = hAPP(c_Relation_Oconverse(tc_List_Olist(_1633089), tc_List_Olist(_1633089)), c_List_Olistrel1(_1633089, _1633091)))], (43025 ^ _782435) ^ [_1633136, _1633138, _1633140] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1633136, _1633136), tc_HOL_Obool)), _1633138), _1633140)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1633136), tc_List_Olist(_1633136)), tc_HOL_Obool)), c_List_Olistrel1(_1633136, _1633138)), c_List_Olistrel1(_1633136, _1633140))))], (43031 ^ _782435) ^ [_1633287, _1633289, _1633291, _1633293, _1633295] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633287), tc_List_Olist(_1633287))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633287), tc_List_Olist(_1633287)), _1633289), _1633291)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633287), c_List_Olistrel1(_1633287, _1633293)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633287), tc_List_Olist(_1633287))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633287), tc_List_Olist(_1633287)), hAPP(hAPP(c_List_Olist_OCons(_1633287), _1633295), _1633289)), hAPP(hAPP(c_List_Olist_OCons(_1633287), _1633295), _1633291))), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633287), c_List_Olistrel1(_1633287, _1633293)))))], (43037 ^ _782435) ^ [_1633542, _1633544, _1633546, _1633548, _1633550] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633542), tc_List_Olist(_1633542))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633542), tc_List_Olist(_1633542)), _1633544), _1633546)), c_List_Olistrel1(_1633542, _1633548))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633542), tc_List_Olist(_1633542))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633542), tc_List_Olist(_1633542)), hAPP(hAPP(c_List_Olist_OCons(_1633542), _1633550), _1633544)), hAPP(hAPP(c_List_Olist_OCons(_1633542), _1633550), _1633546))), c_List_Olistrel1(_1633542, _1633548))))], (43043 ^ _782435) ^ [_1633777, _1633779, _1633781, _1633783] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633777), tc_List_Olist(_1633777))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633777), tc_List_Olist(_1633777)), _1633779), _1633781)), c_List_Olistrel1(_1633777, _1633783))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633777)), _1633779) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633777)), _1633781))], (43049 ^ _782435) ^ [_1633946, _1633948, _1633950, _1633952] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1633946), tc_List_Olist(_1633946))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1633946), tc_List_Olist(_1633946)), _1633948), _1633950)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1633946), c_List_Olistrel1(_1633946, _1633952)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633946)), _1633948) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1633946)), _1633950))], (43055 ^ _782435) ^ [_1634146, _1634148, _1634150, _1634152] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634146), tc_List_Olist(_1634146))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634146), tc_List_Olist(_1634146)), _1634148), _1634150)), c_List_Olistrel1(_1634146, hAPP(c_Relation_Oconverse(_1634146, _1634146), _1634152)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634146), tc_List_Olist(_1634146))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634146), tc_List_Olist(_1634146)), _1634148), _1634150)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1634146), tc_List_Olist(_1634146)), c_List_Olistrel1(_1634146, _1634152)))))], (43061 ^ _782435) ^ [_1634375, _1634377, _1634379, _1634381] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634375), tc_List_Olist(_1634375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634375), tc_List_Olist(_1634375)), _1634377), _1634379)), hAPP(c_Relation_Oconverse(tc_List_Olist(_1634375), tc_List_Olist(_1634375)), c_List_Olistrel1(_1634375, _1634381)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634375), tc_List_Olist(_1634375))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634375), tc_List_Olist(_1634375)), _1634377), _1634379)), c_List_Olistrel1(_1634375, hAPP(c_Relation_Oconverse(_1634375, _1634375), _1634381)))))], (43067 ^ _782435) ^ [_1634610, _1634612, _1634614, _1634616, _1634618] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1634610, _1634610)), hAPP(hAPP(c_Product__Type_OPair(_1634610, _1634610), _1634612), _1634614)), _1634616)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634610), tc_List_Olist(_1634610))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634610), tc_List_Olist(_1634610)), hAPP(hAPP(c_List_Olist_OCons(_1634610), _1634612), _1634618)), hAPP(hAPP(c_List_Olist_OCons(_1634610), _1634614), _1634618))), c_List_Olistrel1(_1634610, _1634616))))], (43073 ^ _782435) ^ [_1634850, _1634852, _1634854, _1634856, _1634858, _1634860] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634850), tc_List_Olist(_1634850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634850), tc_List_Olist(_1634850)), hAPP(hAPP(c_List_Olist_OCons(_1634850), _1634852), _1634854)), hAPP(hAPP(c_List_Olist_OCons(_1634850), _1634856), _1634858))), c_List_Olistrel1(_1634850, _1634860))), 43078 ^ _782435 : [(43079 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1634850, _1634850)), hAPP(hAPP(c_Product__Type_OPair(_1634850, _1634850), _1634852), _1634856)), _1634860)))], (43081 ^ _782435) ^ [] : [-(_1634854 = _1634858)]], 43082 ^ _782435 : [(43083 ^ _782435) ^ [] : [-(_1634852 = _1634856)], (43085 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1634850), tc_List_Olist(_1634850))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1634850), tc_List_Olist(_1634850)), _1634854), _1634858)), c_List_Olistrel1(_1634850, _1634860))))]]], (43087 ^ _782435) ^ [_1635220, _1635222, _1635224, _1635226, _1635228, _1635230] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635220), tc_List_Olist(_1635220))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635220), tc_List_Olist(_1635220)), hAPP(hAPP(c_List_Olist_OCons(_1635220), _1635222), _1635224)), hAPP(hAPP(c_List_Olist_OCons(_1635220), _1635226), _1635228))), c_List_Olistrel1(_1635220, _1635230)))), 43088 ^ _782435 : [(43089 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1635220, _1635220)), hAPP(hAPP(c_Product__Type_OPair(_1635220, _1635220), _1635222), _1635226)), _1635230)), _1635224 = _1635228], (43095 ^ _782435) ^ [] : [_1635222 = _1635226, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635220), tc_List_Olist(_1635220))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635220), tc_List_Olist(_1635220)), _1635224), _1635228)), c_List_Olistrel1(_1635220, _1635230)))]]], (43103 ^ _782435) ^ [_1635648, _1635650, _1635652, _1635654] : [-(c_List_Olist_Olist__size(_1635648, _1635650, hAPP(hAPP(c_List_Olist_OCons(_1635648), _1635652), _1635654)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1635650, _1635652)), c_List_Olist_Olist__size(_1635648, _1635650, _1635654))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (43105 ^ _782435) ^ [_1635708, _1635710, _1635712, _1635714] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1635708), tc_List_Olist(_1635708), c_List_Olistrel(_1635708, _1635710)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1635708)), hAPP(hAPP(c_List_Olist_OCons(_1635708), _1635712), _1635714)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1635708), tc_HOL_Obool)))) = c_List_Oset__Cons(_1635708, hAPP(c_Relation_OImage(_1635708, _1635708, _1635710), hAPP(hAPP(c_Set_Oinsert(_1635708), _1635712), c_Orderings_Obot__class_Obot(tc_fun(_1635708, tc_HOL_Obool)))), hAPP(c_Relation_OImage(tc_List_Olist(_1635708), tc_List_Olist(_1635708), c_List_Olistrel(_1635708, _1635710)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1635708)), _1635714), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1635708), tc_HOL_Obool))))))], (43107 ^ _782435) ^ [_1635831, _1635833, _1635835] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1635831), tc_List_Olist(_1635831))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1635831), tc_List_Olist(_1635831)), _1635833), _1635833)), c_List_Olistrel(_1635831, c_Transitive__Closure_Ortrancl(_1635831, _1635835)))))], (43109 ^ _782435) ^ [_1635891, _1635893, _1635895] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1635891, _1635891), tc_HOL_Obool)), _1635893), _1635895)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1635891), tc_List_Olist(_1635891)), tc_HOL_Obool)), c_List_Olistrel(_1635891, _1635893)), c_List_Olistrel(_1635891, _1635895))))], (43115 ^ _782435) ^ [_1636042, _1636044] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636042), tc_List_Olist(_1636042)), tc_HOL_Obool)), c_List_Olistrel(_1636042, _1636044)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636042), c_List_Olistrel1(_1636042, _1636044)))))], (43117 ^ _782435) ^ [_1636095, _1636097, _1636099, _1636101] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636095), tc_List_Olist(_1636095))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636095), tc_List_Olist(_1636095)), _1636097), _1636099)), c_List_Olistrel(_1636095, _1636101))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636095)), _1636097) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1636095)), _1636099))], (43123 ^ _782435) ^ [_1636264, _1636266, _1636268, _1636270, _1636272] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636264), tc_List_Olist(_1636264))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636264), tc_List_Olist(_1636264)), _1636266), _1636268)), c_List_Olistrel(_1636264, c_Transitive__Closure_Ortrancl(_1636264, _1636270)))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636264), tc_List_Olist(_1636264))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636264), tc_List_Olist(_1636264)), _1636268), _1636272)), c_List_Olistrel(_1636264, c_Transitive__Closure_Ortrancl(_1636264, _1636270)))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636264), tc_List_Olist(_1636264))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636264), tc_List_Olist(_1636264)), _1636266), _1636272)), c_List_Olistrel(_1636264, c_Transitive__Closure_Ortrancl(_1636264, _1636270)))))], (43133 ^ _782435) ^ [_1636603, _1636605] : [-(c_List_Olistrel(_1636603, c_Transitive__Closure_Ortrancl(_1636603, _1636605)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(_1636603), c_List_Olistrel1(_1636603, _1636605)))], (43135 ^ _782435) ^ [_1636642, _1636644, _1636646, _1636648] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636642), tc_List_Olist(_1636642))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636642), tc_List_Olist(_1636642)), _1636644), _1636646)), c_List_Olistrel1(_1636642, _1636648))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1636642), tc_List_Olist(_1636642))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1636642), tc_List_Olist(_1636642)), _1636644), _1636646)), c_List_Olistrel(_1636642, c_Transitive__Closure_Ortrancl(_1636642, _1636648)))))], (43141 ^ _782435) ^ [_1636849, _1636851, _1636853] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1636849, _1636849), tc_HOL_Obool)), _1636851), _1636853)), c_Relation_Orefl__on(_1636849, c_Orderings_Otop__class_Otop(tc_fun(_1636849, tc_HOL_Obool)), _1636853), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1636849), tc_List_Olist(_1636849)), tc_HOL_Obool)), c_List_Olistrel1(_1636849, _1636851)), c_List_Olistrel(_1636849, _1636853))))], (43151 ^ _782435) ^ [_1637066, _1637068, _1637070, _1637072] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637066), tc_List_Olist(_1637066))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637066), tc_List_Olist(_1637066)), _1637068), _1637070)), c_List_Olistrel(_1637066, _1637072))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637066), tc_List_Olist(_1637066))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637066), tc_List_Olist(_1637066)), _1637068), _1637070)), c_Transitive__Closure_Ortrancl(tc_List_Olist(_1637066), c_List_Olistrel1(_1637066, _1637072)))))], (43157 ^ _782435) ^ [_1637277, _1637279, _1637281, _1637283, _1637285, _1637287] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1637277, _1637277)), hAPP(hAPP(c_Product__Type_OPair(_1637277, _1637277), _1637279), _1637281)), _1637283)), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637277), tc_List_Olist(_1637277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637277), tc_List_Olist(_1637277)), _1637285), _1637287)), c_List_Olistrel(_1637277, _1637283))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637277), tc_List_Olist(_1637277))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637277), tc_List_Olist(_1637277)), hAPP(hAPP(c_List_Olist_OCons(_1637277), _1637279), _1637285)), hAPP(hAPP(c_List_Olist_OCons(_1637277), _1637281), _1637287))), c_List_Olistrel(_1637277, _1637283))))], (43167 ^ _782435) ^ [_1637633, _1637635, _1637637, _1637639] : [c_List_Olistrelp(_1637633, hAPP(hAPP(c_COMBC(_1637633, tc_fun(tc_prod(_1637633, _1637633), tc_HOL_Obool), tc_fun(_1637633, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637633, tc_fun(tc_fun(tc_prod(_1637633, _1637633), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1637633, _1637633), tc_HOL_Obool), tc_fun(_1637633, tc_HOL_Obool)), _1637633), c_COMBC(_1637633, tc_fun(tc_prod(_1637633, _1637633), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1637633, tc_prod(_1637633, _1637633)), tc_fun(_1637633, tc_fun(tc_fun(tc_prod(_1637633, _1637633), tc_HOL_Obool), tc_HOL_Obool)), _1637633), hAPP(c_COMBB(tc_prod(_1637633, _1637633), tc_fun(tc_fun(tc_prod(_1637633, _1637633), tc_HOL_Obool), tc_HOL_Obool), _1637633), c_member(tc_prod(_1637633, _1637633)))), c_Product__Type_OPair(_1637633, _1637633)))), _1637635), _1637637, _1637639), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1637633), tc_List_Olist(_1637633))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1637633), tc_List_Olist(_1637633)), _1637637), _1637639)), c_List_Olistrel(_1637633, _1637635))))], (43173 ^ _782435) ^ [_1638010, _1638012, _1638014, _1638016] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638010), tc_List_Olist(_1638010))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638010), tc_List_Olist(_1638010)), _1638014), _1638016)), c_List_Olistrel(_1638010, _1638012))), -(c_List_Olistrelp(_1638010, hAPP(hAPP(c_COMBC(_1638010, tc_fun(tc_prod(_1638010, _1638010), tc_HOL_Obool), tc_fun(_1638010, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638010, tc_fun(tc_fun(tc_prod(_1638010, _1638010), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1638010, _1638010), tc_HOL_Obool), tc_fun(_1638010, tc_HOL_Obool)), _1638010), c_COMBC(_1638010, tc_fun(tc_prod(_1638010, _1638010), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1638010, tc_prod(_1638010, _1638010)), tc_fun(_1638010, tc_fun(tc_fun(tc_prod(_1638010, _1638010), tc_HOL_Obool), tc_HOL_Obool)), _1638010), hAPP(c_COMBB(tc_prod(_1638010, _1638010), tc_fun(tc_fun(tc_prod(_1638010, _1638010), tc_HOL_Obool), tc_HOL_Obool), _1638010), c_member(tc_prod(_1638010, _1638010)))), c_Product__Type_OPair(_1638010, _1638010)))), _1638012), _1638014, _1638016))], (43179 ^ _782435) ^ [_1638393, _1638395, _1638397, _1638399, _1638401] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638393), tc_List_Olist(_1638393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638393), tc_List_Olist(_1638393)), _1638395), hAPP(hAPP(c_List_Olist_OCons(_1638393), _1638397), _1638399))), c_List_Olistrel(_1638393, _1638401))), 43184 ^ _782435 : [(43185 ^ _782435) ^ [] : [-(_1638395 = hAPP(hAPP(c_List_Olist_OCons(_1638393), 43182 ^ [_1638393, _1638395, _1638397, _1638399, _1638401]), 43183 ^ [_1638393, _1638395, _1638397, _1638399, _1638401]))], (43187 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1638393, _1638393)), hAPP(hAPP(c_Product__Type_OPair(_1638393, _1638393), 43182 ^ [_1638393, _1638395, _1638397, _1638399, _1638401]), _1638397)), _1638401)))], (43189 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1638393), tc_List_Olist(_1638393))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1638393), tc_List_Olist(_1638393)), 43183 ^ [_1638393, _1638395, _1638397, _1638399, _1638401]), _1638399)), c_List_Olistrel(_1638393, _1638401))))]]], (43191 ^ _782435) ^ [_1638782, _1638784, _1638786, _1638788, _1638790, _1638792] : [hBOOL(hAPP(hAPP(_1638782, _1638784), _1638786)), c_List_Olistrelp(_1638788, _1638782, _1638790, _1638792), -(c_List_Olistrelp(_1638788, _1638782, hAPP(hAPP(c_List_Olist_OCons(_1638788), _1638784), _1638790), hAPP(hAPP(c_List_Olist_OCons(_1638788), _1638786), _1638792)))], (43201 ^ _782435) ^ [_1639004, _1639006, _1639008, _1639010, _1639012, _1639014] : [c_List_Olistrelp(_1639004, _1639006, hAPP(hAPP(c_List_Olist_OCons(_1639004), _1639008), _1639010), hAPP(hAPP(c_List_Olist_OCons(_1639004), _1639012), _1639014)), 43204 ^ _782435 : [(43205 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1639006, _1639008), _1639012)))], (43207 ^ _782435) ^ [] : [-(c_List_Olistrelp(_1639004, _1639006, _1639010, _1639014))]]], (43209 ^ _782435) ^ [_1639161, _1639163, _1639165, _1639167, _1639169, _1639171] : [-(c_List_Olistrelp(_1639161, _1639163, hAPP(hAPP(c_List_Olist_OCons(_1639161), _1639165), _1639167), hAPP(hAPP(c_List_Olist_OCons(_1639161), _1639169), _1639171))), hBOOL(hAPP(hAPP(_1639163, _1639165), _1639169)), c_List_Olistrelp(_1639161, _1639163, _1639167, _1639171)], (43219 ^ _782435) ^ [_1639358, _1639360, _1639362, _1639364, _1639366] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639358), tc_List_Olist(_1639358))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639358), tc_List_Olist(_1639358)), hAPP(hAPP(c_List_Olist_OCons(_1639358), _1639360), _1639362)), _1639364)), c_List_Olistrel(_1639358, _1639366))), 43224 ^ _782435 : [(43225 ^ _782435) ^ [] : [-(_1639364 = hAPP(hAPP(c_List_Olist_OCons(_1639358), 43222 ^ [_1639358, _1639360, _1639362, _1639364, _1639366]), 43223 ^ [_1639358, _1639360, _1639362, _1639364, _1639366]))], (43227 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1639358, _1639358)), hAPP(hAPP(c_Product__Type_OPair(_1639358, _1639358), _1639360), 43222 ^ [_1639358, _1639360, _1639362, _1639364, _1639366])), _1639366)))], (43229 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1639358), tc_List_Olist(_1639358))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1639358), tc_List_Olist(_1639358)), _1639362), 43223 ^ [_1639358, _1639360, _1639362, _1639364, _1639366])), c_List_Olistrel(_1639358, _1639366))))]]], (43231 ^ _782435) ^ [_1639747, _1639749, _1639751] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1639747, _1639747), tc_HOL_Obool)), _1639749), hAPP(hAPP(c_Product__Type_OSigma(_1639747, _1639747), _1639751), hAPP(c_COMBK(tc_fun(_1639747, tc_HOL_Obool), _1639747), _1639751)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(_1639747), tc_List_Olist(_1639747)), tc_HOL_Obool)), c_List_Olistrel(_1639747, _1639749)), hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(_1639747), tc_List_Olist(_1639747)), c_List_Olists(_1639747, _1639751)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1639747), tc_HOL_Obool), tc_List_Olist(_1639747)), c_List_Olists(_1639747, _1639751))))))], (43237 ^ _782435) ^ [_1639992] : [-(c_List_Olists(_1639992, c_Orderings_Otop__class_Otop(tc_fun(_1639992, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1639992), tc_HOL_Obool)))], (43239 ^ _782435) ^ [_1640030, _1640032, _1640034] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1640030, tc_HOL_Obool)), _1640032), _1640034)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1640030), tc_HOL_Obool)), c_List_Olists(_1640030, _1640032)), c_List_Olists(_1640030, _1640034))))], (43245 ^ _782435) ^ [_1640165, _1640167, _1640169] : [c_Equiv__Relations_Oequiv(_1640165, _1640167, _1640169), -(c_Equiv__Relations_Oequiv(tc_List_Olist(_1640165), c_List_Olists(_1640165, _1640167), c_List_Olistrel(_1640165, _1640169)))], (43251 ^ _782435) ^ [_1640264, _1640266, _1640268] : [c_Relation_Orefl__on(_1640264, _1640266, _1640268), -(c_Relation_Orefl__on(tc_List_Olist(_1640264), c_List_Olists(_1640264, _1640266), c_List_Olistrel(_1640264, _1640268)))], (43257 ^ _782435) ^ [_1640384, _1640386, _1640388, _1640390] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640384)), hAPP(hAPP(c_List_Olist_OCons(_1640384), _1640386), _1640388)), c_List_Olists(_1640384, _1640390))), 43260 ^ _782435 : [(43261 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1640384), _1640386), _1640390)))], (43263 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640384)), _1640388), c_List_Olists(_1640384, _1640390))))]]], (43265 ^ _782435) ^ [_1640565, _1640567, _1640569, _1640571] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640565)), hAPP(hAPP(c_List_Olist_OCons(_1640565), _1640567), _1640569)), c_List_Olists(_1640565, _1640571)))), hBOOL(hAPP(hAPP(c_member(_1640565), _1640567), _1640571)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640565)), _1640569), c_List_Olists(_1640565, _1640571)))], (43275 ^ _782435) ^ [_1640782, _1640784, _1640786] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640782)), _1640784), c_Wellfounded_Oacc(tc_List_Olist(_1640782), c_List_Olistrel1(_1640782, _1640786)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640782)), _1640784), c_List_Olists(_1640782, c_Wellfounded_Oacc(_1640782, _1640786)))))], (43281 ^ _782435) ^ [_1640925, _1640927, _1640929] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640925)), _1640927), c_List_Olists(_1640925, c_Wellfounded_Oacc(_1640925, _1640929)))), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1640925)), _1640927), c_Wellfounded_Oacc(tc_List_Olist(_1640925), c_List_Olistrel1(_1640925, _1640929)))))], (43287 ^ _782435) ^ [_1641089, _1641091, _1641093, _1641095] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641089), tc_List_Olist(_1641089))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641089), tc_List_Olist(_1641089)), _1641091), _1641093)), c_List_Olistrel(_1641089, _1641095))), 43290 ^ _782435 : [(43291 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641089)), _1641091) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641089)), _1641093))], (43293 ^ _782435) ^ [_1641318] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1641318), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641089)), _1641091))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641089, _1641089)), hAPP(hAPP(c_Product__Type_OPair(_1641089, _1641089), hAPP(hAPP(c_List_Onth(_1641089), _1641091), _1641318)), hAPP(hAPP(c_List_Onth(_1641089), _1641093), _1641318))), _1641095)))]]], (43299 ^ _782435) ^ [_1641497, _1641499, _1641501, _1641503] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641497), tc_List_Olist(_1641497))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641497), tc_List_Olist(_1641497)), _1641499), _1641501)), c_List_Olistrel(_1641497, _1641503)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641497)), _1641499) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641497)), _1641501), 43305 ^ _782435 : [(43306 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43304 ^ [_1641497, _1641499, _1641501, _1641503]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1641497)), _1641499))))], (43308 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1641497, _1641497)), hAPP(hAPP(c_Product__Type_OPair(_1641497, _1641497), hAPP(hAPP(c_List_Onth(_1641497), _1641499), 43304 ^ [_1641497, _1641499, _1641501, _1641503])), hAPP(hAPP(c_List_Onth(_1641497), _1641501), 43304 ^ [_1641497, _1641499, _1641501, _1641503]))), _1641503))]]], (43312 ^ _782435) ^ [_1641940, _1641942, _1641944] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1641940, _1641940)), hAPP(hAPP(c_Product__Type_OPair(_1641940, _1641940), 43313 ^ [_1641940, _1641942, _1641944]), 43313 ^ [_1641940, _1641942, _1641944])), _1641942))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1641940), tc_List_Olist(_1641940))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1641940), tc_List_Olist(_1641940)), _1641944), _1641944)), c_List_Olexord(_1641940, _1641942)))], (43319 ^ _782435) ^ [_1642115, _1642117, _1642119] : [-(hAPP(hAPP(c_List_Onth(_1642115), hAPP(hAPP(c_List_Olist_OCons(_1642115), _1642117), _1642119)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = _1642117)], (43321 ^ _782435) ^ [_1642158, _1642160, _1642162, _1642164] : [-(hAPP(hAPP(c_List_Onth(_1642158), hAPP(hAPP(c_List_Olist_OCons(_1642158), _1642160), _1642162)), hAPP(c_Nat_OSuc, _1642164)) = hAPP(hAPP(c_List_Onth(_1642158), _1642162), _1642164))], (43323 ^ _782435) ^ [_1642232, _1642234, _1642236] : [_1642232 = _1642234, 43326 ^ _782435 : [(43327 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642236)), _1642232) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642236)), _1642234))], (43329 ^ _782435) ^ [_1642380] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1642380), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642236)), _1642232))), -(hAPP(hAPP(c_List_Onth(_1642236), _1642232), _1642380) = hAPP(hAPP(c_List_Onth(_1642236), _1642234), _1642380))]]], (43335 ^ _782435) ^ [_1642519, _1642521, _1642523] : [-(_1642519 = _1642521), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642523)), _1642519) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642523)), _1642521), 43341 ^ _782435 : [(43342 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43340 ^ [_1642519, _1642521, _1642523]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1642523)), _1642519))))], (43344 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Onth(_1642523), _1642519), 43340 ^ [_1642519, _1642521, _1642523]) = hAPP(hAPP(c_List_Onth(_1642523), _1642521), 43340 ^ [_1642519, _1642521, _1642523])]]], (43348 ^ _782435) ^ [_1642843] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1642843)), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1642843), tc_HOL_Obool))))], (43350 ^ _782435) ^ [_1642879, _1642881, _1642883, _1642885] : [-(hAPP(hAPP(c_List_Onth(_1642879), hAPP(hAPP(c_List_Olist_OCons(_1642879), _1642881), _1642883)), _1642885) = c_Nat_Onat_Onat__case(_1642879, _1642881, hAPP(c_List_Onth(_1642879), _1642883), _1642885))], (43352 ^ _782435) ^ [_1642949, _1642951, _1642953, _1642955] : [_1642949 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1642951), hAPP(hAPP(c_List_Olist_OCons(_1642951), _1642953), _1642955)), _1642949) = _1642953)], (43358 ^ _782435) ^ [_1643056, _1643058, _1643060, _1643062] : [-(_1643056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1643058), hAPP(hAPP(c_List_Olist_OCons(_1643058), _1643060), _1643062)), _1643056) = hAPP(hAPP(c_List_Onth(_1643058), _1643062), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1643056), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43364 ^ _782435) ^ [_1643143, _1643145, _1643147, _1643149] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643143) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Onth(_1643145), hAPP(hAPP(c_List_Olist_OCons(_1643145), _1643147), _1643149)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643143)) = _1643147)], (43370 ^ _782435) ^ [_1643262, _1643264, _1643266, _1643268] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643262) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Onth(_1643264), hAPP(hAPP(c_List_Olist_OCons(_1643264), _1643266), _1643268)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643262)) = hAPP(hAPP(c_List_Onth(_1643264), _1643268), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1643262)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (43376 ^ _782435) ^ [_1643364, _1643366, _1643368, _1643370] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643364), tc_List_Olist(_1643364))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643364), tc_List_Olist(_1643364)), _1643366), _1643368)), c_List_Olexord(_1643364, _1643370))), 43381 ^ _782435 : [(43382 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643364)), _1643366)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643364)), _1643368))))], (43384 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1643364), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643364)), _1643366)), _1643368) = _1643366)]], 43386 ^ _782435 : [(43387 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43385 ^ [_1643364, _1643366, _1643368, _1643370]), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643364)), _1643366)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643364)), _1643368)))))], (43389 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1643364), 43385 ^ [_1643364, _1643366, _1643368, _1643370]), _1643366) = hAPP(hAPP(c_List_Otake(_1643364), 43385 ^ [_1643364, _1643366, _1643368, _1643370]), _1643368))], (43391 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1643364, _1643364)), hAPP(hAPP(c_Product__Type_OPair(_1643364, _1643364), hAPP(hAPP(c_List_Onth(_1643364), _1643366), 43385 ^ [_1643364, _1643366, _1643368, _1643370])), hAPP(hAPP(c_List_Onth(_1643364), _1643368), 43385 ^ [_1643364, _1643366, _1643368, _1643370]))), _1643370)))]]], (43393 ^ _782435) ^ [_1643904, _1643906, _1643908, _1643910] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1643904), tc_List_Olist(_1643904))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1643904), tc_List_Olist(_1643904)), _1643906), _1643908)), c_List_Olexord(_1643904, _1643910)))), 43394 ^ _782435 : [(43395 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643904)), _1643906)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643904)), _1643908))), hAPP(hAPP(c_List_Otake(_1643904), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643904)), _1643906)), _1643908) = _1643906], (43401 ^ _782435) ^ [_1644211] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1644211), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643904)), _1643906)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1643904)), _1643908)))), hAPP(hAPP(c_List_Otake(_1643904), _1644211), _1643906) = hAPP(hAPP(c_List_Otake(_1643904), _1644211), _1643908), hBOOL(hAPP(hAPP(c_member(tc_prod(_1643904, _1643904)), hAPP(hAPP(c_Product__Type_OPair(_1643904, _1643904), hAPP(hAPP(c_List_Onth(_1643904), _1643906), _1644211)), hAPP(hAPP(c_List_Onth(_1643904), _1643908), _1644211))), _1643910))]]], (43413 ^ _782435) ^ [_1644565, _1644567, _1644569, _1644571] : [43416 ^ _782435 : [(43417 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644565, _1644565)), hAPP(hAPP(c_Product__Type_OPair(_1644565, _1644565), 43414 ^ [_1644565, _1644567, _1644569, _1644571]), 43415 ^ [_1644565, _1644567, _1644569, _1644571])), _1644567))], (43419 ^ _782435) ^ [] : [43414 ^ [_1644565, _1644567, _1644569, _1644571] = 43415 ^ [_1644565, _1644567, _1644569, _1644571]], (43421 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1644565, _1644565)), hAPP(hAPP(c_Product__Type_OPair(_1644565, _1644565), 43415 ^ [_1644565, _1644567, _1644569, _1644571]), 43414 ^ [_1644565, _1644567, _1644569, _1644571])), _1644567))]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644565), tc_List_Olist(_1644565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644565), tc_List_Olist(_1644565)), _1644569), _1644571)), c_List_Olexord(_1644565, _1644567)))), -(_1644569 = _1644571), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1644565), tc_List_Olist(_1644565))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1644565), tc_List_Olist(_1644565)), _1644571), _1644569)), c_List_Olexord(_1644565, _1644567))))], (43433 ^ _782435) ^ [_1645112, _1645114, _1645116] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645112)), _1645114)), _1645116)), -(hAPP(hAPP(c_List_Otake(_1645112), _1645116), _1645114) = _1645114)], (43439 ^ _782435) ^ [_1645231, _1645233, _1645235, _1645237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1645231), _1645233)), -(hAPP(hAPP(c_List_Onth(_1645235), hAPP(hAPP(c_List_Otake(_1645235), _1645233), _1645237)), _1645231) = hAPP(hAPP(c_List_Onth(_1645235), _1645237), _1645231))], (43445 ^ _782435) ^ [_1645370, _1645372, _1645374] : [-(c_List_Osublist(_1645370, _1645372, hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1645374)) = hAPP(hAPP(c_List_Otake(_1645370), _1645374), _1645372))], (43447 ^ _782435) ^ [_1645412, _1645414, _1645416, _1645418] : [-(hAPP(hAPP(c_List_Otake(_1645412), _1645414), hAPP(hAPP(c_List_Otake(_1645412), _1645416), _1645418)) = hAPP(hAPP(c_List_Otake(_1645412), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1645414), _1645416)), _1645418))], (43449 ^ _782435) ^ [_1645471, _1645473, _1645475] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645471)), hAPP(hAPP(c_List_Otake(_1645471), _1645473), _1645475)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1645471)), _1645475)), _1645473))], (43451 ^ _782435) ^ [_1645526, _1645528, _1645530, _1645532] : [-(hAPP(hAPP(c_List_Otake(_1645526), hAPP(c_Nat_OSuc, _1645528)), hAPP(hAPP(c_List_Olist_OCons(_1645526), _1645530), _1645532)) = hAPP(hAPP(c_List_Olist_OCons(_1645526), _1645530), hAPP(hAPP(c_List_Otake(_1645526), _1645528), _1645532)))], (43453 ^ _782435) ^ [_1645590, _1645592, _1645594] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1645590), _1645592)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1645590)), hAPP(c_Set_OCollect(tc_List_Olist(_1645590)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1645590), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1645590)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645590), tc_fun(_1645590, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1645590, tc_HOL_Obool), tc_fun(tc_fun(_1645590, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1645590)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1645590, tc_HOL_Obool))), c_List_Oset(_1645590))), _1645592))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1645590), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1645590)), c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1645590)))), _1645594))))))], (43459 ^ _782435) ^ [_1645893, _1645895, _1645897] : [-(hAPP(c_List_Oset(_1645893), c_List_Osublist(_1645893, _1645895, _1645897)) = hAPP(c_Set_OCollect(_1645893), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1645893), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1645893, 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)), _1645893), 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)), _1645893), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1645893, tc_fun(tc_Nat_Onat, _1645893), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1645893, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1645893), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1645893), c_COMBB(_1645893, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1645893), _1645895))))), 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(_1645893)), _1645895)))), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool), c_member(tc_Nat_Onat)), _1645897))))))], (43461 ^ _782435) ^ [_1646037, _1646039] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1646037), hAPP(c_List_Oset(_1646037), _1646039))))], (43463 ^ _782435) ^ [_1646071, _1646073, _1646075] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646071, tc_HOL_Obool)), hAPP(c_List_Oset(_1646071), hAPP(hAPP(c_List_Otake(_1646071), _1646073), _1646075))), hAPP(c_List_Oset(_1646071), _1646075))))], (43465 ^ _782435) ^ [_1646126, _1646128, _1646130, _1646132] : [hBOOL(hAPP(hAPP(c_member(_1646126), _1646128), hAPP(c_List_Oset(_1646126), hAPP(hAPP(c_List_Otake(_1646126), _1646130), _1646132)))), -(hBOOL(hAPP(hAPP(c_member(_1646126), _1646128), hAPP(c_List_Oset(_1646126), _1646132))))], (43471 ^ _782435) ^ [_1646271, _1646273, _1646275] : [-(hAPP(c_List_Oset(_1646271), hAPP(hAPP(c_List_Olist_OCons(_1646271), _1646273), _1646275)) = hAPP(hAPP(c_Set_Oinsert(_1646271), _1646273), hAPP(c_List_Oset(_1646271), _1646275)))], (43473 ^ _782435) ^ [_1646324, _1646326, _1646328, _1646330] : [hBOOL(hAPP(hAPP(c_member(_1646324), _1646326), hAPP(c_List_Oset(_1646324), hAPP(hAPP(c_List_Olist_OCons(_1646324), _1646328), _1646330)))), -(_1646326 = _1646328), -(hBOOL(hAPP(hAPP(c_member(_1646324), _1646326), hAPP(c_List_Oset(_1646324), _1646330))))], (43483 ^ _782435) ^ [_1646481, _1646483, _1646485, _1646487] : [-(hBOOL(hAPP(hAPP(c_member(_1646481), _1646483), hAPP(c_List_Oset(_1646481), _1646485)))), hBOOL(hAPP(hAPP(c_member(_1646481), _1646483), hAPP(c_List_Oset(_1646481), c_List_Osublist(_1646481, _1646485, _1646487))))], (43489 ^ _782435) ^ [_1646605, _1646607, _1646609, _1646611] : [hBOOL(hAPP(hAPP(c_member(_1646605), _1646607), hAPP(c_List_Oset(_1646605), c_List_Osublist(_1646605, _1646609, _1646611)))), -(hBOOL(hAPP(hAPP(c_member(_1646605), _1646607), hAPP(c_List_Oset(_1646605), _1646609))))], (43495 ^ _782435) ^ [_1646742, _1646744] : [-(hAPP(c_Set_Oimage(tc_List_Olist(_1646742), tc_fun(_1646742, tc_HOL_Obool), c_List_Oset(_1646742)), hAPP(c_List_Oset(tc_List_Olist(_1646742)), c_Enum_Osublists(_1646742, _1646744))) = hAPP(c_Set_OPow(_1646742), hAPP(c_List_Oset(_1646742), _1646744)))], (43497 ^ _782435) ^ [_1646801, _1646803, _1646805] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646801, tc_HOL_Obool)), hAPP(c_List_Oset(_1646801), _1646803)), hAPP(c_List_Oset(_1646801), hAPP(hAPP(c_List_Olist_OCons(_1646801), _1646805), _1646803)))))], (43499 ^ _782435) ^ [_1646856, _1646858, _1646860] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1646856, tc_HOL_Obool)), hAPP(c_List_Oset(_1646856), c_List_Osublist(_1646856, _1646858, _1646860))), hAPP(c_List_Oset(_1646856), _1646858))))], (43501 ^ _782435) ^ [_1646907, _1646909] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Finite__Set_Ocard(_1646907), hAPP(c_List_Oset(_1646907), _1646909))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646907)), _1646909))))], (43503 ^ _782435) ^ [_1646972, _1646974, _1646976] : [43505 ^ _782435 : [(43506 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1646972), 43504 ^ [_1646972, _1646974, _1646976]), hAPP(c_List_Oset(_1646972), _1646974))))], (43508 ^ _782435) ^ [] : [hBOOL(hAPP(_1646976, 43504 ^ [_1646972, _1646974, _1646976]))]], 43509 ^ _782435 : [(43510 ^ _782435) ^ [_1647156] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647156), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1646972)), _1646974))), -(hBOOL(hAPP(_1646976, hAPP(hAPP(c_List_Onth(_1646972), _1646974), _1647156))))]]], (43516 ^ _782435) ^ [_1647283, _1647285, _1647287] : [43518 ^ _782435 : [(43519 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43517 ^ [_1647283, _1647285, _1647287]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1647283)), _1647285))))], (43521 ^ _782435) ^ [] : [hBOOL(hAPP(_1647287, hAPP(hAPP(c_List_Onth(_1647283), _1647285), 43517 ^ [_1647283, _1647285, _1647287])))]], 43522 ^ _782435 : [(43523 ^ _782435) ^ [_1647485] : [hBOOL(hAPP(hAPP(c_member(_1647283), _1647485), hAPP(c_List_Oset(_1647283), _1647285))), -(hBOOL(hAPP(_1647287, _1647485)))]]], (43529 ^ _782435) ^ [_1647602, _1647604, _1647606, _1647608] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647602), _1647604)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1647606, tc_HOL_Obool)), hAPP(c_List_Oset(_1647606), hAPP(hAPP(c_List_Otake(_1647606), _1647602), _1647608))), hAPP(c_List_Oset(_1647606), hAPP(hAPP(c_List_Otake(_1647606), _1647604), _1647608)))))], (43535 ^ _782435) ^ [_1647765, _1647767, _1647769, _1647771, _1647773] : [hBOOL(hAPP(hAPP(c_member(_1647765), _1647767), hAPP(c_List_Oset(_1647765), _1647769))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647771), hAPP(_1647773, _1647767))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1647771), c_List_Olist_Olist__size(_1647765, _1647773, _1647769))))], (43545 ^ _782435) ^ [_1647964, _1647966, _1647968, _1647970, _1647972] : [hBOOL(hAPP(hAPP(c_member(_1647964), _1647966), hAPP(c_List_Oset(_1647964), _1647968))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647970), hAPP(_1647972, _1647966))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1647970), c_List_Olist_Olist__size(_1647964, _1647972, _1647968))))], (43565 ^ _782435) ^ [_1648408, _1648410, _1648412] : [43567 ^ _782435 : [(43568 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1648408), 43566 ^ [_1648408, _1648410, _1648412]), hAPP(c_List_Oset(_1648408), _1648410))))], (43570 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1648408), 43566 ^ [_1648408, _1648410, _1648412]), _1648412))]], -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648408)), _1648410), c_List_Olists(_1648408, _1648412))))], (43555 ^ _782435) ^ [_1648181, _1648183, _1648185] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1648181)), _1648183), c_List_Olists(_1648181, _1648185))), 43558 ^ _782435 : [(43559 ^ _782435) ^ [_1648289] : [hBOOL(hAPP(hAPP(c_member(_1648181), _1648289), hAPP(c_List_Oset(_1648181), _1648183))), -(hBOOL(hAPP(hAPP(c_member(_1648181), _1648289), _1648185)))]]], (43574 ^ _782435) ^ [_1648628, _1648630, _1648632] : [hBOOL(hAPP(hAPP(c_member(_1648628), _1648630), hAPP(c_List_Oset(_1648628), _1648632))), -(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(_1648628)), _1648632))))], (43580 ^ _782435) ^ [_1648767, _1648769, _1648771] : [hBOOL(hAPP(hAPP(c_member(_1648767), _1648769), hAPP(c_List_Oset(_1648767), _1648771))), 43584 ^ _782435 : [(43585 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43583 ^ [_1648767, _1648769, _1648771]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648767)), _1648771))))], (43587 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1648767), _1648771), 43583 ^ [_1648767, _1648769, _1648771]) = _1648769)]]], (43589 ^ _782435) ^ [_1648955, _1648957, _1648959] : [-(hBOOL(hAPP(hAPP(c_member(_1648955), _1648957), hAPP(c_List_Oset(_1648955), _1648959)))), 43590 ^ _782435 : [(43591 ^ _782435) ^ [_1649029] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649029), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1648955)), _1648959))), hAPP(hAPP(c_List_Onth(_1648955), _1648959), _1649029) = _1648957]]], (43599 ^ _782435) ^ [_1649191, _1649193, _1649195] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1649191), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649193)), _1649195))), -(hBOOL(hAPP(hAPP(c_member(_1649193), hAPP(hAPP(c_List_Onth(_1649193), _1649195), _1649191)), hAPP(c_List_Oset(_1649193), _1649195))))], (43605 ^ _782435) ^ [_1649334, _1649336] : [-(c_List_Olists(_1649334, _1649336) = hAPP(c_Set_OCollect(tc_List_Olist(_1649334)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649334), tc_fun(_1649334, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649334, tc_HOL_Obool), tc_fun(tc_fun(_1649334, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649334)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649334, tc_HOL_Obool))), c_List_Oset(_1649334))), _1649336)))], (43607 ^ _782435) ^ [_1649412, _1649414] : [-(hAPP(c_List_Oset(_1649412), _1649414) = hAPP(c_Set_OCollect(_1649412), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, _1649412), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(_1649412, 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)), _1649412), 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)), _1649412), hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_Nat_Onat), c_fconj)), hAPP(hAPP(c_COMBC(_1649412, tc_fun(tc_Nat_Onat, _1649412), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649412, tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, _1649412), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), _1649412), c_COMBB(_1649412, tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(c_List_Onth(_1649412), _1649414))))), 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(_1649412)), _1649414))))))], (43609 ^ _782435) ^ [_1649538, _1649540, _1649542] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1649538), _1649540)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1649538)), hAPP(c_Set_OCollect(tc_List_Olist(_1649538)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1649538), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1649538)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649538), tc_fun(_1649538, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1649538, tc_HOL_Obool), tc_fun(tc_fun(_1649538, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1649538)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1649538, tc_HOL_Obool))), c_List_Oset(_1649538))), _1649540))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1649538), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1649538)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1649538)))), _1649542))))))], (43615 ^ _782435) ^ [_1649862, _1649864, _1649866, _1649868] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1649862), tc_List_Olist(_1649862))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1649862), tc_List_Olist(_1649862)), _1649864), _1649866)), c_List_Olistrel(_1649862, _1649868))), 43618 ^ _782435 : [(43619 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649862)), _1649864) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1649862)), _1649866))], (43621 ^ _782435) ^ [_1650198] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1649862, _1649862)), _1650198), hAPP(c_List_Oset(tc_prod(_1649862, _1649862)), hAPP(hAPP(c_List_Ozip(_1649862, _1649862), _1649864), _1649866)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1649862, _1649862, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1649862, tc_fun(tc_prod(_1649862, _1649862), tc_HOL_Obool), tc_fun(_1649862, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649862, tc_fun(tc_fun(tc_prod(_1649862, _1649862), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1649862, _1649862), tc_HOL_Obool), tc_fun(_1649862, tc_HOL_Obool)), _1649862), c_COMBC(_1649862, tc_fun(tc_prod(_1649862, _1649862), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1649862, tc_prod(_1649862, _1649862)), tc_fun(_1649862, tc_fun(tc_fun(tc_prod(_1649862, _1649862), tc_HOL_Obool), tc_HOL_Obool)), _1649862), hAPP(c_COMBB(tc_prod(_1649862, _1649862), tc_fun(tc_fun(tc_prod(_1649862, _1649862), tc_HOL_Obool), tc_HOL_Obool), _1649862), c_member(tc_prod(_1649862, _1649862)))), c_Product__Type_OPair(_1649862, _1649862)))), _1649868)), _1650198)))]]], (43627 ^ _782435) ^ [_1650591, _1650593, _1650595, _1650597] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1650591), tc_List_Olist(_1650591))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1650591), tc_List_Olist(_1650591)), _1650593), _1650595)), c_List_Olistrel(_1650591, _1650597)))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650591)), _1650593) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1650591)), _1650595), 43633 ^ _782435 : [(43634 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1650591, _1650591)), 43632 ^ [_1650591, _1650593, _1650595, _1650597]), hAPP(c_List_Oset(tc_prod(_1650591, _1650591)), hAPP(hAPP(c_List_Ozip(_1650591, _1650591), _1650593), _1650595)))))], (43636 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1650591, _1650591, tc_HOL_Obool), hAPP(hAPP(c_COMBC(_1650591, tc_fun(tc_prod(_1650591, _1650591), tc_HOL_Obool), tc_fun(_1650591, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650591, tc_fun(tc_fun(tc_prod(_1650591, _1650591), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1650591, _1650591), tc_HOL_Obool), tc_fun(_1650591, tc_HOL_Obool)), _1650591), c_COMBC(_1650591, tc_fun(tc_prod(_1650591, _1650591), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1650591, tc_prod(_1650591, _1650591)), tc_fun(_1650591, tc_fun(tc_fun(tc_prod(_1650591, _1650591), tc_HOL_Obool), tc_HOL_Obool)), _1650591), hAPP(c_COMBB(tc_prod(_1650591, _1650591), tc_fun(tc_fun(tc_prod(_1650591, _1650591), tc_HOL_Obool), tc_HOL_Obool), _1650591), c_member(tc_prod(_1650591, _1650591)))), c_Product__Type_OPair(_1650591, _1650591)))), _1650597)), 43632 ^ [_1650591, _1650593, _1650595, _1650597]))]]], (43640 ^ _782435) ^ [_1651329, _1651331, _1651333] : [-(hAPP(c_List_Oset(tc_List_Olist(_1651329)), c_Enum_On__lists(_1651329, _1651331, _1651333)) = hAPP(c_Set_OCollect(tc_List_Olist(_1651329)), hAPP(hAPP(c_COMBS(tc_List_Olist(_1651329), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1651329)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651329), tc_Nat_Onat, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1651329)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1651329)))), _1651331))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1651329), tc_fun(_1651329, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1651329, tc_HOL_Obool), tc_fun(tc_fun(_1651329, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1651329)), c_Orderings_Oord__class_Oless__eq(tc_fun(_1651329, tc_HOL_Obool))), c_List_Oset(_1651329))), hAPP(c_List_Oset(_1651329), _1651333)))))], (43642 ^ _782435) ^ [_1651474, _1651476, _1651478, _1651480] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(_1651474, _1651476))), hAPP(hAPP(c_List_Ozip(_1651474, _1651476), _1651478), _1651480)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651474)), _1651478)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651476)), _1651480)))], (43644 ^ _782435) ^ [_1651542, _1651544, _1651546, _1651548, _1651550] : [-(hAPP(hAPP(c_List_Otake(tc_prod(_1651542, _1651544)), _1651546), hAPP(hAPP(c_List_Ozip(_1651542, _1651544), _1651548), _1651550)) = hAPP(hAPP(c_List_Ozip(_1651542, _1651544), hAPP(hAPP(c_List_Otake(_1651542), _1651546), _1651548)), hAPP(hAPP(c_List_Otake(_1651544), _1651546), _1651550)))], (43646 ^ _782435) ^ [_1651618, _1651620, _1651622, _1651624, _1651626, _1651628] : [-(hAPP(hAPP(c_List_Ozip(_1651618, _1651620), hAPP(hAPP(c_List_Olist_OCons(_1651618), _1651622), _1651624)), hAPP(hAPP(c_List_Olist_OCons(_1651620), _1651626), _1651628)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(_1651618, _1651620)), hAPP(hAPP(c_Product__Type_OPair(_1651618, _1651620), _1651622), _1651626)), hAPP(hAPP(c_List_Ozip(_1651618, _1651620), _1651624), _1651628)))], (43648 ^ _782435) ^ [_1651723, _1651725, _1651727] : [_1651723 = _1651725, 43651 ^ _782435 : [(43652 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651727)), _1651723) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1651727)), _1651725))], (43654 ^ _782435) ^ [_1651879] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1651727, _1651727)), _1651879), hAPP(c_List_Oset(tc_prod(_1651727, _1651727)), hAPP(hAPP(c_List_Ozip(_1651727, _1651727), _1651723), _1651725)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1651727, _1651727, tc_HOL_Obool), c_fequal), _1651879)))]]], (43660 ^ _782435) ^ [_1652034, _1652036, _1652038] : [-(_1652034 = _1652036), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652038)), _1652034) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1652038)), _1652036), 43666 ^ _782435 : [(43667 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652038, _1652038)), 43665 ^ [_1652034, _1652036, _1652038]), hAPP(c_List_Oset(tc_prod(_1652038, _1652038)), hAPP(hAPP(c_List_Ozip(_1652038, _1652038), _1652034), _1652036)))))], (43669 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1652038, _1652038, tc_HOL_Obool), c_fequal), 43665 ^ [_1652034, _1652036, _1652038]))]]], (43673 ^ _782435) ^ [_1652369, _1652371, _1652373, _1652375] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652369, _1652369)), hAPP(hAPP(c_Product__Type_OPair(_1652369, _1652369), _1652371), _1652373)), hAPP(c_List_Oset(tc_prod(_1652369, _1652369)), hAPP(hAPP(c_List_Ozip(_1652369, _1652369), _1652375), _1652375)))), 43676 ^ _782435 : [(43677 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1652369), _1652371), hAPP(c_List_Oset(_1652369), _1652375))))], (43679 ^ _782435) ^ [] : [-(_1652371 = _1652373)]]], (43681 ^ _782435) ^ [_1652568, _1652570, _1652572, _1652574] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1652568, _1652568)), hAPP(hAPP(c_Product__Type_OPair(_1652568, _1652568), _1652570), _1652572)), hAPP(c_List_Oset(tc_prod(_1652568, _1652568)), hAPP(hAPP(c_List_Ozip(_1652568, _1652568), _1652574), _1652574))))), hBOOL(hAPP(hAPP(c_member(_1652568), _1652570), hAPP(c_List_Oset(_1652568), _1652574))), _1652570 = _1652572], (43691 ^ _782435) ^ [_1652803, _1652805, _1652807, _1652809, _1652811, _1652813] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652803, _1652805)), hAPP(hAPP(c_Product__Type_OPair(_1652803, _1652805), _1652807), _1652809)), hAPP(c_List_Oset(tc_prod(_1652803, _1652805)), hAPP(hAPP(c_List_Ozip(_1652803, _1652805), _1652811), _1652813)))), -(hBOOL(hAPP(hAPP(c_member(_1652803), _1652807), hAPP(c_List_Oset(_1652803), _1652811))))], (43697 ^ _782435) ^ [_1652984, _1652986, _1652988, _1652990, _1652992, _1652994] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1652984, _1652986)), hAPP(hAPP(c_Product__Type_OPair(_1652984, _1652986), _1652988), _1652990)), hAPP(c_List_Oset(tc_prod(_1652984, _1652986)), hAPP(hAPP(c_List_Ozip(_1652984, _1652986), _1652992), _1652994)))), -(hBOOL(hAPP(hAPP(c_member(_1652986), _1652990), hAPP(c_List_Oset(_1652986), _1652994))))], (43703 ^ _782435) ^ [_1653165, _1653167, _1653169, _1653171, _1653173, _1653175] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1653165, _1653167)), hAPP(hAPP(c_Product__Type_OPair(_1653165, _1653167), _1653169), _1653171)), hAPP(c_List_Oset(tc_prod(_1653165, _1653167)), hAPP(hAPP(c_List_Ozip(_1653165, _1653167), _1653173), _1653175)))), 43706 ^ _782435 : [(43707 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653165), _1653169), hAPP(c_List_Oset(_1653165), _1653173))))], (43709 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1653167), _1653171), hAPP(c_List_Oset(_1653167), _1653175))))]]], (43711 ^ _782435) ^ [_1653400, _1653402, _1653404, _1653406, _1653408] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653400), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653402)), _1653404))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1653400), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653406)), _1653408))), -(hAPP(hAPP(c_List_Onth(tc_prod(_1653402, _1653406)), hAPP(hAPP(c_List_Ozip(_1653402, _1653406), _1653404), _1653408)), _1653400) = hAPP(hAPP(c_Product__Type_OPair(_1653402, _1653406), hAPP(hAPP(c_List_Onth(_1653402), _1653404), _1653400)), hAPP(hAPP(c_List_Onth(_1653406), _1653408), _1653400)))], (43721 ^ _782435) ^ [_1653679, _1653681, _1653683, _1653685] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1653679)), _1653681), hAPP(c_List_Oset(tc_List_Olist(_1653679)), c_Enum_On__lists(_1653679, _1653683, _1653685)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653679)), _1653681) = _1653683)], (43727 ^ _782435) ^ [_1653814, _1653816, _1653818] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1653814))), c_Enum_On__lists(_1653814, _1653816, _1653818)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653814)), _1653818)), _1653816))], (43729 ^ _782435) ^ [_1653867, _1653869, _1653871, _1653873] : [-(hAPP(c_List_Oset(tc_prod(_1653867, _1653869)), hAPP(hAPP(c_List_Ozip(_1653867, _1653869), _1653871), _1653873)) = hAPP(c_Set_OCollect(tc_prod(_1653867, _1653869)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_HOL_Obool, tc_prod(_1653867, _1653869)), c_HOL_OEx(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1653867, _1653869), 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(_1653867, _1653869)), 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(_1653867, _1653869)), 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(_1653867, _1653869), tc_fun(tc_Nat_Onat, tc_prod(_1653867, _1653869)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(_1653867, _1653869), tc_HOL_Obool), tc_fun(tc_fun(tc_Nat_Onat, tc_prod(_1653867, _1653869)), tc_fun(tc_Nat_Onat, tc_HOL_Obool)), tc_prod(_1653867, _1653869)), c_COMBB(tc_prod(_1653867, _1653869), tc_HOL_Obool, tc_Nat_Onat)), c_fequal)), hAPP(hAPP(c_COMBS(tc_Nat_Onat, _1653869, tc_prod(_1653867, _1653869)), hAPP(hAPP(c_COMBB(_1653867, tc_fun(_1653869, tc_prod(_1653867, _1653869)), tc_Nat_Onat), c_Product__Type_OPair(_1653867, _1653869)), hAPP(c_List_Onth(_1653867), _1653871))), hAPP(c_List_Onth(_1653869), _1653873)))))), 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(_1653867)), _1653871)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1653869)), _1653873)))))))], (43731 ^ _782435) ^ [_1654092, _1654094, _1654096, _1654098] : [-(hAPP(c_List_Oset(tc_prod(_1654092, _1654094)), c_Enum_Oproduct(_1654092, _1654094, _1654096, _1654098)) = hAPP(hAPP(c_Product__Type_OSigma(_1654092, _1654094), hAPP(c_List_Oset(_1654092), _1654096)), hAPP(c_COMBK(tc_fun(_1654094, tc_HOL_Obool), _1654092), hAPP(c_List_Oset(_1654094), _1654098))))], (43733 ^ _782435) ^ [_1654162, _1654164] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint, _1654162, _1654164) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1654162), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1654164), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43735 ^ _782435) ^ [_1654209, _1654211] : [-(hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654209, _1654211)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1654209, _1654211))], (43737 ^ _782435) ^ [_1654244, _1654246] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1654244, _1654246) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654244, _1654246)))], (43739 ^ _782435) ^ [_1654279, _1654281] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint, _1654279), _1654281) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1654279, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1654281), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (43741 ^ _782435) ^ [_1654322, _1654324] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint, _1654322, _1654324) = hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1654322), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1654324)))], (43743 ^ _782435) ^ [_1654375] : [c_List_Onat__list(_1654375), -(c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1654375)))], (43749 ^ _782435) ^ [_1654448] : [c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint), _1654448)), -(c_List_Onat__list(_1654448))], (43755 ^ _782435) ^ [_1654527, _1654529] : [class_Groups_Ocomm__monoid__add(_1654527), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654527), _1654529) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1654527), hAPP(c_List_Onth(_1654527), _1654529)), 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(_1654527)), _1654529))))], (43771 ^ _782435) ^ [_1654840] : [43773 ^ _782435 : [(43774 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 43772 ^ [_1654840]), hAPP(c_List_Oset(tc_Nat_Onat), _1654840))))], (43776 ^ _782435) ^ [] : [43772 ^ [_1654840] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1654840) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (43761 ^ _782435) ^ [_1654672] : [hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1654672) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 43764 ^ _782435 : [(43765 ^ _782435) ^ [_1654747] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1654747), hAPP(c_List_Oset(tc_Nat_Onat), _1654672))), -(_1654747 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (43780 ^ _782435) ^ [_1654996, _1654998, _1655000] : [class_Groups_Omonoid__add(_1654996), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1654996), hAPP(hAPP(c_List_Olist_OCons(_1654996), _1654998), _1655000)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1654996), _1654998), hAPP(c_List_Omonoid__add__class_Olistsum(_1654996), _1655000)))], (43786 ^ _782435) ^ [_1655125, _1655127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655125), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1655127))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1655127), _1655125)), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), _1655127))))], (43792 ^ _782435) ^ [_1655246, _1655248, _1655250, _1655252] : [43794 ^ _782435 : [(43795 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1655246), 43793 ^ [_1655246, _1655248, _1655250, _1655252]), hAPP(c_List_Oset(_1655246), _1655248))))], (43797 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1655250, 43793 ^ [_1655246, _1655248, _1655250, _1655252])), hAPP(_1655252, 43793 ^ [_1655246, _1655248, _1655250, _1655252])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), c_List_Olist_Olist__size(_1655246, _1655250, _1655248)), c_List_Olist_Olist__size(_1655246, _1655252, _1655248))))], (43801 ^ _782435) ^ [_1655496, _1655498, _1655500] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1655496), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655498)), _1655500))), -(c_List_Obutlast(_1655498, hAPP(hAPP(c_List_Otake(_1655498), _1655496), _1655500)) = hAPP(hAPP(c_List_Otake(_1655498), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1655496), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1655500))], (43807 ^ _782435) ^ [_1655649, _1655651, _1655653] : [hBOOL(hAPP(hAPP(c_member(_1655649), _1655651), hAPP(c_List_Oset(_1655649), c_List_Obutlast(_1655649, _1655653)))), -(hBOOL(hAPP(hAPP(c_member(_1655649), _1655651), hAPP(c_List_Oset(_1655649), _1655653))))], (43813 ^ _782435) ^ [_1655782, _1655784, _1655786] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1655782), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655784)), _1655786))), -(hAPP(hAPP(c_List_Otake(_1655784), _1655782), c_List_Obutlast(_1655784, _1655786)) = hAPP(hAPP(c_List_Otake(_1655784), _1655782), _1655786))], (43819 ^ _782435) ^ [_1655923, _1655925] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655923)), c_List_Obutlast(_1655923, _1655925)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655923)), _1655925)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (43821 ^ _782435) ^ [_1655971, _1655973] : [-(c_List_Obutlast(_1655971, _1655973) = hAPP(hAPP(c_List_Otake(_1655971), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1655971)), _1655973)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1655973))], (43823 ^ _782435) ^ [_1656020, _1656022, _1656024] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1656020), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), _1656022))), -(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat, _1656022), _1656020), _1656024)) = 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), _1656022)), _1656024)), hAPP(hAPP(c_List_Onth(tc_Nat_Onat), _1656022), _1656020)))], (43829 ^ _782435) ^ [_1656181, _1656183, _1656185, _1656187] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656181), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656183)), _1656185))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1656181), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656183)), _1656187))), 43839 ^ _782435 : [(43840 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43838 ^ [_1656181, _1656183, _1656185, _1656187]), _1656181)))], (43842 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Onth(_1656183), _1656185), 43838 ^ [_1656181, _1656183, _1656185, _1656187]) = hAPP(hAPP(c_List_Onth(_1656183), _1656187), 43838 ^ [_1656181, _1656183, _1656185, _1656187])]], -(hAPP(hAPP(c_List_Otake(_1656183), _1656181), _1656185) = hAPP(hAPP(c_List_Otake(_1656183), _1656181), _1656187))], (43846 ^ _782435) ^ [_1656598, _1656600, _1656602, _1656604] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656598)), _1656600)), _1656602)), -(hAPP(hAPP(c_List_Olist__update(_1656598, _1656600), _1656602), _1656604) = _1656600)], (43852 ^ _782435) ^ [_1656717, _1656719, _1656721, _1656723, _1656725] : [-(_1656717 = _1656719), -(hAPP(hAPP(c_List_Onth(_1656721), hAPP(hAPP(c_List_Olist__update(_1656721, _1656723), _1656717), _1656725)), _1656719) = hAPP(hAPP(c_List_Onth(_1656721), _1656723), _1656719))], (43858 ^ _782435) ^ [_1656784, _1656786, _1656788] : [-(hAPP(hAPP(c_List_Olist__update(_1656784, _1656786), _1656788), hAPP(hAPP(c_List_Onth(_1656784), _1656786), _1656788)) = _1656786)], (43860 ^ _782435) ^ [_1656828, _1656830, _1656832, _1656834] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656828)), hAPP(hAPP(c_List_Olist__update(_1656828, _1656830), _1656832), _1656834)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1656828)), _1656830))], (43862 ^ _782435) ^ [_1656880, _1656882, _1656884, _1656886, _1656888] : [-(hAPP(hAPP(c_List_Olist__update(_1656880, hAPP(hAPP(c_List_Olist_OCons(_1656880), _1656882), _1656884)), _1656886), _1656888) = c_Nat_Onat_Onat__case(tc_List_Olist(_1656880), hAPP(hAPP(c_List_Olist_OCons(_1656880), _1656888), _1656884), hAPP(hAPP(c_COMBB(tc_List_Olist(_1656880), tc_List_Olist(_1656880), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1656880), _1656882)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, _1656880, tc_List_Olist(_1656880)), c_List_Olist__update(_1656880, _1656884)), _1656888)), _1656886))], (43864 ^ _782435) ^ [_1656977, _1656979, _1656981, _1656983] : [-(hAPP(hAPP(c_List_Olist__update(_1656977, hAPP(hAPP(c_List_Olist_OCons(_1656977), _1656979), _1656981)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1656983) = hAPP(hAPP(c_List_Olist_OCons(_1656977), _1656983), _1656981))], (43866 ^ _782435) ^ [_1657031, _1657033, _1657035, _1657037, _1657039] : [-(hAPP(hAPP(c_List_Olist__update(_1657031, hAPP(hAPP(c_List_Olist_OCons(_1657031), _1657033), _1657035)), hAPP(c_Nat_OSuc, _1657037)), _1657039) = hAPP(hAPP(c_List_Olist_OCons(_1657031), _1657033), hAPP(hAPP(c_List_Olist__update(_1657031, _1657035), _1657037), _1657039)))], (43868 ^ _782435) ^ [_1657099, _1657101, _1657103, _1657105, _1657107] : [-(hAPP(hAPP(c_List_Olist__update(_1657099, hAPP(hAPP(c_List_Olist__update(_1657099, _1657101), _1657103), _1657105)), _1657103), _1657107) = hAPP(hAPP(c_List_Olist__update(_1657099, _1657101), _1657103), _1657107))], (43870 ^ _782435) ^ [_1657153, _1657155, _1657157, _1657159, _1657161, _1657163] : [-(_1657153 = _1657155), -(hAPP(hAPP(c_List_Olist__update(_1657157, hAPP(hAPP(c_List_Olist__update(_1657157, _1657159), _1657153), _1657161)), _1657155), _1657163) = hAPP(hAPP(c_List_Olist__update(_1657157, hAPP(hAPP(c_List_Olist__update(_1657157, _1657159), _1657155), _1657163)), _1657153), _1657161))], (43876 ^ _782435) ^ [_1657233, _1657235, _1657237, _1657239, _1657241, _1657243] : [-(hAPP(hAPP(c_List_Olist__update(tc_prod(_1657233, _1657235), hAPP(hAPP(c_List_Ozip(_1657233, _1657235), _1657237), _1657239)), _1657241), _1657243) = hAPP(hAPP(c_List_Ozip(_1657233, _1657235), hAPP(hAPP(c_List_Olist__update(_1657233, _1657237), _1657241), hAPP(c_Product__Type_Ofst(_1657233, _1657235), _1657243))), hAPP(hAPP(c_List_Olist__update(_1657235, _1657239), _1657241), hAPP(c_Product__Type_Osnd(_1657233, _1657235), _1657243))))], (43878 ^ _782435) ^ [_1657326, _1657328, _1657330, _1657332, _1657334, _1657336, _1657338] : [-(hAPP(hAPP(c_List_Ozip(_1657326, _1657328), hAPP(hAPP(c_List_Olist__update(_1657326, _1657330), _1657332), _1657334)), hAPP(hAPP(c_List_Olist__update(_1657328, _1657336), _1657332), _1657338)) = hAPP(hAPP(c_List_Olist__update(tc_prod(_1657326, _1657328), hAPP(hAPP(c_List_Ozip(_1657326, _1657328), _1657330), _1657336)), _1657332), hAPP(hAPP(c_Product__Type_OPair(_1657326, _1657328), _1657334), _1657338)))], (43880 ^ _782435) ^ [_1657418, _1657420, _1657422, _1657424, _1657426] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657418, tc_HOL_Obool)), hAPP(c_List_Oset(_1657418), _1657420)), _1657422)), hBOOL(hAPP(hAPP(c_member(_1657418), _1657424), _1657422)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657418, tc_HOL_Obool)), hAPP(c_List_Oset(_1657418), hAPP(hAPP(c_List_Olist__update(_1657418, _1657420), _1657426), _1657424))), _1657422)))], (43890 ^ _782435) ^ [_1657651, _1657653, _1657655, _1657657] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1657651, tc_HOL_Obool)), hAPP(c_List_Oset(_1657651), hAPP(hAPP(c_List_Olist__update(_1657651, _1657653), _1657655), _1657657))), hAPP(hAPP(c_Set_Oinsert(_1657651), _1657657), hAPP(c_List_Oset(_1657651), _1657653)))))], (43892 ^ _782435) ^ [_1657717, _1657719, _1657721, _1657723] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657717), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657719)), _1657721))), -(hAPP(hAPP(c_List_Onth(_1657719), hAPP(hAPP(c_List_Olist__update(_1657719, _1657721), _1657717), _1657723)), _1657717) = _1657723)], (43898 ^ _782435) ^ [_1657856, _1657858, _1657860, _1657862] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1657856), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1657858)), _1657860))), 43901 ^ _782435 : [(43902 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Olist__update(_1657858, _1657860), _1657856), _1657862) = _1657860, -(hAPP(hAPP(c_List_Onth(_1657858), _1657860), _1657856) = _1657862)], (43908 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Onth(_1657858), _1657860), _1657856) = _1657862, -(hAPP(hAPP(c_List_Olist__update(_1657858, _1657860), _1657856), _1657862) = _1657860)]]], (43914 ^ _782435) ^ [_1658150, _1658152, _1658154, _1658156, _1658158] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658150), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658152)), _1658154))), 43917 ^ _782435 : [(43918 ^ _782435) ^ [] : [_1658150 = _1658156, -(hAPP(hAPP(c_List_Onth(_1658152), hAPP(hAPP(c_List_Olist__update(_1658152, _1658154), _1658150), _1658158)), _1658156) = _1658158)], (43924 ^ _782435) ^ [] : [-(_1658150 = _1658156), -(hAPP(hAPP(c_List_Onth(_1658152), hAPP(hAPP(c_List_Olist__update(_1658152, _1658154), _1658150), _1658158)), _1658156) = hAPP(hAPP(c_List_Onth(_1658152), _1658154), _1658156))]]], (43930 ^ _782435) ^ [_1658446, _1658448, _1658450, _1658452] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1658446), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658448)), _1658450))), -(hBOOL(hAPP(hAPP(c_member(_1658448), _1658452), hAPP(c_List_Oset(_1658448), hAPP(hAPP(c_List_Olist__update(_1658448, _1658450), _1658446), _1658452)))))], (43936 ^ _782435) ^ [_1658608, _1658610, _1658612, _1658614] : [_1658608 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658610)), _1658612)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Obutlast(_1658610, hAPP(hAPP(c_List_Olist__update(_1658610, _1658612), _1658608), _1658614)) = c_List_Obutlast(_1658610, _1658612))], (43942 ^ _782435) ^ [_1658739, _1658741, _1658743, _1658745] : [-(_1658739 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658741)), _1658743)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Obutlast(_1658741, hAPP(hAPP(c_List_Olist__update(_1658741, _1658743), _1658739), _1658745)) = hAPP(hAPP(c_List_Olist__update(_1658741, c_List_Obutlast(_1658741, _1658743)), _1658739), _1658745))], (43948 ^ _782435) ^ [_1658839, _1658841, _1658843, _1658845] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1658839), tc_List_Olist(_1658839))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1658839), tc_List_Olist(_1658839)), _1658841), _1658843)), c_List_Olistrel1(_1658839, _1658845))), 43953 ^ _782435 : [(43954 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1658839, _1658839)), hAPP(hAPP(c_Product__Type_OPair(_1658839, _1658839), hAPP(hAPP(c_List_Onth(_1658839), _1658841), 43952 ^ [_1658839, _1658841, _1658843, _1658845])), 43951 ^ [_1658839, _1658841, _1658843, _1658845])), _1658845)))], (43956 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 43952 ^ [_1658839, _1658841, _1658843, _1658845]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1658839)), _1658841))))], (43958 ^ _782435) ^ [] : [-(_1658843 = hAPP(hAPP(c_List_Olist__update(_1658839, _1658841), 43952 ^ [_1658839, _1658841, _1658843, _1658845]), 43951 ^ [_1658839, _1658841, _1658843, _1658845]))]]], (43960 ^ _782435) ^ [_1659187, _1659189, _1659191, _1659193] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1659187), tc_List_Olist(_1659187))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1659187), tc_List_Olist(_1659187)), _1659189), _1659191)), c_List_Olistrel1(_1659187, _1659193)))), 43961 ^ _782435 : [(43962 ^ _782435) ^ [_1659320, _1659322] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1659187, _1659187)), hAPP(hAPP(c_Product__Type_OPair(_1659187, _1659187), hAPP(hAPP(c_List_Onth(_1659187), _1659189), _1659320)), _1659322)), _1659193)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1659320), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1659187)), _1659189))), _1659191 = hAPP(hAPP(c_List_Olist__update(_1659187, _1659189), _1659320), _1659322)]]], (43974 ^ _782435) ^ [_1659620, _1659622, _1659624, _1659626] : [hBOOL(hAPP(c_List_Odistinct(_1659620), _1659622)), -(hBOOL(hAPP(hAPP(c_member(_1659620), _1659624), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1659620, tc_HOL_Obool)), hAPP(c_List_Oset(_1659620), _1659622)), hAPP(hAPP(c_Set_Oinsert(_1659620), hAPP(hAPP(c_List_Onth(_1659620), _1659622), _1659626)), c_Orderings_Obot__class_Obot(tc_fun(_1659620, tc_HOL_Obool))))))), -(hBOOL(hAPP(c_List_Odistinct(_1659620), hAPP(hAPP(c_List_Olist__update(_1659620, _1659622), _1659626), _1659624))))], (43984 ^ _782435) ^ [_1659838, _1659840, _1659842] : [hBOOL(hAPP(c_List_Odistinct(_1659838), _1659840)), -(hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1659838)), c_Enum_On__lists(_1659838, _1659842, _1659840))))], (43990 ^ _782435) ^ [_1659945, _1659947, _1659949, _1659951] : [hBOOL(hAPP(c_List_Odistinct(_1659945), _1659947)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1659945, _1659949)), hAPP(hAPP(c_List_Ozip(_1659945, _1659949), _1659947), _1659951))))], (43996 ^ _782435) ^ [_1660066, _1660068, _1660070, _1660072] : [hBOOL(hAPP(c_List_Odistinct(_1660066), _1660068)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1660070, _1660066)), hAPP(hAPP(c_List_Ozip(_1660070, _1660066), _1660072), _1660068))))], (44002 ^ _782435) ^ [_1660187, _1660189, _1660191] : [hBOOL(hAPP(c_List_Odistinct(_1660187), _1660189)), -(hBOOL(hAPP(c_List_Odistinct(_1660187), c_List_Osublist(_1660187, _1660189, _1660191))))], (44008 ^ _782435) ^ [_1660290, _1660292, _1660294, _1660296] : [hBOOL(hAPP(c_List_Odistinct(_1660290), _1660292)), hBOOL(hAPP(c_List_Odistinct(_1660294), _1660296)), -(hBOOL(hAPP(c_List_Odistinct(tc_prod(_1660290, _1660294)), c_Enum_Oproduct(_1660290, _1660294, _1660292, _1660296))))], (44018 ^ _782435) ^ [_1660467, _1660469] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint), c_List_Oupto(_1660467, _1660469))))], (44020 ^ _782435) ^ [_1660497, _1660499, _1660501] : [hBOOL(hAPP(c_List_Odistinct(_1660497), _1660499)), -(hBOOL(hAPP(c_List_Odistinct(_1660497), hAPP(hAPP(c_List_Otake(_1660497), _1660501), _1660499))))], (44026 ^ _782435) ^ [_1660626, _1660628, _1660630] : [hBOOL(hAPP(c_List_Odistinct(_1660626), hAPP(hAPP(c_List_Olist_OCons(_1660626), _1660628), _1660630))), 44029 ^ _782435 : [(44030 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1660626), _1660628), hAPP(c_List_Oset(_1660626), _1660630)))], (44032 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1660626), _1660630)))]]], (44034 ^ _782435) ^ [_1660793, _1660795, _1660797] : [-(hBOOL(hAPP(c_List_Odistinct(_1660793), hAPP(hAPP(c_List_Olist_OCons(_1660793), _1660795), _1660797)))), -(hBOOL(hAPP(hAPP(c_member(_1660793), _1660795), hAPP(c_List_Oset(_1660793), _1660797)))), hBOOL(hAPP(c_List_Odistinct(_1660793), _1660797))], (44044 ^ _782435) ^ [_1660987, _1660989] : [hAPP(c_Finite__Set_Ocard(_1660987), hAPP(c_List_Oset(_1660987), _1660989)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1660987)), _1660989), -(hBOOL(hAPP(c_List_Odistinct(_1660987), _1660989)))], (44050 ^ _782435) ^ [_1661106, _1661108] : [hBOOL(hAPP(c_List_Odistinct(_1661106), _1661108)), -(hAPP(c_Finite__Set_Ocard(_1661106), hAPP(c_List_Oset(_1661106), _1661108)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661106)), _1661108))], (44056 ^ _782435) ^ [_1661225, _1661227, _1661229, _1661231] : [hBOOL(hAPP(c_List_Odistinct(_1661225), _1661227)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661229), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661225)), _1661227))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661231), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661225)), _1661227))), 44067 ^ _782435 : [(44068 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Onth(_1661225), _1661227), _1661229) = hAPP(hAPP(c_List_Onth(_1661225), _1661227), _1661231), -(_1661229 = _1661231)], (44074 ^ _782435) ^ [] : [_1661229 = _1661231, -(hAPP(hAPP(c_List_Onth(_1661225), _1661227), _1661229) = hAPP(hAPP(c_List_Onth(_1661225), _1661227), _1661231))]]], (44098 ^ _782435) ^ [_1662135, _1662137] : [44100 ^ _782435 : [(44101 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44099 ^ [_1662135, _1662137]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662135)), _1662137))))], (44104 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 44102 ^ [_1662135, _1662137]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662135)), _1662137))))], (44106 ^ _782435) ^ [] : [44099 ^ [_1662135, _1662137] = 44102 ^ [_1662135, _1662137]], (44108 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Onth(_1662135), _1662137), 44099 ^ [_1662135, _1662137]) = hAPP(hAPP(c_List_Onth(_1662135), _1662137), 44102 ^ [_1662135, _1662137]))]], -(hBOOL(hAPP(c_List_Odistinct(_1662135), _1662137)))], (44080 ^ _782435) ^ [_1661675, _1661677] : [hBOOL(hAPP(c_List_Odistinct(_1661675), _1661677)), 44083 ^ _782435 : [(44084 ^ _782435) ^ [_1661807] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661807), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661675)), _1661677))), 44087 ^ _782435 : [(44088 ^ _782435) ^ [_1661934] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1661934), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1661675)), _1661677))), -(_1661807 = _1661934), hAPP(hAPP(c_List_Onth(_1661675), _1661677), _1661807) = hAPP(hAPP(c_List_Onth(_1661675), _1661677), _1661934)]]]]], (44112 ^ _782435) ^ [_1662567, _1662569] : [class_Groups_Ocomm__monoid__add(_1662567), hBOOL(hAPP(c_List_Odistinct(_1662567), _1662569)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1662567), _1662569) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1662567, _1662567), c_COMBI(_1662567)), hAPP(c_List_Oset(_1662567), _1662569)))], (44122 ^ _782435) ^ [_1662753, _1662755] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1662753), _1662755)), -(c_Nitpick_Ocard_H(_1662753, _1662755) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1662753)), c_Hilbert__Choice_OEps(tc_List_Olist(_1662753), hAPP(hAPP(c_COMBS(tc_List_Olist(_1662753), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1662753)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1662753), tc_fun(_1662753, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1662753, tc_HOL_Obool), tc_fun(tc_fun(_1662753, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1662753)), c_fequal), c_List_Oset(_1662753))), _1662755))), c_List_Odistinct(_1662753)))))], (44128 ^ _782435) ^ [_1662990, _1662992] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1662990), _1662992))), -(c_Nitpick_Ocard_H(_1662990, _1662992) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44134 ^ _782435) ^ [_1663035, _1663037, _1663039] : [hBOOL(hAPP(c_List_Odistinct(_1663035), _1663037)), -(hAPP(c_List_Oset(_1663035), c_List_Oremove1(_1663035, _1663039, _1663037)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1663035, tc_HOL_Obool)), hAPP(c_List_Oset(_1663035), _1663037)), hAPP(hAPP(c_Set_Oinsert(_1663035), _1663039), c_Orderings_Obot__class_Obot(tc_fun(_1663035, tc_HOL_Obool)))))], (44140 ^ _782435) ^ [_1663198, _1663200, _1663202] : [hBOOL(hAPP(c_List_Odistinct(_1663198), _1663200)), -(hBOOL(hAPP(c_List_Odistinct(_1663198), c_List_Oremove1(_1663198, _1663202, _1663200))))], (44146 ^ _782435) ^ [_1663316, _1663318, _1663320, _1663322] : [_1663316 = _1663318, -(c_List_Oremove1(_1663320, _1663316, hAPP(hAPP(c_List_Olist_OCons(_1663320), _1663318), _1663322)) = _1663322)], (44152 ^ _782435) ^ [_1663415, _1663417, _1663419, _1663421] : [-(_1663415 = _1663417), -(c_List_Oremove1(_1663419, _1663415, hAPP(hAPP(c_List_Olist_OCons(_1663419), _1663417), _1663421)) = hAPP(hAPP(c_List_Olist_OCons(_1663419), _1663417), c_List_Oremove1(_1663419, _1663415, _1663421)))], (44158 ^ _782435) ^ [_1663481, _1663483, _1663485, _1663487] : [-(c_List_Oremove1(_1663481, _1663483, c_List_Oremove1(_1663481, _1663485, _1663487)) = c_List_Oremove1(_1663481, _1663485, c_List_Oremove1(_1663481, _1663483, _1663487)))], (44160 ^ _782435) ^ [_1663522, _1663524, _1663526] : [-(hBOOL(hAPP(hAPP(c_member(_1663522), _1663524), hAPP(c_List_Oset(_1663522), _1663526)))), -(c_List_Oremove1(_1663522, _1663524, _1663526) = _1663526)], (44166 ^ _782435) ^ [_1663575, _1663577, _1663579, _1663581] : [-(hBOOL(hAPP(hAPP(c_member(_1663575), _1663577), hAPP(c_List_Oset(_1663575), _1663579)))), hBOOL(hAPP(hAPP(c_member(_1663575), _1663577), hAPP(c_List_Oset(_1663575), c_List_Oremove1(_1663575, _1663581, _1663579))))], (44172 ^ _782435) ^ [_1663698, _1663700, _1663702, _1663704] : [-(_1663698 = _1663700), 44175 ^ _782435 : [(44176 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663702), _1663698), hAPP(c_List_Oset(_1663702), c_List_Oremove1(_1663702, _1663700, _1663704)))), -(hBOOL(hAPP(hAPP(c_member(_1663702), _1663698), hAPP(c_List_Oset(_1663702), _1663704))))], (44182 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1663702), _1663698), hAPP(c_List_Oset(_1663702), _1663704))), -(hBOOL(hAPP(hAPP(c_member(_1663702), _1663698), hAPP(c_List_Oset(_1663702), c_List_Oremove1(_1663702, _1663700, _1663704)))))]]], (44188 ^ _782435) ^ [_1663999, _1664001, _1664003] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1663999, tc_HOL_Obool)), hAPP(c_List_Oset(_1663999), c_List_Oremove1(_1663999, _1664001, _1664003))), hAPP(c_List_Oset(_1663999), _1664003))))], (44190 ^ _782435) ^ [_1664062, _1664064, _1664066] : [hBOOL(hAPP(hAPP(c_member(_1664062), _1664064), hAPP(c_List_Oset(_1664062), _1664066))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664062)), c_List_Oremove1(_1664062, _1664064, _1664066)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664062)), _1664066)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (44196 ^ _782435) ^ [_1664207, _1664209, _1664211] : [-(hBOOL(hAPP(hAPP(c_member(_1664207), _1664209), hAPP(c_List_Oset(_1664207), _1664211)))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664207)), c_List_Oremove1(_1664207, _1664209, _1664211)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1664207)), _1664211))], (44202 ^ _782435) ^ [_1664277, _1664279, _1664281] : [class_Orderings_Olinorder(_1664277), hBOOL(hAPP(c_Finite__Set_Ofinite(_1664277), _1664279)), -(c_List_Olinorder__class_Osorted__list__of__set(_1664277, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1664277, tc_HOL_Obool)), _1664279), hAPP(hAPP(c_Set_Oinsert(_1664277), _1664281), c_Orderings_Obot__class_Obot(tc_fun(_1664277, tc_HOL_Obool))))) = c_List_Oremove1(_1664277, _1664281, c_List_Olinorder__class_Osorted__list__of__set(_1664277, _1664279)))], (44212 ^ _782435) ^ [_1664499, _1664501, _1664503, _1664505] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664499) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1664501), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664499)), hAPP(hAPP(c_List_Olist_OCons(_1664501), _1664503), _1664505)) = c_List_Olist_ONil(_1664501))], (44218 ^ _782435) ^ [_1664622, _1664624, _1664626, _1664628] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664622) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1664624), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664622)), hAPP(hAPP(c_List_Olist_OCons(_1664624), _1664626), _1664628)) = hAPP(hAPP(c_List_Olist_OCons(_1664624), _1664626), hAPP(hAPP(c_List_Otake(_1664624), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1664622)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1664628)))], (44224 ^ _782435) ^ [_1664711, _1664713] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1664711)), c_List_Olist_ONil(_1664711)), c_List_Olists(_1664711, _1664713))))], (44226 ^ _782435) ^ [_1664750, _1664752, _1664754] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664750), tc_List_Olist(_1664750))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664750), tc_List_Olist(_1664750)), _1664752), c_List_Olist_ONil(_1664750))), c_List_Olistrel(_1664750, _1664754))), -(_1664752 = c_List_Olist_ONil(_1664750))], (44232 ^ _782435) ^ [_1664897, _1664899, _1664901] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1664897), tc_List_Olist(_1664897))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1664897), tc_List_Olist(_1664897)), c_List_Olist_ONil(_1664897)), _1664899)), c_List_Olistrel(_1664897, _1664901))), -(_1664899 = c_List_Olist_ONil(_1664897))], (44238 ^ _782435) ^ [_1665044] : [-(hBOOL(hAPP(c_List_Odistinct(_1665044), c_List_Olist_ONil(_1665044))))], (44240 ^ _782435) ^ [_1665072, _1665074] : [-(_1665072 = c_List_Olist_ONil(_1665074)), hBOOL(hAPP(c_List_Odistinct(_1665074), _1665072)), -(hBOOL(hAPP(c_List_Odistinct(_1665074), c_List_Obutlast(_1665074, _1665072))))], (44250 ^ _782435) ^ [_1665223, _1665225] : [-(c_List_Oremove1(_1665223, _1665225, c_List_Olist_ONil(_1665223)) = c_List_Olist_ONil(_1665223))], (44252 ^ _782435) ^ [_1665256, _1665258, _1665260] : [-(hAPP(hAPP(c_List_Ozip(_1665256, _1665258), c_List_Olist_ONil(_1665256)), _1665260) = c_List_Olist_ONil(tc_prod(_1665256, _1665258)))], (44254 ^ _782435) ^ [_1665299, _1665301, _1665303] : [-(hAPP(hAPP(c_List_Ozip(_1665299, _1665301), _1665303), c_List_Olist_ONil(_1665301)) = c_List_Olist_ONil(tc_prod(_1665299, _1665301)))], (44256 ^ _782435) ^ [_1665342] : [class_Orderings_Olinorder(_1665342), -(c_List_Olinorder__class_Osorted__list__of__set(_1665342, c_Orderings_Obot__class_Obot(tc_fun(_1665342, tc_HOL_Obool))) = c_List_Olist_ONil(_1665342))], (44262 ^ _782435) ^ [_1665435, _1665437] : [-(c_List_Osublist(_1665435, c_List_Olist_ONil(_1665435), _1665437) = c_List_Olist_ONil(_1665435))], (44264 ^ _782435) ^ [_1665468, _1665470] : [-(c_List_Olistrelp(_1665468, _1665470, c_List_Olist_ONil(_1665468), c_List_Olist_ONil(_1665468)))], (44266 ^ _782435) ^ [_1665499, _1665501] : [-(c_List_Olistrelp(_1665499, _1665501, c_List_Olist_ONil(_1665499), c_List_Olist_ONil(_1665499)))], (44268 ^ _782435) ^ [_1665530, _1665532] : [-(c_List_Olist_Olist__size(_1665530, _1665532, c_List_Olist_ONil(_1665530)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44270 ^ _782435) ^ [_1665561, _1665563] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1665561), _1665563)), -(c_List_Oupto(_1665563, _1665561) = c_List_Olist_ONil(tc_Int_Oint))], (44276 ^ _782435) ^ [_1665654, _1665656, _1665658] : [-(c_Enum_Oproduct(_1665654, _1665656, c_List_Olist_ONil(_1665654), _1665658) = c_List_Olist_ONil(tc_prod(_1665654, _1665656)))], (44278 ^ _782435) ^ [_1665708, _1665710, _1665712] : [c_List_Olist_ONil(_1665708) = hAPP(hAPP(c_List_Olist_OCons(_1665708), _1665710), _1665712)], (44280 ^ _782435) ^ [_1665760, _1665762, _1665764] : [hAPP(hAPP(c_List_Olist_OCons(_1665760), _1665762), _1665764) = c_List_Olist_ONil(_1665760)], (44282 ^ _782435) ^ [_1665797] : [-(c_Enum_Osublists(_1665797, c_List_Olist_ONil(_1665797)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1665797)), c_List_Olist_ONil(_1665797)), c_List_Olist_ONil(tc_List_Olist(_1665797))))], (44284 ^ _782435) ^ [_1665841, _1665843] : [-(hAPP(hAPP(c_List_Otake(_1665841), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1665843) = c_List_Olist_ONil(_1665841))], (44296 ^ _782435) ^ [_1666006, _1666008, _1666010] : [44297 ^ _782435 : [(44298 ^ _782435) ^ [] : [_1666008 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (44300 ^ _782435) ^ [] : [_1666010 = c_List_Olist_ONil(_1666006)]], -(hAPP(hAPP(c_List_Otake(_1666006), _1666008), _1666010) = c_List_Olist_ONil(_1666006))], (44286 ^ _782435) ^ [_1665894, _1665896, _1665898] : [hAPP(hAPP(c_List_Otake(_1665894), _1665896), _1665898) = c_List_Olist_ONil(_1665894), -(_1665896 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1665898 = c_List_Olist_ONil(_1665894))], (44304 ^ _782435) ^ [_1666149, _1666151] : [-(hAPP(hAPP(c_List_Otake(_1666149), _1666151), c_List_Olist_ONil(_1666149)) = c_List_Olist_ONil(_1666149))], (44306 ^ _782435) ^ [_1666195, _1666197] : [_1666195 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_Enum_On__lists(_1666197, _1666195, c_List_Olist_ONil(_1666197)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666197)), c_List_Olist_ONil(_1666197)), c_List_Olist_ONil(tc_List_Olist(_1666197))))], (44312 ^ _782435) ^ [_1666310, _1666312] : [-(_1666310 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_Enum_On__lists(_1666312, _1666310, c_List_Olist_ONil(_1666312)) = c_List_Olist_ONil(tc_List_Olist(_1666312)))], (44318 ^ _782435) ^ [_1666358, _1666360] : [-(c_Enum_On__lists(_1666358, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1666360) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1666358)), c_List_Olist_ONil(_1666358)), c_List_Olist_ONil(tc_List_Olist(_1666358))))], (44320 ^ _782435) ^ [_1666418, _1666420] : [hAPP(c_List_Oset(_1666418), _1666420) = c_Orderings_Obot__class_Obot(tc_fun(_1666418, tc_HOL_Obool)), -(_1666420 = c_List_Olist_ONil(_1666418))], (44326 ^ _782435) ^ [_1666515, _1666517] : [_1666517 = c_List_Olist_ONil(_1666515), -(hAPP(c_List_Oset(_1666515), _1666517) = c_Orderings_Obot__class_Obot(tc_fun(_1666515, tc_HOL_Obool)))], (44332 ^ _782435) ^ [_1666633, _1666635] : [c_Orderings_Obot__class_Obot(tc_fun(_1666633, tc_HOL_Obool)) = hAPP(c_List_Oset(_1666633), _1666635), -(_1666635 = c_List_Olist_ONil(_1666633))], (44338 ^ _782435) ^ [_1666730, _1666732] : [_1666732 = c_List_Olist_ONil(_1666730), -(c_Orderings_Obot__class_Obot(tc_fun(_1666730, tc_HOL_Obool)) = hAPP(c_List_Oset(_1666730), _1666732))], (44344 ^ _782435) ^ [_1666833] : [-(hAPP(c_List_Oset(_1666833), c_List_Olist_ONil(_1666833)) = c_Orderings_Obot__class_Obot(tc_fun(_1666833, tc_HOL_Obool)))], (44346 ^ _782435) ^ [_1666880, _1666882, _1666884] : [_1666880 = c_List_Olist_ONil(_1666882), -(c_List_Obutlast(_1666882, hAPP(hAPP(c_List_Olist_OCons(_1666882), _1666884), _1666880)) = c_List_Olist_ONil(_1666882))], (44352 ^ _782435) ^ [_1666983, _1666985, _1666987] : [-(_1666983 = c_List_Olist_ONil(_1666985)), -(c_List_Obutlast(_1666985, hAPP(hAPP(c_List_Olist_OCons(_1666985), _1666987), _1666983)) = hAPP(hAPP(c_List_Olist_OCons(_1666985), _1666987), c_List_Obutlast(_1666985, _1666983)))], (44358 ^ _782435) ^ [_1667062, _1667064] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667062)), _1667064) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(_1667064 = c_List_Olist_ONil(_1667062))], (44364 ^ _782435) ^ [_1667153, _1667155] : [_1667155 = c_List_Olist_ONil(_1667153), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667153)), _1667155) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44370 ^ _782435) ^ [_1667250] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1667250)), c_List_Olist_ONil(_1667250)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (44372 ^ _782435) ^ [_1667282] : [-(c_List_Obutlast(_1667282, c_List_Olist_ONil(_1667282)) = c_List_Olist_ONil(_1667282))], (44374 ^ _782435) ^ [_1667312] : [class_Groups_Omonoid__add(_1667312), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1667312), c_List_Olist_ONil(_1667312)) = c_Groups_Ozero__class_Ozero(_1667312))], (44380 ^ _782435) ^ [_1667403, _1667405, _1667407] : [-(hAPP(hAPP(c_List_Olist__update(_1667403, c_List_Olist_ONil(_1667403)), _1667405), _1667407) = c_List_Olist_ONil(_1667403))], (44382 ^ _782435) ^ [_1667443, _1667445, _1667447] : [-(hAPP(hAPP(c_List_Olist__update(_1667443, c_List_Olist_ONil(_1667443)), _1667445), _1667447) = c_List_Olist_ONil(_1667443))], (44384 ^ _782435) ^ [_1667504, _1667506, _1667508, _1667510] : [hAPP(hAPP(c_List_Olist__update(_1667504, _1667506), _1667508), _1667510) = c_List_Olist_ONil(_1667504), -(_1667506 = c_List_Olist_ONil(_1667504))], (44390 ^ _782435) ^ [_1667607, _1667609, _1667611, _1667613] : [_1667609 = c_List_Olist_ONil(_1667607), -(hAPP(hAPP(c_List_Olist__update(_1667607, _1667609), _1667611), _1667613) = c_List_Olist_ONil(_1667607))], (44396 ^ _782435) ^ [_1667716, _1667718] : [-(c_List_Osublist(_1667716, _1667718, c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))) = c_List_Olist_ONil(_1667716))], (44398 ^ _782435) ^ [_1667762, _1667764] : [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(_1667762)), _1667764))), _1667764 = c_List_Olist_ONil(_1667762)], (44404 ^ _782435) ^ [_1667856, _1667858] : [-(_1667858 = c_List_Olist_ONil(_1667856)), -(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(_1667856)), _1667858))))], (44410 ^ _782435) ^ [_1667905, _1667907, _1667909] : [-(hAPP(hAPP(c_List_Otake(_1667905), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1667905), _1667907), _1667909)) = hAPP(hAPP(c_List_Olist_OCons(_1667905), _1667907), c_List_Olist_ONil(_1667905)))], (44412 ^ _782435) ^ [_1667973, _1667975, _1667977] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1667973), tc_List_Olist(_1667973))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1667973), tc_List_Olist(_1667973)), c_List_Olist_ONil(_1667973)), _1667975)), c_List_Olistrel1(_1667973, _1667977)))], (44414 ^ _782435) ^ [_1668047, _1668049, _1668051] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668047), tc_List_Olist(_1668047))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668047), tc_List_Olist(_1668047)), _1668049), c_List_Olist_ONil(_1668047))), c_List_Olistrel1(_1668047, _1668051)))], (44416 ^ _782435) ^ [_1668106, _1668108] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668106), tc_List_Olist(_1668106))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668106), tc_List_Olist(_1668106)), c_List_Olist_ONil(_1668106)), c_List_Olist_ONil(_1668106))), c_List_Olistrel(_1668106, _1668108))))], (44418 ^ _782435) ^ [_1668180, _1668182, _1668184] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668180), tc_List_Olist(_1668180))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668180), tc_List_Olist(_1668180)), _1668182), c_List_Olist_ONil(_1668180))), c_List_Olexord(_1668180, _1668184)))], (44420 ^ _782435) ^ [_1668254, _1668256, _1668258] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668254), tc_List_Olist(_1668254))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668254), tc_List_Olist(_1668254)), _1668256), c_List_Olist_ONil(_1668254))), c_List_Olex(_1668254, _1668258)))], (44422 ^ _782435) ^ [_1668328, _1668330, _1668332] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1668328), tc_List_Olist(_1668328))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1668328), tc_List_Olist(_1668328)), c_List_Olist_ONil(_1668328)), _1668330)), c_List_Olex(_1668328, _1668332)))], (44424 ^ _782435) ^ [_1668387, _1668389, _1668391, _1668393] : [-(hAPP(hAPP(c_List_Otake(_1668387), _1668389), hAPP(hAPP(c_List_Olist_OCons(_1668387), _1668391), _1668393)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1668387), c_List_Olist_ONil(_1668387), hAPP(hAPP(c_COMBB(tc_List_Olist(_1668387), tc_List_Olist(_1668387), tc_Nat_Onat), hAPP(c_List_Olist_OCons(_1668387), _1668391)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1668387), tc_List_Olist(_1668387)), c_List_Otake(_1668387)), _1668393)), _1668389))], (44426 ^ _782435) ^ [_1668485, _1668487] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1668485), _1668487)), -(c_List_Oupto(_1668485, _1668487) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1668485), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1668485), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1668487)))], (44432 ^ _782435) ^ [_1668602, _1668604] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1668602), _1668604))), -(c_List_Oupto(_1668602, _1668604) = c_List_Olist_ONil(tc_Int_Oint))], (44438 ^ _782435) ^ [_1668660, _1668662, _1668664] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668660)), -(c_List_Osublist(_1668662, hAPP(hAPP(c_List_Olist_OCons(_1668662), _1668664), c_List_Olist_ONil(_1668662)), _1668660) = hAPP(hAPP(c_List_Olist_OCons(_1668662), _1668664), c_List_Olist_ONil(_1668662)))], (44444 ^ _782435) ^ [_1668785, _1668787, _1668789] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1668785))), -(c_List_Osublist(_1668787, hAPP(hAPP(c_List_Olist_OCons(_1668787), _1668789), c_List_Olist_ONil(_1668787)), _1668785) = c_List_Olist_ONil(_1668787))], (44450 ^ _782435) ^ [_1668843] : [-(c_List_Olists(_1668843, c_Orderings_Obot__class_Obot(tc_fun(_1668843, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1668843)), c_List_Olist_ONil(_1668843)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1668843), tc_HOL_Obool))))], (44452 ^ _782435) ^ [_1668908, _1668910, _1668912, _1668914] : [_1668908 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Otake(_1668910), _1668908), hAPP(hAPP(c_List_Olist_OCons(_1668910), _1668912), _1668914)) = c_List_Olist_ONil(_1668910))], (44458 ^ _782435) ^ [_1669019, _1669021, _1669023, _1669025] : [-(_1669019 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Otake(_1669021), _1669019), hAPP(hAPP(c_List_Olist_OCons(_1669021), _1669023), _1669025)) = hAPP(hAPP(c_List_Olist_OCons(_1669021), _1669023), hAPP(hAPP(c_List_Otake(_1669021), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1669019), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1669025)))], (44464 ^ _782435) ^ [_1669108, _1669110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669108)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669110))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669108), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669110)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669108)), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669108)), c_Groups_Oone__class_Oone(tc_Int_Oint)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669110))))], (44470 ^ _782435) ^ [_1669267, _1669269] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669267)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669269)))), -(c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669267), hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint), _1669269)) = c_List_Olist_ONil(tc_Int_Oint))], (44476 ^ _782435) ^ [_1669325, _1669327] : [-(hAPP(c_Relation_OImage(tc_List_Olist(_1669325), tc_List_Olist(_1669325), c_List_Olistrel(_1669325, _1669327)), hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669325)), c_List_Olist_ONil(_1669325)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669325), tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669325)), c_List_Olist_ONil(_1669325)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669325), tc_HOL_Obool))))], (44478 ^ _782435) ^ [_1669402, _1669404] : [-(c_List_Oset__Cons(_1669402, _1669404, hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669402)), c_List_Olist_ONil(_1669402)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669402), tc_HOL_Obool)))) = hAPP(c_Set_Oimage(_1669402, tc_List_Olist(_1669402), hAPP(hAPP(c_COMBC(_1669402, tc_List_Olist(_1669402), tc_List_Olist(_1669402)), c_List_Olist_OCons(_1669402)), c_List_Olist_ONil(_1669402))), _1669404))], (44480 ^ _782435) ^ [_1669477, _1669479] : [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), _1669477), _1669479))), 44483 ^ _782435 : [(44484 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1669477), _1669479)), -(c_List_Oupto(_1669477, _1669479) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint), _1669477), c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1669477), c_Groups_Oone__class_Oone(tc_Int_Oint)), _1669479)))], (44490 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), _1669477), _1669479))), -(c_List_Oupto(_1669477, _1669479) = c_List_Olist_ONil(tc_Int_Oint))]]], (44496 ^ _782435) ^ [_1669727, _1669729, _1669731] : [-(_1669727 = c_List_Olist_ONil(_1669729)), -(hBOOL(hAPP(hAPP(c_member(_1669729), hAPP(c_Product__Type_Ofst(_1669729, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect(_1669729, _1669727), _1669731))), hAPP(c_List_Oset(_1669729), _1669727))))], (44502 ^ _782435) ^ [_1669791] : [-(c_List_Olistset(_1669791, c_List_Olist_ONil(tc_fun(_1669791, tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(_1669791)), c_List_Olist_ONil(_1669791)), c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(_1669791), tc_HOL_Obool))))], (44504 ^ _782435) ^ [_1669841, _1669843, _1669845, _1669847, _1669849] : [-(hAPP(hAPP(c_List_Ozip(_1669841, _1669843), _1669845), hAPP(hAPP(c_List_Olist_OCons(_1669843), _1669847), _1669849)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1669841, _1669843)), _1669841, c_List_Olist_ONil(tc_prod(_1669841, _1669843)), hAPP(hAPP(c_COMBC(_1669841, tc_fun(tc_List_Olist(_1669841), tc_List_Olist(tc_prod(_1669841, _1669843))), tc_fun(tc_List_Olist(_1669841), tc_List_Olist(tc_prod(_1669841, _1669843)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1669841, _1669843)), tc_List_Olist(tc_prod(_1669841, _1669843))), tc_fun(tc_fun(tc_List_Olist(_1669841), tc_List_Olist(tc_prod(_1669841, _1669843))), tc_fun(tc_List_Olist(_1669841), tc_List_Olist(tc_prod(_1669841, _1669843)))), _1669841), c_COMBB(tc_List_Olist(tc_prod(_1669841, _1669843)), tc_List_Olist(tc_prod(_1669841, _1669843)), tc_List_Olist(_1669841))), hAPP(hAPP(c_COMBB(tc_prod(_1669841, _1669843), tc_fun(tc_List_Olist(tc_prod(_1669841, _1669843)), tc_List_Olist(tc_prod(_1669841, _1669843))), _1669841), c_List_Olist_OCons(tc_prod(_1669841, _1669843))), hAPP(hAPP(c_COMBC(_1669841, _1669843, tc_prod(_1669841, _1669843)), c_Product__Type_OPair(_1669841, _1669843)), _1669847)))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1669841), tc_List_Olist(_1669843), tc_List_Olist(tc_prod(_1669841, _1669843))), c_List_Ozip(_1669841, _1669843)), _1669849))), _1669845))], (44506 ^ _782435) ^ [_1670068, _1670070, _1670072, _1670074, _1670076, _1670078] : [-(hAPP(c_List_Olist_Olist__case(_1670068, _1670070, _1670072, _1670074), hAPP(hAPP(c_List_Olist_OCons(_1670070), _1670076), _1670078)) = hAPP(hAPP(_1670074, _1670076), _1670078))], (44508 ^ _782435) ^ [_1670123, _1670125, _1670127, _1670129] : [-(hAPP(c_List_Olist_Olist__case(_1670123, _1670125, _1670127, _1670129), c_List_Olist_ONil(_1670125)) = _1670127)], (44510 ^ _782435) ^ [_1670162, _1670164, _1670166] : [-(c_List_Olistset(_1670162, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1670162, tc_HOL_Obool)), _1670164), _1670166)) = c_List_Oset__Cons(_1670162, _1670164, c_List_Olistset(_1670162, _1670166)))], (44512 ^ _782435) ^ [_1670210, _1670212, _1670214, _1670216, _1670218] : [-(hAPP(hAPP(c_List_Ozip(_1670210, _1670212), hAPP(hAPP(c_List_Olist_OCons(_1670210), _1670214), _1670216)), _1670218) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(_1670210, _1670212)), _1670212, c_List_Olist_ONil(tc_prod(_1670210, _1670212)), hAPP(hAPP(c_COMBC(_1670212, tc_fun(tc_List_Olist(_1670212), tc_List_Olist(tc_prod(_1670210, _1670212))), tc_fun(tc_List_Olist(_1670212), tc_List_Olist(tc_prod(_1670210, _1670212)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(_1670210, _1670212)), tc_List_Olist(tc_prod(_1670210, _1670212))), tc_fun(tc_fun(tc_List_Olist(_1670212), tc_List_Olist(tc_prod(_1670210, _1670212))), tc_fun(tc_List_Olist(_1670212), tc_List_Olist(tc_prod(_1670210, _1670212)))), _1670212), c_COMBB(tc_List_Olist(tc_prod(_1670210, _1670212)), tc_List_Olist(tc_prod(_1670210, _1670212)), tc_List_Olist(_1670212))), hAPP(hAPP(c_COMBB(tc_prod(_1670210, _1670212), tc_fun(tc_List_Olist(tc_prod(_1670210, _1670212)), tc_List_Olist(tc_prod(_1670210, _1670212))), _1670212), c_List_Olist_OCons(tc_prod(_1670210, _1670212))), hAPP(c_Product__Type_OPair(_1670210, _1670212), _1670214)))), hAPP(c_List_Ozip(_1670210, _1670212), _1670216))), _1670218))], (44514 ^ _782435) ^ [_1670411, _1670413, _1670415] : [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), _1670411), _1670413))), -(hBOOL(hAPP(hAPP(_1670415, _1670411), _1670413))), 44521 ^ _782435 : [(44522 ^ _782435) ^ [] : [-(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 ^ [_1670411, _1670413, _1670415]), 44520 ^ [_1670411, _1670413, _1670415]))))], (44530 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1670415, 44519 ^ [_1670411, _1670413, _1670415]), 44520 ^ [_1670411, _1670413, _1670415]))], (44524 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint), 44519 ^ [_1670411, _1670413, _1670415]), 44520 ^ [_1670411, _1670413, _1670415])), -(hBOOL(hAPP(hAPP(_1670415, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 44519 ^ [_1670411, _1670413, _1670415]), c_Groups_Oone__class_Oone(tc_Int_Oint))), 44520 ^ [_1670411, _1670413, _1670415])))]]], (44534 ^ _782435) ^ [_1670920, _1670922, _1670924, _1670926, _1670928] : [_1670920 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1670922, _1670924, _1670926), _1670920), _1670928) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1670924), _1670922), c_List_Olist_ONil(_1670924)), _1670928))], (44540 ^ _782435) ^ [_1671043, _1671045, _1671047, _1671049, _1671051] : [-(_1671043 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(hAPP(c_Lazy__Sequence_Oanamorph(_1671045, _1671047, _1671049), _1671043), _1671051) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(_1671047), _1671045), tc_prod(_1671047, _1671045), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671047), _1671045), c_List_Olist_ONil(_1671047)), _1671051), hAPP(c_Product__Type_Oprod_Oprod__case(_1671047, _1671045, tc_prod(tc_List_Olist(_1671047), _1671045)), hAPP(hAPP(c_COMBC(_1671047, tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045)), tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045))), hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(_1671047), _1671045), tc_prod(tc_List_Olist(_1671047), _1671045)), tc_fun(tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045)), tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045))), _1671047), c_COMBB(tc_prod(tc_List_Olist(_1671047), _1671045), tc_prod(tc_List_Olist(_1671047), _1671045), _1671045)), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1671047), tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045))), tc_fun(tc_prod(tc_List_Olist(_1671047), _1671045), tc_prod(tc_List_Olist(_1671047), _1671045)), _1671047), c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1671047), _1671045, tc_prod(tc_List_Olist(_1671047), _1671045))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1671047), tc_List_Olist(_1671047)), tc_fun(tc_List_Olist(_1671047), tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045))), _1671047), hAPP(c_COMBB(tc_List_Olist(_1671047), tc_fun(_1671045, tc_prod(tc_List_Olist(_1671047), _1671045)), tc_List_Olist(_1671047)), c_Product__Type_OPair(tc_List_Olist(_1671047), _1671045))), c_List_Olist_OCons(_1671047))))), hAPP(c_Lazy__Sequence_Oanamorph(_1671045, _1671047, _1671049), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1671043), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))))), hAPP(_1671049, _1671051)))], (44546 ^ _782435) ^ [_1671337, _1671339, _1671341, _1671343] : [-(c_List_Osublist(_1671337, hAPP(hAPP(c_List_Olist_OCons(_1671337), _1671339), _1671341), _1671343) = hAPP(hAPP(c_List_Oappend(_1671337), hAPP(hAPP(hAPP(c_If(tc_List_Olist(_1671337)), hAPP(hAPP(c_member(tc_Nat_Onat), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1671343)), hAPP(hAPP(c_List_Olist_OCons(_1671337), _1671339), c_List_Olist_ONil(_1671337))), c_List_Olist_ONil(_1671337))), c_List_Osublist(_1671337, _1671341, 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)), _1671343)))))], (44548 ^ _782435) ^ [_1671451, _1671453, _1671455, _1671457, _1671459, _1671461] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671451), tc_List_Olist(_1671451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671451), tc_List_Olist(_1671451)), hAPP(hAPP(c_List_Oappend(_1671451), _1671453), hAPP(hAPP(c_List_Olist_OCons(_1671451), _1671455), c_List_Olist_ONil(_1671451)))), hAPP(hAPP(c_List_Oappend(_1671451), _1671457), hAPP(hAPP(c_List_Olist_OCons(_1671451), _1671459), c_List_Olist_ONil(_1671451))))), c_List_Olistrel1(_1671451, _1671461))), 44553 ^ _782435 : [(44554 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671451), tc_List_Olist(_1671451))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671451), tc_List_Olist(_1671451)), _1671453), _1671457)), c_List_Olistrel1(_1671451, _1671461))))], (44556 ^ _782435) ^ [] : [-(_1671455 = _1671459)]], 44557 ^ _782435 : [(44558 ^ _782435) ^ [] : [-(_1671453 = _1671457)], (44560 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1671451, _1671451)), hAPP(hAPP(c_Product__Type_OPair(_1671451, _1671451), _1671455), _1671459)), _1671461)))]]], (44562 ^ _782435) ^ [_1671861, _1671863, _1671865, _1671867, _1671869, _1671871] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671861), tc_List_Olist(_1671861))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671861), tc_List_Olist(_1671861)), hAPP(hAPP(c_List_Oappend(_1671861), _1671863), hAPP(hAPP(c_List_Olist_OCons(_1671861), _1671865), c_List_Olist_ONil(_1671861)))), hAPP(hAPP(c_List_Oappend(_1671861), _1671867), hAPP(hAPP(c_List_Olist_OCons(_1671861), _1671869), c_List_Olist_ONil(_1671861))))), c_List_Olistrel1(_1671861, _1671871)))), 44563 ^ _782435 : [(44564 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1671861), tc_List_Olist(_1671861))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1671861), tc_List_Olist(_1671861)), _1671863), _1671867)), c_List_Olistrel1(_1671861, _1671871))), _1671865 = _1671869], (44570 ^ _782435) ^ [] : [_1671863 = _1671867, hBOOL(hAPP(hAPP(c_member(tc_prod(_1671861, _1671861)), hAPP(hAPP(c_Product__Type_OPair(_1671861, _1671861), _1671865), _1671869)), _1671871))]]], (44578 ^ _782435) ^ [_1672353, _1672355, _1672357, _1672359, _1672361] : [hAPP(hAPP(c_List_Oappend(_1672353), _1672355), _1672357) = hAPP(hAPP(c_List_Olist_OCons(_1672353), _1672359), _1672361), 44583 ^ _782435 : [(44584 ^ _782435) ^ [] : [-(_1672355 = c_List_Olist_ONil(_1672353))], (44586 ^ _782435) ^ [] : [-(_1672357 = hAPP(hAPP(c_List_Olist_OCons(_1672353), _1672359), _1672361))]], 44588 ^ _782435 : [(44589 ^ _782435) ^ [] : [-(_1672355 = hAPP(hAPP(c_List_Olist_OCons(_1672353), _1672359), 44587 ^ [_1672353, _1672355, _1672357, _1672359, _1672361]))], (44591 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1672353), 44587 ^ [_1672353, _1672355, _1672357, _1672359, _1672361]), _1672357) = _1672361)]]], (44593 ^ _782435) ^ [_1672646, _1672648, _1672650, _1672652, _1672654] : [-(hAPP(hAPP(c_List_Oappend(_1672646), _1672648), _1672650) = hAPP(hAPP(c_List_Olist_OCons(_1672646), _1672652), _1672654)), 44594 ^ _782435 : [(44595 ^ _782435) ^ [] : [_1672648 = c_List_Olist_ONil(_1672646), _1672650 = hAPP(hAPP(c_List_Olist_OCons(_1672646), _1672652), _1672654)], (44601 ^ _782435) ^ [_1672829] : [_1672648 = hAPP(hAPP(c_List_Olist_OCons(_1672646), _1672652), _1672829), hAPP(hAPP(c_List_Oappend(_1672646), _1672829), _1672650) = _1672654]]], (44609 ^ _782435) ^ [_1673017, _1673019, _1673021, _1673023, _1673025] : [hAPP(hAPP(c_List_Olist_OCons(_1673017), _1673019), _1673021) = hAPP(hAPP(c_List_Oappend(_1673017), _1673023), _1673025), 44614 ^ _782435 : [(44615 ^ _782435) ^ [] : [-(_1673023 = c_List_Olist_ONil(_1673017))], (44617 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673017), _1673019), _1673021) = _1673025)]], 44619 ^ _782435 : [(44620 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673017), _1673019), 44618 ^ [_1673017, _1673019, _1673021, _1673023, _1673025]) = _1673023)], (44622 ^ _782435) ^ [] : [-(_1673021 = hAPP(hAPP(c_List_Oappend(_1673017), 44618 ^ [_1673017, _1673019, _1673021, _1673023, _1673025]), _1673025))]]], (44624 ^ _782435) ^ [_1673310, _1673312, _1673314, _1673316, _1673318] : [-(hAPP(hAPP(c_List_Olist_OCons(_1673310), _1673312), _1673314) = hAPP(hAPP(c_List_Oappend(_1673310), _1673316), _1673318)), 44625 ^ _782435 : [(44626 ^ _782435) ^ [] : [_1673316 = c_List_Olist_ONil(_1673310), hAPP(hAPP(c_List_Olist_OCons(_1673310), _1673312), _1673314) = _1673318], (44632 ^ _782435) ^ [_1673493] : [hAPP(hAPP(c_List_Olist_OCons(_1673310), _1673312), _1673493) = _1673316, _1673314 = hAPP(hAPP(c_List_Oappend(_1673310), _1673493), _1673318)]]], (44640 ^ _782435) ^ [_1673681, _1673683, _1673685, _1673687, _1673689] : [hAPP(hAPP(c_List_Oappend(_1673681), _1673683), hAPP(hAPP(c_List_Olist_OCons(_1673681), _1673685), c_List_Olist_ONil(_1673681))) = hAPP(hAPP(c_List_Oappend(_1673681), _1673687), hAPP(hAPP(c_List_Olist_OCons(_1673681), _1673689), c_List_Olist_ONil(_1673681))), 44643 ^ _782435 : [(44644 ^ _782435) ^ [] : [-(_1673683 = _1673687)], (44646 ^ _782435) ^ [] : [-(_1673685 = _1673689)]]], (44648 ^ _782435) ^ [_1673858, _1673860, _1673862, _1673864, _1673866] : [-(hAPP(hAPP(c_List_Oappend(_1673858), _1673860), hAPP(hAPP(c_List_Olist_OCons(_1673858), _1673862), c_List_Olist_ONil(_1673858))) = hAPP(hAPP(c_List_Oappend(_1673858), _1673864), hAPP(hAPP(c_List_Olist_OCons(_1673858), _1673866), c_List_Olist_ONil(_1673858)))), _1673860 = _1673864, _1673862 = _1673866], (44658 ^ _782435) ^ [_1674073, _1674075, _1674077, _1674079] : [-(hAPP(hAPP(c_List_Oappend(_1674073), hAPP(hAPP(c_List_Olist_OCons(_1674073), _1674075), _1674077)), _1674079) = hAPP(hAPP(c_List_Olist_OCons(_1674073), _1674075), hAPP(hAPP(c_List_Oappend(_1674073), _1674077), _1674079)))], (44660 ^ _782435) ^ [_1674134, _1674136, _1674138, _1674140, _1674142, _1674144] : [hAPP(hAPP(c_List_Olist_OCons(_1674134), _1674136), _1674138) = _1674140, _1674142 = hAPP(hAPP(c_List_Oappend(_1674134), _1674138), _1674144), -(hAPP(hAPP(c_List_Olist_OCons(_1674134), _1674136), _1674142) = hAPP(hAPP(c_List_Oappend(_1674134), _1674140), _1674144))], (44670 ^ _782435) ^ [_1674364, _1674366, _1674368, _1674370] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674364)), hAPP(hAPP(c_List_Oappend(_1674364), _1674366), _1674368)), c_List_Olists(_1674364, _1674370))), 44673 ^ _782435 : [(44674 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674364)), _1674366), c_List_Olists(_1674364, _1674370))))], (44676 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674364)), _1674368), c_List_Olists(_1674364, _1674370))))]]], (44678 ^ _782435) ^ [_1674555, _1674557, _1674559, _1674561] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674555)), hAPP(hAPP(c_List_Oappend(_1674555), _1674557), _1674559)), c_List_Olists(_1674555, _1674561)))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674555)), _1674557), c_List_Olists(_1674555, _1674561))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1674555)), _1674559), c_List_Olists(_1674555, _1674561)))], (44688 ^ _782435) ^ [_1674782, _1674784, _1674786, _1674788, _1674790, _1674792] : [hAPP(hAPP(c_List_Oappend(_1674782), _1674784), _1674786) = _1674788, _1674790 = hAPP(hAPP(c_List_Oappend(_1674782), _1674786), _1674792), -(hAPP(hAPP(c_List_Oappend(_1674782), _1674784), _1674790) = hAPP(hAPP(c_List_Oappend(_1674782), _1674788), _1674792))], (44698 ^ _782435) ^ [_1675012, _1675014, _1675016, _1675018] : [hAPP(hAPP(c_List_Oappend(_1675012), _1675014), _1675016) = hAPP(hAPP(c_List_Oappend(_1675012), _1675018), _1675016), -(_1675014 = _1675018)], (44704 ^ _782435) ^ [_1675121, _1675123, _1675125, _1675127] : [_1675123 = _1675127, -(hAPP(hAPP(c_List_Oappend(_1675121), _1675123), _1675125) = hAPP(hAPP(c_List_Oappend(_1675121), _1675127), _1675125))], (44710 ^ _782435) ^ [_1675257, _1675259, _1675261, _1675263] : [hAPP(hAPP(c_List_Oappend(_1675257), _1675259), _1675261) = hAPP(hAPP(c_List_Oappend(_1675257), _1675259), _1675263), -(_1675261 = _1675263)], (44716 ^ _782435) ^ [_1675366, _1675368, _1675370, _1675372] : [_1675370 = _1675372, -(hAPP(hAPP(c_List_Oappend(_1675366), _1675368), _1675370) = hAPP(hAPP(c_List_Oappend(_1675366), _1675368), _1675372))], (44722 ^ _782435) ^ [_1675505, _1675507, _1675509, _1675511, _1675513] : [hAPP(hAPP(c_List_Oappend(_1675505), _1675507), _1675509) = hAPP(hAPP(c_List_Oappend(_1675505), _1675511), _1675513), 44728 ^ _782435 : [(44729 ^ _782435) ^ [] : [-(_1675507 = hAPP(hAPP(c_List_Oappend(_1675505), _1675511), 44725 ^ [_1675505, _1675507, _1675509, _1675511, _1675513]))], (44731 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1675505), 44725 ^ [_1675505, _1675507, _1675509, _1675511, _1675513]), _1675509) = _1675513)]], 44732 ^ _782435 : [(44733 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1675505), _1675507), 44725 ^ [_1675505, _1675507, _1675509, _1675511, _1675513]) = _1675511)], (44735 ^ _782435) ^ [] : [-(_1675509 = hAPP(hAPP(c_List_Oappend(_1675505), 44725 ^ [_1675505, _1675507, _1675509, _1675511, _1675513]), _1675513))]]], (44737 ^ _782435) ^ [_1675836, _1675838, _1675840, _1675842, _1675844] : [-(hAPP(hAPP(c_List_Oappend(_1675836), _1675838), _1675840) = hAPP(hAPP(c_List_Oappend(_1675836), _1675842), _1675844)), 44738 ^ _782435 : [(44739 ^ _782435) ^ [_1675948] : [_1675838 = hAPP(hAPP(c_List_Oappend(_1675836), _1675842), _1675948), hAPP(hAPP(c_List_Oappend(_1675836), _1675948), _1675840) = _1675844], (44745 ^ _782435) ^ [_1676060] : [hAPP(hAPP(c_List_Oappend(_1675836), _1675838), _1676060) = _1675842, _1675840 = hAPP(hAPP(c_List_Oappend(_1675836), _1676060), _1675844)]]], (44753 ^ _782435) ^ [_1676224, _1676226, _1676228, _1676230] : [-(hAPP(hAPP(c_List_Oappend(_1676224), hAPP(hAPP(c_List_Oappend(_1676224), _1676226), _1676228)), _1676230) = hAPP(hAPP(c_List_Oappend(_1676224), _1676226), hAPP(hAPP(c_List_Oappend(_1676224), _1676228), _1676230)))], (44755 ^ _782435) ^ [_1676285, _1676287, _1676289] : [-(hAPP(c_List_Oset(_1676285), hAPP(hAPP(c_List_Oappend(_1676285), _1676287), _1676289)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1676285, tc_HOL_Obool)), hAPP(c_List_Oset(_1676285), _1676287)), hAPP(c_List_Oset(_1676285), _1676289)))], (44757 ^ _782435) ^ [_1676346, _1676348, _1676350, _1676352, _1676354, _1676356] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676346)), _1676348) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676350)), _1676352), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676346)), _1676354) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676350)), _1676356), -(hAPP(hAPP(c_List_Ozip(_1676346, _1676350), hAPP(hAPP(c_List_Oappend(_1676346), _1676348), _1676354)), hAPP(hAPP(c_List_Oappend(_1676350), _1676352), _1676356)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1676346, _1676350)), hAPP(hAPP(c_List_Ozip(_1676346, _1676350), _1676348), _1676352)), hAPP(hAPP(c_List_Ozip(_1676346, _1676350), _1676354), _1676356)))], (44767 ^ _782435) ^ [_1676655, _1676657, _1676659] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676655)), hAPP(hAPP(c_List_Oappend(_1676655), _1676657), _1676659)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676655)), _1676657)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1676655)), _1676659)))], (44769 ^ _782435) ^ [_1676717, _1676719, _1676721] : [class_Groups_Omonoid__add(_1676717), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1676717), hAPP(hAPP(c_List_Oappend(_1676717), _1676719), _1676721)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1676717), hAPP(c_List_Omonoid__add__class_Olistsum(_1676717), _1676719)), hAPP(c_List_Omonoid__add__class_Olistsum(_1676717), _1676721)))], (44775 ^ _782435) ^ [_1676868, _1676870, _1676872] : [_1676868 = c_List_Olist_ONil(_1676870), -(c_List_Obutlast(_1676870, hAPP(hAPP(c_List_Oappend(_1676870), _1676872), _1676868)) = c_List_Obutlast(_1676870, _1676872))], (44781 ^ _782435) ^ [_1676973, _1676975, _1676977] : [-(_1676973 = c_List_Olist_ONil(_1676975)), -(c_List_Obutlast(_1676975, hAPP(hAPP(c_List_Oappend(_1676975), _1676977), _1676973)) = hAPP(hAPP(c_List_Oappend(_1676975), _1676977), c_List_Obutlast(_1676975, _1676973)))], (44787 ^ _782435) ^ [_1677037, _1677039] : [-(hAPP(hAPP(c_List_Oappend(_1677037), c_List_Olist_ONil(_1677037)), _1677039) = _1677039)], (44789 ^ _782435) ^ [_1677090, _1677092, _1677094] : [c_List_Olist_ONil(_1677090) = hAPP(hAPP(c_List_Oappend(_1677090), _1677092), _1677094), 44792 ^ _782435 : [(44793 ^ _782435) ^ [] : [-(_1677092 = c_List_Olist_ONil(_1677090))], (44795 ^ _782435) ^ [] : [-(_1677094 = c_List_Olist_ONil(_1677090))]]], (44797 ^ _782435) ^ [_1677219, _1677221, _1677223] : [-(c_List_Olist_ONil(_1677219) = hAPP(hAPP(c_List_Oappend(_1677219), _1677221), _1677223)), _1677221 = c_List_Olist_ONil(_1677219), _1677223 = c_List_Olist_ONil(_1677219)], (44807 ^ _782435) ^ [_1677382, _1677384] : [-(hAPP(hAPP(c_List_Oappend(_1677382), _1677384), c_List_Olist_ONil(_1677382)) = _1677384)], (44809 ^ _782435) ^ [_1677435, _1677437, _1677439] : [_1677435 = hAPP(hAPP(c_List_Oappend(_1677437), _1677435), _1677439), -(_1677439 = c_List_Olist_ONil(_1677437))], (44815 ^ _782435) ^ [_1677530, _1677532, _1677534] : [_1677534 = c_List_Olist_ONil(_1677532), -(_1677530 = hAPP(hAPP(c_List_Oappend(_1677532), _1677530), _1677534))], (44821 ^ _782435) ^ [_1677649, _1677651, _1677653] : [_1677649 = hAPP(hAPP(c_List_Oappend(_1677651), _1677653), _1677649), -(_1677653 = c_List_Olist_ONil(_1677651))], (44827 ^ _782435) ^ [_1677744, _1677746, _1677748] : [_1677748 = c_List_Olist_ONil(_1677746), -(_1677744 = hAPP(hAPP(c_List_Oappend(_1677746), _1677748), _1677744))], (44833 ^ _782435) ^ [_1677863, _1677865, _1677867] : [hAPP(hAPP(c_List_Oappend(_1677863), _1677865), _1677867) = c_List_Olist_ONil(_1677863), 44836 ^ _782435 : [(44837 ^ _782435) ^ [] : [-(_1677865 = c_List_Olist_ONil(_1677863))], (44839 ^ _782435) ^ [] : [-(_1677867 = c_List_Olist_ONil(_1677863))]]], (44841 ^ _782435) ^ [_1677992, _1677994, _1677996] : [-(hAPP(hAPP(c_List_Oappend(_1677992), _1677994), _1677996) = c_List_Olist_ONil(_1677992)), _1677994 = c_List_Olist_ONil(_1677992), _1677996 = c_List_Olist_ONil(_1677992)], (44851 ^ _782435) ^ [_1678173, _1678175, _1678177] : [hAPP(hAPP(c_List_Oappend(_1678173), _1678175), _1678177) = _1678175, -(_1678177 = c_List_Olist_ONil(_1678173))], (44857 ^ _782435) ^ [_1678268, _1678270, _1678272] : [_1678272 = c_List_Olist_ONil(_1678268), -(hAPP(hAPP(c_List_Oappend(_1678268), _1678270), _1678272) = _1678270)], (44863 ^ _782435) ^ [_1678387, _1678389, _1678391] : [hAPP(hAPP(c_List_Oappend(_1678387), _1678389), _1678391) = _1678391, -(_1678389 = c_List_Olist_ONil(_1678387))], (44869 ^ _782435) ^ [_1678482, _1678484, _1678486] : [_1678484 = c_List_Olist_ONil(_1678482), -(hAPP(hAPP(c_List_Oappend(_1678482), _1678484), _1678486) = _1678486)], (44875 ^ _782435) ^ [_1678583, _1678585, _1678587] : [_1678583 = _1678585, -(_1678583 = hAPP(hAPP(c_List_Oappend(_1678587), c_List_Olist_ONil(_1678587)), _1678585))], (44881 ^ _782435) ^ [_1678682, _1678684, _1678686, _1678688] : [-(hAPP(hAPP(c_List_Onth(_1678682), hAPP(hAPP(c_List_Oappend(_1678682), _1678684), hAPP(hAPP(c_List_Olist_OCons(_1678682), _1678686), _1678688))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678682)), _1678684)) = _1678686)], (44883 ^ _782435) ^ [_1678742, _1678744, _1678746, _1678748] : [-(hAPP(hAPP(c_List_Onth(_1678742), hAPP(hAPP(c_List_Oappend(_1678742), _1678744), _1678746)), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678742)), _1678744)), _1678748)) = hAPP(hAPP(c_List_Onth(_1678742), _1678746), _1678748))], (44885 ^ _782435) ^ [_1678808, _1678810, _1678812, _1678814] : [-(hAPP(hAPP(c_List_Otake(_1678808), _1678810), hAPP(hAPP(c_List_Oappend(_1678808), _1678812), _1678814)) = hAPP(hAPP(c_List_Oappend(_1678808), hAPP(hAPP(c_List_Otake(_1678808), _1678810), _1678812)), hAPP(hAPP(c_List_Otake(_1678808), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1678810), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678808)), _1678812))), _1678814)))], (44887 ^ _782435) ^ [_1678890, _1678892, _1678894, _1678896, _1678898] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1678890), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1678892)), _1678894))), -(hAPP(hAPP(c_List_Olist__update(_1678892, hAPP(hAPP(c_List_Oappend(_1678892), _1678894), _1678896)), _1678890), _1678898) = hAPP(hAPP(c_List_Oappend(_1678892), hAPP(hAPP(c_List_Olist__update(_1678892, _1678894), _1678890), _1678898)), _1678896))], (44893 ^ _782435) ^ [_1679065, _1679067, _1679069, _1679071, _1679073] : [-(hAPP(hAPP(c_List_Olist__update(_1679065, hAPP(hAPP(c_List_Oappend(_1679065), _1679067), hAPP(hAPP(c_List_Olist_OCons(_1679065), _1679069), _1679071))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1679065)), _1679067)), _1679073) = hAPP(hAPP(c_List_Oappend(_1679065), _1679067), hAPP(hAPP(c_List_Olist_OCons(_1679065), _1679073), _1679071)))], (44895 ^ _782435) ^ [_1679159, _1679161, _1679163, _1679165] : [hBOOL(hAPP(hAPP(c_member(_1679159), _1679161), hAPP(c_List_Oset(_1679159), _1679163))), -(c_List_Oremove1(_1679159, _1679161, hAPP(hAPP(c_List_Oappend(_1679159), _1679163), _1679165)) = hAPP(hAPP(c_List_Oappend(_1679159), c_List_Oremove1(_1679159, _1679161, _1679163)), _1679165))], (44901 ^ _782435) ^ [_1679306, _1679308, _1679310, _1679312] : [-(hBOOL(hAPP(hAPP(c_member(_1679306), _1679308), hAPP(c_List_Oset(_1679306), _1679310)))), -(c_List_Oremove1(_1679306, _1679308, hAPP(hAPP(c_List_Oappend(_1679306), _1679310), _1679312)) = hAPP(hAPP(c_List_Oappend(_1679306), _1679310), c_List_Oremove1(_1679306, _1679308, _1679312)))], (44907 ^ _782435) ^ [_1679384, _1679386, _1679388, _1679390] : [44908 ^ _782435 : [(44909 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679384), _1679386), hAPP(c_List_Oset(_1679384), c_List_Obutlast(_1679384, _1679388))))], (44911 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1679384), _1679386), hAPP(c_List_Oset(_1679384), c_List_Obutlast(_1679384, _1679390))))]], -(hBOOL(hAPP(hAPP(c_member(_1679384), _1679386), hAPP(c_List_Oset(_1679384), c_List_Obutlast(_1679384, hAPP(hAPP(c_List_Oappend(_1679384), _1679388), _1679390))))))], (44915 ^ _782435) ^ [_1679609, _1679611, _1679613] : [-(c_List_Obutlast(_1679609, hAPP(hAPP(c_List_Oappend(_1679609), _1679611), hAPP(hAPP(c_List_Olist_OCons(_1679609), _1679613), c_List_Olist_ONil(_1679609)))) = _1679611)], (44917 ^ _782435) ^ [_1679657, _1679659, _1679661, _1679663, _1679665, _1679667] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679657), tc_List_Olist(_1679657))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679657), tc_List_Olist(_1679657)), hAPP(hAPP(c_List_Oappend(_1679657), _1679659), _1679665)), hAPP(hAPP(c_List_Oappend(_1679657), _1679661), _1679667))), c_List_Olistrel1(_1679657, _1679663)))), 44918 ^ _782435 : [(44919 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679657), tc_List_Olist(_1679657))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679657), tc_List_Olist(_1679657)), _1679659), _1679661)), c_List_Olistrel1(_1679657, _1679663))), _1679665 = _1679667], (44925 ^ _782435) ^ [] : [_1679659 = _1679661, hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1679657), tc_List_Olist(_1679657))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1679657), tc_List_Olist(_1679657)), _1679665), _1679667)), c_List_Olistrel1(_1679657, _1679663)))]]], (44933 ^ _782435) ^ [_1680105, _1680107, _1680109, _1680111, _1680113] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1680105), tc_List_Olist(_1680105))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680105), tc_List_Olist(_1680105)), _1680107), _1680109)), c_List_Olexord(_1680105, _1680111))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1680105), tc_List_Olist(_1680105))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1680105), tc_List_Olist(_1680105)), hAPP(hAPP(c_List_Oappend(_1680105), _1680113), _1680107)), hAPP(hAPP(c_List_Oappend(_1680105), _1680113), _1680109))), c_List_Olexord(_1680105, _1680111))))], (44939 ^ _782435) ^ [_1680358, _1680360, _1680362] : [hBOOL(hAPP(c_List_Odistinct(_1680358), hAPP(hAPP(c_List_Oappend(_1680358), _1680360), _1680362))), 44942 ^ _782435 : [(44943 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680358), _1680360)))], (44945 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1680358), _1680362)))], (44947 ^ _782435) ^ [] : [-(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680358, tc_HOL_Obool)), hAPP(c_List_Oset(_1680358), _1680360)), hAPP(c_List_Oset(_1680358), _1680362)) = c_Orderings_Obot__class_Obot(tc_fun(_1680358, tc_HOL_Obool)))]]], (44949 ^ _782435) ^ [_1680575, _1680577, _1680579] : [-(hBOOL(hAPP(c_List_Odistinct(_1680575), hAPP(hAPP(c_List_Oappend(_1680575), _1680577), _1680579)))), hBOOL(hAPP(c_List_Odistinct(_1680575), _1680577)), hBOOL(hAPP(c_List_Odistinct(_1680575), _1680579)), hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1680575, tc_HOL_Obool)), hAPP(c_List_Oset(_1680575), _1680577)), hAPP(c_List_Oset(_1680575), _1680579)) = c_Orderings_Obot__class_Obot(tc_fun(_1680575, tc_HOL_Obool))], (44963 ^ _782435) ^ [_1680871, _1680873, _1680875, _1680877] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1680871), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1680873)), _1680875))), -(hAPP(hAPP(c_List_Onth(_1680873), hAPP(hAPP(c_List_Oappend(_1680873), _1680875), _1680877)), _1680871) = hAPP(hAPP(c_List_Onth(_1680873), _1680875), _1680871))], (44969 ^ _782435) ^ [_1681018, _1681020, _1681022, _1681024] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681018), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681020)), _1681022)))), -(hAPP(hAPP(c_List_Onth(_1681020), hAPP(hAPP(c_List_Oappend(_1681020), _1681022), _1681024)), _1681018) = hAPP(hAPP(c_List_Onth(_1681020), _1681024), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681018), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681020)), _1681022))))], (44975 ^ _782435) ^ [_1681127, _1681129, _1681131, _1681133, _1681135] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681127), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681129)), _1681131))), -(hAPP(hAPP(c_List_Olist__update(_1681129, hAPP(hAPP(c_List_Oappend(_1681129), _1681131), _1681133)), _1681127), _1681135) = hAPP(hAPP(c_List_Oappend(_1681129), hAPP(hAPP(c_List_Olist__update(_1681129, _1681131), _1681127), _1681135)), _1681133))], (44981 ^ _782435) ^ [_1681296, _1681298, _1681300, _1681302, _1681304] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1681296), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681298)), _1681300)))), -(hAPP(hAPP(c_List_Olist__update(_1681298, hAPP(hAPP(c_List_Oappend(_1681298), _1681300), _1681302)), _1681296), _1681304) = hAPP(hAPP(c_List_Oappend(_1681298), _1681300), hAPP(hAPP(c_List_Olist__update(_1681298, _1681302), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1681296), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1681298)), _1681300))), _1681304)))], (44987 ^ _782435) ^ [_1681399, _1681401, _1681403, _1681405] : [-(c_List_Osublist(_1681399, hAPP(hAPP(c_List_Oappend(_1681399), _1681401), _1681403), _1681405) = hAPP(hAPP(c_List_Oappend(_1681399), c_List_Osublist(_1681399, _1681401, _1681405)), c_List_Osublist(_1681399, _1681403, 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(_1681399)), _1681401)))), _1681405)))))], (44989 ^ _782435) ^ [_1681478, _1681480, _1681482, _1681484, _1681486, _1681488, _1681490, _1681492] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681478, _1681478)), hAPP(hAPP(c_Product__Type_OPair(_1681478, _1681478), _1681480), _1681482)), _1681484)), _1681486 = hAPP(hAPP(c_List_Oappend(_1681478), _1681488), hAPP(hAPP(c_List_Olist_OCons(_1681478), _1681480), _1681490)), _1681492 = hAPP(hAPP(c_List_Oappend(_1681478), _1681488), hAPP(hAPP(c_List_Olist_OCons(_1681478), _1681482), _1681490)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681478), tc_List_Olist(_1681478))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681478), tc_List_Olist(_1681478)), _1681486), _1681492)), c_List_Olistrel1(_1681478, _1681484))))], (45003 ^ _782435) ^ [_1681857, _1681859, _1681861, _1681863, _1681865, _1681867, _1681869] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1681857, _1681857)), hAPP(hAPP(c_Product__Type_OPair(_1681857, _1681857), _1681859), _1681861)), _1681863)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1681857), tc_List_Olist(_1681857))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1681857), tc_List_Olist(_1681857)), hAPP(hAPP(c_List_Oappend(_1681857), _1681865), hAPP(hAPP(c_List_Olist_OCons(_1681857), _1681859), _1681867))), hAPP(hAPP(c_List_Oappend(_1681857), _1681865), hAPP(hAPP(c_List_Olist_OCons(_1681857), _1681861), _1681869)))), c_List_Olexord(_1681857, _1681863))))], (45009 ^ _782435) ^ [_1682106, _1682108, _1682110] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1682106), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1682108)), _1682110))), -(hAPP(hAPP(c_List_Otake(_1682108), hAPP(c_Nat_OSuc, _1682106)), _1682110) = hAPP(hAPP(c_List_Oappend(_1682108), hAPP(hAPP(c_List_Otake(_1682108), _1682106), _1682110)), hAPP(hAPP(c_List_Olist_OCons(_1682108), hAPP(hAPP(c_List_Onth(_1682108), _1682110), _1682106)), c_List_Olist_ONil(_1682108))))], (45015 ^ _782435) ^ [_1682299, _1682301, _1682303, _1682305] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682299), tc_List_Olist(_1682299))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682299), tc_List_Olist(_1682299)), _1682301), _1682303)), c_List_Olistrel1(_1682299, _1682305))), 45020 ^ _782435 : [(45021 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682299, _1682299)), hAPP(hAPP(c_Product__Type_OPair(_1682299, _1682299), 45018 ^ [_1682299, _1682301, _1682303, _1682305]), 45019 ^ [_1682299, _1682301, _1682303, _1682305])), _1682305)))], (45025 ^ _782435) ^ [] : [-(_1682301 = hAPP(hAPP(c_List_Oappend(_1682299), 45022 ^ [_1682299, _1682301, _1682303, _1682305]), hAPP(hAPP(c_List_Olist_OCons(_1682299), 45018 ^ [_1682299, _1682301, _1682303, _1682305]), 45023 ^ [_1682299, _1682301, _1682303, _1682305])))], (45027 ^ _782435) ^ [] : [-(_1682303 = hAPP(hAPP(c_List_Oappend(_1682299), 45022 ^ [_1682299, _1682301, _1682303, _1682305]), hAPP(hAPP(c_List_Olist_OCons(_1682299), 45019 ^ [_1682299, _1682301, _1682303, _1682305]), 45023 ^ [_1682299, _1682301, _1682303, _1682305])))]]], (45029 ^ _782435) ^ [_1682704, _1682706, _1682708, _1682710, _1682712] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682704), tc_List_Olist(_1682704))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682704), tc_List_Olist(_1682704)), hAPP(hAPP(c_List_Oappend(_1682704), _1682706), _1682708)), hAPP(hAPP(c_List_Oappend(_1682704), _1682706), _1682710))), c_List_Olexord(_1682704, _1682712))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1682704, _1682704)), hAPP(hAPP(c_Product__Type_OPair(_1682704, _1682704), 45034 ^ [_1682704, _1682706, _1682708, _1682710, _1682712]), 45034 ^ [_1682704, _1682706, _1682708, _1682710, _1682712])), _1682712))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1682704), tc_List_Olist(_1682704))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1682704), tc_List_Olist(_1682704)), _1682708), _1682710)), c_List_Olexord(_1682704, _1682712))))], (45040 ^ _782435) ^ [_1683023, _1683025] : [-(hAPP(c_List_Orotate1(_1683023), _1683025) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1683023), _1683023, c_List_Olist_ONil(_1683023), hAPP(hAPP(c_COMBB(tc_List_Olist(_1683023), tc_fun(tc_List_Olist(_1683023), tc_List_Olist(_1683023)), _1683023), hAPP(c_COMBC(tc_List_Olist(_1683023), tc_List_Olist(_1683023), tc_List_Olist(_1683023)), c_List_Oappend(_1683023))), hAPP(hAPP(c_COMBC(_1683023, tc_List_Olist(_1683023), tc_List_Olist(_1683023)), c_List_Olist_OCons(_1683023)), c_List_Olist_ONil(_1683023)))), _1683025))], (45042 ^ _782435) ^ [_1683117, _1683119, _1683121, _1683123] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1683117), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1683119)), _1683121))), -(hAPP(hAPP(c_List_Olist__update(_1683119, _1683121), _1683117), _1683123) = hAPP(hAPP(c_List_Oappend(_1683119), hAPP(hAPP(c_List_Otake(_1683119), _1683117), _1683121)), hAPP(hAPP(c_List_Olist_OCons(_1683119), _1683123), hAPP(hAPP(c_List_Odrop(_1683119), hAPP(c_Nat_OSuc, _1683117)), _1683121))))], (45048 ^ _782435) ^ [_1683310, _1683312, _1683314] : [-(hAPP(hAPP(c_List_Oappend(_1683310), hAPP(hAPP(c_List_Otake(_1683310), _1683312), _1683314)), hAPP(hAPP(c_List_Odrop(_1683310), _1683312), _1683314)) = _1683314)], (45050 ^ _782435) ^ [_1683361, _1683363, _1683365] : [-(hAPP(hAPP(c_List_Odrop(_1683361), c_Groups_Oone__class_Oone(tc_Nat_Onat)), hAPP(hAPP(c_List_Olist_OCons(_1683361), _1683363), _1683365)) = _1683365)], (45052 ^ _782435) ^ [_1683404, _1683406, _1683408, _1683410] : [-(hAPP(hAPP(c_List_Odrop(_1683404), hAPP(c_Nat_OSuc, _1683406)), hAPP(hAPP(c_List_Olist_OCons(_1683404), _1683408), _1683410)) = hAPP(hAPP(c_List_Odrop(_1683404), _1683406), _1683410))], (45054 ^ _782435) ^ [_1683460, _1683462, _1683464, _1683466, _1683468] : [hAPP(hAPP(c_List_Odrop(_1683460), _1683462), _1683464) = hAPP(hAPP(c_List_Olist_OCons(_1683460), _1683466), _1683468), -(hAPP(hAPP(c_List_Onth(_1683460), _1683464), _1683462) = _1683466)], (45060 ^ _782435) ^ [_1683591, _1683593, _1683595] : [hBOOL(hAPP(c_List_Odistinct(_1683591), _1683593)), -(hBOOL(hAPP(c_List_Odistinct(_1683591), hAPP(hAPP(c_List_Odrop(_1683591), _1683595), _1683593))))], (45066 ^ _782435) ^ [_1683717, _1683719] : [hBOOL(hAPP(c_List_Odistinct(_1683717), hAPP(c_List_Orotate1(_1683717), _1683719))), -(hBOOL(hAPP(c_List_Odistinct(_1683717), _1683719)))], (45072 ^ _782435) ^ [_1683816, _1683818] : [hBOOL(hAPP(c_List_Odistinct(_1683816), _1683818)), -(hBOOL(hAPP(c_List_Odistinct(_1683816), hAPP(c_List_Orotate1(_1683816), _1683818))))], (45078 ^ _782435) ^ [_1683921, _1683923, _1683925, _1683927, _1683929] : [-(hAPP(hAPP(c_List_Odrop(tc_prod(_1683921, _1683923)), _1683925), hAPP(hAPP(c_List_Ozip(_1683921, _1683923), _1683927), _1683929)) = hAPP(hAPP(c_List_Ozip(_1683921, _1683923), hAPP(hAPP(c_List_Odrop(_1683921), _1683925), _1683927)), hAPP(hAPP(c_List_Odrop(_1683923), _1683925), _1683929)))], (45080 ^ _782435) ^ [_1683997, _1683999] : [-(hAPP(hAPP(c_List_Odrop(_1683997), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1683999) = _1683999)], (45082 ^ _782435) ^ [_1684030, _1684032, _1684034, _1684036] : [-(hAPP(hAPP(c_List_Odrop(_1684030), _1684032), hAPP(hAPP(c_List_Odrop(_1684030), _1684034), _1684036)) = hAPP(hAPP(c_List_Odrop(_1684030), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684032), _1684034)), _1684036))], (45084 ^ _782435) ^ [_1684089, _1684091, _1684093, _1684095] : [-(hAPP(hAPP(c_List_Odrop(_1684089), _1684091), hAPP(hAPP(c_List_Otake(_1684089), _1684093), _1684095)) = hAPP(hAPP(c_List_Otake(_1684089), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1684093), _1684091)), hAPP(hAPP(c_List_Odrop(_1684089), _1684091), _1684095)))], (45086 ^ _782435) ^ [_1684156, _1684158, _1684160, _1684162] : [-(hAPP(hAPP(c_List_Otake(_1684156), _1684158), hAPP(hAPP(c_List_Odrop(_1684156), _1684160), _1684162)) = hAPP(hAPP(c_List_Odrop(_1684156), _1684160), hAPP(hAPP(c_List_Otake(_1684156), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1684158), _1684160)), _1684162)))], (45088 ^ _782435) ^ [_1684223, _1684225, _1684227, _1684229] : [hBOOL(hAPP(hAPP(c_member(_1684223), _1684225), hAPP(c_List_Oset(_1684223), hAPP(hAPP(c_List_Odrop(_1684223), _1684227), _1684229)))), -(hBOOL(hAPP(hAPP(c_member(_1684223), _1684225), hAPP(c_List_Oset(_1684223), _1684229))))], (45094 ^ _782435) ^ [_1684368, _1684370] : [-(hAPP(c_List_Oset(_1684368), hAPP(c_List_Orotate1(_1684368), _1684370)) = hAPP(c_List_Oset(_1684368), _1684370))], (45096 ^ _782435) ^ [_1684408, _1684410, _1684412] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684408, tc_HOL_Obool)), hAPP(c_List_Oset(_1684408), hAPP(hAPP(c_List_Odrop(_1684408), _1684410), _1684412))), hAPP(c_List_Oset(_1684408), _1684412))))], (45098 ^ _782435) ^ [_1684463, _1684465, _1684467] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684463)), hAPP(hAPP(c_List_Odrop(_1684463), _1684465), _1684467)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684463)), _1684467)), _1684465))], (45100 ^ _782435) ^ [_1684518, _1684520] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684518)), hAPP(c_List_Orotate1(_1684518), _1684520)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1684518)), _1684520))], (45102 ^ _782435) ^ [_1684562, _1684564, _1684566] : [-(c_List_Obutlast(_1684562, hAPP(hAPP(c_List_Odrop(_1684562), _1684564), _1684566)) = hAPP(hAPP(c_List_Odrop(_1684562), _1684564), c_List_Obutlast(_1684562, _1684566)))], (45104 ^ _782435) ^ [_1684611, _1684613, _1684615] : [-(hAPP(hAPP(c_List_Odrop(_1684611), _1684613), c_List_Obutlast(_1684611, _1684615)) = c_List_Obutlast(_1684611, hAPP(hAPP(c_List_Odrop(_1684611), _1684613), _1684615)))], (45106 ^ _782435) ^ [_1684660, _1684662] : [-(hAPP(hAPP(c_List_Odrop(_1684660), _1684662), c_List_Olist_ONil(_1684660)) = c_List_Olist_ONil(_1684660))], (45108 ^ _782435) ^ [_1684712, _1684714] : [hAPP(c_List_Orotate1(_1684712), _1684714) = c_List_Olist_ONil(_1684712), -(_1684714 = c_List_Olist_ONil(_1684712))], (45114 ^ _782435) ^ [_1684803, _1684805] : [_1684805 = c_List_Olist_ONil(_1684803), -(hAPP(c_List_Orotate1(_1684803), _1684805) = c_List_Olist_ONil(_1684803))], (45120 ^ _782435) ^ [_1684900, _1684902, _1684904, _1684906] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1684900), _1684902)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1684904, tc_HOL_Obool)), hAPP(c_List_Oset(_1684904), hAPP(hAPP(c_List_Odrop(_1684904), _1684902), _1684906))), hAPP(c_List_Oset(_1684904), hAPP(hAPP(c_List_Odrop(_1684904), _1684900), _1684906)))))], (45126 ^ _782435) ^ [_1685081, _1685083, _1685085] : [hAPP(hAPP(c_List_Odrop(_1685081), _1685083), _1685085) = c_List_Olist_ONil(_1685081), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685081)), _1685085)), _1685083)))], (45132 ^ _782435) ^ [_1685200, _1685202, _1685204] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685200)), _1685204)), _1685202)), -(hAPP(hAPP(c_List_Odrop(_1685200), _1685202), _1685204) = c_List_Olist_ONil(_1685200))], (45138 ^ _782435) ^ [_1685325, _1685327, _1685329] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685325)), _1685327)), _1685329)), -(hAPP(hAPP(c_List_Odrop(_1685325), _1685329), _1685327) = c_List_Olist_ONil(_1685325))], (45144 ^ _782435) ^ [_1685448, _1685450, _1685452, _1685454] : [-(hAPP(hAPP(c_List_Odrop(_1685448), _1685450), hAPP(hAPP(c_List_Oappend(_1685448), _1685452), _1685454)) = hAPP(hAPP(c_List_Oappend(_1685448), hAPP(hAPP(c_List_Odrop(_1685448), _1685450), _1685452)), hAPP(hAPP(c_List_Odrop(_1685448), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1685450), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685448)), _1685452))), _1685454)))], (45146 ^ _782435) ^ [_1685551, _1685553, _1685555, _1685557] : [hAPP(hAPP(c_List_Oappend(_1685551), _1685553), _1685555) = _1685557, 45149 ^ _782435 : [(45150 ^ _782435) ^ [] : [-(_1685553 = hAPP(hAPP(c_List_Otake(_1685551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685551)), _1685553)), _1685557))], (45152 ^ _782435) ^ [] : [-(_1685555 = hAPP(hAPP(c_List_Odrop(_1685551), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685551)), _1685553)), _1685557))]]], (45154 ^ _782435) ^ [_1685730, _1685732, _1685734, _1685736] : [-(hAPP(hAPP(c_List_Oappend(_1685730), _1685732), _1685734) = _1685736), _1685732 = hAPP(hAPP(c_List_Otake(_1685730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685730)), _1685732)), _1685736), _1685734 = hAPP(hAPP(c_List_Odrop(_1685730), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1685730)), _1685732)), _1685736)], (45164 ^ _782435) ^ [_1685945, _1685947, _1685949, _1685951] : [-(hAPP(hAPP(c_List_Odrop(_1685945), _1685947), hAPP(hAPP(c_List_Olist_OCons(_1685945), _1685949), _1685951)) = c_Nat_Onat_Onat__case(tc_List_Olist(_1685945), hAPP(hAPP(c_List_Olist_OCons(_1685945), _1685949), _1685951), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(_1685945), tc_List_Olist(_1685945)), c_List_Odrop(_1685945)), _1685951), _1685947))], (45166 ^ _782435) ^ [_1686036, _1686038, _1686040, _1686042] : [_1686036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1686038), _1686036), hAPP(hAPP(c_List_Olist_OCons(_1686038), _1686040), _1686042)) = hAPP(hAPP(c_List_Olist_OCons(_1686038), _1686040), _1686042))], (45172 ^ _782435) ^ [_1686159, _1686161, _1686163, _1686165] : [-(_1686159 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1686161), _1686159), hAPP(hAPP(c_List_Olist_OCons(_1686161), _1686163), _1686165)) = hAPP(hAPP(c_List_Odrop(_1686161), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1686159), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1686165))], (45178 ^ _782435) ^ [_1686231, _1686233, _1686235, _1686237] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686231), _1686233)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686235)), _1686237))), -(hAPP(hAPP(c_List_Onth(_1686235), hAPP(hAPP(c_List_Odrop(_1686235), _1686231), _1686237)), _1686233) = hAPP(hAPP(c_List_Onth(_1686235), _1686237), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1686231), _1686233)))], (45184 ^ _782435) ^ [_1686432, _1686434, _1686436, _1686438, _1686440] : [hAPP(hAPP(c_List_Oappend(_1686432), _1686434), _1686436) = hAPP(hAPP(c_List_Oappend(_1686432), _1686438), _1686440), 45187 ^ _782435 : [(45188 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686434)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686438))), 45191 ^ _782435 : [(45192 ^ _782435) ^ [] : [-(_1686434 = hAPP(hAPP(c_List_Otake(_1686432), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686434)), _1686438))], (45194 ^ _782435) ^ [] : [-(_1686436 = hAPP(hAPP(c_List_Oappend(_1686432), hAPP(hAPP(c_List_Odrop(_1686432), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686434)), _1686438)), _1686440))]]], (45196 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686434)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686438)))), 45199 ^ _782435 : [(45200 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Otake(_1686432), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686438)), _1686434) = _1686438)], (45202 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Oappend(_1686432), hAPP(hAPP(c_List_Odrop(_1686432), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686432)), _1686438)), _1686434)), _1686436) = _1686440)]]]]], (45204 ^ _782435) ^ [_1686945, _1686947, _1686949, _1686951, _1686953] : [-(hAPP(hAPP(c_List_Oappend(_1686945), _1686947), _1686949) = hAPP(hAPP(c_List_Oappend(_1686945), _1686951), _1686953)), 45207 ^ _782435 : [(45208 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686947)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686951))))], (45210 ^ _782435) ^ [] : [_1686947 = hAPP(hAPP(c_List_Otake(_1686945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686947)), _1686951), _1686949 = hAPP(hAPP(c_List_Oappend(_1686945), hAPP(hAPP(c_List_Odrop(_1686945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686947)), _1686951)), _1686953)]], 45215 ^ _782435 : [(45216 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686947)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686951)))], (45218 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Otake(_1686945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686951)), _1686947) = _1686951, hAPP(hAPP(c_List_Oappend(_1686945), hAPP(hAPP(c_List_Odrop(_1686945), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1686945)), _1686951)), _1686947)), _1686949) = _1686953]]], (45226 ^ _782435) ^ [_1687533, _1687535, _1687537] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1687533), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1687535)), _1687537))), -(hAPP(hAPP(c_List_Olist_OCons(_1687535), hAPP(hAPP(c_List_Onth(_1687535), _1687537), _1687533)), hAPP(hAPP(c_List_Odrop(_1687535), hAPP(c_Nat_OSuc, _1687533)), _1687537)) = hAPP(hAPP(c_List_Odrop(_1687535), _1687533), _1687537))], (45232 ^ _782435) ^ [_1687704, _1687706, _1687708, _1687710] : [-(hAPP(c_List_Orotate1(_1687704), c_List_Olist_ONil(_1687704)) = c_List_Olist_ONil(_1687704))], (45234 ^ _782435) ^ [_1687739, _1687741, _1687743, _1687745] : [-(hAPP(c_List_Orotate1(_1687741), hAPP(hAPP(c_List_Olist_OCons(_1687741), _1687743), _1687745)) = hAPP(hAPP(c_List_Oappend(_1687741), _1687745), hAPP(hAPP(c_List_Olist_OCons(_1687741), _1687743), c_List_Olist_ONil(_1687741))))], (45236 ^ _782435) ^ [_1687816, _1687818, _1687820, _1687822] : [hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687816) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(hAPP(c_List_Odrop(_1687818), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687816)), hAPP(hAPP(c_List_Olist_OCons(_1687818), _1687820), _1687822)) = hAPP(hAPP(c_List_Olist_OCons(_1687818), _1687820), _1687822))], (45242 ^ _782435) ^ [_1687951, _1687953, _1687955, _1687957] : [-(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687951) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(hAPP(c_List_Odrop(_1687953), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687951)), hAPP(hAPP(c_List_Olist_OCons(_1687953), _1687955), _1687957)) = hAPP(hAPP(c_List_Odrop(_1687953), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1687951)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1687957))], (45248 ^ _782435) ^ [_1688032, _1688034, _1688036, _1688038] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1688032), _1688034)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688036)), _1688038))), -(hAPP(hAPP(c_List_Otake(_1688036), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1688032), _1688034)), _1688038) = hAPP(hAPP(c_List_Oappend(_1688036), hAPP(hAPP(c_List_Otake(_1688036), _1688032), _1688038)), hAPP(hAPP(c_List_Otake(_1688036), _1688034), hAPP(hAPP(c_List_Odrop(_1688036), _1688032), _1688038))))], (45254 ^ _782435) ^ [_1688241, _1688243] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688241)), _1688243)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate1(_1688241), _1688243) = _1688243)], (45260 ^ _782435) ^ [_1688352, _1688354, _1688356, _1688358, _1688360] : [-(hAPP(hAPP(c_List_Ozip(_1688352, _1688354), _1688356), hAPP(hAPP(c_List_Oappend(_1688354), _1688358), _1688360)) = hAPP(hAPP(c_List_Oappend(tc_prod(_1688352, _1688354)), hAPP(hAPP(c_List_Ozip(_1688352, _1688354), hAPP(hAPP(c_List_Otake(_1688352), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688354)), _1688358)), _1688356)), _1688358)), hAPP(hAPP(c_List_Ozip(_1688352, _1688354), hAPP(hAPP(c_List_Odrop(_1688352), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688354)), _1688358)), _1688356)), _1688360)))], (45262 ^ _782435) ^ [_1688459, _1688461, _1688463, _1688465, _1688467] : [-(hAPP(hAPP(c_List_Ozip(_1688459, _1688461), hAPP(hAPP(c_List_Oappend(_1688459), _1688463), _1688465)), _1688467) = hAPP(hAPP(c_List_Oappend(tc_prod(_1688459, _1688461)), hAPP(hAPP(c_List_Ozip(_1688459, _1688461), _1688463), hAPP(hAPP(c_List_Otake(_1688461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688459)), _1688463)), _1688467))), hAPP(hAPP(c_List_Ozip(_1688459, _1688461), _1688465), hAPP(hAPP(c_List_Odrop(_1688461), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688459)), _1688463)), _1688467))))], (45264 ^ _782435) ^ [_1688566, _1688568, _1688570] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688566), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688568)), _1688570))), -(_1688570 = hAPP(hAPP(c_List_Oappend(_1688568), hAPP(hAPP(c_List_Otake(_1688568), _1688566), _1688570)), hAPP(hAPP(c_List_Olist_OCons(_1688568), hAPP(hAPP(c_List_Onth(_1688568), _1688570), _1688566)), hAPP(hAPP(c_List_Odrop(_1688568), hAPP(c_Nat_OSuc, _1688566)), _1688570))))], (45270 ^ _782435) ^ [_1688755, _1688757, _1688759] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688755), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688757)), _1688759))), -(hAPP(hAPP(c_List_Oappend(_1688757), hAPP(hAPP(c_List_Otake(_1688757), _1688755), _1688759)), hAPP(hAPP(c_List_Olist_OCons(_1688757), hAPP(c_List_Ohd(_1688757), hAPP(hAPP(c_List_Odrop(_1688757), _1688755), _1688759))), c_List_Olist_ONil(_1688757))) = hAPP(hAPP(c_List_Otake(_1688757), hAPP(c_Nat_OSuc, _1688755)), _1688759))], (45276 ^ _782435) ^ [_1688957, _1688959, _1688961] : [-(_1688957 = c_List_Olist_ONil(_1688959)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1688961), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1688959)), _1688957))), -(hAPP(c_List_Ohd(_1688959), hAPP(hAPP(c_List_Odrop(_1688959), _1688961), _1688957)) = hAPP(hAPP(c_List_Onth(_1688959), _1688957), _1688961))], (45286 ^ _782435) ^ [_1689156, _1689158, _1689160] : [-(hAPP(c_List_Ohd(_1689156), hAPP(hAPP(c_List_Olist_OCons(_1689156), _1689158), _1689160)) = _1689158)], (45288 ^ _782435) ^ [_1689192, _1689194, _1689196] : [-(_1689192 = c_List_Olist_ONil(_1689194)), -(hAPP(c_List_Ohd(_1689194), hAPP(hAPP(c_List_Oappend(_1689194), _1689192), _1689196)) = hAPP(c_List_Ohd(_1689194), _1689192))], (45294 ^ _782435) ^ [_1689262, _1689264, _1689266] : [_1689262 = c_List_Olist_ONil(_1689264), -(hAPP(c_List_Ohd(_1689264), hAPP(hAPP(c_List_Oappend(_1689264), _1689262), _1689266)) = hAPP(c_List_Ohd(_1689264), _1689266))], (45300 ^ _782435) ^ [_1689375, _1689377, _1689379] : [-(_1689375 = c_List_Olist_ONil(_1689377)), -(hAPP(c_List_Ohd(_1689377), hAPP(hAPP(c_List_Oappend(_1689377), _1689375), _1689379)) = hAPP(c_List_Ohd(_1689377), _1689375))], (45306 ^ _782435) ^ [_1689431, _1689433] : [-(_1689431 = c_List_Olist_ONil(_1689433)), -(hBOOL(hAPP(hAPP(c_member(_1689433), hAPP(c_List_Ohd(_1689433), _1689431)), hAPP(c_List_Oset(_1689433), _1689431))))], (45312 ^ _782435) ^ [_1689482, _1689484] : [-(_1689482 = c_List_Olist_ONil(_1689484)), -(hAPP(c_List_Ohd(_1689484), _1689482) = hAPP(hAPP(c_List_Onth(_1689484), _1689482), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (45318 ^ _782435) ^ [_1689529, _1689531] : [-(_1689529 = c_List_Olist_ONil(_1689531)), -(hAPP(c_List_Orotate1(_1689531), _1689529) = hAPP(hAPP(c_List_Oappend(_1689531), hAPP(c_List_Otl(_1689531), _1689529)), hAPP(hAPP(c_List_Olist_OCons(_1689531), hAPP(c_List_Ohd(_1689531), _1689529)), c_List_Olist_ONil(_1689531))))], (45324 ^ _782435) ^ [_1689596, _1689598, _1689600] : [-(_1689596 = c_List_Olist_ONil(_1689598)), -(hAPP(c_List_Ohd(_1689598), hAPP(c_List_Orotate(_1689598, _1689600), _1689596)) = hAPP(hAPP(c_List_Onth(_1689598), _1689596), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1689600, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1689598)), _1689596))))], (45330 ^ _782435) ^ [_1689666, _1689668, _1689670] : [-(hAPP(hAPP(c_List_Odrop(_1689666), _1689668), hAPP(c_List_Otl(_1689666), _1689670)) = hAPP(c_List_Otl(_1689666), hAPP(hAPP(c_List_Odrop(_1689666), _1689668), _1689670)))], (45332 ^ _782435) ^ [_1689719, _1689721, _1689723] : [-(hAPP(c_List_Otl(_1689719), hAPP(hAPP(c_List_Odrop(_1689719), _1689721), _1689723)) = hAPP(hAPP(c_List_Odrop(_1689719), _1689721), hAPP(c_List_Otl(_1689719), _1689723)))], (45334 ^ _782435) ^ [_1689772, _1689774, _1689776] : [-(hAPP(c_List_Otl(_1689772), hAPP(hAPP(c_List_Olist_OCons(_1689772), _1689774), _1689776)) = _1689776)], (45336 ^ _782435) ^ [_1689812, _1689814] : [hBOOL(hAPP(c_List_Odistinct(_1689812), _1689814)), -(hBOOL(hAPP(c_List_Odistinct(_1689812), hAPP(c_List_Otl(_1689812), _1689814))))], (45342 ^ _782435) ^ [_1689933, _1689935, _1689937] : [hBOOL(hAPP(c_List_Odistinct(_1689933), hAPP(c_List_Orotate(_1689933, _1689935), _1689937))), -(hBOOL(hAPP(c_List_Odistinct(_1689933), _1689937)))], (45348 ^ _782435) ^ [_1690036, _1690038, _1690040] : [hBOOL(hAPP(c_List_Odistinct(_1690036), _1690040)), -(hBOOL(hAPP(c_List_Odistinct(_1690036), hAPP(c_List_Orotate(_1690036, _1690038), _1690040))))], (45354 ^ _782435) ^ [_1690145, _1690147, _1690149] : [-(c_List_Orotate(_1690145, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690147), _1690149)) = hAPP(c_Fun_Ocomp(tc_List_Olist(_1690145), tc_List_Olist(_1690145), tc_List_Olist(_1690145), c_List_Orotate(_1690145, _1690147)), c_List_Orotate(_1690145, _1690149)))], (45356 ^ _782435) ^ [_1690201] : [-(c_List_Orotate(_1690201, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(_1690201)))], (45358 ^ _782435) ^ [_1690231, _1690233, _1690235, _1690237] : [-(hAPP(c_List_Orotate(_1690231, _1690233), hAPP(c_List_Orotate(_1690231, _1690235), _1690237)) = hAPP(c_List_Orotate(_1690231, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1690233), _1690235)), _1690237))], (45360 ^ _782435) ^ [_1690284, _1690286, _1690288] : [-(hAPP(c_List_Oset(_1690284), hAPP(c_List_Orotate(_1690284, _1690286), _1690288)) = hAPP(c_List_Oset(_1690284), _1690288))], (45362 ^ _782435) ^ [_1690327, _1690329, _1690331] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690327)), hAPP(c_List_Orotate(_1690327, _1690329), _1690331)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690327)), _1690331))], (45364 ^ _782435) ^ [_1690374] : [-(hAPP(c_List_Otl(_1690374), c_List_Olist_ONil(_1690374)) = c_List_Olist_ONil(_1690374))], (45366 ^ _782435) ^ [_1690424, _1690426, _1690428] : [hAPP(c_List_Orotate(_1690424, _1690426), _1690428) = c_List_Olist_ONil(_1690424), -(_1690428 = c_List_Olist_ONil(_1690424))], (45372 ^ _782435) ^ [_1690519, _1690521, _1690523] : [_1690523 = c_List_Olist_ONil(_1690519), -(hAPP(c_List_Orotate(_1690519, _1690521), _1690523) = c_List_Olist_ONil(_1690519))], (45378 ^ _782435) ^ [_1690620, _1690622] : [-(c_List_Orotate(_1690620, _1690622) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(_1690620), tc_List_Olist(_1690620)), _1690622), c_List_Orotate1(_1690620)))], (45380 ^ _782435) ^ [_1690663, _1690665, _1690667] : [-(hAPP(c_List_Orotate1(_1690663), hAPP(c_List_Orotate(_1690663, _1690665), _1690667)) = hAPP(c_List_Orotate(_1690663, _1690665), hAPP(c_List_Orotate1(_1690663), _1690667)))], (45382 ^ _782435) ^ [_1690708, _1690710, _1690712] : [-(_1690708 = c_List_Olist_ONil(_1690710)), -(hAPP(c_List_Otl(_1690710), hAPP(hAPP(c_List_Oappend(_1690710), _1690708), _1690712)) = hAPP(hAPP(c_List_Oappend(_1690710), hAPP(c_List_Otl(_1690710), _1690708)), _1690712))], (45388 ^ _782435) ^ [_1690774, _1690776, _1690778] : [-(hAPP(hAPP(c_List_Otake(_1690774), _1690776), hAPP(c_List_Otl(_1690774), _1690778)) = hAPP(c_List_Otl(_1690774), hAPP(hAPP(c_List_Otake(_1690774), hAPP(c_Nat_OSuc, _1690776)), _1690778)))], (45390 ^ _782435) ^ [_1690830, _1690832, _1690834] : [-(hAPP(c_List_Orotate(_1690830, _1690832), _1690834) = hAPP(c_List_Orotate(_1690830, c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1690832, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1690830)), _1690834))), _1690834))], (45392 ^ _782435) ^ [_1690880, _1690882, _1690884] : [-(hAPP(hAPP(c_List_Odrop(_1690880), hAPP(c_Nat_OSuc, _1690882)), _1690884) = hAPP(hAPP(c_List_Odrop(_1690880), _1690882), hAPP(c_List_Otl(_1690880), _1690884)))], (45394 ^ _782435) ^ [_1690931, _1690933, _1690935] : [-(hAPP(c_List_Orotate(_1690931, hAPP(c_Nat_OSuc, _1690933)), _1690935) = hAPP(c_List_Orotate1(_1690931), hAPP(c_List_Orotate(_1690931, _1690933), _1690935)))], (45396 ^ _782435) ^ [_1690978, _1690980, _1690982] : [-(hAPP(c_List_Otl(_1690978), hAPP(hAPP(c_List_Oappend(_1690978), _1690980), _1690982)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(_1690978), _1690978, hAPP(c_List_Otl(_1690978), _1690982), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1690978), tc_List_Olist(_1690978)), _1690978), hAPP(hAPP(c_COMBC(tc_List_Olist(_1690978), tc_List_Olist(_1690978), tc_List_Olist(_1690978)), c_List_Oappend(_1690978)), _1690982))), _1690980))], (45398 ^ _782435) ^ [_1691064, _1691066, _1691068] : [c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691064, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691066)), _1691068)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Orotate(_1691066, _1691064), _1691068) = _1691068)], (45404 ^ _782435) ^ [_1691177, _1691179, _1691181] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691177)), _1691179)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(hAPP(c_List_Orotate(_1691177, _1691181), _1691179) = _1691179)], (45410 ^ _782435) ^ [_1691292, _1691294] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691292)), hAPP(c_List_Otl(_1691292), _1691294)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691292)), _1691294)), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (45412 ^ _782435) ^ [_1691342, _1691344, _1691346] : [-(hAPP(c_List_Otl(_1691342), hAPP(hAPP(c_List_Otake(_1691342), _1691344), _1691346)) = hAPP(hAPP(c_List_Otake(_1691342), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1691344), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_List_Otl(_1691342), _1691346)))], (45414 ^ _782435) ^ [_1691397, _1691399, _1691401] : [-(_1691397 = c_List_Olist_ONil(_1691399)), -(hAPP(hAPP(c_List_Otake(_1691399), hAPP(c_Nat_OSuc, _1691401)), _1691397) = hAPP(hAPP(c_List_Olist_OCons(_1691399), hAPP(c_List_Ohd(_1691399), _1691397)), hAPP(hAPP(c_List_Otake(_1691399), _1691401), hAPP(c_List_Otl(_1691399), _1691397))))], (45420 ^ _782435) ^ [_1691474, _1691476, _1691478] : [-(hAPP(c_List_Orotate(_1691474, _1691476), _1691478) = hAPP(hAPP(c_List_Oappend(_1691474), hAPP(hAPP(c_List_Odrop(_1691474), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691476, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691474)), _1691478))), _1691478)), hAPP(hAPP(c_List_Otake(_1691474), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1691476, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1691474)), _1691478))), _1691478)))], (45422 ^ _782435) ^ [_1691553, _1691555] : [class_Lattices_Oab__semigroup__idem__mult(_1691553), -(_1691555 = c_List_Olist_ONil(_1691553)), -(hAPP(c_Finite__Set_Ofold1(_1691553, c_Groups_Otimes__class_Otimes(_1691553)), hAPP(c_List_Oset(_1691553), _1691555)) = hAPP(c_List_Ofoldl(_1691553, _1691553, c_Groups_Otimes__class_Otimes(_1691553), hAPP(c_List_Ohd(_1691553), _1691555)), hAPP(c_List_Otl(_1691553), _1691555)))], (45432 ^ _782435) ^ [_1691713, _1691715, _1691717, _1691719] : [45433 ^ _782435 : [(45434 ^ _782435) ^ [_1691810, _1691812] : [_1691713 = hAPP(hAPP(c_List_Olist_OCons(_1691715), _1691812), _1691810)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1691715), tc_List_Olist(_1691715))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1691715), tc_List_Olist(_1691715)), _1691717), hAPP(hAPP(c_List_Oappend(_1691715), _1691717), _1691713))), c_List_Olexord(_1691715, _1691719))))], (45438 ^ _782435) ^ [_1691909, _1691911, _1691913, _1691915] : [-(hAPP(c_List_Ofoldl(_1691909, _1691911, _1691913, _1691915), c_List_Olist_ONil(_1691911)) = _1691915)], (45440 ^ _782435) ^ [_1691948, _1691950, _1691952] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1691948), _1691950)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1691948), hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1691950), _1691952))))], (45446 ^ _782435) ^ [_1692063, _1692065, _1692067, _1692069] : [class_Groups_Osemigroup__add(_1692063), -(hAPP(c_List_Ofoldl(_1692063, _1692063, c_Groups_Oplus__class_Oplus(_1692063), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692063), _1692065), _1692067)), _1692069) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692063), _1692065), hAPP(c_List_Ofoldl(_1692063, _1692063, c_Groups_Oplus__class_Oplus(_1692063), _1692067), _1692069)))], (45452 ^ _782435) ^ [_1692214, _1692216, _1692218] : [class_Groups_Omonoid__add(_1692214), -(hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1692214), _1692216), hAPP(c_List_Ofoldl(_1692214, _1692214, c_Groups_Oplus__class_Oplus(_1692214), c_Groups_Ozero__class_Ozero(_1692214)), _1692218)) = hAPP(c_List_Ofoldl(_1692214, _1692214, c_Groups_Oplus__class_Oplus(_1692214), _1692216), _1692218))], (45458 ^ _782435) ^ [_1692351, _1692353, _1692355, _1692357, _1692359, _1692361] : [-(hAPP(c_List_Ofoldl(_1692351, _1692353, _1692355, _1692357), hAPP(hAPP(c_List_Olist_OCons(_1692353), _1692359), _1692361)) = hAPP(c_List_Ofoldl(_1692351, _1692353, _1692355, hAPP(hAPP(_1692355, _1692357), _1692359)), _1692361))], (45460 ^ _782435) ^ [_1692414, _1692416, _1692418, _1692420, _1692422, _1692424] : [-(hAPP(c_List_Ofoldl(_1692414, _1692416, _1692418, _1692420), hAPP(hAPP(c_List_Oappend(_1692416), _1692422), _1692424)) = hAPP(c_List_Ofoldl(_1692414, _1692416, _1692418, hAPP(c_List_Ofoldl(_1692414, _1692416, _1692418, _1692420), _1692422)), _1692424))], (45462 ^ _782435) ^ [_1692479] : [class_Groups_Omonoid__add(_1692479), -(c_List_Omonoid__add__class_Olistsum(_1692479) = c_List_Ofoldl(_1692479, _1692479, c_Groups_Oplus__class_Oplus(_1692479), c_Groups_Ozero__class_Ozero(_1692479)))], (45468 ^ _782435) ^ [_1692589, _1692591] : [hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692589), _1692591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45471 ^ _782435 : [(45472 ^ _782435) ^ [] : [-(_1692589 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (45474 ^ _782435) ^ [_1692703] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1692703), hAPP(c_List_Oset(tc_Nat_Onat), _1692591))), -(_1692703 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))]]], (45480 ^ _782435) ^ [_1692800, _1692802] : [-(hAPP(c_List_Ofoldl(tc_Nat_Onat, tc_Nat_Onat, c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1692800), _1692802) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), _1692800 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), 45486 ^ _782435 : [(45487 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 45485 ^ [_1692800, _1692802]), hAPP(c_List_Oset(tc_Nat_Onat), _1692802))))], (45489 ^ _782435) ^ [] : [45485 ^ [_1692800, _1692802] = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (45493 ^ _782435) ^ [_1693026, _1693028, _1693030, _1693032, _1693034] : [c_Finite__Set_Ofun__left__comm__idem(_1693026, _1693028, _1693030), -(hAPP(hAPP(c_Finite__Set_Ofold(_1693026, _1693028, _1693030), _1693032), hAPP(c_List_Oset(_1693026), _1693034)) = hAPP(c_List_Ofoldl(_1693028, _1693026, hAPP(c_COMBC(_1693026, _1693028, _1693028), _1693030), _1693032), _1693034))], (45499 ^ _782435) ^ [_1693171, _1693173] : [class_Complete__Lattice_Ocomplete__lattice(_1693171), -(c_Complete__Lattice_OSup__class_OSup(_1693171, hAPP(c_List_Oset(_1693171), _1693173)) = hAPP(c_List_Ofoldl(_1693171, _1693171, c_Lattices_Osemilattice__sup__class_Osup(_1693171), c_Orderings_Obot__class_Obot(_1693171)), _1693173))], (45505 ^ _782435) ^ [_1693286, _1693288] : [class_Complete__Lattice_Ocomplete__lattice(_1693286), -(c_Complete__Lattice_OInf__class_OInf(_1693286, hAPP(c_List_Oset(_1693286), _1693288)) = hAPP(c_List_Ofoldl(_1693286, _1693286, c_Lattices_Osemilattice__inf__class_Oinf(_1693286), c_Orderings_Otop__class_Otop(_1693286)), _1693288))], (45511 ^ _782435) ^ [_1693401, _1693403, _1693405] : [class_Lattices_Olattice(_1693401), -(c_Big__Operators_Olattice__class_OSup__fin(_1693401, hAPP(c_List_Oset(_1693401), hAPP(hAPP(c_List_Olist_OCons(_1693401), _1693403), _1693405))) = hAPP(c_List_Ofoldl(_1693401, _1693401, c_Lattices_Osemilattice__sup__class_Osup(_1693401), _1693403), _1693405))], (45517 ^ _782435) ^ [_1693530, _1693532, _1693534] : [class_Lattices_Olattice(_1693530), -(c_Big__Operators_Olattice__class_OInf__fin(_1693530, hAPP(c_List_Oset(_1693530), hAPP(hAPP(c_List_Olist_OCons(_1693530), _1693532), _1693534))) = hAPP(c_List_Ofoldl(_1693530, _1693530, c_Lattices_Osemilattice__inf__class_Oinf(_1693530), _1693532), _1693534))], (45523 ^ _782435) ^ [_1693659, _1693661, _1693663] : [class_Orderings_Olinorder(_1693659), -(c_Big__Operators_Olinorder__class_OMin(_1693659, hAPP(c_List_Oset(_1693659), hAPP(hAPP(c_List_Olist_OCons(_1693659), _1693661), _1693663))) = hAPP(c_List_Ofoldl(_1693659, _1693659, c_Orderings_Oord__class_Omin(_1693659), _1693661), _1693663))], (45529 ^ _782435) ^ [_1693788, _1693790, _1693792] : [class_Orderings_Olinorder(_1693788), -(c_Big__Operators_Olinorder__class_OMax(_1693788, hAPP(c_List_Oset(_1693788), hAPP(hAPP(c_List_Olist_OCons(_1693788), _1693790), _1693792))) = hAPP(c_List_Ofoldl(_1693788, _1693788, c_Orderings_Oord__class_Omax(_1693788), _1693790), _1693792))], (45535 ^ _782435) ^ [_1693917, _1693919, _1693921] : [class_Orderings_Olinorder(_1693917), -(c_Big__Operators_Olattice_OInf__fin(_1693917, c_Orderings_Oord__class_Omin(_1693917), hAPP(c_List_Oset(_1693917), hAPP(hAPP(c_List_Olist_OCons(_1693917), _1693919), _1693921))) = hAPP(c_List_Ofoldl(_1693917, _1693917, c_Orderings_Oord__class_Omin(_1693917), _1693919), _1693921))], (45541 ^ _782435) ^ [_1694052, _1694054, _1694056] : [class_Orderings_Olinorder(_1694052), -(c_Big__Operators_Olattice_OSup__fin(_1694052, c_Orderings_Oord__class_Omax(_1694052), hAPP(c_List_Oset(_1694052), hAPP(hAPP(c_List_Olist_OCons(_1694052), _1694054), _1694056))) = hAPP(c_List_Ofoldl(_1694052, _1694052, c_Orderings_Oord__class_Omax(_1694052), _1694054), _1694056))], (45547 ^ _782435) ^ [_1694187, _1694189, _1694191, _1694193] : [class_Complete__Lattice_Ocomplete__lattice(_1694187), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1694189, _1694187), hAPP(c_List_Oset(_1694189), _1694191)), _1694193) = hAPP(c_List_Ofoldl(_1694187, _1694189, hAPP(c_COMBC(_1694189, _1694187, _1694187), hAPP(hAPP(c_COMBB(_1694187, tc_fun(_1694187, _1694187), _1694189), c_Lattices_Osemilattice__sup__class_Osup(_1694187)), _1694193)), c_Orderings_Obot__class_Obot(_1694187)), _1694191))], (45553 ^ _782435) ^ [_1694358, _1694360, _1694362, _1694364] : [class_Complete__Lattice_Ocomplete__lattice(_1694358), -(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1694360, _1694358), hAPP(c_List_Oset(_1694360), _1694362)), _1694364) = hAPP(c_List_Ofoldl(_1694358, _1694360, hAPP(c_COMBC(_1694360, _1694358, _1694358), hAPP(hAPP(c_COMBB(_1694358, tc_fun(_1694358, _1694358), _1694360), c_Lattices_Osemilattice__inf__class_Oinf(_1694358)), _1694364)), c_Orderings_Otop__class_Otop(_1694358)), _1694362))], (45559 ^ _782435) ^ [_1694529, _1694531] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1694529), hAPP(c_List_Oset(tc_Nat_Onat), _1694531))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1694529), 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)), _1694531))))], (45565 ^ _782435) ^ [_1694638, _1694640, _1694642] : [class_Orderings_Olinorder(_1694638), hBOOL(hAPP(c_Finite__Set_Ofinite(_1694638), _1694640)), -(c_List_Olinorder__class_Osorted__list__of__set(_1694638, hAPP(hAPP(c_Set_Oinsert(_1694638), _1694642), _1694640)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1694638, _1694638, c_COMBI(_1694638)), _1694642), c_List_Olinorder__class_Osorted__list__of__set(_1694638, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1694638, tc_HOL_Obool)), _1694640), hAPP(hAPP(c_Set_Oinsert(_1694638), _1694642), c_Orderings_Obot__class_Obot(tc_fun(_1694638, tc_HOL_Obool)))))))], (45575 ^ _782435) ^ [_1694895, _1694897, _1694899] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1694895), tc_List_Olist(_1694895))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1694895), tc_List_Olist(_1694895)), c_List_Olist_ONil(_1694895)), _1694897)), c_List_Olexord(_1694895, _1694899))), -(_1694897 = hAPP(hAPP(c_List_Olist_OCons(_1694895), 45578 ^ [_1694895, _1694897, _1694899]), 45579 ^ [_1694895, _1694897, _1694899]))], (45583 ^ _782435) ^ [_1695078, _1695080, _1695082] : [45584 ^ _782435 : [(45585 ^ _782435) ^ [_1695167, _1695169] : [_1695080 = hAPP(hAPP(c_List_Olist_OCons(_1695078), _1695169), _1695167)]], -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1695078), tc_List_Olist(_1695078))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1695078), tc_List_Olist(_1695078)), c_List_Olist_ONil(_1695078)), _1695080)), c_List_Olexord(_1695078, _1695082))))], (45589 ^ _782435) ^ [_1695262, _1695264, _1695266, _1695268] : [class_Orderings_Olinorder(_1695262), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695264, _1695262, _1695266), _1695268), c_List_Olist_ONil(_1695264)) = hAPP(hAPP(c_List_Olist_OCons(_1695264), _1695268), c_List_Olist_ONil(_1695264)))], (45595 ^ _782435) ^ [_1695385, _1695387, _1695389, _1695391, _1695393, _1695395] : [class_Orderings_Olinorder(_1695385), 45598 ^ _782435 : [(45599 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695385), hAPP(_1695387, _1695389)), hAPP(_1695387, _1695391))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695393, _1695385, _1695387), _1695389), hAPP(hAPP(c_List_Olist_OCons(_1695393), _1695391), _1695395)) = hAPP(hAPP(c_List_Olist_OCons(_1695393), _1695389), hAPP(hAPP(c_List_Olist_OCons(_1695393), _1695391), _1695395)))], (45605 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1695385), hAPP(_1695387, _1695389)), hAPP(_1695387, _1695391)))), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695393, _1695385, _1695387), _1695389), hAPP(hAPP(c_List_Olist_OCons(_1695393), _1695391), _1695395)) = hAPP(hAPP(c_List_Olist_OCons(_1695393), _1695391), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695393, _1695385, _1695387), _1695389), _1695395)))]]], (45611 ^ _782435) ^ [_1695767, _1695769, _1695771] : [class_Orderings_Olinorder(_1695767), -(c_List_Oremove1(_1695767, _1695769, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695767, _1695767, c_COMBI(_1695767)), _1695769), _1695771)) = _1695771)], (45617 ^ _782435) ^ [_1695876, _1695878, _1695880, _1695882] : [class_Orderings_Olinorder(_1695876), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695876, _1695876, c_COMBI(_1695876)), _1695878), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695876, _1695876, c_COMBI(_1695876)), _1695880), _1695882)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695876, _1695876, c_COMBI(_1695876)), _1695880), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1695876, _1695876, c_COMBI(_1695876)), _1695878), _1695882)))], (45623 ^ _782435) ^ [_1696051, _1696053, _1696055, _1696057, _1696059, _1696061] : [class_Orderings_Olinorder(_1696051), -(hAPP(_1696053, _1696055) = hAPP(_1696053, _1696057)), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696059, _1696051, _1696053), _1696057), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696059, _1696051, _1696053), _1696055), _1696061)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696059, _1696051, _1696053), _1696055), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696059, _1696051, _1696053), _1696057), _1696061)))], (45633 ^ _782435) ^ [_1696241] : [class_Orderings_Olinorder(_1696241), -(c_Finite__Set_Ofun__left__comm(_1696241, tc_List_Olist(_1696241), c_List_Olinorder__class_Oinsort__key(_1696241, _1696241, c_COMBI(_1696241))))], (45639 ^ _782435) ^ [_1696332, _1696334, _1696336, _1696338, _1696340] : [class_Orderings_Olinorder(_1696332), -(hAPP(c_List_Oset(_1696334), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696334, _1696332, _1696336), _1696338), _1696340)) = hAPP(hAPP(c_Set_Oinsert(_1696334), _1696338), hAPP(c_List_Oset(_1696334), _1696340)))], (45645 ^ _782435) ^ [_1696469, _1696471, _1696473, _1696475, _1696477] : [class_Orderings_Olinorder(_1696469), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696471)), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696471, _1696469, _1696473), _1696475), _1696477)) = hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1696471)), _1696477)))], (45651 ^ _782435) ^ [_1696604, _1696606, _1696608, _1696610, _1696612] : [class_Orderings_Olinorder(_1696604), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696606, _1696604, _1696608), _1696610), _1696612) = c_List_Olist_ONil(_1696606)], (45657 ^ _782435) ^ [_1696710, _1696712, _1696714, _1696716, _1696718] : [class_Orderings_Olinorder(_1696710), 45660 ^ _782435 : [(45661 ^ _782435) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1696712), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696712, _1696710, _1696714), _1696716), _1696718))), 45664 ^ _782435 : [(45665 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1696712), _1696716), hAPP(c_List_Oset(_1696712), _1696718)))], (45667 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696712), _1696718)))]]], (45669 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1696712), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1696712, _1696710, _1696714), _1696716), _1696718)))), -(hBOOL(hAPP(hAPP(c_member(_1696712), _1696716), hAPP(c_List_Oset(_1696712), _1696718)))), hBOOL(hAPP(c_List_Odistinct(_1696712), _1696718))]]], (45679 ^ _782435) ^ [_1697112, _1697114, _1697116, _1697118, _1697120] : [class_Orderings_Olinorder(_1697112), -(hBOOL(hAPP(hAPP(c_member(_1697112), hAPP(_1697114, _1697116)), hAPP(c_Set_Oimage(_1697118, _1697112, _1697114), hAPP(c_List_Oset(_1697118), _1697120))))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697118, _1697112, _1697114, _1697116, _1697120) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697118, _1697112, _1697114), _1697116), _1697120))], (45689 ^ _782435) ^ [_1697284, _1697286, _1697288] : [class_Orderings_Olinorder(_1697284), -(hBOOL(hAPP(hAPP(c_member(_1697284), _1697286), hAPP(c_List_Oset(_1697284), _1697288)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697284, _1697284, c_COMBI(_1697284), _1697286, _1697288) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1697284, _1697284, c_COMBI(_1697284)), _1697286), _1697288))], (45699 ^ _782435) ^ [_1697440, _1697442, _1697444, _1697446, _1697448] : [class_Orderings_Olinorder(_1697440), hBOOL(hAPP(c_List_Odistinct(_1697442), _1697444)), -(hBOOL(hAPP(c_List_Odistinct(_1697442), c_List_Olinorder__class_Oinsort__insert__key(_1697442, _1697440, _1697446, _1697448, _1697444))))], (45709 ^ _782435) ^ [_1697607, _1697609, _1697611] : [class_Orderings_Olinorder(_1697607), hBOOL(hAPP(hAPP(c_member(_1697607), _1697609), hAPP(c_List_Oset(_1697607), _1697611))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697607, _1697607, c_COMBI(_1697607), _1697609, _1697611) = _1697611)], (45719 ^ _782435) ^ [_1697778, _1697780, _1697782] : [class_Orderings_Olinorder(_1697778), -(hAPP(c_List_Oset(_1697778), c_List_Olinorder__class_Oinsort__insert__key(_1697778, _1697778, c_COMBI(_1697778), _1697780, _1697782)) = hAPP(hAPP(c_Set_Oinsert(_1697778), _1697780), hAPP(c_List_Oset(_1697778), _1697782)))], (45725 ^ _782435) ^ [_1697907, _1697909, _1697911, _1697913, _1697915] : [class_Orderings_Olinorder(_1697907), hBOOL(hAPP(hAPP(c_member(_1697907), hAPP(_1697909, _1697911)), hAPP(c_Set_Oimage(_1697913, _1697907, _1697909), hAPP(c_List_Oset(_1697913), _1697915)))), -(c_List_Olinorder__class_Oinsort__insert__key(_1697913, _1697907, _1697909, _1697911, _1697915) = _1697915)], (45735 ^ _782435) ^ [_1698101, _1698103, _1698105, _1698107] : [-(_1698101 = c_List_Olist_ONil(_1698103)), 45738 ^ _782435 : [(45739 ^ _782435) ^ [] : [_1698105 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698103)), _1698101)), c_Groups_Oone__class_Oone(tc_Nat_Onat)), -(c_List_Olast(_1698103, hAPP(hAPP(c_List_Olist__update(_1698103, _1698101), _1698105), _1698107)) = _1698107)], (45745 ^ _782435) ^ [] : [-(_1698105 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698103)), _1698101)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), -(c_List_Olast(_1698103, hAPP(hAPP(c_List_Olist__update(_1698103, _1698101), _1698105), _1698107)) = c_List_Olast(_1698103, _1698101))]]], (45751 ^ _782435) ^ [_1698387, _1698389] : [-(_1698387 = c_List_Olist_ONil(_1698389)), -(c_List_Olast(_1698389, _1698387) = hAPP(hAPP(c_List_Onth(_1698389), _1698387), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1698389)), _1698387)), c_Groups_Oone__class_Oone(tc_Nat_Onat))))], (45757 ^ _782435) ^ [_1698449, _1698451, _1698453] : [_1698449 = c_List_Olist_ONil(_1698451), -(c_List_Olast(_1698451, hAPP(hAPP(c_List_Oappend(_1698451), _1698453), _1698449)) = c_List_Olast(_1698451, _1698453))], (45763 ^ _782435) ^ [_1698556, _1698558, _1698560] : [-(_1698556 = c_List_Olist_ONil(_1698558)), -(c_List_Olast(_1698558, hAPP(hAPP(c_List_Oappend(_1698558), _1698560), _1698556)) = c_List_Olast(_1698558, _1698556))], (45769 ^ _782435) ^ [_1698622, _1698624, _1698626] : [_1698622 = c_List_Olist_ONil(_1698624), -(c_List_Olast(_1698624, hAPP(hAPP(c_List_Oappend(_1698624), _1698626), _1698622)) = c_List_Olast(_1698624, _1698626))], (45775 ^ _782435) ^ [_1698727, _1698729, _1698731] : [-(_1698727 = c_List_Olist_ONil(_1698729)), -(c_List_Olast(_1698729, hAPP(hAPP(c_List_Oappend(_1698729), _1698731), _1698727)) = c_List_Olast(_1698729, _1698727))], (45781 ^ _782435) ^ [_1698783, _1698785, _1698787] : [_1698783 = c_List_Olist_ONil(_1698785), -(c_List_Olast(_1698785, hAPP(hAPP(c_List_Olist_OCons(_1698785), _1698787), _1698783)) = _1698787)], (45787 ^ _782435) ^ [_1698884, _1698886, _1698888] : [-(_1698884 = c_List_Olist_ONil(_1698886)), -(c_List_Olast(_1698886, hAPP(hAPP(c_List_Olist_OCons(_1698886), _1698888), _1698884)) = c_List_Olast(_1698886, _1698884))], (45793 ^ _782435) ^ [_1698950, _1698952, _1698954] : [_1698950 = c_List_Olist_ONil(_1698952), -(c_List_Olast(_1698952, hAPP(hAPP(c_List_Olist_OCons(_1698952), _1698954), _1698950)) = _1698954)], (45799 ^ _782435) ^ [_1699049, _1699051, _1699053] : [-(_1699049 = c_List_Olist_ONil(_1699051)), -(c_List_Olast(_1699051, hAPP(hAPP(c_List_Olist_OCons(_1699051), _1699053), _1699049)) = c_List_Olast(_1699051, _1699049))], (45805 ^ _782435) ^ [_1699101, _1699103] : [-(_1699101 = c_List_Olist_ONil(_1699103)), -(hBOOL(hAPP(hAPP(c_member(_1699103), c_List_Olast(_1699103, _1699101)), hAPP(c_List_Oset(_1699103), _1699101))))], (45811 ^ _782435) ^ [_1699154, _1699156, _1699158] : [-(c_List_Olast(_1699154, hAPP(hAPP(c_List_Oappend(_1699154), _1699156), hAPP(hAPP(c_List_Olist_OCons(_1699154), _1699158), c_List_Olist_ONil(_1699154)))) = _1699158)], (45813 ^ _782435) ^ [_1699202, _1699204, _1699206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1699202), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1699204)), _1699206))), -(c_List_Olast(_1699204, hAPP(hAPP(c_List_Odrop(_1699204), _1699202), _1699206)) = c_List_Olast(_1699204, _1699206))], (45819 ^ _782435) ^ [_1699329, _1699331] : [-(_1699329 = c_List_Olist_ONil(_1699331)), -(hAPP(hAPP(c_List_Oappend(_1699331), c_List_Obutlast(_1699331, _1699329)), hAPP(hAPP(c_List_Olist_OCons(_1699331), c_List_Olast(_1699331, _1699329)), c_List_Olist_ONil(_1699331))) = _1699329)], (45825 ^ _782435) ^ [_1699412, _1699414, _1699416, _1699418] : [hAPP(hAPP(c_List_Oappend(_1699412), _1699414), hAPP(hAPP(c_List_Olist_OCons(_1699412), _1699416), c_List_Olist_ONil(_1699412))) = _1699418, 45828 ^ _782435 : [(45829 ^ _782435) ^ [] : [_1699418 = c_List_Olist_ONil(_1699412)], (45831 ^ _782435) ^ [] : [-(c_List_Obutlast(_1699412, _1699418) = _1699414)], (45833 ^ _782435) ^ [] : [-(c_List_Olast(_1699412, _1699418) = _1699416)]]], (45835 ^ _782435) ^ [_1699601, _1699603, _1699605, _1699607] : [-(hAPP(hAPP(c_List_Oappend(_1699601), _1699603), hAPP(hAPP(c_List_Olist_OCons(_1699601), _1699605), c_List_Olist_ONil(_1699601))) = _1699607), -(_1699607 = c_List_Olist_ONil(_1699601)), c_List_Obutlast(_1699601, _1699607) = _1699603, c_List_Olast(_1699601, _1699607) = _1699605], (45849 ^ _782435) ^ [_1699869, _1699871, _1699873] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699869)), _1699871), c_List_Olists(_1699869, _1699873))), -(_1699871 = c_List_Olist_ONil(_1699869)), 45858 ^ _782435 : [(45859 ^ _782435) ^ [] : [-(_1699871 = hAPP(hAPP(c_List_Olist_OCons(_1699869), 45856 ^ [_1699869, _1699871, _1699873]), 45857 ^ [_1699869, _1699871, _1699873]))], (45861 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1699869), 45856 ^ [_1699869, _1699871, _1699873]), _1699873)))], (45863 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1699869)), 45857 ^ [_1699869, _1699871, _1699873]), c_List_Olists(_1699869, _1699873))))]]], (45865 ^ _782435) ^ [_1700152, _1700154, _1700156] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700152)), _1700154), c_List_Olists(_1700152, _1700156)))), 45866 ^ _782435 : [(45867 ^ _782435) ^ [] : [_1700154 = c_List_Olist_ONil(_1700152)], (45869 ^ _782435) ^ [_1700280, _1700282] : [_1700154 = hAPP(hAPP(c_List_Olist_OCons(_1700152), _1700282), _1700280), hBOOL(hAPP(hAPP(c_member(_1700152), _1700282), _1700156)), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1700152)), _1700280), c_List_Olists(_1700152, _1700156)))]]], (45881 ^ _782435) ^ [_1700514, _1700516] : [-(_1700514 = c_List_Olist_ONil(_1700516)), -(c_Random_Oselect__weight(_1700516, hAPP(hAPP(c_List_Omap(_1700516, tc_prod(tc_Code__Numeral_Ocode__numeral, _1700516)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1700516), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1700514)) = c_Random_Oselect(_1700516, _1700514))], (45887 ^ _782435) ^ [_1700576, _1700578, _1700580] : [c_Fun_Oinj__on(_1700576, _1700578, _1700580, c_Orderings_Otop__class_Otop(tc_fun(_1700576, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1700576), tc_List_Olist(_1700578), hAPP(c_List_Omap(_1700576, _1700578), _1700580), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1700576), tc_HOL_Obool))))], (45893 ^ _782435) ^ [_1700703, _1700705, _1700707, _1700709] : [-(_1700703 = c_List_Olist_ONil(_1700705)), -(c_List_Olast(_1700707, hAPP(hAPP(c_List_Omap(_1700705, _1700707), _1700709), _1700703)) = hAPP(_1700709, c_List_Olast(_1700705, _1700703)))], (45899 ^ _782435) ^ [_1700763, _1700765, _1700767, _1700769, _1700771] : [c_Fun_Oinj__on(_1700763, _1700765, _1700767, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1700763, tc_HOL_Obool)), hAPP(c_List_Oset(_1700763), _1700769)), hAPP(c_List_Oset(_1700763), _1700771))), 45902 ^ _782435 : [(45903 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Omap(_1700763, _1700765), _1700767), _1700769) = hAPP(hAPP(c_List_Omap(_1700763, _1700765), _1700767), _1700771), -(_1700769 = _1700771)], (45909 ^ _782435) ^ [] : [_1700769 = _1700771, -(hAPP(hAPP(c_List_Omap(_1700763, _1700765), _1700767), _1700769) = hAPP(hAPP(c_List_Omap(_1700763, _1700765), _1700767), _1700771))]]], (45915 ^ _782435) ^ [_1701088, _1701090, _1701092, _1701094, _1701096] : [hAPP(hAPP(c_List_Omap(_1701088, _1701090), _1701092), _1701094) = hAPP(hAPP(c_List_Omap(_1701088, _1701090), _1701092), _1701096), c_Fun_Oinj__on(_1701088, _1701090, _1701092, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1701088, tc_HOL_Obool)), hAPP(c_List_Oset(_1701088), _1701094)), hAPP(c_List_Oset(_1701088), _1701096))), -(_1701094 = _1701096)], (45925 ^ _782435) ^ [_1701311, _1701313, _1701315, _1701317, _1701319, _1701321, _1701323] : [-(hAPP(c_List_Ofoldl(_1701311, _1701313, _1701315, _1701317), hAPP(hAPP(c_List_Omap(_1701319, _1701313), _1701321), _1701323)) = hAPP(c_List_Ofoldl(_1701311, _1701319, hAPP(hAPP(c_COMBC(_1701311, tc_fun(_1701319, _1701313), tc_fun(_1701319, _1701311)), hAPP(hAPP(c_COMBB(tc_fun(_1701313, _1701311), tc_fun(tc_fun(_1701319, _1701313), tc_fun(_1701319, _1701311)), _1701311), c_COMBB(_1701313, _1701311, _1701319)), _1701315)), _1701321), _1701317), _1701323))], (45927 ^ _782435) ^ [_1701413, _1701415, _1701417, _1701419, _1701421] : [-(hAPP(c_List_Orotate(_1701413, _1701415), hAPP(hAPP(c_List_Omap(_1701417, _1701413), _1701419), _1701421)) = hAPP(hAPP(c_List_Omap(_1701417, _1701413), _1701419), hAPP(c_List_Orotate(_1701417, _1701415), _1701421)))], (45929 ^ _782435) ^ [_1701474, _1701476, _1701478, _1701480] : [-(hAPP(hAPP(c_List_Omap(_1701474, _1701476), _1701478), hAPP(c_List_Otl(_1701474), _1701480)) = hAPP(c_List_Otl(_1701476), hAPP(hAPP(c_List_Omap(_1701474, _1701476), _1701478), _1701480)))], (45931 ^ _782435) ^ [_1701552, _1701554, _1701556, _1701558] : [hAPP(hAPP(c_List_Omap(_1701552, _1701554), _1701556), _1701558) = c_List_Olist_ONil(_1701554), -(_1701558 = c_List_Olist_ONil(_1701552))], (45937 ^ _782435) ^ [_1701655, _1701657, _1701659, _1701661] : [_1701661 = c_List_Olist_ONil(_1701655), -(hAPP(hAPP(c_List_Omap(_1701655, _1701657), _1701659), _1701661) = c_List_Olist_ONil(_1701657))], (45943 ^ _782435) ^ [_1701764, _1701766, _1701768] : [-(hAPP(hAPP(c_List_Omap(_1701764, _1701766), _1701768), c_List_Olist_ONil(_1701764)) = c_List_Olist_ONil(_1701766))], (45945 ^ _782435) ^ [_1701825, _1701827, _1701829, _1701831] : [c_List_Olist_ONil(_1701825) = hAPP(hAPP(c_List_Omap(_1701827, _1701825), _1701829), _1701831), -(_1701831 = c_List_Olist_ONil(_1701827))], (45951 ^ _782435) ^ [_1701928, _1701930, _1701932, _1701934] : [_1701934 = c_List_Olist_ONil(_1701930), -(c_List_Olist_ONil(_1701928) = hAPP(hAPP(c_List_Omap(_1701930, _1701928), _1701932), _1701934))], (45957 ^ _782435) ^ [_1702037, _1702039, _1702041, _1702043, _1702045, _1702047] : [-(hAPP(hAPP(c_List_Omap(_1702037, _1702039), _1702041), hAPP(hAPP(c_List_Olist__update(_1702037, _1702043), _1702045), _1702047)) = hAPP(hAPP(c_List_Olist__update(_1702039, hAPP(hAPP(c_List_Omap(_1702037, _1702039), _1702041), _1702043)), _1702045), hAPP(_1702041, _1702047)))], (45959 ^ _782435) ^ [_1702109, _1702111, _1702113, _1702115, _1702117] : [class_Groups_Ocomm__monoid__add(_1702109), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702109), hAPP(hAPP(c_List_Omap(_1702111, _1702109), hAPP(hAPP(c_COMBS(_1702111, _1702109, _1702109), hAPP(hAPP(c_COMBB(_1702109, tc_fun(_1702109, _1702109), _1702111), c_Groups_Oplus__class_Oplus(_1702109)), _1702113)), _1702115)), _1702117)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1702109), hAPP(c_List_Omonoid__add__class_Olistsum(_1702109), hAPP(hAPP(c_List_Omap(_1702111, _1702109), _1702113), _1702117))), hAPP(c_List_Omonoid__add__class_Olistsum(_1702109), hAPP(hAPP(c_List_Omap(_1702111, _1702109), _1702115), _1702117))))], (45965 ^ _782435) ^ [_1702340, _1702342, _1702344] : [class_Groups_Omonoid__add(_1702340), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702340), hAPP(hAPP(c_List_Omap(_1702342, _1702340), hAPP(c_COMBK(_1702340, _1702342), c_Groups_Ozero__class_Ozero(_1702340))), _1702344)) = c_Groups_Ozero__class_Ozero(_1702340))], (45971 ^ _782435) ^ [_1702465, _1702467, _1702469, _1702471, _1702473] : [class_Rings_Osemiring__0(_1702465), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702465), hAPP(hAPP(c_List_Omap(_1702467, _1702465), hAPP(hAPP(c_COMBC(_1702467, _1702465, _1702465), hAPP(hAPP(c_COMBB(_1702465, tc_fun(_1702465, _1702465), _1702467), c_Groups_Otimes__class_Otimes(_1702465)), _1702469)), _1702471)), _1702473)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1702465), hAPP(c_List_Omonoid__add__class_Olistsum(_1702465), hAPP(hAPP(c_List_Omap(_1702467, _1702465), _1702469), _1702473))), _1702471))], (45977 ^ _782435) ^ [_1702668, _1702670, _1702672, _1702674, _1702676] : [class_Rings_Osemiring__0(_1702668), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702668), hAPP(hAPP(c_List_Omap(_1702670, _1702668), hAPP(hAPP(c_COMBB(_1702668, _1702668, _1702670), hAPP(c_Groups_Otimes__class_Otimes(_1702668), _1702672)), _1702674)), _1702676)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1702668), _1702672), hAPP(c_List_Omonoid__add__class_Olistsum(_1702668), hAPP(hAPP(c_List_Omap(_1702670, _1702668), _1702674), _1702676))))], (45983 ^ _782435) ^ [_1702851, _1702853, _1702855, _1702857, _1702859] : [class_Groups_Oab__group__add(_1702851), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1702851), hAPP(hAPP(c_List_Omap(_1702853, _1702851), hAPP(hAPP(c_COMBS(_1702853, _1702851, _1702851), hAPP(hAPP(c_COMBB(_1702851, tc_fun(_1702851, _1702851), _1702853), c_Groups_Ominus__class_Ominus(_1702851)), _1702855)), _1702857)), _1702859)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1702851), hAPP(c_List_Omonoid__add__class_Olistsum(_1702851), hAPP(hAPP(c_List_Omap(_1702853, _1702851), _1702855), _1702859))), hAPP(c_List_Omonoid__add__class_Olistsum(_1702851), hAPP(hAPP(c_List_Omap(_1702853, _1702851), _1702857), _1702859))))], (45989 ^ _782435) ^ [_1703082, _1703084, _1703086, _1703088] : [-(hAPP(hAPP(c_List_Omap(_1703082, _1703084), _1703086), c_List_Obutlast(_1703082, _1703088)) = c_List_Obutlast(_1703084, hAPP(hAPP(c_List_Omap(_1703082, _1703084), _1703086), _1703088)))], (45991 ^ _782435) ^ [_1703135, _1703137, _1703139, _1703141, _1703143, _1703145, _1703147] : [hAPP(hAPP(c_List_Omap(_1703135, _1703137), _1703139), _1703141) = hAPP(hAPP(c_List_Omap(_1703143, _1703137), _1703145), _1703147), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703135)), _1703141) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703143)), _1703147))], (45997 ^ _782435) ^ [_1703286, _1703288, _1703290, _1703292] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703286)), hAPP(hAPP(c_List_Omap(_1703288, _1703286), _1703290), _1703292)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1703288)), _1703292))], (46009 ^ _782435) ^ [_1703606, _1703608, _1703610, _1703612, _1703614] : [46011 ^ _782435 : [(46012 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1703606), 46010 ^ [_1703606, _1703608, _1703610, _1703612, _1703614]), hAPP(c_List_Oset(_1703606), _1703612))))], (46014 ^ _782435) ^ [] : [hAPP(_1703610, 46010 ^ [_1703606, _1703608, _1703610, _1703612, _1703614]) = hAPP(_1703614, 46010 ^ [_1703606, _1703608, _1703610, _1703612, _1703614])]], -(hAPP(hAPP(c_List_Omap(_1703606, _1703608), _1703610), _1703612) = hAPP(hAPP(c_List_Omap(_1703606, _1703608), _1703614), _1703612))], (45999 ^ _782435) ^ [_1703362, _1703364, _1703366, _1703368, _1703370] : [hAPP(hAPP(c_List_Omap(_1703362, _1703364), _1703366), _1703368) = hAPP(hAPP(c_List_Omap(_1703362, _1703364), _1703370), _1703368), 46002 ^ _782435 : [(46003 ^ _782435) ^ [_1703485] : [hBOOL(hAPP(hAPP(c_member(_1703362), _1703485), hAPP(c_List_Oset(_1703362), _1703368))), -(hAPP(_1703366, _1703485) = hAPP(_1703370, _1703485))]]], (46018 ^ _782435) ^ [_1703863, _1703865, _1703867, _1703869, _1703871] : [-(hAPP(hAPP(c_List_Otake(_1703863), _1703865), hAPP(hAPP(c_List_Omap(_1703867, _1703863), _1703869), _1703871)) = hAPP(hAPP(c_List_Omap(_1703867, _1703863), _1703869), hAPP(hAPP(c_List_Otake(_1703867), _1703865), _1703871)))], (46020 ^ _782435) ^ [_1703928, _1703930, _1703932, _1703934, _1703936] : [hAPP(hAPP(c_List_Omap(_1703928, _1703930), _1703932), _1703934) = hAPP(hAPP(c_List_Omap(_1703928, _1703930), _1703932), _1703936), c_Fun_Oinj__on(_1703928, _1703930, _1703932, c_Orderings_Otop__class_Otop(tc_fun(_1703928, tc_HOL_Obool))), -(_1703934 = _1703936)], (46030 ^ _782435) ^ [_1704119, _1704121, _1704123, _1704125, _1704127] : [c_Fun_Oinj__on(_1704119, _1704121, _1704123, c_Orderings_Otop__class_Otop(tc_fun(_1704119, tc_HOL_Obool))), 46033 ^ _782435 : [(46034 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Omap(_1704119, _1704121), _1704123), _1704125) = hAPP(hAPP(c_List_Omap(_1704119, _1704121), _1704123), _1704127), -(_1704125 = _1704127)], (46040 ^ _782435) ^ [] : [_1704125 = _1704127, -(hAPP(hAPP(c_List_Omap(_1704119, _1704121), _1704123), _1704125) = hAPP(hAPP(c_List_Omap(_1704119, _1704121), _1704123), _1704127))]]], (46046 ^ _782435) ^ [_1704412, _1704414] : [-(hAPP(hAPP(c_List_Omap(_1704412, _1704412), c_COMBI(_1704412)), _1704414) = _1704414)], (46048 ^ _782435) ^ [_1704448, _1704450, _1704452, _1704454] : [-(hAPP(c_List_Oset(_1704448), hAPP(hAPP(c_List_Omap(_1704450, _1704448), _1704452), _1704454)) = hAPP(c_Set_Oimage(_1704450, _1704448, _1704452), hAPP(c_List_Oset(_1704450), _1704454)))], (46050 ^ _782435) ^ [_1704503, _1704505, _1704507, _1704509, _1704511] : [-(hAPP(hAPP(c_List_Omap(_1704503, _1704505), _1704507), hAPP(hAPP(c_List_Olist_OCons(_1704503), _1704509), _1704511)) = hAPP(hAPP(c_List_Olist_OCons(_1704505), hAPP(_1704507, _1704509)), hAPP(hAPP(c_List_Omap(_1704503, _1704505), _1704507), _1704511)))], (46052 ^ _782435) ^ [_1704571, _1704573] : [-(hAPP(hAPP(c_List_Ozip(_1704571, _1704571), _1704573), _1704573) = hAPP(hAPP(c_List_Omap(_1704571, tc_prod(_1704571, _1704571)), hAPP(hAPP(c_COMBS(_1704571, _1704571, tc_prod(_1704571, _1704571)), c_Product__Type_OPair(_1704571, _1704571)), c_COMBI(_1704571))), _1704573))], (46054 ^ _782435) ^ [_1704635, _1704637, _1704639, _1704641, _1704643, _1704645, _1704647, _1704649] : [-(hAPP(hAPP(c_List_Ozip(_1704635, _1704637), hAPP(hAPP(c_List_Omap(_1704639, _1704635), _1704641), _1704643)), hAPP(hAPP(c_List_Omap(_1704645, _1704637), _1704647), _1704649)) = hAPP(hAPP(c_List_Omap(tc_prod(_1704639, _1704645), tc_prod(_1704635, _1704637)), hAPP(c_Product__Type_Oprod_Oprod__case(_1704639, _1704645, tc_prod(_1704635, _1704637)), hAPP(hAPP(c_COMBC(_1704639, tc_fun(_1704645, _1704637), tc_fun(_1704645, tc_prod(_1704635, _1704637))), hAPP(hAPP(c_COMBB(tc_fun(_1704637, tc_prod(_1704635, _1704637)), tc_fun(tc_fun(_1704645, _1704637), tc_fun(_1704645, tc_prod(_1704635, _1704637))), _1704639), c_COMBB(_1704637, tc_prod(_1704635, _1704637), _1704645)), hAPP(hAPP(c_COMBB(_1704635, tc_fun(_1704637, tc_prod(_1704635, _1704637)), _1704639), c_Product__Type_OPair(_1704635, _1704637)), _1704641))), _1704647))), hAPP(hAPP(c_List_Ozip(_1704639, _1704645), _1704643), _1704649)))], (46056 ^ _782435) ^ [_1704806, _1704808, _1704810, _1704812, _1704814, _1704816] : [-(hAPP(hAPP(c_List_Ozip(_1704806, _1704808), hAPP(hAPP(c_List_Omap(_1704810, _1704806), _1704812), _1704814)), _1704816) = hAPP(hAPP(c_List_Omap(tc_prod(_1704810, _1704808), tc_prod(_1704806, _1704808)), hAPP(c_Product__Type_Oprod_Oprod__case(_1704810, _1704808, tc_prod(_1704806, _1704808)), hAPP(hAPP(c_COMBB(_1704806, tc_fun(_1704808, tc_prod(_1704806, _1704808)), _1704810), c_Product__Type_OPair(_1704806, _1704808)), _1704812))), hAPP(hAPP(c_List_Ozip(_1704810, _1704808), _1704814), _1704816)))], (46058 ^ _782435) ^ [_1704910, _1704912, _1704914, _1704916, _1704918, _1704920, _1704922, _1704924] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1704910, _1704912), _1704914), _1704916), hAPP(hAPP(c_List_Ozip(_1704910, _1704912), hAPP(hAPP(c_List_Omap(_1704918, _1704910), _1704920), _1704922)), _1704924)) = hAPP(hAPP(c_List_Omap(tc_prod(_1704918, _1704912), _1704914), hAPP(c_Product__Type_Oprod_Oprod__case(_1704918, _1704912, _1704914), hAPP(hAPP(c_COMBB(tc_fun(_1704912, tc_prod(_1704910, _1704912)), tc_fun(_1704912, _1704914), _1704918), hAPP(c_COMBB(tc_prod(_1704910, _1704912), _1704914, _1704912), _1704916)), hAPP(hAPP(c_COMBB(_1704910, tc_fun(_1704912, tc_prod(_1704910, _1704912)), _1704918), c_Product__Type_OPair(_1704910, _1704912)), _1704920)))), hAPP(hAPP(c_List_Ozip(_1704918, _1704912), _1704922), _1704924)))], (46060 ^ _782435) ^ [_1705053, _1705055, _1705057, _1705059, _1705061, _1705063, _1705065, _1705067] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1705053, _1705055), _1705057), _1705059), hAPP(hAPP(c_List_Ozip(_1705053, _1705055), _1705061), hAPP(hAPP(c_List_Omap(_1705063, _1705055), _1705065), _1705067))) = hAPP(hAPP(c_List_Omap(tc_prod(_1705053, _1705063), _1705057), hAPP(c_Product__Type_Oprod_Oprod__case(_1705053, _1705063, _1705057), hAPP(hAPP(c_COMBB(tc_fun(_1705063, tc_prod(_1705053, _1705055)), tc_fun(_1705063, _1705057), _1705053), hAPP(c_COMBB(tc_prod(_1705053, _1705055), _1705057, _1705063), _1705059)), hAPP(hAPP(c_COMBC(_1705053, tc_fun(_1705063, _1705055), tc_fun(_1705063, tc_prod(_1705053, _1705055))), hAPP(hAPP(c_COMBB(tc_fun(_1705055, tc_prod(_1705053, _1705055)), tc_fun(tc_fun(_1705063, _1705055), tc_fun(_1705063, tc_prod(_1705053, _1705055))), _1705053), c_COMBB(_1705055, tc_prod(_1705053, _1705055), _1705063)), c_Product__Type_OPair(_1705053, _1705055))), _1705065)))), hAPP(hAPP(c_List_Ozip(_1705053, _1705063), _1705061), _1705067)))], (46062 ^ _782435) ^ [_1705234, _1705236, _1705238, _1705240, _1705242, _1705244] : [-(hAPP(hAPP(c_List_Ozip(_1705234, _1705236), _1705238), hAPP(hAPP(c_List_Omap(_1705240, _1705236), _1705242), _1705244)) = hAPP(hAPP(c_List_Omap(tc_prod(_1705234, _1705240), tc_prod(_1705234, _1705236)), hAPP(c_Product__Type_Oprod_Oprod__case(_1705234, _1705240, tc_prod(_1705234, _1705236)), hAPP(hAPP(c_COMBC(_1705234, tc_fun(_1705240, _1705236), tc_fun(_1705240, tc_prod(_1705234, _1705236))), hAPP(hAPP(c_COMBB(tc_fun(_1705236, tc_prod(_1705234, _1705236)), tc_fun(tc_fun(_1705240, _1705236), tc_fun(_1705240, tc_prod(_1705234, _1705236))), _1705234), c_COMBB(_1705236, tc_prod(_1705234, _1705236), _1705240)), c_Product__Type_OPair(_1705234, _1705236))), _1705242))), hAPP(hAPP(c_List_Ozip(_1705234, _1705240), _1705238), _1705244)))], (46064 ^ _782435) ^ [_1705376, _1705378, _1705380, _1705382, _1705384] : [-(hAPP(hAPP(c_List_Omap(_1705376, _1705378), _1705380), hAPP(hAPP(c_List_Oappend(_1705376), _1705382), _1705384)) = hAPP(hAPP(c_List_Oappend(_1705378), hAPP(hAPP(c_List_Omap(_1705376, _1705378), _1705380), _1705382)), hAPP(hAPP(c_List_Omap(_1705376, _1705378), _1705380), _1705384)))], (46066 ^ _782435) ^ [_1705446, _1705448, _1705450, _1705452] : [-(_1705446 = c_List_Olist_ONil(_1705448)), -(hAPP(c_List_Ohd(_1705450), hAPP(hAPP(c_List_Omap(_1705448, _1705450), _1705452), _1705446)) = hAPP(_1705452, hAPP(c_List_Ohd(_1705448), _1705446)))], (46072 ^ _782435) ^ [_1705510, _1705512, _1705514, _1705516, _1705518] : [-(hAPP(hAPP(c_List_Odrop(_1705510), _1705512), hAPP(hAPP(c_List_Omap(_1705514, _1705510), _1705516), _1705518)) = hAPP(hAPP(c_List_Omap(_1705514, _1705510), _1705516), hAPP(hAPP(c_List_Odrop(_1705514), _1705512), _1705518)))], (46074 ^ _782435) ^ [_1705575, _1705577, _1705579, _1705581, _1705583] : [-(c_List_Olist_Olist__size(_1705575, _1705577, hAPP(hAPP(c_List_Omap(_1705579, _1705575), _1705581), _1705583)) = c_List_Olist_Olist__size(_1705579, hAPP(c_Fun_Ocomp(_1705575, tc_Nat_Onat, _1705579, _1705577), _1705581), _1705583))], (46076 ^ _782435) ^ [_1705631, _1705633, _1705635, _1705637, _1705639] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1705631), tc_List_Olist(_1705633), tc_List_Olist(_1705635), hAPP(c_List_Omap(_1705631, _1705633), _1705637)), hAPP(c_List_Omap(_1705635, _1705631), _1705639)) = hAPP(c_List_Omap(_1705635, _1705633), hAPP(c_Fun_Ocomp(_1705631, _1705633, _1705635, _1705637), _1705639)))], (46078 ^ _782435) ^ [_1705702, _1705704, _1705706, _1705708, _1705710] : [-(hAPP(c_Fun_Ocomp(tc_List_Olist(_1705702), tc_List_Olist(_1705704), tc_List_Olist(_1705706), hAPP(c_List_Omap(_1705702, _1705704), _1705708)), hAPP(c_List_Omap(_1705706, _1705702), _1705710)) = hAPP(c_List_Omap(_1705706, _1705704), hAPP(c_Fun_Ocomp(_1705702, _1705704, _1705706, _1705708), _1705710)))], (46080 ^ _782435) ^ [_1705773, _1705775, _1705777, _1705779, _1705781, _1705783] : [-(hAPP(hAPP(c_List_Omap(_1705773, _1705775), _1705777), hAPP(hAPP(c_List_Omap(_1705779, _1705773), _1705781), _1705783)) = hAPP(hAPP(c_List_Omap(_1705779, _1705775), hAPP(c_Fun_Ocomp(_1705773, _1705775, _1705779, _1705777), _1705781)), _1705783))], (46082 ^ _782435) ^ [_1705841, _1705843, _1705845, _1705847, _1705849, _1705851] : [-(hAPP(hAPP(c_List_Omap(_1705841, _1705843), _1705845), hAPP(hAPP(c_List_Omap(_1705847, _1705841), _1705849), _1705851)) = hAPP(hAPP(c_List_Omap(_1705847, _1705843), hAPP(c_Fun_Ocomp(_1705841, _1705843, _1705847, _1705845), _1705849)), _1705851))], (46084 ^ _782435) ^ [_1705909] : [-(hAPP(c_List_Omap(_1705909, _1705909), c_COMBI(_1705909)) = c_Fun_Oid(tc_List_Olist(_1705909)))], (46086 ^ _782435) ^ [_1705944] : [-(hAPP(c_List_Omap(_1705944, _1705944), c_Fun_Oid(_1705944)) = c_Fun_Oid(tc_List_Olist(_1705944)))], (46088 ^ _782435) ^ [_1705979, _1705981, _1705983, _1705985, _1705987] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1705979), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1705981)), _1705983))), -(hAPP(hAPP(c_List_Onth(_1705985), hAPP(hAPP(c_List_Omap(_1705981, _1705985), _1705987), _1705983)), _1705979) = hAPP(_1705987, hAPP(hAPP(c_List_Onth(_1705981), _1705983), _1705979)))], (46094 ^ _782435) ^ [_1706138, _1706140, _1706142, _1706144, _1706146, _1706148] : [-(hBOOL(hAPP(hAPP(c_member(_1706138), _1706140), hAPP(c_List_Oset(_1706138), _1706142)))), -(hAPP(hAPP(c_List_Omap(_1706138, _1706144), c_Fun_Ofun__upd(_1706138, _1706144, _1706146, _1706140, _1706148)), _1706142) = hAPP(hAPP(c_List_Omap(_1706138, _1706144), _1706146), _1706142))], (46100 ^ _782435) ^ [_1706239, _1706241, _1706243, _1706245] : [hBOOL(hAPP(c_List_Odistinct(_1706239), hAPP(hAPP(c_List_Omap(_1706241, _1706239), _1706243), _1706245))), 46103 ^ _782435 : [(46104 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1706241), _1706245)))], (46106 ^ _782435) ^ [] : [-(c_Fun_Oinj__on(_1706241, _1706239, _1706243, hAPP(c_List_Oset(_1706241), _1706245)))]]], (46108 ^ _782435) ^ [_1706390, _1706392, _1706394, _1706396] : [-(hBOOL(hAPP(c_List_Odistinct(_1706390), hAPP(hAPP(c_List_Omap(_1706392, _1706390), _1706394), _1706396)))), hBOOL(hAPP(c_List_Odistinct(_1706392), _1706396)), c_Fun_Oinj__on(_1706392, _1706390, _1706394, hAPP(c_List_Oset(_1706392), _1706396))], (46118 ^ _782435) ^ [_1706577, _1706579] : [class_Groups_Oordered__ab__group__add__abs(_1706577), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1706577), hAPP(c_Groups_Oabs__class_Oabs(_1706577), hAPP(c_List_Omonoid__add__class_Olistsum(_1706577), _1706579))), hAPP(c_List_Omonoid__add__class_Olistsum(_1706577), hAPP(hAPP(c_List_Omap(_1706577, _1706577), c_Groups_Oabs__class_Oabs(_1706577)), _1706579)))))], (46124 ^ _782435) ^ [_1706718, _1706720, _1706722, _1706724] : [class_Groups_Oab__group__add(_1706718), -(hAPP(c_Groups_Ouminus__class_Ouminus(_1706718), hAPP(c_List_Omonoid__add__class_Olistsum(_1706718), hAPP(hAPP(c_List_Omap(_1706720, _1706718), _1706722), _1706724))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1706718), hAPP(hAPP(c_List_Omap(_1706720, _1706718), hAPP(c_Fun_Ocomp(_1706718, _1706718, _1706720, c_Groups_Ouminus__class_Ouminus(_1706718)), _1706722)), _1706724)))], (46130 ^ _782435) ^ [_1706901, _1706903, _1706905] : [c_Fun_Oinj__on(tc_List_Olist(_1706901), tc_List_Olist(_1706903), hAPP(c_List_Omap(_1706901, _1706903), _1706905), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1706901), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1706901, _1706903, _1706905, c_Orderings_Otop__class_Otop(tc_fun(_1706901, tc_HOL_Obool))))], (46136 ^ _782435) ^ [_1707028, _1707030, _1707032] : [c_Fun_Oinj__on(_1707028, _1707030, _1707032, c_Orderings_Otop__class_Otop(tc_fun(_1707028, tc_HOL_Obool))), -(c_Fun_Oinj__on(tc_List_Olist(_1707028), tc_List_Olist(_1707030), hAPP(c_List_Omap(_1707028, _1707030), _1707032), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1707028), tc_HOL_Obool))))], (46142 ^ _782435) ^ [_1707161, _1707163, _1707165] : [c_Fun_Oinj__on(tc_List_Olist(_1707161), tc_List_Olist(_1707163), hAPP(c_List_Omap(_1707161, _1707163), _1707165), c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(_1707161), tc_HOL_Obool))), -(c_Fun_Oinj__on(_1707161, _1707163, _1707165, c_Orderings_Otop__class_Otop(tc_fun(_1707161, tc_HOL_Obool))))], (46148 ^ _782435) ^ [_1707292, _1707294, _1707296, _1707298] : [class_Groups_Ocomm__monoid__add(_1707292), hBOOL(hAPP(c_List_Odistinct(_1707294), _1707296)), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707292), hAPP(hAPP(c_List_Omap(_1707294, _1707292), _1707298), _1707296)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1707294, _1707292), _1707298), hAPP(c_List_Oset(_1707294), _1707296)))], (46158 ^ _782435) ^ [_1707491, _1707493, _1707495, _1707497] : [class_Rings_Osemiring__1(_1707491), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707491), hAPP(hAPP(c_List_Omap(_1707493, _1707491), hAPP(c_COMBK(_1707491, _1707493), _1707495)), _1707497)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1707491), hAPP(c_Nat_Osemiring__1__class_Oof__nat(_1707491), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1707493)), _1707497))), _1707495))], (46164 ^ _782435) ^ [_1707650, _1707652, _1707654, _1707656, _1707658] : [-(c_Enum_Oproduct(_1707650, _1707652, hAPP(hAPP(c_List_Olist_OCons(_1707650), _1707654), _1707656), _1707658) = hAPP(hAPP(c_List_Oappend(tc_prod(_1707650, _1707652)), hAPP(hAPP(c_List_Omap(_1707652, tc_prod(_1707650, _1707652)), hAPP(c_Product__Type_OPair(_1707650, _1707652), _1707654)), _1707658)), c_Enum_Oproduct(_1707650, _1707652, _1707656, _1707658)))], (46166 ^ _782435) ^ [_1707728, _1707730, _1707732, _1707734, _1707736] : [class_Groups_Ocomm__monoid__add(_1707728), hBOOL(hAPP(hAPP(c_member(_1707730), _1707732), hAPP(c_List_Oset(_1707730), _1707734))), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1707728), hAPP(hAPP(c_List_Omap(_1707730, _1707728), _1707736), _1707734)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1707728), hAPP(_1707736, _1707732)), hAPP(c_List_Omonoid__add__class_Olistsum(_1707728), hAPP(hAPP(c_List_Omap(_1707730, _1707728), _1707736), c_List_Oremove1(_1707730, _1707732, _1707734)))))], (46176 ^ _782435) ^ [_1707977, _1707979, _1707981, _1707983] : [c_Fun_Oinj__on(_1707977, _1707979, _1707981, c_Complete__Lattice_OSup__class_OSup(tc_fun(_1707977, tc_HOL_Obool), hAPP(c_Set_Oimage(tc_List_Olist(_1707977), tc_fun(_1707977, tc_HOL_Obool), c_List_Oset(_1707977)), _1707983))), -(c_Fun_Oinj__on(tc_List_Olist(_1707977), tc_List_Olist(_1707979), hAPP(c_List_Omap(_1707977, _1707979), _1707981), _1707983))], (46182 ^ _782435) ^ [_1708126, _1708128, _1708130, _1708132] : [class_Groups_Ocomm__monoid__add(_1708126), 46185 ^ _782435 : [(46186 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1708128), _1708130)), -(c_Nitpick_Osetsum_H(_1708128, _1708126, _1708132, _1708130) = hAPP(c_List_Omonoid__add__class_Olistsum(_1708126), hAPP(hAPP(c_List_Omap(_1708128, _1708126), _1708132), c_Hilbert__Choice_OEps(tc_List_Olist(_1708128), hAPP(hAPP(c_COMBS(tc_List_Olist(_1708128), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_List_Olist(_1708128)), c_fconj), hAPP(hAPP(c_COMBC(tc_List_Olist(_1708128), tc_fun(_1708128, tc_HOL_Obool), tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_fun(_1708128, tc_HOL_Obool), tc_fun(tc_fun(_1708128, tc_HOL_Obool), tc_HOL_Obool), tc_List_Olist(_1708128)), c_fequal), c_List_Oset(_1708128))), _1708130))), c_List_Odistinct(_1708128))))))], (46192 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1708128), _1708130))), -(c_Nitpick_Osetsum_H(_1708128, _1708126, _1708132, _1708130) = c_Groups_Ozero__class_Ozero(_1708126))]]], (46198 ^ _782435) ^ [_1708514, _1708516, _1708518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708514), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1708516)), _1708518))), -(hAPP(c_Random_Opick(_1708516, hAPP(hAPP(c_List_Omap(_1708516, tc_prod(tc_Code__Numeral_Ocode__numeral, _1708516)), hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral, _1708516), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), _1708518)), hAPP(c_Code__Numeral_Oof__nat, _1708514)) = hAPP(hAPP(c_List_Onth(_1708516), _1708518), _1708514))], (46204 ^ _782435) ^ [_1708687, _1708689, _1708691] : [-(c_Enum_Osublists(_1708687, hAPP(hAPP(c_List_Olist_OCons(_1708687), _1708689), _1708691)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(_1708687)), tc_List_Olist(tc_List_Olist(_1708687))), c_Enum_Osublists(_1708687, _1708691)), hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(_1708687)), tc_List_Olist(tc_List_Olist(_1708687)), tc_List_Olist(tc_List_Olist(_1708687))), hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(_1708687)), tc_fun(tc_List_Olist(tc_List_Olist(_1708687)), tc_List_Olist(tc_List_Olist(_1708687))), tc_List_Olist(tc_List_Olist(_1708687))), c_List_Oappend(tc_List_Olist(_1708687))), hAPP(c_List_Omap(tc_List_Olist(_1708687), tc_List_Olist(_1708687)), hAPP(c_List_Olist_OCons(_1708687), _1708689)))), c_COMBI(tc_List_Olist(tc_List_Olist(_1708687))))))], (46206 ^ _782435) ^ [_1708836, _1708838] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1708836)), hAPP(c_Code__Numeral_Oof__nat, _1708838))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708836), _1708838)))], (46212 ^ _782435) ^ [_1708941, _1708943] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1708941), _1708943)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1708941)), hAPP(c_Code__Numeral_Oof__nat, _1708943))))], (46218 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1709085, _1709087] : [hAPP(c_Code__Numeral_Oof__nat, _1709085) = hAPP(c_Code__Numeral_Oof__nat, _1709087), -(_1709085 = _1709087)], (46226 ^ _782435) ^ [_1709170, _1709172] : [_1709170 = _1709172, -(hAPP(c_Code__Numeral_Oof__nat, _1709170) = hAPP(c_Code__Numeral_Oof__nat, _1709172))], (46232 ^ _782435) ^ [] : [-(c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral))], (46234 ^ _782435) ^ [_1709279, _1709281] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1709279)), hAPP(c_Code__Numeral_Oof__nat, _1709281)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1709279), _1709281)))], (46236 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1709343, _1709345] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709343), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1709345), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), 46245 ^ _782435 : [(46246 ^ _782435) ^ [] : [hAPP(c_Code__Numeral_Oof__nat, _1709343) = hAPP(c_Code__Numeral_Oof__nat, _1709345), -(_1709343 = _1709345)], (46252 ^ _782435) ^ [] : [_1709343 = _1709345, -(hAPP(c_Code__Numeral_Oof__nat, _1709343) = hAPP(c_Code__Numeral_Oof__nat, _1709345))]]], (46258 ^ _782435) ^ [_1709640, _1709642, _1709644, _1709646] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709640)), _1709642) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709644)), _1709646), -(hAPP(hAPP(c_List_Omap(tc_prod(_1709640, _1709644), _1709640), c_Product__Type_Ofst(_1709640, _1709644)), hAPP(hAPP(c_List_Ozip(_1709640, _1709644), _1709642), _1709646)) = _1709642)], (46264 ^ _782435) ^ [_1709797, _1709799, _1709801, _1709803] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709797)), _1709799) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1709801)), _1709803), -(hAPP(hAPP(c_List_Omap(tc_prod(_1709797, _1709801), _1709801), c_Product__Type_Osnd(_1709797, _1709801)), hAPP(hAPP(c_List_Ozip(_1709797, _1709801), _1709799), _1709803)) = _1709803)], (46270 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1709972, _1709974, _1709976] : [-(hAPP(hAPP(c_List_Ozip(_1709972, _1709974), hAPP(hAPP(c_List_Omap(tc_prod(_1709972, _1709974), _1709972), c_Product__Type_Ofst(_1709972, _1709974)), _1709976)), hAPP(hAPP(c_List_Omap(tc_prod(_1709972, _1709974), _1709974), c_Product__Type_Osnd(_1709972, _1709974)), _1709976)) = _1709976)], (46274 ^ _782435) ^ [_1710038, _1710040] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710038)), hAPP(c_Code__Numeral_Oof__nat, _1710040)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1710038), _1710040)))], (46276 ^ _782435) ^ [_1710099, _1710101] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710099)), hAPP(c_Code__Numeral_Oof__nat, _1710101))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710099), _1710101)))], (46282 ^ _782435) ^ [_1710204, _1710206] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1710204), _1710206)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), hAPP(c_Code__Numeral_Oof__nat, _1710204)), hAPP(c_Code__Numeral_Oof__nat, _1710206))))], (46288 ^ _782435) ^ [_1710315, _1710317] : [hBOOL(hAPP(c_List_Odistinct(_1710315), _1710317)), -(hBOOL(hAPP(c_List_Odistinct(tc_fun(_1710315, tc_HOL_Obool)), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1710315), tc_fun(_1710315, tc_HOL_Obool)), c_List_Oset(_1710315)), c_Enum_Osublists(_1710315, _1710317)))))], (46294 ^ _782435) ^ [_1710452, _1710454, _1710456] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1710452), hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710454), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1710454)), _1710456)))), -(hBOOL(hAPP(hAPP(c_member(_1710454), hAPP(c_Random_Opick(_1710454, _1710456), _1710452)), hAPP(c_List_Oset(_1710454), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1710454), _1710454), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1710454)), _1710456)))))], (46300 ^ _782435) ^ [_1710643, _1710645, _1710647, _1710649, _1710651] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710643)), _1710645) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1710647)), _1710649), 46303 ^ _782435 : [(46304 ^ _782435) ^ [] : [hAPP(hAPP(c_List_Ozip(_1710643, _1710647), _1710645), _1710649) = _1710651, 46307 ^ _782435 : [(46308 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710643, _1710647), _1710643), c_Product__Type_Ofst(_1710643, _1710647)), _1710651) = _1710645)], (46310 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1710643, _1710647), _1710647), c_Product__Type_Osnd(_1710643, _1710647)), _1710651) = _1710649)]]], (46312 ^ _782435) ^ [] : [-(hAPP(hAPP(c_List_Ozip(_1710643, _1710647), _1710645), _1710649) = _1710651), hAPP(hAPP(c_List_Omap(tc_prod(_1710643, _1710647), _1710643), c_Product__Type_Ofst(_1710643, _1710647)), _1710651) = _1710645, hAPP(hAPP(c_List_Omap(tc_prod(_1710643, _1710647), _1710647), c_Product__Type_Osnd(_1710643, _1710647)), _1710651) = _1710649]]], (46322 ^ _782435) ^ [_1711091, _1711093, _1711095] : [-(c_List_Olist_Olist__size(_1711091, _1711093, _1711095) = 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(_1711091, tc_Nat_Onat), _1711093), _1711095))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1711091)), _1711095)))], (46324 ^ _782435) ^ [_1711153] : [-(_1711153 = 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)), _1711153)))], (46330 ^ _782435) ^ [_1711185] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1711185)), _1711185 = hAPP(c_Code__Numeral_Oof__nat, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (46336 ^ _782435) ^ [_1711267, _1711269, _1711271, _1711273] : [class_Groups_Ocomm__monoid__add(_1711267), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1711267), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1711267), _1711269), c_List_Oupto(_1711271, _1711273))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1711267), _1711269), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1711271, _1711273))))], (46342 ^ _782435) ^ [_1711410, _1711412, _1711414, _1711416] : [class_Groups_Ocomm__monoid__add(_1711410), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint, _1711410), _1711412), hAPP(c_List_Oset(tc_Int_Oint), c_List_Oupto(_1711414, _1711416))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1711410), hAPP(hAPP(c_List_Omap(tc_Int_Oint, _1711410), _1711412), c_List_Oupto(_1711414, _1711416))))], (46348 ^ _782435) ^ [_1711553, _1711555, _1711557] : [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, _1711553), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1711553)), _1711555)))), -(hBOOL(hAPP(hAPP(c_member(_1711553), hAPP(c_Product__Type_Ofst(_1711553, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_Random_Oselect__weight(_1711553, _1711555), _1711557))), hAPP(c_List_Oset(_1711553), hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral, _1711553), _1711553), c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral, _1711553)), _1711555)))))], (46354 ^ _782435) ^ [_1711750, _1711752] : [-(c_Random_Oselect__weight(_1711750, _1711752) = 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(_1711750, 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, _1711750), tc_Code__Numeral_Ocode__numeral), c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral, _1711750)), _1711752)))), hAPP(hAPP(c_COMBB(_1711750, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1711750, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1711750, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random_Opick(_1711750, _1711752))))], (46356 ^ _782435) ^ [_1711834, _1711836] : [-(c_Random_Oselect(_1711834, _1711836) = 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(_1711834, 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(_1711834)), _1711836)))), hAPP(hAPP(c_COMBB(_1711834, tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1711834, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_Code__Numeral_Ocode__numeral), c_Product__Type_OPair(_1711834, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, _1711834, tc_Code__Numeral_Ocode__numeral), hAPP(c_List_Onth(_1711834), _1711836)), c_Code__Numeral_Onat__of))))], (46358 ^ _782435) ^ [_1711922, _1711924] : [-(hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, hAPP(c_Code__Numeral_Oof__nat, _1711922)), hAPP(c_Code__Numeral_Oof__nat, _1711924)) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1711922), _1711924)))], (46360 ^ _782435) ^ [_1711968] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1711968)) = _1711968)], (46362 ^ _782435) ^ [_1711997] : [-(hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Code__Numeral_Onat__of, _1711997)) = _1711997)], (46364 ^ _782435) ^ [_1712026] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Code__Numeral_Oof__nat, _1712026)) = _1712026)], (46366 ^ _782435) ^ [_1712055, _1712057] : [-(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral), _1712055), _1712057) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712055)), hAPP(c_Code__Numeral_Onat__of, _1712057))))], (46368 ^ _782435) ^ [_1712116, _1712118] : [hAPP(c_Code__Numeral_Onat__of, _1712116) = hAPP(c_Code__Numeral_Onat__of, _1712118), -(_1712116 = _1712118)], (46374 ^ _782435) ^ [_1712201, _1712203] : [_1712201 = _1712203, -(hAPP(c_Code__Numeral_Onat__of, _1712201) = hAPP(c_Code__Numeral_Onat__of, _1712203))], (46380 ^ _782435) ^ [_1712307, _1712309] : [hAPP(c_Code__Numeral_Onat__of, _1712307) = hAPP(c_Code__Numeral_Onat__of, _1712309), -(_1712307 = _1712309)], (46386 ^ _782435) ^ [_1712392, _1712394] : [_1712392 = _1712394, -(hAPP(c_Code__Numeral_Onat__of, _1712392) = hAPP(c_Code__Numeral_Onat__of, _1712394))], (46392 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1712516, _1712518] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1712516), _1712518)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712516)), hAPP(c_Code__Numeral_Onat__of, _1712518))))], (46400 ^ _782435) ^ [_1712621, _1712623] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712621)), hAPP(c_Code__Numeral_Onat__of, _1712623))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1712621), _1712623)))], (46406 ^ _782435) ^ [_1712732] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712732)), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (46408 ^ _782435) ^ [_1712763] : [-(hAPP(c_Code__Numeral_Onat__of, hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral), _1712763)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1712763))], (46410 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1712828, _1712830] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1712828), _1712830)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712828)), hAPP(c_Code__Numeral_Onat__of, _1712830))))], (46418 ^ _782435) ^ [_1712933, _1712935] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1712933)), hAPP(c_Code__Numeral_Onat__of, _1712935))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1712933), _1712935)))], (46424 ^ _782435) ^ [_1713044] : [-(hAPP(c_Code__Numeral_Onat__of, _1713044) = c_Code__Numeral_Onat__of__aux(_1713044, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (46426 ^ _782435) ^ [_1713073, _1713075] : [-(c_Code__Numeral_Onat__of__aux(_1713073, _1713075) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713073)), _1713075))], (46428 ^ _782435) ^ [_1713110] : [-(c_Code__Numeral_OSuc__code__numeral(_1713110) = hAPP(c_Code__Numeral_Oof__nat, hAPP(c_Nat_OSuc, hAPP(c_Code__Numeral_Onat__of, _1713110))))], (46430 ^ _782435) ^ [_1713144, _1713146] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1713144), _1713146) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713144)), hAPP(c_Code__Numeral_Onat__of, _1713146))))], (46432 ^ _782435) ^ [_1713190] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1713190), 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, _1713190)) = _1713190)], (46438 ^ _782435) ^ [_1713287, _1713289] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral), _1713287), _1713289) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713287)), hAPP(c_Code__Numeral_Onat__of, _1713289))))], (46440 ^ _782435) ^ [_1713333, _1713335] : [-(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral), _1713333), _1713335) = hAPP(c_Code__Numeral_Oof__nat, hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat), hAPP(c_Code__Numeral_Onat__of, _1713333)), hAPP(c_Code__Numeral_Onat__of, _1713335))))], (46442 ^ _782435) ^ [] : [-(c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral))], (46444 ^ _782435) ^ [_1713397, _1713399] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1713397), _1713399) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral, _1713397), _1713399))], (46446 ^ _782435) ^ [_1713434, _1713436] : [-(c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral, _1713434, _1713436) = hAPP(c_Code__Numeral_Oof__nat, c_Divides_Odiv__class_Omod(tc_Nat_Onat, hAPP(c_Code__Numeral_Onat__of, _1713434), hAPP(c_Code__Numeral_Onat__of, _1713436))))], (46448 ^ _782435) ^ [_1713472] : [-(_1713472 = 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, _1713472)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_Code__Numeral_Onat__of, _1713472))))], (46454 ^ _782435) ^ [_1713523, _1713525, _1713527, _1713529, _1713531] : [class_Groups_Omonoid__add(_1713523), class_Groups_Oordered__ab__semigroup__add(_1713523), 46464 ^ _782435 : [(46465 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1713525), 46463 ^ [_1713523, _1713525, _1713527, _1713529, _1713531]), hAPP(c_List_Oset(_1713525), _1713527))))], (46467 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713523), hAPP(_1713529, 46463 ^ [_1713523, _1713525, _1713527, _1713529, _1713531])), hAPP(_1713531, 46463 ^ [_1713523, _1713525, _1713527, _1713529, _1713531])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1713523), hAPP(c_List_Omonoid__add__class_Olistsum(_1713523), hAPP(hAPP(c_List_Omap(_1713525, _1713523), _1713529), _1713527))), hAPP(c_List_Omonoid__add__class_Olistsum(_1713523), hAPP(hAPP(c_List_Omap(_1713525, _1713523), _1713531), _1713527)))))], (46471 ^ _782435) ^ [_1713947, _1713949] : [-(hAPP(c_New__DSequence_Opos__not__seq(_1713947), _1713949) = c_Lazy__Sequence_Ohb__not__seq(hAPP(_1713947, 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)))), _1713949))))], (46473 ^ _782435) ^ [_1713985, _1713987, _1713989, _1713991, _1713993] : [c_List_Opartition(_1713985, _1713987, _1713989) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1713985), tc_List_Olist(_1713985)), _1713991), _1713993), -(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1713985, tc_HOL_Obool)), hAPP(c_List_Oset(_1713985), _1713991)), hAPP(c_List_Oset(_1713985), _1713993)) = hAPP(c_List_Oset(_1713985), _1713989))], (46479 ^ _782435) ^ [_1714154, _1714156, _1714158, _1714160] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1714154)), _1714156), c_List_Olists(_1714154, _1714158))), hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1714154)), _1714156), c_List_Olists(_1714154, _1714160))), -(hBOOL(hAPP(c_List_Olistsp(_1714154, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714154, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1714154, tc_fun(_1714154, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714154)), _1714158)), hAPP(hAPP(c_COMBC(_1714154, tc_fun(_1714154, tc_HOL_Obool), tc_HOL_Obool), c_member(_1714154)), _1714160))), _1714156)))], (46489 ^ _782435) ^ [_1714431, _1714433] : [-(hBOOL(hAPP(c_List_Olistsp(_1714431, _1714433), c_List_Olist_ONil(_1714431))))], (46491 ^ _782435) ^ [_1714463, _1714465] : [-(hBOOL(hAPP(c_List_Olistsp(_1714463, _1714465), c_List_Olist_ONil(_1714463))))], (46503 ^ _782435) ^ [_1714711, _1714713, _1714715] : [46505 ^ _782435 : [(46506 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1714711), 46504 ^ [_1714711, _1714713, _1714715]), hAPP(c_List_Oset(_1714711), _1714715))))], (46508 ^ _782435) ^ [] : [hBOOL(hAPP(_1714713, 46504 ^ [_1714711, _1714713, _1714715]))]], -(hBOOL(hAPP(c_List_Olistsp(_1714711, _1714713), _1714715)))], (46493 ^ _782435) ^ [_1714513, _1714515, _1714517] : [hBOOL(hAPP(c_List_Olistsp(_1714513, _1714515), _1714517)), 46496 ^ _782435 : [(46497 ^ _782435) ^ [_1714602] : [hBOOL(hAPP(hAPP(c_member(_1714513), _1714602), hAPP(c_List_Oset(_1714513), _1714517))), -(hBOOL(hAPP(_1714515, _1714602)))]]], (46512 ^ _782435) ^ [_1714901, _1714903, _1714905, _1714907] : [hBOOL(hAPP(c_List_Olistsp(_1714901, _1714903), _1714905)), hBOOL(hAPP(c_List_Olistsp(_1714901, _1714907), _1714905)), -(hBOOL(hAPP(c_List_Olistsp(_1714901, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1714901, tc_HOL_Obool)), _1714903), _1714907)), _1714905)))], (46522 ^ _782435) ^ [_1715090, _1715092, _1715094] : [-(c_List_Olistsp(_1715090, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1715090, tc_HOL_Obool)), _1715092), _1715094)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1715090), tc_HOL_Obool)), c_List_Olistsp(_1715090, _1715092)), c_List_Olistsp(_1715090, _1715094)))], (46524 ^ _782435) ^ [_1715171, _1715173, _1715175, _1715177] : [hBOOL(hAPP(c_List_Olistsp(_1715171, hAPP(hAPP(c_COMBS(_1715171, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715171), c_fconj), _1715173)), _1715175)), _1715177)), 46527 ^ _782435 : [(46528 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715171, _1715173), _1715177)))], (46530 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715171, _1715175), _1715177)))]]], (46532 ^ _782435) ^ [_1715344, _1715346, _1715348, _1715350] : [-(hBOOL(hAPP(c_List_Olistsp(_1715344, hAPP(hAPP(c_COMBS(_1715344, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1715344), c_fconj), _1715346)), _1715348)), _1715350))), hBOOL(hAPP(c_List_Olistsp(_1715344, _1715346), _1715350)), hBOOL(hAPP(c_List_Olistsp(_1715344, _1715348), _1715350))], (46542 ^ _782435) ^ [_1715574, _1715576, _1715578, _1715580] : [hBOOL(hAPP(c_List_Olistsp(_1715574, _1715576), hAPP(hAPP(c_List_Olist_OCons(_1715574), _1715578), _1715580))), 46545 ^ _782435 : [(46546 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1715576, _1715578)))], (46548 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715574, _1715576), _1715580)))]]], (46550 ^ _782435) ^ [_1715717, _1715719, _1715721, _1715723] : [-(hBOOL(hAPP(c_List_Olistsp(_1715717, _1715719), hAPP(hAPP(c_List_Olist_OCons(_1715717), _1715721), _1715723)))), hBOOL(hAPP(_1715719, _1715721)), hBOOL(hAPP(c_List_Olistsp(_1715717, _1715719), _1715723))], (46560 ^ _782435) ^ [_1715917, _1715919, _1715921, _1715923] : [hBOOL(hAPP(c_List_Olistsp(_1715917, _1715919), hAPP(hAPP(c_List_Oappend(_1715917), _1715921), _1715923))), 46563 ^ _782435 : [(46564 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715917, _1715919), _1715921)))], (46566 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Olistsp(_1715917, _1715919), _1715923)))]]], (46568 ^ _782435) ^ [_1716066, _1716068, _1716070, _1716072] : [-(hBOOL(hAPP(c_List_Olistsp(_1716066, _1716068), hAPP(hAPP(c_List_Oappend(_1716066), _1716070), _1716072)))), hBOOL(hAPP(c_List_Olistsp(_1716066, _1716068), _1716070)), hBOOL(hAPP(c_List_Olistsp(_1716066, _1716068), _1716072))], (46578 ^ _782435) ^ [_1716251, _1716253, _1716255] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1716251, tc_HOL_Obool)), _1716253), _1716255)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(_1716251), tc_HOL_Obool)), c_List_Olistsp(_1716251, _1716253)), c_List_Olistsp(_1716251, _1716255))))], (46584 ^ _782435) ^ [_1716386, _1716388, _1716390, _1716392, _1716394] : [c_List_Opartition(_1716386, _1716388, _1716390) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716386), tc_List_Olist(_1716386)), _1716392), _1716394), 46587 ^ _782435 : [(46588 ^ _782435) ^ [_1716539] : [hBOOL(hAPP(hAPP(c_member(_1716386), _1716539), hAPP(c_List_Oset(_1716386), _1716392))), -(hBOOL(hAPP(_1716388, _1716539)))], (46594 ^ _782435) ^ [_1716648] : [hBOOL(hAPP(hAPP(c_member(_1716386), _1716648), hAPP(c_List_Oset(_1716386), _1716394))), hBOOL(hAPP(_1716388, _1716648))]]], (46600 ^ _782435) ^ [_1716768, _1716770] : [-(c_List_Opartition(_1716768, _1716770, c_List_Olist_ONil(_1716768)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1716768), tc_List_Olist(_1716768)), c_List_Olist_ONil(_1716768)), c_List_Olist_ONil(_1716768)))], (46602 ^ _782435) ^ [_1716834, _1716836, _1716838] : [hBOOL(hAPP(c_List_Olistsp(_1716834, hAPP(hAPP(c_COMBC(_1716834, tc_fun(_1716834, tc_HOL_Obool), tc_HOL_Obool), c_member(_1716834)), _1716836)), _1716838)), -(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1716834)), _1716838), c_List_Olists(_1716834, _1716836))))], (46608 ^ _782435) ^ [_1716973, _1716975, _1716977] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1716973)), _1716977), c_List_Olists(_1716973, _1716975))), -(hBOOL(hAPP(c_List_Olistsp(_1716973, hAPP(hAPP(c_COMBC(_1716973, tc_fun(_1716973, tc_HOL_Obool), tc_HOL_Obool), c_member(_1716973)), _1716975)), _1716977)))], (46614 ^ _782435) ^ [_1717118, _1717120, _1717122, _1717124] : [-(c_List_Opartition(_1717118, _1717120, hAPP(hAPP(c_List_Olist_OCons(_1717118), _1717122), _1717124)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1717118), tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), hAPP(hAPP(c_COMBS(tc_List_Olist(_1717118), tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717118), tc_fun(tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), tc_fun(tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), tc_List_Olist(_1717118)), c_COMBS(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), tc_fun(tc_List_Olist(_1717118), tc_fun(tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), tc_List_Olist(_1717118)), hAPP(c_COMBB(tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_fun(tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), tc_List_Olist(_1717118)), hAPP(c_If(tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), hAPP(_1717120, _1717122)))), hAPP(hAPP(c_COMBB(tc_List_Olist(_1717118), tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), tc_List_Olist(_1717118)), c_Product__Type_OPair(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), hAPP(c_List_Olist_OCons(_1717118), _1717122))))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717118), tc_fun(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118))), tc_fun(tc_fun(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_fun(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), tc_List_Olist(_1717118)), c_COMBB(tc_List_Olist(_1717118), tc_prod(tc_List_Olist(_1717118), tc_List_Olist(_1717118)), tc_List_Olist(_1717118))), c_Product__Type_OPair(tc_List_Olist(_1717118), tc_List_Olist(_1717118)))), hAPP(c_List_Olist_OCons(_1717118), _1717122)))), c_List_Opartition(_1717118, _1717120, _1717124)))], (46616 ^ _782435) ^ [_1717537, _1717539, _1717541] : [-(c_List_Olistsp(_1717537, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1717537, tc_HOL_Obool)), hAPP(hAPP(c_COMBC(_1717537, tc_fun(_1717537, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717537)), _1717539)), hAPP(hAPP(c_COMBC(_1717537, tc_fun(_1717537, tc_HOL_Obool), tc_HOL_Obool), c_member(_1717537)), _1717541))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(_1717537), tc_HOL_Obool)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717537), tc_fun(tc_List_Olist(_1717537), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1717537))), c_List_Olists(_1717537, _1717539))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1717537), tc_fun(tc_List_Olist(_1717537), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_List_Olist(_1717537))), c_List_Olists(_1717537, _1717541))))], (46618 ^ _782435) ^ [_1717693, _1717695, _1717697, _1717699, _1717701] : [c_List_Olist__all2(_1717693, _1717695, _1717697, _1717699, _1717701), 46621 ^ _782435 : [(46622 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717693)), _1717699) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1717695)), _1717701))], (46624 ^ _782435) ^ [_1717859] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1717693, _1717695)), _1717859), hAPP(c_List_Oset(tc_prod(_1717693, _1717695)), hAPP(hAPP(c_List_Ozip(_1717693, _1717695), _1717699), _1717701)))), -(hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1717693, _1717695, tc_HOL_Obool), _1717697), _1717859)))]]], (46630 ^ _782435) ^ [_1718018, _1718020, _1718022, _1718024, _1718026] : [-(c_List_Olist__all2(_1718018, _1718020, _1718022, _1718024, _1718026)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718018)), _1718024) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718020)), _1718026), 46636 ^ _782435 : [(46637 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1718018, _1718020)), 46635 ^ [_1718018, _1718020, _1718022, _1718024, _1718026]), hAPP(c_List_Oset(tc_prod(_1718018, _1718020)), hAPP(hAPP(c_List_Ozip(_1718018, _1718020), _1718024), _1718026)))))], (46639 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1718018, _1718020, tc_HOL_Obool), _1718022), 46635 ^ [_1718018, _1718020, _1718022, _1718024, _1718026]))]]], (46643 ^ _782435) ^ [_1718359, _1718361, _1718363, _1718365] : [46645 ^ _782435 : [(46646 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46644 ^ [_1718359, _1718361, _1718363, _1718365]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1718359)), _1718361))))], (46648 ^ _782435) ^ [] : [hBOOL(hAPP(_1718363, hAPP(hAPP(c_List_Onth(_1718359), _1718361), 46644 ^ [_1718359, _1718361, _1718363, _1718365])))]], hBOOL(hAPP(hAPP(c_member(_1718359), _1718365), hAPP(c_List_Oset(_1718359), _1718361))), -(hBOOL(hAPP(_1718363, _1718365)))], (46656 ^ _782435) ^ [_1718685, _1718687, _1718689, _1718691, _1718693, _1718695, _1718697] : [c_List_Olist__all2(_1718685, _1718687, _1718689, hAPP(hAPP(c_List_Omap(_1718691, _1718685), _1718693), _1718695), _1718697), -(c_List_Olist__all2(_1718691, _1718687, hAPP(hAPP(c_COMBB(_1718685, tc_fun(_1718687, tc_HOL_Obool), _1718691), _1718689), _1718693), _1718695, _1718697))], (46662 ^ _782435) ^ [_1718824, _1718826, _1718828, _1718830, _1718832, _1718834, _1718836] : [c_List_Olist__all2(_1718830, _1718826, hAPP(hAPP(c_COMBB(_1718824, tc_fun(_1718826, tc_HOL_Obool), _1718830), _1718828), _1718832), _1718834, _1718836), -(c_List_Olist__all2(_1718824, _1718826, _1718828, hAPP(hAPP(c_List_Omap(_1718830, _1718824), _1718832), _1718834), _1718836))], (46668 ^ _782435) ^ [_1718999, _1719001, _1719003, _1719005, _1719007, _1719009, _1719011] : [c_List_Olist__all2(_1718999, _1719001, _1719003, _1719005, hAPP(hAPP(c_List_Omap(_1719007, _1719001), _1719009), _1719011)), -(c_List_Olist__all2(_1718999, _1719007, hAPP(hAPP(c_COMBC(_1718999, tc_fun(_1719007, _1719001), tc_fun(_1719007, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719001, tc_HOL_Obool), tc_fun(tc_fun(_1719007, _1719001), tc_fun(_1719007, tc_HOL_Obool)), _1718999), c_COMBB(_1719001, tc_HOL_Obool, _1719007)), _1719003)), _1719009), _1719005, _1719011))], (46674 ^ _782435) ^ [_1719196, _1719198, _1719200, _1719202, _1719204, _1719206, _1719208] : [c_List_Olist__all2(_1719196, _1719204, hAPP(hAPP(c_COMBC(_1719196, tc_fun(_1719204, _1719198), tc_fun(_1719204, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1719198, tc_HOL_Obool), tc_fun(tc_fun(_1719204, _1719198), tc_fun(_1719204, tc_HOL_Obool)), _1719196), c_COMBB(_1719198, tc_HOL_Obool, _1719204)), _1719200)), _1719206), _1719202, _1719208), -(c_List_Olist__all2(_1719196, _1719198, _1719200, _1719202, hAPP(hAPP(c_List_Omap(_1719204, _1719198), _1719206), _1719208)))], (46680 ^ _782435) ^ [_1719399, _1719401, _1719403, _1719405, _1719407, _1719409, _1719411] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719399)), _1719401) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1719403)), _1719405), 46683 ^ _782435 : [(46684 ^ _782435) ^ [] : [c_List_Olist__all2(_1719399, _1719403, _1719407, hAPP(hAPP(c_List_Oappend(_1719399), _1719401), _1719409), hAPP(hAPP(c_List_Oappend(_1719403), _1719405), _1719411)), 46687 ^ _782435 : [(46688 ^ _782435) ^ [] : [-(c_List_Olist__all2(_1719399, _1719403, _1719407, _1719401, _1719405))], (46690 ^ _782435) ^ [] : [-(c_List_Olist__all2(_1719399, _1719403, _1719407, _1719409, _1719411))]]], (46692 ^ _782435) ^ [] : [-(c_List_Olist__all2(_1719399, _1719403, _1719407, hAPP(hAPP(c_List_Oappend(_1719399), _1719401), _1719409), hAPP(hAPP(c_List_Oappend(_1719403), _1719405), _1719411))), c_List_Olist__all2(_1719399, _1719403, _1719407, _1719401, _1719405), c_List_Olist__all2(_1719399, _1719403, _1719407, _1719409, _1719411)]]], (46702 ^ _782435) ^ [_1719821, _1719823, _1719825, _1719827, _1719829, _1719831, _1719833] : [c_List_Olist__all2(_1719821, _1719823, _1719825, _1719827, _1719829), c_List_Olist__all2(_1719821, _1719823, _1719825, _1719831, _1719833), -(c_List_Olist__all2(_1719821, _1719823, _1719825, hAPP(hAPP(c_List_Oappend(_1719821), _1719827), _1719831), hAPP(hAPP(c_List_Oappend(_1719823), _1719829), _1719833)))], (46712 ^ _782435) ^ [_1720020, _1720022, _1720024, _1720026, _1720028, _1720030] : [c_List_Olist__all2(_1720020, _1720022, _1720024, _1720026, _1720028), -(c_List_Olist__all2(_1720020, _1720022, _1720024, hAPP(hAPP(c_List_Odrop(_1720020), _1720030), _1720026), hAPP(hAPP(c_List_Odrop(_1720022), _1720030), _1720028)))], (46718 ^ _782435) ^ [_1720179, _1720181, _1720183, _1720185, _1720187, _1720189, _1720191] : [c_List_Olist__all2(_1720179, _1720181, _1720183, hAPP(hAPP(c_List_Olist_OCons(_1720179), _1720185), _1720187), hAPP(hAPP(c_List_Olist_OCons(_1720181), _1720189), _1720191)), 46721 ^ _782435 : [(46722 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1720183, _1720185), _1720189)))], (46724 ^ _782435) ^ [] : [-(c_List_Olist__all2(_1720179, _1720181, _1720183, _1720187, _1720191))]]], (46726 ^ _782435) ^ [_1720342, _1720344, _1720346, _1720348, _1720350, _1720352, _1720354] : [-(c_List_Olist__all2(_1720342, _1720344, _1720346, hAPP(hAPP(c_List_Olist_OCons(_1720342), _1720348), _1720350), hAPP(hAPP(c_List_Olist_OCons(_1720344), _1720352), _1720354))), hBOOL(hAPP(hAPP(_1720346, _1720348), _1720352)), c_List_Olist__all2(_1720342, _1720344, _1720346, _1720350, _1720354)], (46736 ^ _782435) ^ [_1720565, _1720567, _1720569] : [_1720565 = _1720567, -(c_List_Olist__all2(_1720569, _1720569, c_fequal, _1720565, _1720567))], (46742 ^ _782435) ^ [_1720646, _1720648, _1720650] : [c_List_Olist__all2(_1720650, _1720650, c_fequal, _1720646, _1720648), -(_1720646 = _1720648)], (46748 ^ _782435) ^ [_1720733, _1720735, _1720737, _1720739, _1720741, _1720743] : [c_List_Olist__all2(_1720733, _1720735, _1720737, _1720739, _1720741), -(c_List_Olist__all2(_1720733, _1720735, _1720737, hAPP(hAPP(c_List_Otake(_1720733), _1720743), _1720739), hAPP(hAPP(c_List_Otake(_1720735), _1720743), _1720741)))], (46754 ^ _782435) ^ [_1720862, _1720864, _1720866, _1720868, _1720870] : [c_List_Olist__all2(_1720862, _1720864, _1720866, _1720868, _1720870), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720862)), _1720868) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1720864)), _1720870))], (46760 ^ _782435) ^ [_1721000, _1721002, _1721004, _1721006] : [c_List_Olist__all2(_1721000, _1721002, _1721004, c_List_Olist_ONil(_1721000), _1721006), -(_1721006 = c_List_Olist_ONil(_1721002))], (46766 ^ _782435) ^ [_1721091, _1721093, _1721095, _1721097] : [_1721097 = c_List_Olist_ONil(_1721093), -(c_List_Olist__all2(_1721091, _1721093, _1721095, c_List_Olist_ONil(_1721091), _1721097))], (46772 ^ _782435) ^ [_1721209, _1721211, _1721213, _1721215] : [c_List_Olist__all2(_1721209, _1721211, _1721213, _1721215, c_List_Olist_ONil(_1721211)), -(_1721215 = c_List_Olist_ONil(_1721209))], (46778 ^ _782435) ^ [_1721300, _1721302, _1721304, _1721306] : [_1721306 = c_List_Olist_ONil(_1721300), -(c_List_Olist__all2(_1721300, _1721302, _1721304, _1721306, c_List_Olist_ONil(_1721302)))], (46784 ^ _782435) ^ [_1721397, _1721399, _1721401, _1721403, _1721405, _1721407] : [c_List_Olist__all2(_1721397, _1721399, _1721401, _1721403, _1721405), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721407), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721399)), _1721405))), -(hBOOL(hAPP(hAPP(_1721401, hAPP(hAPP(c_List_Onth(_1721397), _1721403), _1721407)), hAPP(hAPP(c_List_Onth(_1721399), _1721405), _1721407))))], (46794 ^ _782435) ^ [_1721614, _1721616, _1721618, _1721620, _1721622, _1721624] : [c_List_Olist__all2(_1721614, _1721616, _1721618, _1721620, _1721622), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1721624), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721614)), _1721620))), -(hBOOL(hAPP(hAPP(_1721618, hAPP(hAPP(c_List_Onth(_1721614), _1721620), _1721624)), hAPP(hAPP(c_List_Onth(_1721616), _1721622), _1721624))))], (46804 ^ _782435) ^ [_1721855, _1721857, _1721859, _1721861, _1721863] : [c_List_Olist__all2(_1721855, _1721857, _1721859, _1721861, _1721863), 46807 ^ _782435 : [(46808 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721855)), _1721861) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721857)), _1721863))], (46810 ^ _782435) ^ [_1722018] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722018), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1721855)), _1721861))), -(hBOOL(hAPP(hAPP(_1721859, hAPP(hAPP(c_List_Onth(_1721855), _1721861), _1722018)), hAPP(hAPP(c_List_Onth(_1721857), _1721863), _1722018))))]]], (46816 ^ _782435) ^ [_1722171, _1722173, _1722175, _1722177, _1722179] : [-(c_List_Olist__all2(_1722171, _1722173, _1722175, _1722177, _1722179)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722171)), _1722177) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722173)), _1722179), 46822 ^ _782435 : [(46823 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 46821 ^ [_1722171, _1722173, _1722175, _1722177, _1722179]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722171)), _1722177))))], (46825 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1722175, hAPP(hAPP(c_List_Onth(_1722171), _1722177), 46821 ^ [_1722171, _1722173, _1722175, _1722177, _1722179])), hAPP(hAPP(c_List_Onth(_1722173), _1722179), 46821 ^ [_1722171, _1722173, _1722175, _1722177, _1722179])))]]], (46829 ^ _782435) ^ [_1722531, _1722533, _1722535, _1722537, _1722539, _1722541, _1722543, _1722545] : [c_List_Olist__all2(_1722531, _1722533, _1722535, _1722537, _1722539), hBOOL(hAPP(hAPP(_1722535, _1722541), _1722543)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722545), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722533)), _1722539))), -(c_List_Olist__all2(_1722531, _1722533, _1722535, hAPP(hAPP(c_List_Olist__update(_1722531, _1722537), _1722545), _1722541), hAPP(hAPP(c_List_Olist__update(_1722533, _1722539), _1722545), _1722543)))], (46843 ^ _782435) ^ [_1722830, _1722832, _1722834, _1722836, _1722838, _1722840, _1722842, _1722844] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1722830), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1722832)), _1722834))), c_List_Olist__all2(_1722832, _1722836, _1722838, _1722834, _1722840), hBOOL(hAPP(hAPP(_1722838, _1722842), _1722844)), -(c_List_Olist__all2(_1722832, _1722836, _1722838, hAPP(hAPP(c_List_Olist__update(_1722832, _1722834), _1722830), _1722842), hAPP(hAPP(c_List_Olist__update(_1722836, _1722840), _1722830), _1722844)))], (46857 ^ _782435) ^ [_1723129, _1723131, _1723133, _1723135, _1723137] : [46859 ^ _782435 : [(46860 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1723129, _1723131)), 46858 ^ [_1723129, _1723131, _1723133, _1723135, _1723137]), hAPP(c_List_Oset(tc_prod(_1723129, _1723131)), hAPP(hAPP(c_List_Ozip(_1723129, _1723131), _1723133), _1723135)))))], (46862 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1723129, _1723131, tc_HOL_Obool), _1723137), 46858 ^ [_1723129, _1723131, _1723133, _1723135, _1723137]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723129)), _1723133) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723131)), _1723135), -(c_List_Olist__all2(_1723129, _1723131, _1723137, _1723133, _1723135))], (46870 ^ _782435) ^ [_1723468, _1723470, _1723472, _1723474, _1723476] : [c_Finite__Set_Ofun__left__comm(_1723468, _1723470, _1723472), -(hAPP(hAPP(c_Finite__Set_Ofold(_1723468, _1723470, _1723472), _1723474), hAPP(c_List_Oset(_1723468), _1723476)) = hAPP(c_List_Ofoldl(_1723470, _1723468, hAPP(c_COMBC(_1723468, _1723470, _1723470), _1723472), _1723474), c_List_Oremdups(_1723468, _1723476)))], (46876 ^ _782435) ^ [_1723619, _1723621] : [-(hBOOL(hAPP(c_List_Odistinct(_1723619), c_List_Oremdups(_1723619, _1723621))))], (46878 ^ _782435) ^ [_1723651, _1723653] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723651)), c_List_Oremdups(_1723651, _1723653))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1723651)), _1723653))))], (46880 ^ _782435) ^ [_1723713, _1723715] : [c_List_Oremdups(_1723713, _1723715) = c_List_Olist_ONil(_1723713), -(_1723715 = c_List_Olist_ONil(_1723713))], (46886 ^ _782435) ^ [_1723800, _1723802] : [_1723802 = c_List_Olist_ONil(_1723800), -(c_List_Oremdups(_1723800, _1723802) = c_List_Olist_ONil(_1723800))], (46892 ^ _782435) ^ [_1723908, _1723910] : [c_List_Olist_ONil(_1723908) = c_List_Oremdups(_1723908, _1723910), -(_1723910 = c_List_Olist_ONil(_1723908))], (46898 ^ _782435) ^ [_1723995, _1723997] : [_1723997 = c_List_Olist_ONil(_1723995), -(c_List_Olist_ONil(_1723995) = c_List_Oremdups(_1723995, _1723997))], (46904 ^ _782435) ^ [_1724088] : [-(c_List_Oremdups(_1724088, c_List_Olist_ONil(_1724088)) = c_List_Olist_ONil(_1724088))], (46906 ^ _782435) ^ [_1724133, _1724135] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724133)), c_List_Oremdups(_1724133, _1724135)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724133)), _1724135), -(c_List_Oremdups(_1724133, _1724135) = _1724135)], (46912 ^ _782435) ^ [_1724246, _1724248] : [c_List_Oremdups(_1724246, _1724248) = _1724248, -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724246)), c_List_Oremdups(_1724246, _1724248)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1724246)), _1724248))], (46918 ^ _782435) ^ [_1724365, _1724367] : [-(hAPP(c_List_Oset(_1724365), c_List_Oremdups(_1724365, _1724367)) = hAPP(c_List_Oset(_1724365), _1724367))], (46920 ^ _782435) ^ [_1724403, _1724405] : [-(c_List_Oremdups(_1724403, c_List_Oremdups(_1724403, _1724405)) = c_List_Oremdups(_1724403, _1724405))], (46922 ^ _782435) ^ [_1724437, _1724439] : [hBOOL(hAPP(c_List_Odistinct(_1724437), _1724439)), -(c_List_Oremdups(_1724437, _1724439) = _1724439)], (46928 ^ _782435) ^ [_1724543, _1724545] : [c_List_Oremdups(_1724543, _1724545) = _1724545, -(hBOOL(hAPP(c_List_Odistinct(_1724543), _1724545)))], (46934 ^ _782435) ^ [_1724630, _1724632] : [hBOOL(hAPP(c_List_Odistinct(_1724630), _1724632)), -(c_List_Oremdups(_1724630, _1724632) = _1724632)], (46940 ^ _782435) ^ [_1724723, _1724725, _1724727, _1724729] : [-(c_List_Oremdups(_1724723, hAPP(hAPP(c_List_Omap(_1724725, _1724723), _1724727), c_List_Oremdups(_1724725, _1724729))) = c_List_Oremdups(_1724723, hAPP(hAPP(c_List_Omap(_1724725, _1724723), _1724727), _1724729)))], (46942 ^ _782435) ^ [_1724779, _1724781, _1724783] : [hBOOL(hAPP(c_List_Odistinct(_1724779), _1724781)), -(c_List_Oremove1(_1724779, _1724783, c_List_Oremdups(_1724779, _1724781)) = c_List_Oremdups(_1724779, c_List_Oremove1(_1724779, _1724783, _1724781)))], (46948 ^ _782435) ^ [_1724906, _1724908, _1724910] : [hBOOL(hAPP(hAPP(c_member(_1724906), _1724908), hAPP(c_List_Oset(_1724906), _1724910))), -(c_List_Oremdups(_1724906, hAPP(hAPP(c_List_Olist_OCons(_1724906), _1724908), _1724910)) = c_List_Oremdups(_1724906, _1724910))], (46954 ^ _782435) ^ [_1725031, _1725033, _1725035] : [-(hBOOL(hAPP(hAPP(c_member(_1725031), _1725033), hAPP(c_List_Oset(_1725031), _1725035)))), -(c_List_Oremdups(_1725031, hAPP(hAPP(c_List_Olist_OCons(_1725031), _1725033), _1725035)) = hAPP(hAPP(c_List_Olist_OCons(_1725031), _1725033), c_List_Oremdups(_1725031, _1725035)))], (46960 ^ _782435) ^ [_1725105, _1725107] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725105)), c_List_Oremdups(_1725105, _1725107)) = hAPP(c_Finite__Set_Ocard(_1725105), hAPP(c_List_Oset(_1725105), _1725107)))], (46962 ^ _782435) ^ [_1725150, _1725152] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725150)), c_List_Oremdups(_1725150, c_List_Oconcat(_1725150, _1725152))) = hAPP(c_Finite__Set_Ocard(_1725150), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1725150), tc_fun(_1725150, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1725150)), _1725152)), c_List_Oset(_1725150))))], (46964 ^ _782435) ^ [_1725216, _1725218] : [class_Orderings_Olinorder(_1725216), -(c_List_Olinorder__class_Osorted__list__of__set(_1725216, hAPP(c_List_Oset(_1725216), _1725218)) = c_List_Olinorder__class_Osort__key(_1725216, _1725216, c_COMBI(_1725216), c_List_Oremdups(_1725216, _1725218)))], (46970 ^ _782435) ^ [_1725327] : [-(c_List_Oconcat(_1725327, c_List_Olist_ONil(tc_List_Olist(_1725327))) = c_List_Olist_ONil(_1725327))], (46972 ^ _782435) ^ [_1725359, _1725361] : [-(c_List_Oconcat(_1725359, _1725361) = hAPP(c_List_Ofoldl(tc_List_Olist(_1725359), tc_List_Olist(_1725359), c_List_Oappend(_1725359), c_List_Olist_ONil(_1725359)), _1725361))], (46974 ^ _782435) ^ [_1725403, _1725405, _1725407] : [-(hAPP(c_List_Ofoldl(tc_List_Olist(_1725403), tc_List_Olist(_1725403), c_List_Oappend(_1725403), _1725405), _1725407) = hAPP(hAPP(c_List_Oappend(_1725403), _1725405), c_List_Oconcat(_1725403, _1725407)))], (46976 ^ _782435) ^ [_1725455, _1725457, _1725459, _1725461] : [class_Orderings_Olinorder(_1725455), 46979 ^ _782435 : [(46980 ^ _782435) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725457), c_List_Olinorder__class_Osort__key(_1725457, _1725455, _1725459, _1725461))), -(hBOOL(hAPP(c_List_Odistinct(_1725457), _1725461)))], (46986 ^ _782435) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1725457), _1725461)), -(hBOOL(hAPP(c_List_Odistinct(_1725457), c_List_Olinorder__class_Osort__key(_1725457, _1725455, _1725459, _1725461))))]]], (46992 ^ _782435) ^ [_1725711, _1725713, _1725715, _1725717] : [class_Orderings_Olinorder(_1725711), -(hAPP(c_List_Oset(_1725713), c_List_Olinorder__class_Osort__key(_1725713, _1725711, _1725715, _1725717)) = hAPP(c_List_Oset(_1725713), _1725717))], (46998 ^ _782435) ^ [_1725820, _1725822, _1725824, _1725826] : [class_Orderings_Olinorder(_1725820), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725822)), c_List_Olinorder__class_Osort__key(_1725822, _1725820, _1725824, _1725826)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1725822)), _1725826))], (47004 ^ _782435) ^ [_1725937, _1725939, _1725941] : [class_Orderings_Olinorder(_1725937), -(c_List_Olinorder__class_Osort__key(_1725939, _1725937, _1725941, c_List_Olist_ONil(_1725939)) = c_List_Olist_ONil(_1725939))], (47010 ^ _782435) ^ [_1726032, _1726034, _1726036] : [-(c_List_Oconcat(_1726032, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1726032)), _1726034), _1726036)) = hAPP(hAPP(c_List_Oappend(_1726032), _1726034), c_List_Oconcat(_1726032, _1726036)))], (47022 ^ _782435) ^ [_1726304, _1726306] : [47024 ^ _782435 : [(47025 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726304)), 47023 ^ [_1726304, _1726306]), hAPP(c_List_Oset(tc_List_Olist(_1726304)), _1726306))))], (47027 ^ _782435) ^ [] : [47023 ^ [_1726304, _1726306] = c_List_Olist_ONil(_1726304)]], -(c_List_Oconcat(_1726304, _1726306) = c_List_Olist_ONil(_1726304))], (47012 ^ _782435) ^ [_1726098, _1726100] : [c_List_Oconcat(_1726098, _1726100) = c_List_Olist_ONil(_1726098), 47015 ^ _782435 : [(47016 ^ _782435) ^ [_1726189] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726098)), _1726189), hAPP(c_List_Oset(tc_List_Olist(_1726098)), _1726100))), -(_1726189 = c_List_Olist_ONil(_1726098))]]], (47041 ^ _782435) ^ [_1726716, _1726718] : [47043 ^ _782435 : [(47044 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726716)), 47042 ^ [_1726716, _1726718]), hAPP(c_List_Oset(tc_List_Olist(_1726716)), _1726718))))], (47046 ^ _782435) ^ [] : [47042 ^ [_1726716, _1726718] = c_List_Olist_ONil(_1726716)]], -(c_List_Olist_ONil(_1726716) = c_List_Oconcat(_1726716, _1726718))], (47031 ^ _782435) ^ [_1726510, _1726512] : [c_List_Olist_ONil(_1726510) = c_List_Oconcat(_1726510, _1726512), 47034 ^ _782435 : [(47035 ^ _782435) ^ [_1726601] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1726510)), _1726601), hAPP(c_List_Oset(tc_List_Olist(_1726510)), _1726512))), -(_1726601 = c_List_Olist_ONil(_1726510))]]], (47050 ^ _782435) ^ [_1726907, _1726909, _1726911, _1726913] : [-(hAPP(hAPP(c_List_Omap(_1726907, _1726909), _1726911), c_List_Oconcat(_1726907, _1726913)) = c_List_Oconcat(_1726909, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1726907), tc_List_Olist(_1726909)), hAPP(c_List_Omap(_1726907, _1726909), _1726911)), _1726913)))], (47052 ^ _782435) ^ [_1726970, _1726972] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1726970)), c_List_Oconcat(_1726970, _1726972)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1726970), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1726970))), _1726972)))], (47054 ^ _782435) ^ [_1727023, _1727025] : [-(hAPP(c_List_Oset(_1727023), c_List_Oconcat(_1727023, _1727025)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(_1727023), tc_fun(_1727023, tc_HOL_Obool)), hAPP(c_List_Oset(tc_List_Olist(_1727023)), _1727025)), c_List_Oset(_1727023)))], (47056 ^ _782435) ^ [_1727079, _1727081, _1727083, _1727085, _1727087] : [class_Orderings_Olinorder(_1727079), -(c_List_Olinorder__class_Osort__key(_1727081, _1727079, _1727083, hAPP(hAPP(c_List_Olist_OCons(_1727081), _1727085), _1727087)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1727081, _1727079, _1727083), _1727085), c_List_Olinorder__class_Osort__key(_1727081, _1727079, _1727083, _1727087)))], (47062 ^ _782435) ^ [_1727216, _1727218, _1727220] : [-(c_List_Oconcat(_1727216, hAPP(hAPP(c_List_Oappend(tc_List_Olist(_1727216)), _1727218), _1727220)) = hAPP(hAPP(c_List_Oappend(_1727216), c_List_Oconcat(_1727216, _1727218)), c_List_Oconcat(_1727216, _1727220)))], (47064 ^ _782435) ^ [_1727270, _1727272] : [class_Orderings_Olinorder(_1727270), -(c_List_Olinorder__class_Osort__key(_1727270, _1727270, c_COMBI(_1727270), _1727272) = hAPP(c_List_Ofoldl(tc_List_Olist(_1727270), _1727270, hAPP(c_COMBC(_1727270, tc_List_Olist(_1727270), tc_List_Olist(_1727270)), c_List_Olinorder__class_Oinsort__key(_1727270, _1727270, c_COMBI(_1727270))), c_List_Olist_ONil(_1727270)), _1727272))], (47070 ^ _782435) ^ [_1727417, _1727419, _1727421] : [47072 ^ _782435 : [(47073 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1727417), tc_List_Olist(_1727417))), 47071 ^ [_1727417, _1727419, _1727421]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1727417), tc_List_Olist(_1727417))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1727417), tc_List_Olist(_1727417)), _1727419), _1727421)))))], (47075 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1727417), tc_List_Olist(_1727417), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1727417), tc_fun(tc_List_Olist(_1727417), tc_Nat_Onat), tc_fun(tc_List_Olist(_1727417), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1727417), tc_Nat_Onat), tc_fun(tc_List_Olist(_1727417), tc_HOL_Obool)), tc_List_Olist(_1727417)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1727417))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1727417)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1727417))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1727417)))), 47071 ^ [_1727417, _1727419, _1727421]))]], hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1727417))), _1727419) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1727417))), _1727421), 47080 ^ _782435 : [(47081 ^ _782435) ^ [] : [c_List_Oconcat(_1727417, _1727419) = c_List_Oconcat(_1727417, _1727421), -(_1727419 = _1727421)], (47087 ^ _782435) ^ [] : [_1727419 = _1727421, -(c_List_Oconcat(_1727417, _1727419) = c_List_Oconcat(_1727417, _1727421))]]], (47093 ^ _782435) ^ [_1728144, _1728146, _1728148] : [c_List_Oconcat(_1728144, _1728146) = c_List_Oconcat(_1728144, _1728148), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728144))), _1728146) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1728144))), _1728148), 47103 ^ _782435 : [(47104 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1728144), tc_List_Olist(_1728144))), 47102 ^ [_1728144, _1728146, _1728148]), hAPP(c_List_Oset(tc_prod(tc_List_Olist(_1728144), tc_List_Olist(_1728144))), hAPP(hAPP(c_List_Ozip(tc_List_Olist(_1728144), tc_List_Olist(_1728144)), _1728146), _1728148)))))], (47106 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(_1728144), tc_List_Olist(_1728144), tc_HOL_Obool), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728144), tc_fun(tc_List_Olist(_1728144), tc_Nat_Onat), tc_fun(tc_List_Olist(_1728144), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_fun(tc_fun(tc_List_Olist(_1728144), tc_Nat_Onat), tc_fun(tc_List_Olist(_1728144), tc_HOL_Obool)), tc_List_Olist(_1728144)), c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1728144))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_HOL_Obool), tc_List_Olist(_1728144)), c_fequal), c_Nat_Osize__class_Osize(tc_List_Olist(_1728144))))), c_Nat_Osize__class_Osize(tc_List_Olist(_1728144)))), 47102 ^ [_1728144, _1728146, _1728148]))]], -(_1728146 = _1728148)], (47110 ^ _782435) ^ [_1728785, _1728787, _1728789, _1728791] : [-(c_List_Oconcat(_1728785, hAPP(hAPP(c_List_Omap(_1728787, tc_List_Olist(_1728785)), hAPP(hAPP(c_COMBC(_1728787, tc_List_Olist(_1728785), tc_List_Olist(_1728785)), hAPP(hAPP(c_COMBB(_1728785, tc_fun(tc_List_Olist(_1728785), tc_List_Olist(_1728785)), _1728787), c_List_Olist_OCons(_1728785)), _1728789)), c_List_Olist_ONil(_1728785))), _1728791)) = hAPP(hAPP(c_List_Omap(_1728787, _1728785), _1728789), _1728791))], (47112 ^ _782435) ^ [_1728872, _1728874, _1728876] : [-(c_Enum_On__lists(_1728872, hAPP(c_Nat_OSuc, _1728874), _1728876) = c_List_Oconcat(tc_List_Olist(_1728872), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728872), tc_List_Olist(tc_List_Olist(_1728872))), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728872), tc_List_Olist(_1728872), tc_List_Olist(tc_List_Olist(_1728872))), hAPP(hAPP(c_COMBB(tc_fun(_1728872, tc_List_Olist(_1728872)), tc_fun(tc_List_Olist(_1728872), tc_List_Olist(tc_List_Olist(_1728872))), tc_List_Olist(_1728872)), c_List_Omap(_1728872, tc_List_Olist(_1728872))), hAPP(c_COMBC(_1728872, tc_List_Olist(_1728872), tc_List_Olist(_1728872)), c_List_Olist_OCons(_1728872)))), _1728876)), c_Enum_On__lists(_1728872, _1728874, _1728876))))], (47114 ^ _782435) ^ [_1728992, _1728994, _1728996, _1728998] : [-(c_List_Otranspose(_1728992, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1728992)), hAPP(hAPP(c_List_Olist_OCons(_1728992), _1728994), _1728996)), _1728998)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1728992)), hAPP(hAPP(c_List_Olist_OCons(_1728992), _1728994), c_List_Oconcat(_1728992, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728992), tc_List_Olist(_1728992)), c_List_Olist_Olist__case(tc_List_Olist(_1728992), _1728992, c_List_Olist_ONil(_1728992), hAPP(hAPP(c_COMBB(tc_List_Olist(_1728992), tc_fun(tc_List_Olist(_1728992), tc_List_Olist(_1728992)), _1728992), c_COMBK(tc_List_Olist(_1728992), tc_List_Olist(_1728992))), hAPP(hAPP(c_COMBC(_1728992, tc_List_Olist(_1728992), tc_List_Olist(_1728992)), c_List_Olist_OCons(_1728992)), c_List_Olist_ONil(_1728992))))), _1728998)))), c_List_Otranspose(_1728992, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1728992)), _1728996), c_List_Oconcat(tc_List_Olist(_1728992), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1728992), tc_List_Olist(tc_List_Olist(_1728992))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1728992)), _1728992, c_List_Olist_ONil(tc_List_Olist(_1728992)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1728992), tc_List_Olist(tc_List_Olist(_1728992))), _1728992), hAPP(hAPP(c_COMBC(tc_List_Olist(_1728992), tc_List_Olist(tc_List_Olist(_1728992)), tc_List_Olist(tc_List_Olist(_1728992))), c_List_Olist_OCons(tc_List_Olist(_1728992))), c_List_Olist_ONil(tc_List_Olist(_1728992)))))), _1728998))))))], (47116 ^ _782435) ^ [_1729218, _1729220] : [-(c_List_Oconcat(_1729218, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729218), tc_List_Olist(_1729218)), c_List_Olist_Olist__case(tc_List_Olist(_1729218), _1729218, c_List_Olist_ONil(_1729218), hAPP(hAPP(c_COMBB(tc_List_Olist(_1729218), tc_fun(tc_List_Olist(_1729218), tc_List_Olist(_1729218)), _1729218), c_COMBK(tc_List_Olist(_1729218), tc_List_Olist(_1729218))), hAPP(hAPP(c_COMBC(_1729218, tc_List_Olist(_1729218), tc_List_Olist(_1729218)), c_List_Olist_OCons(_1729218)), c_List_Olist_ONil(_1729218))))), _1729220)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729218), _1729218), c_List_Ohd(_1729218)), hAPP(c_List_Ofilter(tc_List_Olist(_1729218), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1729218)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1729218), tc_List_Olist(_1729218), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1729218)))), _1729220)))], (47118 ^ _782435) ^ [_1729361, _1729363, _1729365] : [-(hAPP(c_List_Ofilter(_1729361, _1729363), c_List_Oconcat(_1729361, _1729365)) = c_List_Oconcat(_1729361, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1729361), tc_List_Olist(_1729361)), c_List_Ofilter(_1729361, _1729363)), _1729365)))], (47120 ^ _782435) ^ [_1729416, _1729418, _1729420, _1729422, _1729424] : [class_Orderings_Olinorder(_1729416), -(hAPP(c_List_Ofilter(_1729418, _1729420), c_List_Olinorder__class_Osort__key(_1729418, _1729416, _1729422, _1729424)) = c_List_Olinorder__class_Osort__key(_1729418, _1729416, _1729422, hAPP(c_List_Ofilter(_1729418, _1729420), _1729424)))], (47126 ^ _782435) ^ [_1729541, _1729543, _1729545, _1729547, _1729549] : [-(hAPP(c_List_Ofilter(_1729541, _1729543), hAPP(hAPP(c_List_Omap(_1729545, _1729541), _1729547), _1729549)) = hAPP(hAPP(c_List_Omap(_1729545, _1729541), _1729547), hAPP(c_List_Ofilter(_1729545, hAPP(c_Fun_Ocomp(_1729541, tc_HOL_Obool, _1729545, _1729543), _1729547)), _1729549)))], (47128 ^ _782435) ^ [_1729610, _1729612, _1729614, _1729616, _1729618] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729610)), hAPP(c_List_Ofilter(_1729610, _1729612), hAPP(hAPP(c_List_Omap(_1729614, _1729610), _1729616), _1729618))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1729614)), hAPP(c_List_Ofilter(_1729614, hAPP(c_Fun_Ocomp(_1729610, tc_HOL_Obool, _1729614, _1729612), _1729616)), _1729618)))], (47130 ^ _782435) ^ [_1729684, _1729686, _1729688, _1729690, _1729692, _1729694] : [class_Orderings_Olinorder(_1729684), -(hBOOL(hAPP(_1729686, _1729688))), -(hAPP(c_List_Ofilter(_1729690, _1729686), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1729690, _1729684, _1729692), _1729688), _1729694)) = hAPP(c_List_Ofilter(_1729690, _1729686), _1729694))], (47140 ^ _782435) ^ [_1729830, _1729832] : [-(hAPP(c_List_Ofilter(_1729830, _1729832), c_List_Olist_ONil(_1729830)) = c_List_Olist_ONil(_1729830))], (47142 ^ _782435) ^ [_1729865] : [-(c_List_Otranspose(_1729865, c_List_Olist_ONil(tc_List_Olist(_1729865))) = c_List_Olist_ONil(tc_List_Olist(_1729865)))], (47154 ^ _782435) ^ [_1730122, _1730124, _1730126] : [47156 ^ _782435 : [(47157 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730122), 47155 ^ [_1730122, _1730124, _1730126]), hAPP(c_List_Oset(_1730122), _1730126))))], (47159 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1730124, 47155 ^ [_1730122, _1730124, _1730126])))]], -(hAPP(c_List_Ofilter(_1730122, _1730124), _1730126) = c_List_Olist_ONil(_1730122))], (47144 ^ _782435) ^ [_1729917, _1729919, _1729921] : [hAPP(c_List_Ofilter(_1729917, _1729919), _1729921) = c_List_Olist_ONil(_1729917), 47147 ^ _782435 : [(47148 ^ _782435) ^ [_1730014] : [hBOOL(hAPP(hAPP(c_member(_1729917), _1730014), hAPP(c_List_Oset(_1729917), _1729921))), hBOOL(hAPP(_1729919, _1730014))]]], (47163 ^ _782435) ^ [_1730239, _1730241, _1730243] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730239)), hAPP(c_List_Ofilter(_1730239, _1730241), _1730243))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730239)), _1730243))))], (47165 ^ _782435) ^ [_1730291, _1730293, _1730295] : [-(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730291)), hAPP(c_List_Ofilter(_1730291, _1730293), _1730295))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730291)), hAPP(c_List_Ofilter(_1730291, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1730291), c_fNot), _1730293)), _1730295))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1730291)), _1730295))], (47167 ^ _782435) ^ [_1730367, _1730369, _1730371] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1730367, tc_HOL_Obool)), hAPP(c_List_Oset(_1730367), hAPP(c_List_Ofilter(_1730367, _1730369), _1730371))), hAPP(c_List_Oset(_1730367), _1730371))))], (47179 ^ _782435) ^ [_1730638, _1730640, _1730642] : [47181 ^ _782435 : [(47182 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1730638), 47180 ^ [_1730638, _1730640, _1730642]), hAPP(c_List_Oset(_1730638), _1730642))))], (47184 ^ _782435) ^ [] : [hBOOL(hAPP(_1730640, 47180 ^ [_1730638, _1730640, _1730642]))]], -(hAPP(c_List_Ofilter(_1730638, _1730640), _1730642) = _1730642)], (47169 ^ _782435) ^ [_1730438, _1730440, _1730442] : [hAPP(c_List_Ofilter(_1730438, _1730440), _1730442) = _1730442, 47172 ^ _782435 : [(47173 ^ _782435) ^ [_1730529] : [hBOOL(hAPP(hAPP(c_member(_1730438), _1730529), hAPP(c_List_Oset(_1730438), _1730442))), -(hBOOL(hAPP(_1730440, _1730529)))]]], (47188 ^ _782435) ^ [_1730830, _1730832, _1730834, _1730836] : [-(hAPP(c_List_Ofilter(_1730830, _1730832), hAPP(c_List_Ofilter(_1730830, _1730834), _1730836)) = hAPP(c_List_Ofilter(_1730830, hAPP(hAPP(c_COMBS(_1730830, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1730830), c_fconj), _1730834)), _1730832)), _1730836))], (47190 ^ _782435) ^ [_1730893, _1730895, _1730897, _1730899] : [-(hBOOL(hAPP(_1730893, _1730895))), -(c_List_Oremove1(_1730897, _1730895, hAPP(c_List_Ofilter(_1730897, _1730893), _1730899)) = hAPP(c_List_Ofilter(_1730897, _1730893), _1730899))], (47196 ^ _782435) ^ [_1730951, _1730953, _1730955, _1730957] : [-(hAPP(c_List_Ofilter(_1730951, _1730953), c_List_Oremove1(_1730951, _1730955, _1730957)) = c_List_Oremove1(_1730951, _1730955, hAPP(c_List_Ofilter(_1730951, _1730953), _1730957)))], (47198 ^ _782435) ^ [_1731015, _1731017, _1731019, _1731021] : [hBOOL(hAPP(_1731015, _1731017)), -(hAPP(c_List_Ofilter(_1731019, _1731015), hAPP(hAPP(c_List_Olist_OCons(_1731019), _1731017), _1731021)) = hAPP(hAPP(c_List_Olist_OCons(_1731019), _1731017), hAPP(c_List_Ofilter(_1731019, _1731015), _1731021)))], (47204 ^ _782435) ^ [_1731150, _1731152, _1731154, _1731156] : [-(hBOOL(hAPP(_1731150, _1731152))), -(hAPP(c_List_Ofilter(_1731154, _1731150), hAPP(hAPP(c_List_Olist_OCons(_1731154), _1731152), _1731156)) = hAPP(c_List_Ofilter(_1731154, _1731150), _1731156))], (47210 ^ _782435) ^ [_1731214, _1731216, _1731218, _1731220] : [-(hAPP(c_List_Ofilter(_1731214, _1731216), hAPP(hAPP(c_List_Oappend(_1731214), _1731218), _1731220)) = hAPP(hAPP(c_List_Oappend(_1731214), hAPP(c_List_Ofilter(_1731214, _1731216), _1731218)), hAPP(c_List_Ofilter(_1731214, _1731216), _1731220)))], (47212 ^ _782435) ^ [_1731277, _1731279, _1731281] : [hBOOL(hAPP(c_List_Odistinct(_1731277), _1731279)), -(hBOOL(hAPP(c_List_Odistinct(_1731277), hAPP(c_List_Ofilter(_1731277, _1731281), _1731279))))], (47218 ^ _782435) ^ [_1731384, _1731386, _1731388] : [-(hAPP(c_Product__Type_Ofst(tc_List_Olist(_1731384), tc_List_Olist(_1731384)), c_List_Opartition(_1731384, _1731386, _1731388)) = hAPP(c_List_Ofilter(_1731384, _1731386), _1731388))], (47220 ^ _782435) ^ [_1731431, _1731433, _1731435] : [-(c_List_Opartition(_1731431, _1731433, _1731435) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1731431), tc_List_Olist(_1731431)), hAPP(c_List_Ofilter(_1731431, _1731433), _1731435)), hAPP(c_List_Ofilter(_1731431, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1731431, c_fNot), _1731433)), _1731435)))], (47222 ^ _782435) ^ [_1731495, _1731497, _1731499] : [-(hAPP(c_Product__Type_Osnd(tc_List_Olist(_1731495), tc_List_Olist(_1731495)), c_List_Opartition(_1731495, _1731497, _1731499)) = hAPP(c_List_Ofilter(_1731495, hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, _1731495, c_fNot), _1731497)), _1731499))], (47224 ^ _782435) ^ [_1731550, _1731552, _1731554] : [-(c_List_Oremdups(_1731550, hAPP(c_List_Ofilter(_1731550, _1731552), _1731554)) = hAPP(c_List_Ofilter(_1731550, _1731552), c_List_Oremdups(_1731550, _1731554)))], (47226 ^ _782435) ^ [_1731595, _1731597] : [-(c_List_Otranspose(_1731595, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1731595)), c_List_Olist_ONil(_1731595)), _1731597)) = c_List_Otranspose(_1731595, _1731597))], (47228 ^ _782435) ^ [_1731638, _1731640, _1731642] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731638), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1731640))), c_List_Otranspose(_1731640, _1731642)))), -(hAPP(hAPP(c_List_Onth(tc_List_Olist(_1731640)), c_List_Otranspose(_1731640, _1731642)), _1731638) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731640), _1731640), hAPP(hAPP(c_COMBC(tc_List_Olist(_1731640), tc_Nat_Onat, _1731640), c_List_Onth(_1731640)), _1731638)), hAPP(c_List_Ofilter(tc_List_Olist(_1731640), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1731640)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1731638)), c_Nat_Osize__class_Osize(tc_List_Olist(_1731640)))), _1731642)))], (47234 ^ _782435) ^ [_1731881, _1731883, _1731885, _1731887] : [-(c_List_Otranspose(_1731881, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731883), tc_List_Olist(_1731881)), hAPP(c_List_Omap(_1731883, _1731881), _1731885)), _1731887)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1731883), tc_List_Olist(_1731881)), hAPP(c_List_Omap(_1731883, _1731881), _1731885)), c_List_Otranspose(_1731883, _1731887)))], (47236 ^ _782435) ^ [_1731954, _1731956, _1731958] : [-(hAPP(c_List_Oset(_1731954), hAPP(c_List_Ofilter(_1731954, _1731956), _1731958)) = hAPP(c_Set_OCollect(_1731954), hAPP(hAPP(c_COMBS(_1731954, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1731954), c_fconj), hAPP(hAPP(c_COMBC(_1731954, tc_fun(_1731954, tc_HOL_Obool), tc_HOL_Obool), c_member(_1731954)), hAPP(c_List_Oset(_1731954), _1731958)))), _1731956)))], (47238 ^ _782435) ^ [_1732037, _1732039, _1732041, _1732043] : [hBOOL(hAPP(hAPP(c_member(_1732037), _1732039), hAPP(c_List_Oset(_1732037), _1732041))), -(hBOOL(hAPP(_1732043, _1732039))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732037)), hAPP(c_List_Ofilter(_1732037, _1732043), _1732041))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732037)), _1732041))))], (47248 ^ _782435) ^ [_1732211, _1732213, _1732215] : [-(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1732211, tc_HOL_Obool)), hAPP(c_List_Oset(_1732211), _1732213)), hAPP(hAPP(c_Set_Oinsert(_1732211), _1732215), c_Orderings_Obot__class_Obot(tc_fun(_1732211, tc_HOL_Obool)))) = hAPP(c_List_Oset(_1732211), hAPP(c_List_Ofilter(_1732211, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1732211), c_fNot), hAPP(hAPP(c_COMBC(_1732211, _1732211, tc_HOL_Obool), c_fequal), _1732215))), _1732213)))], (47250 ^ _782435) ^ [_1732298, _1732300, _1732302] : [hBOOL(hAPP(c_List_Odistinct(_1732298), _1732300)), -(hAPP(c_List_Ofilter(_1732298, hAPP(hAPP(c_COMBC(_1732298, tc_fun(_1732298, tc_HOL_Obool), tc_HOL_Obool), c_member(_1732298)), hAPP(c_List_Oset(_1732298), c_List_Osublist(_1732298, _1732300, _1732302)))), _1732300) = c_List_Osublist(_1732298, _1732300, _1732302))], (47266 ^ _782435) ^ [_1732678, _1732680] : [47268 ^ _782435 : [(47269 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732678)), 47267 ^ [_1732678, _1732680]), hAPP(c_List_Oset(tc_List_Olist(_1732678)), _1732680))))], (47271 ^ _782435) ^ [] : [47267 ^ [_1732678, _1732680] = c_List_Olist_ONil(_1732678)]], -(c_List_Otranspose(_1732678, _1732680) = c_List_Olist_ONil(tc_List_Olist(_1732678)))], (47256 ^ _782435) ^ [_1732468, _1732470] : [c_List_Otranspose(_1732468, _1732470) = c_List_Olist_ONil(tc_List_Olist(_1732468)), 47259 ^ _782435 : [(47260 ^ _782435) ^ [_1732563] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1732468)), _1732563), hAPP(c_List_Oset(tc_List_Olist(_1732468)), _1732470))), -(_1732563 = c_List_Olist_ONil(_1732468))]]], (47275 ^ _782435) ^ [_1732873, _1732875, _1732877] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1732873)), hAPP(c_List_Ofilter(_1732873, _1732875), _1732877)) = 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(_1732873)), _1732877)))), hAPP(hAPP(c_COMBB(_1732873, tc_HOL_Obool, tc_Nat_Onat), _1732875), hAPP(c_List_Onth(_1732873), _1732877))))))], (47277 ^ _782435) ^ [_1732953, _1732955] : [-(c_List_Oconcat(tc_List_Olist(_1732953), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732953), tc_List_Olist(tc_List_Olist(_1732953))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1732953)), _1732953, c_List_Olist_ONil(tc_List_Olist(_1732953)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1732953), tc_List_Olist(tc_List_Olist(_1732953))), _1732953), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732953), tc_List_Olist(tc_List_Olist(_1732953)), tc_List_Olist(tc_List_Olist(_1732953))), c_List_Olist_OCons(tc_List_Olist(_1732953))), c_List_Olist_ONil(tc_List_Olist(_1732953)))))), _1732955)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(_1732953), tc_List_Olist(_1732953)), c_List_Otl(_1732953)), hAPP(c_List_Ofilter(tc_List_Olist(_1732953), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1732953)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1732953), tc_List_Olist(_1732953), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1732953)))), _1732955)))], (47279 ^ _782435) ^ [_1733105, _1733107, _1733109, _1733111] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1733105)), c_List_Otranspose__rel(_1733105)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733105)), hAPP(hAPP(c_List_Olist_OCons(_1733105), _1733107), _1733109)), _1733111))), -(c_List_Otranspose(_1733105, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733105)), hAPP(hAPP(c_List_Olist_OCons(_1733105), _1733107), _1733109)), _1733111)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733105)), hAPP(hAPP(c_List_Olist_OCons(_1733105), _1733107), c_List_Oconcat(_1733105, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733105), tc_List_Olist(_1733105)), c_List_Olist_Olist__case(tc_List_Olist(_1733105), _1733105, c_List_Olist_ONil(_1733105), hAPP(hAPP(c_COMBB(tc_List_Olist(_1733105), tc_fun(tc_List_Olist(_1733105), tc_List_Olist(_1733105)), _1733105), c_COMBK(tc_List_Olist(_1733105), tc_List_Olist(_1733105))), hAPP(hAPP(c_COMBC(_1733105, tc_List_Olist(_1733105), tc_List_Olist(_1733105)), c_List_Olist_OCons(_1733105)), c_List_Olist_ONil(_1733105))))), _1733111)))), c_List_Otranspose(_1733105, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733105)), _1733109), c_List_Oconcat(tc_List_Olist(_1733105), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1733105), tc_List_Olist(tc_List_Olist(_1733105))), c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(_1733105)), _1733105, c_List_Olist_ONil(tc_List_Olist(_1733105)), hAPP(c_COMBK(tc_fun(tc_List_Olist(_1733105), tc_List_Olist(tc_List_Olist(_1733105))), _1733105), hAPP(hAPP(c_COMBC(tc_List_Olist(_1733105), tc_List_Olist(tc_List_Olist(_1733105)), tc_List_Olist(tc_List_Olist(_1733105))), c_List_Olist_OCons(tc_List_Olist(_1733105))), c_List_Olist_ONil(tc_List_Olist(_1733105)))))), _1733111))))))], (47285 ^ _782435) ^ [_1733638, _1733640] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1733638)), c_List_Otranspose__rel(_1733638)), hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733638)), c_List_Olist_ONil(_1733638)), _1733640))), -(c_List_Otranspose(_1733638, hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(_1733638)), c_List_Olist_ONil(_1733638)), _1733640)) = c_List_Otranspose(_1733638, _1733640))], (47291 ^ _782435) ^ [_1733797, _1733799, _1733801, _1733803] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1733797, tc_Nat_Onat), _1733797), c_Product__Type_Ofst(_1733797, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1733797, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1733797, tc_Nat_Onat)), _1733799), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_prod(_1733797, tc_Nat_Onat)), c_Nat_OSuc), c_Product__Type_Osnd(_1733797, tc_Nat_Onat)))), hAPP(hAPP(c_List_Ozip(_1733797, tc_Nat_Onat), _1733801), _1733803))) = hAPP(hAPP(c_List_Omap(tc_prod(_1733797, tc_Nat_Onat), _1733797), c_Product__Type_Ofst(_1733797, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1733797, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_prod(_1733797, tc_Nat_Onat)), _1733799), c_Product__Type_Osnd(_1733797, tc_Nat_Onat))), hAPP(hAPP(c_List_Ozip(_1733797, tc_Nat_Onat), _1733801), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), _1733803)))))], (47293 ^ _782435) ^ [_1733940, _1733942] : [-(c_Random_Oselect__weight(_1733940, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1733940), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1733940, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1733940, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1733940)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1733942)) = c_Random_Oselect__weight(_1733940, _1733942))], (47295 ^ _782435) ^ [_1734003, _1734005] : [-(c_Random_Opick(_1734003, hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral, _1734003), hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral, _1734003, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(_1734003, tc_HOL_Obool), tc_Code__Numeral_Ocode__numeral), c_COMBK(tc_HOL_Obool, _1734003)), hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))), _1734005)) = c_Random_Opick(_1734003, _1734005))], (47297 ^ _782435) ^ [_1734066] : [hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(_1734066)), c_List_Otranspose__rel(_1734066)), c_List_Olist_ONil(tc_List_Olist(_1734066)))), -(c_List_Otranspose(_1734066, c_List_Olist_ONil(tc_List_Olist(_1734066))) = c_List_Olist_ONil(tc_List_Olist(_1734066)))], (47303 ^ _782435) ^ [_1734193, _1734195] : [-(c_List_Ofoldr(tc_List_Olist(_1734193), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734193)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734193))), c_List_Otranspose(_1734193, _1734195), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1734193))), hAPP(c_List_Ofilter(tc_List_Olist(_1734193), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1734193)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734193), tc_List_Olist(_1734193), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1734193)))), _1734195)))], (47305 ^ _782435) ^ [_1734290, _1734292, _1734294, _1734296] : [-(hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat), hAPP(c_Nat_OSuc, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1734290)), _1734292))), c_List_Ofoldr(tc_List_Olist(_1734294), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734294)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734294))), _1734296, 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(_1734290)), _1734292)), c_List_Ofoldr(tc_List_Olist(_1734294), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734294)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734294), tc_Nat_Onat, tc_Nat_Onat), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1734294)), c_Groups_Ominus__class_Ominus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1734294)))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), hAPP(c_List_Ofilter(tc_List_Olist(_1734294), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1734294)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1734294), tc_List_Olist(_1734294), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1734294)))), _1734296), c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))))], (47307 ^ _782435) ^ [_1734459, _1734461, _1734463, _1734465] : [-(c_List_Ofoldr(_1734459, _1734461, _1734463, c_List_Olist_ONil(_1734459), _1734465) = _1734465)], (47309 ^ _782435) ^ [_1734496, _1734498, _1734500, _1734502, _1734504, _1734506] : [-(c_List_Ofoldr(_1734496, _1734498, _1734500, hAPP(hAPP(c_List_Olist_OCons(_1734496), _1734502), _1734504), _1734506) = hAPP(hAPP(_1734500, _1734502), c_List_Ofoldr(_1734496, _1734498, _1734500, _1734504, _1734506)))], (47311 ^ _782435) ^ [_1734555, _1734557, _1734559, _1734561, _1734563, _1734565] : [-(c_List_Ofoldr(_1734555, _1734557, _1734559, hAPP(hAPP(c_List_Oappend(_1734555), _1734561), _1734563), _1734565) = c_List_Ofoldr(_1734555, _1734557, _1734559, _1734561, c_List_Ofoldr(_1734555, _1734557, _1734559, _1734563, _1734565)))], (47313 ^ _782435) ^ [_1734614, _1734616, _1734618] : [class_Groups_Oab__semigroup__add(_1734614), -(c_List_Ofoldr(_1734614, _1734614, c_Groups_Oplus__class_Oplus(_1734614), _1734616, _1734618) = hAPP(c_List_Ofoldl(_1734614, _1734614, c_Groups_Oplus__class_Oplus(_1734614), _1734618), _1734616))], (47319 ^ _782435) ^ [_1734727, _1734729, _1734731, _1734733, _1734735, _1734737, _1734739] : [-(c_List_Ofoldr(_1734727, _1734729, _1734731, hAPP(hAPP(c_List_Omap(_1734733, _1734727), _1734735), _1734737), _1734739) = c_List_Ofoldr(_1734733, _1734729, hAPP(c_Fun_Ocomp(_1734727, tc_fun(_1734729, _1734729), _1734733, _1734731), _1734735), _1734737, _1734739))], (47321 ^ _782435) ^ [_1734794, _1734796] : [class_Groups_Omonoid__add(_1734794), -(hAPP(c_List_Ofoldl(_1734794, _1734794, c_Groups_Oplus__class_Oplus(_1734794), c_Groups_Ozero__class_Ozero(_1734794)), _1734796) = c_List_Ofoldr(_1734794, _1734794, c_Groups_Oplus__class_Oplus(_1734794), _1734796, c_Groups_Ozero__class_Ozero(_1734794)))], (47327 ^ _782435) ^ [_1734913, _1734915, _1734917] : [class_Groups_Omonoid__add(_1734913), -(hAPP(c_List_Ofoldl(_1734913, _1734913, c_Groups_Oplus__class_Oplus(_1734913), _1734915), _1734917) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1734913), _1734915), c_List_Ofoldr(_1734913, _1734913, c_Groups_Oplus__class_Oplus(_1734913), _1734917, c_Groups_Ozero__class_Ozero(_1734913))))], (47333 ^ _782435) ^ [_1735046, _1735048] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1735046))), c_List_Otranspose(_1735046, _1735048)) = c_List_Ofoldr(tc_List_Olist(_1735046), tc_Nat_Onat, hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_List_Olist(_1735046)), c_Orderings_Oord__class_Omax(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_List_Olist(_1735046))), _1735048, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))], (47335 ^ _782435) ^ [_1735107, _1735109, _1735111] : [-(c_List_Osublist(_1735107, _1735109, _1735111) = hAPP(hAPP(c_List_Omap(tc_prod(_1735107, tc_Nat_Onat), _1735107), c_Product__Type_Ofst(_1735107, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735107, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735107, 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(_1735107, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1735107, tc_Nat_Onat))), _1735111)), hAPP(hAPP(c_List_Ozip(_1735107, tc_Nat_Onat), _1735109), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735107)), _1735109))))))], (47337 ^ _782435) ^ [_1735210, _1735212, _1735214, _1735216] : [-(hAPP(hAPP(c_List_Omap(tc_prod(_1735210, tc_Nat_Onat), _1735210), c_Product__Type_Ofst(_1735210, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735210, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735210, 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(_1735210, tc_Nat_Onat)), c_member(tc_Nat_Onat)), c_Product__Type_Osnd(_1735210, tc_Nat_Onat))), _1735212)), hAPP(hAPP(c_List_Ozip(_1735210, tc_Nat_Onat), _1735214), c_List_Oupt(_1735216, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735216), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735210)), _1735214)))))) = hAPP(hAPP(c_List_Omap(tc_prod(_1735210, tc_Nat_Onat), _1735210), c_Product__Type_Ofst(_1735210, tc_Nat_Onat)), hAPP(c_List_Ofilter(tc_prod(_1735210, tc_Nat_Onat), hAPP(hAPP(c_COMBC(tc_prod(_1735210, 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(_1735210, tc_Nat_Onat)), c_member(tc_Nat_Onat)), hAPP(hAPP(c_COMBC(tc_prod(_1735210, 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(_1735210, tc_Nat_Onat)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Product__Type_Osnd(_1735210, tc_Nat_Onat))), _1735216))), _1735212)), hAPP(hAPP(c_List_Ozip(_1735210, tc_Nat_Onat), _1735214), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1735210)), _1735214))))))], (47339 ^ _782435) ^ [_1735415, _1735417] : [-(hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1735415), _1735417) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1735415, _1735417)))], (47341 ^ _782435) ^ [_1735452, _1735454] : [-(hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1735452, _1735454)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1735452), _1735454))], (47343 ^ _782435) ^ [_1735489, _1735491] : [-(hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat), c_List_Oupt(_1735489, _1735491))))], (47345 ^ _782435) ^ [_1735519, _1735521, _1735523] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735519), _1735521)), -(c_List_Oupt(_1735519, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735521), _1735523)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735519, _1735521)), c_List_Oupt(_1735521, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735521), _1735523))))], (47351 ^ _782435) ^ [_1735671, _1735673] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735671), _1735673)), -(c_List_Oupt(_1735671, hAPP(c_Nat_OSuc, _1735673)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735671, _1735673)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1735673), c_List_Olist_ONil(tc_Nat_Onat))))], (47357 ^ _782435) ^ [_1735794, _1735796] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735794), _1735796))), -(c_List_Oupt(_1735794, hAPP(c_Nat_OSuc, _1735796)) = c_List_Olist_ONil(tc_Nat_Onat))], (47363 ^ _782435) ^ [_1735843, _1735845] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1735843), _1735845)), -(c_List_Oupt(_1735843, hAPP(c_Nat_OSuc, _1735845)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), c_List_Oupt(_1735843, _1735845)), hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1735845), c_List_Olist_ONil(tc_Nat_Onat))))], (47369 ^ _782435) ^ [_1735972, _1735974, _1735976] : [-(hAPP(hAPP(c_List_Odrop(tc_Nat_Onat), _1735972), c_List_Oupt(_1735974, _1735976)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1735974), _1735972), _1735976))], (47371 ^ _782435) ^ [_1736017, _1736019] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736017), _1736019)), -(hAPP(c_List_Ohd(tc_Nat_Onat), c_List_Oupt(_1736017, _1736019)) = _1736017)], (47377 ^ _782435) ^ [_1736125, _1736127] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736125), _1736127)), -(c_List_Oupt(_1736125, _1736127) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1736125), c_List_Oupt(hAPP(c_Nat_OSuc, _1736125), _1736127)))], (47383 ^ _782435) ^ [_1736236, _1736238] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736236), _1736238))), -(c_List_Oupt(_1736236, _1736238) = c_List_Olist_ONil(tc_Nat_Onat))], (47389 ^ _782435) ^ [_1736282, _1736284] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1736282), _1736284)), -(c_List_Oupt(_1736282, _1736284) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1736282), c_List_Oupt(hAPP(c_Nat_OSuc, _1736282), _1736284)))], (47395 ^ _782435) ^ [_1736399, _1736401, _1736403] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736399), _1736401)), _1736403)), -(hAPP(hAPP(c_List_Otake(tc_Nat_Onat), _1736401), c_List_Oupt(_1736399, _1736403)) = c_List_Oupt(_1736399, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1736399), _1736401)))], (47401 ^ _782435) ^ [_1736536, _1736538] : [-(c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat, hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1736536), _1736538)) = c_List_Oupt(_1736536, _1736538))], (47413 ^ _782435) ^ [_1736690, _1736692] : [47414 ^ _782435 : [(47415 ^ _782435) ^ [] : [_1736692 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (47417 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736692), _1736690))]], -(c_List_Oupt(_1736690, _1736692) = c_List_Olist_ONil(tc_Nat_Onat))], (47403 ^ _782435) ^ [_1736588, _1736590] : [c_List_Oupt(_1736588, _1736590) = c_List_Olist_ONil(tc_Nat_Onat), -(_1736590 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736590), _1736588)))], (47421 ^ _782435) ^ [_1736823, _1736825] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1736823), _1736825)), -(c_List_Oupt(_1736825, _1736823) = c_List_Olist_ONil(tc_Nat_Onat))], (47427 ^ _782435) ^ [_1736916] : [-(c_List_Oupt(_1736916, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat))], (47429 ^ _782435) ^ [_1736942, _1736944] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)), c_List_Oupt(_1736942, _1736944)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1736944), _1736942))], (47431 ^ _782435) ^ [_1736988, _1736990] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736988)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736990))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736988), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736990)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736988)), c_List_Oupt(hAPP(c_Nat_OSuc, hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736988)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1736990))))], (47437 ^ _782435) ^ [_1737141, _1737143] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737141)), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737143)))), -(c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737141), hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat), _1737143)) = c_List_Olist_ONil(tc_Nat_Onat))], (47443 ^ _782435) ^ [_1737220, _1737222, _1737224, _1737226] : [c_List_Oupt(_1737220, _1737222) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1737224), _1737226), 47446 ^ _782435 : [(47447 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737220), _1737222)))], (47449 ^ _782435) ^ [] : [-(_1737220 = _1737224)], (47451 ^ _782435) ^ [] : [-(c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737220), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1737222) = _1737226)]]], (47453 ^ _782435) ^ [_1737393, _1737395, _1737397, _1737399] : [-(c_List_Oupt(_1737393, _1737395) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat), _1737397), _1737399)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737393), _1737395)), _1737393 = _1737397, c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737393), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1737395) = _1737399], (47467 ^ _782435) ^ [_1737634, _1737636] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1737634), _1737636)), -(c_List_Olast(tc_Nat_Onat, c_List_Oupt(_1737634, _1737636)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1737636), c_Groups_Oone__class_Oone(tc_Nat_Onat)))], (47473 ^ _782435) ^ [_1737745, _1737747] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Nat_Onat), c_Nat_OSuc), c_List_Oupt(_1737745, _1737747)) = c_List_Oupt(hAPP(c_Nat_OSuc, _1737745), hAPP(c_Nat_OSuc, _1737747)))], (47475 ^ _782435) ^ [_1737785, _1737787] : [-(c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat, _1737785, _1737787) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1737785, hAPP(c_Nat_OSuc, _1737787))))], (47477 ^ _782435) ^ [_1737823] : [-(hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat), _1737823) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1737823)))], (47479 ^ _782435) ^ [_1737855, _1737857, _1737859] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737855), _1737857)), _1737859)), -(hAPP(hAPP(c_List_Onth(tc_Nat_Onat), c_List_Oupt(_1737855, _1737859)), _1737857) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1737855), _1737857))], (47485 ^ _782435) ^ [_1737986, _1737988] : [-(c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat, _1737986, _1737988) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1737986), hAPP(c_Nat_OSuc, _1737988))))], (47487 ^ _782435) ^ [_1738027, _1738029] : [-(c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat, _1738027, _1738029) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(hAPP(c_Nat_OSuc, _1738027), _1738029)))], (47489 ^ _782435) ^ [_1738065] : [-(hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat), _1738065) = hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_OSuc, _1738065))))], (47491 ^ _782435) ^ [_1738100, _1738102] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738100), hAPP(c_List_Onth(_1738100), _1738102)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738100)), _1738102))) = _1738102)], (47493 ^ _782435) ^ [_1738149, _1738151, _1738153, _1738155] : [class_Groups_Ocomm__monoid__add(_1738149), -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1738149), _1738151), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1738153, _1738155))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1738149), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738149), _1738151), c_List_Oupt(_1738153, _1738155))))], (47499 ^ _782435) ^ [_1738292, _1738294, _1738296, _1738298] : [class_Groups_Ocomm__monoid__add(_1738292), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1738292), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738292), _1738294), c_List_Oupt(_1738296, _1738298))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat, _1738292), _1738294), hAPP(c_List_Oset(tc_Nat_Onat), c_List_Oupt(_1738296, _1738298))))], (47505 ^ _782435) ^ [_1738435, _1738437, _1738439, _1738441, _1738443] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1738435), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1738437), _1738439))), -(hAPP(hAPP(c_List_Onth(_1738441), hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1738441), _1738443), c_List_Oupt(_1738439, _1738437))), _1738435) = hAPP(_1738443, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1738439), _1738435)))], (47511 ^ _782435) ^ [_1738598, _1738600, _1738602] : [47512 ^ _782435 : [(47513 ^ _782435) ^ [] : [-(_1738598 = c_List_Olist_ONil(tc_List_Olist(_1738600)))], (47515 ^ _782435) ^ [] : [_1738602 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 47519 ^ _782435 : [(47520 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47518 ^ [_1738598, _1738600, _1738602]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738600))), _1738598))))], (47522 ^ _782435) ^ [] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1738600)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1738600)), _1738598), 47518 ^ [_1738598, _1738600, _1738602])) = _1738602]], -(c_List_Otranspose(_1738600, _1738598) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_List_Olist(_1738600)), hAPP(hAPP(c_COMBC(tc_Nat_Onat, tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1738600)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, _1738600), tc_fun(tc_List_Olist(tc_Nat_Onat), tc_List_Olist(_1738600)), tc_Nat_Onat), c_List_Omap(tc_Nat_Onat, _1738600)), hAPP(c_COMBC(tc_Nat_Onat, tc_Nat_Onat, _1738600), hAPP(hAPP(c_COMBB(tc_List_Olist(_1738600), tc_fun(tc_Nat_Onat, _1738600), tc_Nat_Onat), c_List_Onth(_1738600)), hAPP(c_List_Onth(tc_List_Olist(_1738600)), _1738598))))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1738600))), _1738598)))), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1738602)))], (47526 ^ _782435) ^ [_1739108, _1739110, _1739112, _1739114, _1739116] : [class_Orderings_Olinorder(_1739108), hBOOL(hAPP(hAPP(c_member(_1739110), _1739112), hAPP(c_List_Oset(_1739110), _1739114))), c_List_Olinorder__class_Osorted(_1739108, hAPP(hAPP(c_List_Omap(_1739110, _1739108), _1739116), _1739114)), hAPP(c_List_Ohd(_1739110), hAPP(c_List_Ofilter(_1739110, hAPP(hAPP(c_COMBB(_1739108, tc_HOL_Obool, _1739110), hAPP(c_fequal, hAPP(_1739116, _1739112))), _1739116)), _1739114)) = _1739112, -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739110, _1739108, _1739116), _1739112), c_List_Oremove1(_1739110, _1739112, _1739114)) = _1739114)], (47544 ^ _782435) ^ [_1739487] : [class_Orderings_Olinorder(_1739487), -(c_List_Olinorder__class_Osorted(_1739487, c_List_Olist_ONil(_1739487)))], (47550 ^ _782435) ^ [_1739564, _1739566] : [class_Orderings_Olinorder(_1739564), -(c_List_Olinorder__class_Osorted(_1739564, hAPP(hAPP(c_List_Olist_OCons(_1739564), _1739566), c_List_Olist_ONil(_1739564))))], (47556 ^ _782435) ^ [_1739659, _1739661] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, c_List_Oupt(_1739659, _1739661)))], (47558 ^ _782435) ^ [_1739687, _1739689] : [class_Orderings_Olinorder(_1739687), -(c_List_Olinorder__class_Osorted(_1739687, c_List_Olinorder__class_Osort__key(_1739687, _1739687, c_COMBI(_1739687), _1739689)))], (47564 ^ _782435) ^ [_1739776, _1739778, _1739780] : [class_Orderings_Olinorder(_1739776), 47567 ^ _782435 : [(47568 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1739776, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739776, _1739776, c_COMBI(_1739776)), _1739778), _1739780)), -(c_List_Olinorder__class_Osorted(_1739776, _1739780))], (47574 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1739776, _1739780), -(c_List_Olinorder__class_Osorted(_1739776, hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1739776, _1739776, c_COMBI(_1739776)), _1739778), _1739780)))]]], (47580 ^ _782435) ^ [_1740023, _1740025] : [class_Orderings_Olinorder(_1740023), c_List_Olinorder__class_Osorted(_1740023, _1740025), -(c_List_Olinorder__class_Osorted(_1740023, hAPP(c_List_Otl(_1740023), _1740025)))], (47590 ^ _782435) ^ [_1740160] : [class_Orderings_Olinorder(_1740160), -(c_List_Olinorder__class_Osorted(_1740160, c_List_Olist_ONil(_1740160)))], (47596 ^ _782435) ^ [_1740237, _1740239] : [class_Orderings_Olinorder(_1740237), -(_1740239 = c_List_Olist_ONil(_1740237)), c_List_Olinorder__class_Osorted(_1740237, _1740239), -(c_List_Olinorder__class_Osorted(_1740237, c_List_Obutlast(_1740237, _1740239)))], (47610 ^ _782435) ^ [_1740429, _1740431, _1740433] : [class_Orderings_Olinorder(_1740429), c_List_Olinorder__class_Osorted(_1740429, _1740431), -(c_List_Olinorder__class_Osorted(_1740429, hAPP(hAPP(c_List_Otake(_1740429), _1740433), _1740431)))], (47620 ^ _782435) ^ [_1740576, _1740578] : [-(c_List_Olinorder__class_Osorted(tc_Int_Oint, c_List_Oupto(_1740576, _1740578)))], (47622 ^ _782435) ^ [_1740604, _1740606, _1740608] : [class_Orderings_Olinorder(_1740604), c_List_Olinorder__class_Osorted(_1740604, _1740606), -(c_List_Olinorder__class_Osorted(_1740604, c_List_Oremove1(_1740604, _1740608, _1740606)))], (47632 ^ _782435) ^ [_1740743, _1740745, _1740747, _1740749] : [class_Orderings_Olinorder(_1740743), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1740743), _1740745), _1740747)), c_List_Olinorder__class_Osorted(_1740743, hAPP(hAPP(c_List_Olist_OCons(_1740743), _1740747), _1740749)), -(c_List_Olinorder__class_Osorted(_1740743, hAPP(hAPP(c_List_Olist_OCons(_1740743), _1740745), hAPP(hAPP(c_List_Olist_OCons(_1740743), _1740747), _1740749))))], (47646 ^ _782435) ^ [_1740996, _1740998, _1741000, _1741002] : [class_Orderings_Olinorder(_1740996), 47649 ^ _782435 : [(47650 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1740996, hAPP(hAPP(c_List_Olist_OCons(_1740996), _1740998), hAPP(hAPP(c_List_Olist_OCons(_1740996), _1741000), _1741002))), 47653 ^ _782435 : [(47654 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1740996), _1740998), _1741000)))], (47656 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1740996, hAPP(hAPP(c_List_Olist_OCons(_1740996), _1741000), _1741002)))]]], (47658 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1740996, hAPP(hAPP(c_List_Olist_OCons(_1740996), _1740998), hAPP(hAPP(c_List_Olist_OCons(_1740996), _1741000), _1741002)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1740996), _1740998), _1741000)), c_List_Olinorder__class_Osorted(_1740996, hAPP(hAPP(c_List_Olist_OCons(_1740996), _1741000), _1741002))]]], (47668 ^ _782435) ^ [_1741382, _1741384, _1741386] : [class_Orderings_Olinorder(_1741382), c_List_Olinorder__class_Osorted(_1741382, _1741384), -(c_List_Olinorder__class_Osorted(_1741382, hAPP(hAPP(c_List_Odrop(_1741382), _1741386), _1741384)))], (47678 ^ _782435) ^ [_1741529, _1741531, _1741533] : [class_Orderings_Olinorder(_1741529), c_List_Olinorder__class_Osorted(_1741529, _1741531), -(c_List_Olinorder__class_Osorted(_1741529, c_List_Olinorder__class_Oinsort__insert__key(_1741529, _1741529, c_COMBI(_1741529), _1741533, _1741531)))], (47688 ^ _782435) ^ [_1741676, _1741678] : [class_Orderings_Olinorder(_1741676), c_List_Olinorder__class_Osorted(_1741676, _1741678), -(c_List_Olinorder__class_Osorted(_1741676, c_List_Oremdups(_1741676, _1741678)))], (47698 ^ _782435) ^ [_1741809, _1741811, _1741813] : [class_Orderings_Olinorder(_1741809), c_List_Olinorder__class_Osorted(_1741809, _1741811), hBOOL(hAPP(c_List_Odistinct(_1741809), _1741811)), c_List_Olinorder__class_Osorted(_1741809, _1741813), hBOOL(hAPP(c_List_Odistinct(_1741809), _1741813)), hAPP(c_List_Oset(_1741809), _1741811) = hAPP(c_List_Oset(_1741809), _1741813), -(_1741811 = _1741813)], (47724 ^ _782435) ^ [_1742192, _1742194, _1742196, _1742198] : [class_Orderings_Olinorder(_1742192), -(c_List_Olinorder__class_Osorted(_1742192, hAPP(hAPP(c_List_Omap(_1742194, _1742192), _1742196), c_List_Olinorder__class_Osort__key(_1742194, _1742192, _1742196, _1742198))))], (47730 ^ _782435) ^ [_1742299, _1742301, _1742303, _1742305, _1742307] : [class_Orderings_Olinorder(_1742299), c_List_Olinorder__class_Osorted(_1742299, hAPP(hAPP(c_List_Omap(_1742301, _1742299), _1742303), _1742305)), -(c_List_Olinorder__class_Osorted(_1742299, hAPP(hAPP(c_List_Omap(_1742301, _1742299), _1742303), c_List_Olinorder__class_Oinsort__insert__key(_1742301, _1742299, _1742303, _1742307, _1742305))))], (47740 ^ _782435) ^ [_1742486, _1742488, _1742490, _1742492, _1742494] : [class_Orderings_Olinorder(_1742486), c_List_Olinorder__class_Osorted(_1742486, hAPP(hAPP(c_List_Omap(_1742488, _1742486), _1742490), _1742492)), -(c_List_Olinorder__class_Osorted(_1742486, hAPP(hAPP(c_List_Omap(_1742488, _1742486), _1742490), c_List_Oremove1(_1742488, _1742494, _1742492))))], (47750 ^ _782435) ^ [_1742669, _1742671, _1742673, _1742675, _1742677] : [class_Orderings_Olinorder(_1742669), 47753 ^ _782435 : [(47754 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1742669, hAPP(hAPP(c_List_Omap(_1742671, _1742669), _1742673), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742671, _1742669, _1742673), _1742675), _1742677))), -(c_List_Olinorder__class_Osorted(_1742669, hAPP(hAPP(c_List_Omap(_1742671, _1742669), _1742673), _1742677)))], (47760 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1742669, hAPP(hAPP(c_List_Omap(_1742671, _1742669), _1742673), _1742677)), -(c_List_Olinorder__class_Osorted(_1742669, hAPP(hAPP(c_List_Omap(_1742671, _1742669), _1742673), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1742671, _1742669, _1742673), _1742675), _1742677))))]]], (47766 ^ _782435) ^ [_1742976, _1742978, _1742980, _1742982, _1742984] : [class_Orderings_Olinorder(_1742976), c_List_Olinorder__class_Osorted(_1742976, hAPP(hAPP(c_List_Omap(_1742978, _1742976), _1742980), _1742982)), -(c_List_Olinorder__class_Osorted(_1742976, hAPP(hAPP(c_List_Omap(_1742978, _1742976), _1742980), hAPP(c_List_Ofilter(_1742978, _1742984), _1742982))))], (47776 ^ _782435) ^ [_1743163, _1743165, _1743167, _1743169, _1743171] : [class_Orderings_Olinorder(_1743163), -(c_List_Olinorder__class_Osorted(_1743163, hAPP(hAPP(c_List_Omap(_1743165, _1743163), _1743167), hAPP(c_List_Ofilter(_1743165, hAPP(hAPP(c_COMBC(_1743165, _1743163, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1743163, tc_fun(_1743163, tc_HOL_Obool), _1743165), c_fequal), _1743167)), hAPP(_1743169, _1743171))), _1743171))))], (47782 ^ _782435) ^ [_1743326, _1743328, _1743330] : [class_Orderings_Olinorder(_1743326), -(c_List_Olinorder__class_Osorted(_1743326, hAPP(c_List_Ofilter(_1743326, hAPP(hAPP(c_COMBC(_1743326, _1743326, tc_HOL_Obool), c_fequal), hAPP(_1743328, _1743330))), _1743330)))], (47788 ^ _782435) ^ [_1743441, _1743443, _1743445] : [class_Orderings_Olinorder(_1743441), 47791 ^ _782435 : [(47792 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1743441, hAPP(hAPP(c_List_Olist_OCons(_1743441), _1743443), _1743445)), 47795 ^ _782435 : [(47796 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743441, _1743445))], (47798 ^ _782435) ^ [_1743627] : [hBOOL(hAPP(hAPP(c_member(_1743441), _1743627), hAPP(c_List_Oset(_1743441), _1743445))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743441), _1743443), _1743627)))]]], (47804 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743441, hAPP(hAPP(c_List_Olist_OCons(_1743441), _1743443), _1743445))), c_List_Olinorder__class_Osorted(_1743441, _1743445), 47810 ^ _782435 : [(47811 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743441), 47809 ^ [_1743441, _1743443, _1743445]), hAPP(c_List_Oset(_1743441), _1743445))))], (47813 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743441), _1743443), 47809 ^ [_1743441, _1743443, _1743445]))]]]]], (47817 ^ _782435) ^ [_1743966, _1743968, _1743970] : [class_Orderings_Olinorder(_1743966), 47820 ^ _782435 : [(47821 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1743966, hAPP(hAPP(c_List_Oappend(_1743966), _1743968), _1743970)), 47824 ^ _782435 : [(47825 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743966, _1743968))], (47827 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743966, _1743970))], (47829 ^ _782435) ^ [_1744202] : [hBOOL(hAPP(hAPP(c_member(_1743966), _1744202), hAPP(c_List_Oset(_1743966), _1743968))), 47832 ^ _782435 : [(47833 ^ _782435) ^ [_1744312] : [hBOOL(hAPP(hAPP(c_member(_1743966), _1744312), hAPP(c_List_Oset(_1743966), _1743970))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743966), _1744202), _1744312)))]]]]], (47839 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1743966, hAPP(hAPP(c_List_Oappend(_1743966), _1743968), _1743970))), c_List_Olinorder__class_Osorted(_1743966, _1743968), c_List_Olinorder__class_Osorted(_1743966, _1743970), 47849 ^ _782435 : [(47850 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743966), 47848 ^ [_1743966, _1743968, _1743970]), hAPP(c_List_Oset(_1743966), _1743968))))], (47853 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1743966), 47851 ^ [_1743966, _1743968, _1743970]), hAPP(c_List_Oset(_1743966), _1743970))))], (47855 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1743966), 47848 ^ [_1743966, _1743968, _1743970]), 47851 ^ [_1743966, _1743968, _1743970]))]]]]], (47859 ^ _782435) ^ [_1744814, _1744816, _1744818, _1744820, _1744822, _1744824] : [class_Orderings_Olinorder(_1744814), c_List_Olinorder__class_Osorted(_1744814, hAPP(hAPP(c_List_Omap(_1744816, _1744814), _1744818), _1744820)), hBOOL(hAPP(_1744822, _1744824)), -(hAPP(c_List_Ofilter(_1744816, _1744822), hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744816, _1744814, _1744818), _1744824), _1744820)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1744816, _1744814, _1744818), _1744824), hAPP(c_List_Ofilter(_1744816, _1744822), _1744820)))], (47873 ^ _782435) ^ [_1745103, _1745105, _1745107] : [class_Orderings_Olinorder(_1745103), 47876 ^ _782435 : [(47877 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1745103, hAPP(hAPP(c_List_Olist_OCons(_1745103), _1745105), _1745107)), 47880 ^ _782435 : [(47887 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745103, _1745107))], (47881 ^ _782435) ^ [_1745271] : [hBOOL(hAPP(hAPP(c_member(_1745103), _1745271), hAPP(c_List_Oset(_1745103), _1745107))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745103), _1745105), _1745271)))]]], (47889 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745103, hAPP(hAPP(c_List_Olist_OCons(_1745103), _1745105), _1745107))), 47893 ^ _782435 : [(47894 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1745103), 47892 ^ [_1745103, _1745105, _1745107]), hAPP(c_List_Oset(_1745103), _1745107))))], (47896 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1745103), _1745105), 47892 ^ [_1745103, _1745105, _1745107]))]], c_List_Olinorder__class_Osorted(_1745103, _1745107)]]], (47902 ^ _782435) ^ [_1745629, _1745631] : [class_Orderings_Olinorder(_1745629), hBOOL(hAPP(c_Finite__Set_Ofinite(_1745629), _1745631)), 47909 ^ _782435 : [(47910 ^ _782435) ^ [] : [-(hAPP(c_List_Oset(_1745629), c_List_Olinorder__class_Osorted__list__of__set(_1745629, _1745631)) = _1745631)], (47912 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1745629, c_List_Olinorder__class_Osorted__list__of__set(_1745629, _1745631)))], (47914 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1745629), c_List_Olinorder__class_Osorted__list__of__set(_1745629, _1745631))))]]], (47916 ^ _782435) ^ [_1745850, _1745852, _1745854] : [class_Orderings_Olinorder(_1745850), hBOOL(hAPP(hAPP(c_member(_1745850), _1745852), hAPP(c_List_Oset(_1745850), _1745854))), c_List_Olinorder__class_Osorted(_1745850, _1745854), -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1745850, _1745850, c_COMBI(_1745850)), _1745852), c_List_Oremove1(_1745850, _1745852, _1745854)) = _1745854)], (47930 ^ _782435) ^ [_1746091, _1746093, _1746095, _1746097] : [class_Orderings_Olinorder(_1746091), c_List_Olinorder__class_Osorted(_1746091, _1746093), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746095), _1746097)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746097), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746091)), _1746093))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746091), hAPP(hAPP(c_List_Onth(_1746091), _1746093), _1746095)), hAPP(hAPP(c_List_Onth(_1746091), _1746093), _1746097))))], (47948 ^ _782435) ^ [_1746418, _1746420] : [class_Orderings_Olinorder(_1746418), 47951 ^ _782435 : [(47966 ^ _782435) ^ [] : [47968 ^ _782435 : [(47969 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 47967 ^ [_1746418, _1746420]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746418)), _1746420))))], (47972 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 47970 ^ [_1746418, _1746420]), 47967 ^ [_1746418, _1746420])))], (47974 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746418), hAPP(hAPP(c_List_Onth(_1746418), _1746420), 47970 ^ [_1746418, _1746420])), hAPP(hAPP(c_List_Onth(_1746418), _1746420), 47967 ^ [_1746418, _1746420])))]], -(c_List_Olinorder__class_Osorted(_1746418, _1746420))], (47952 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1746418, _1746420), 47955 ^ _782435 : [(47956 ^ _782435) ^ [_1746589] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1746589), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1746418)), _1746420))), 47959 ^ _782435 : [(47960 ^ _782435) ^ [_1746706] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1746706), _1746589)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1746418), hAPP(hAPP(c_List_Onth(_1746418), _1746420), _1746706)), hAPP(hAPP(c_List_Onth(_1746418), _1746420), _1746589))))]]]]]]], (47978 ^ _782435) ^ [_1747142, _1747144, _1747146, _1747148, _1747150] : [class_Orderings_Olinorder(_1747142), c_Fun_Oinj__on(_1747144, _1747142, _1747146, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1747144, tc_HOL_Obool)), hAPP(c_List_Oset(_1747144), _1747148)), hAPP(c_List_Oset(_1747144), _1747150))), c_List_Olinorder__class_Osorted(_1747142, hAPP(hAPP(c_List_Omap(_1747144, _1747142), _1747146), _1747148)), hBOOL(hAPP(c_List_Odistinct(_1747142), hAPP(hAPP(c_List_Omap(_1747144, _1747142), _1747146), _1747148))), c_List_Olinorder__class_Osorted(_1747142, hAPP(hAPP(c_List_Omap(_1747144, _1747142), _1747146), _1747150)), hBOOL(hAPP(c_List_Odistinct(_1747142), hAPP(hAPP(c_List_Omap(_1747144, _1747142), _1747146), _1747150))), hAPP(c_List_Oset(_1747144), _1747148) = hAPP(c_List_Oset(_1747144), _1747150), -(_1747148 = _1747150)], (48008 ^ _782435) ^ [_1747725, _1747727, _1747729] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747725), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1747725))), _1747727))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747729), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1747725))), _1747727))), -(hAPP(hAPP(c_List_Omap(tc_List_Olist(_1747725), _1747725), hAPP(hAPP(c_COMBC(tc_List_Olist(_1747725), tc_Nat_Onat, _1747725), c_List_Onth(_1747725)), _1747729)), hAPP(c_List_Ofilter(tc_List_Olist(_1747725), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1747725)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1747729)), c_Nat_Osize__class_Osize(tc_List_Olist(_1747725)))), c_List_Otranspose(_1747725, _1747727))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(_1747725)), _1747727), _1747729))], (48018 ^ _782435) ^ [_1748052, _1748054, _1748056, _1748058] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1748052), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1748052))), _1748054))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748056), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748052))), c_List_Otranspose(_1748052, _1748054)))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748058), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1748052))), hAPP(c_List_Ofilter(tc_List_Olist(_1748052), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1748052)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1748056)), c_Nat_Osize__class_Osize(tc_List_Olist(_1748052)))), _1748054)))), -(hAPP(hAPP(c_List_Onth(_1748052), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1748052)), c_List_Otranspose(_1748052, _1748054)), _1748056)), _1748058) = hAPP(hAPP(c_List_Onth(_1748052), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1748052)), _1748054), _1748058)), _1748056))], (48032 ^ _782435) ^ [_1748475, _1748477] : [-(c_Fun_Oinj__on(tc_List_Olist(_1748475), tc_List_Olist(_1748475), c_List_Orev(_1748475), _1748477))], (48034 ^ _782435) ^ [_1748523, _1748525] : [hAPP(c_List_Orev(_1748523), _1748525) = c_List_Olist_ONil(_1748523), -(_1748525 = c_List_Olist_ONil(_1748523))], (48040 ^ _782435) ^ [_1748614, _1748616] : [_1748616 = c_List_Olist_ONil(_1748614), -(hAPP(c_List_Orev(_1748614), _1748616) = c_List_Olist_ONil(_1748614))], (48046 ^ _782435) ^ [_1748726, _1748728] : [c_List_Olist_ONil(_1748726) = hAPP(c_List_Orev(_1748726), _1748728), -(_1748728 = c_List_Olist_ONil(_1748726))], (48052 ^ _782435) ^ [_1748817, _1748819] : [_1748819 = c_List_Olist_ONil(_1748817), -(c_List_Olist_ONil(_1748817) = hAPP(c_List_Orev(_1748817), _1748819))], (48058 ^ _782435) ^ [_1748914] : [-(hAPP(c_List_Orev(_1748914), c_List_Olist_ONil(_1748914)) = c_List_Olist_ONil(_1748914))], (48060 ^ _782435) ^ [_1748964, _1748966, _1748968] : [hAPP(hAPP(c_List_Olist_OCons(_1748964), _1748966), c_List_Olist_ONil(_1748964)) = hAPP(c_List_Orev(_1748964), _1748968), -(_1748968 = hAPP(hAPP(c_List_Olist_OCons(_1748964), _1748966), c_List_Olist_ONil(_1748964)))], (48066 ^ _782435) ^ [_1749089, _1749091, _1749093] : [_1749093 = hAPP(hAPP(c_List_Olist_OCons(_1749089), _1749091), c_List_Olist_ONil(_1749089)), -(hAPP(hAPP(c_List_Olist_OCons(_1749089), _1749091), c_List_Olist_ONil(_1749089)) = hAPP(c_List_Orev(_1749089), _1749093))], (48072 ^ _782435) ^ [_1749238, _1749240, _1749242] : [hAPP(c_List_Orev(_1749238), _1749240) = hAPP(hAPP(c_List_Olist_OCons(_1749238), _1749242), c_List_Olist_ONil(_1749238)), -(_1749240 = hAPP(hAPP(c_List_Olist_OCons(_1749238), _1749242), c_List_Olist_ONil(_1749238)))], (48078 ^ _782435) ^ [_1749363, _1749365, _1749367] : [_1749365 = hAPP(hAPP(c_List_Olist_OCons(_1749363), _1749367), c_List_Olist_ONil(_1749363)), -(hAPP(c_List_Orev(_1749363), _1749365) = hAPP(hAPP(c_List_Olist_OCons(_1749363), _1749367), c_List_Olist_ONil(_1749363)))], (48084 ^ _782435) ^ [_1749494, _1749496, _1749498] : [-(hAPP(c_List_Orev(_1749494), hAPP(hAPP(c_List_Oappend(_1749494), _1749496), _1749498)) = hAPP(hAPP(c_List_Oappend(_1749494), hAPP(c_List_Orev(_1749494), _1749498)), hAPP(c_List_Orev(_1749494), _1749496)))], (48086 ^ _782435) ^ [_1749567, _1749569] : [hBOOL(hAPP(c_List_Odistinct(_1749567), hAPP(c_List_Orev(_1749567), _1749569))), -(hBOOL(hAPP(c_List_Odistinct(_1749567), _1749569)))], (48092 ^ _782435) ^ [_1749666, _1749668] : [hBOOL(hAPP(c_List_Odistinct(_1749666), _1749668)), -(hBOOL(hAPP(c_List_Odistinct(_1749666), hAPP(c_List_Orev(_1749666), _1749668))))], (48098 ^ _782435) ^ [_1749771, _1749773] : [-(hAPP(c_List_Orev(_1749771), c_List_Oconcat(_1749771, _1749773)) = c_List_Oconcat(_1749771, hAPP(hAPP(c_List_Omap(tc_List_Olist(_1749771), tc_List_Olist(_1749771)), c_List_Orev(_1749771)), hAPP(c_List_Orev(tc_List_Olist(_1749771)), _1749773))))], (48100 ^ _782435) ^ [_1749829, _1749831, _1749833, _1749835] : [-(hAPP(c_List_Orev(_1749829), hAPP(hAPP(c_List_Omap(_1749831, _1749829), _1749833), _1749835)) = hAPP(hAPP(c_List_Omap(_1749831, _1749829), _1749833), hAPP(c_List_Orev(_1749831), _1749835)))], (48102 ^ _782435) ^ [_1749886, _1749888, _1749890] : [-(hAPP(c_List_Orev(_1749886), hAPP(c_List_Ofilter(_1749886, _1749888), _1749890)) = hAPP(c_List_Ofilter(_1749886, _1749888), hAPP(c_List_Orev(_1749886), _1749890)))], (48104 ^ _782435) ^ [_1749935, _1749937, _1749939, _1749941] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749935)), _1749937) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1749939)), _1749941), -(hAPP(hAPP(c_List_Ozip(_1749935, _1749939), hAPP(c_List_Orev(_1749935), _1749937)), hAPP(c_List_Orev(_1749939), _1749941)) = hAPP(c_List_Orev(tc_prod(_1749935, _1749939)), hAPP(hAPP(c_List_Ozip(_1749935, _1749939), _1749937), _1749941)))], (48110 ^ _782435) ^ [_1750116, _1750118] : [-(hAPP(c_List_Oset(_1750116), hAPP(c_List_Orev(_1750116), _1750118)) = hAPP(c_List_Oset(_1750116), _1750118))], (48112 ^ _782435) ^ [_1750156, _1750158] : [class_Groups_Ocomm__monoid__add(_1750156), -(hAPP(c_List_Omonoid__add__class_Olistsum(_1750156), hAPP(c_List_Orev(_1750156), _1750158)) = hAPP(c_List_Omonoid__add__class_Olistsum(_1750156), _1750158))], (48118 ^ _782435) ^ [_1750279, _1750281, _1750283] : [hAPP(c_List_Orev(_1750279), _1750281) = hAPP(c_List_Orev(_1750279), _1750283), -(_1750281 = _1750283)], (48124 ^ _782435) ^ [_1750374, _1750376, _1750378] : [_1750376 = _1750378, -(hAPP(c_List_Orev(_1750374), _1750376) = hAPP(c_List_Orev(_1750374), _1750378))], (48130 ^ _782435) ^ [_1750493, _1750495, _1750497] : [hAPP(c_List_Orev(_1750493), _1750495) = _1750497, -(_1750495 = hAPP(c_List_Orev(_1750493), _1750497))], (48136 ^ _782435) ^ [_1750588, _1750590, _1750592] : [_1750590 = hAPP(c_List_Orev(_1750588), _1750592), -(hAPP(c_List_Orev(_1750588), _1750590) = _1750592)], (48142 ^ _782435) ^ [_1750689, _1750691] : [-(hAPP(c_List_Orev(_1750689), hAPP(c_List_Orev(_1750689), _1750691)) = _1750691)], (48144 ^ _782435) ^ [_1750724, _1750726] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750724)), hAPP(c_List_Orev(_1750724), _1750726)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1750724)), _1750726))], (48146 ^ _782435) ^ [_1750792, _1750794, _1750796, _1750798, _1750800] : [c_List_Olist__all2(_1750792, _1750794, _1750796, hAPP(c_List_Orev(_1750792), _1750798), _1750800), -(c_List_Olist__all2(_1750792, _1750794, _1750796, _1750798, hAPP(c_List_Orev(_1750794), _1750800)))], (48152 ^ _782435) ^ [_1750903, _1750905, _1750907, _1750909, _1750911] : [c_List_Olist__all2(_1750903, _1750905, _1750907, _1750909, hAPP(c_List_Orev(_1750905), _1750911)), -(c_List_Olist__all2(_1750903, _1750905, _1750907, hAPP(c_List_Orev(_1750903), _1750909), _1750911))], (48158 ^ _782435) ^ [_1751044, _1751046, _1751048, _1751050, _1751052] : [c_List_Olist__all2(_1751044, _1751046, _1751048, hAPP(c_List_Orev(_1751044), _1751050), hAPP(c_List_Orev(_1751046), _1751052)), -(c_List_Olist__all2(_1751044, _1751046, _1751048, _1751050, _1751052))], (48164 ^ _782435) ^ [_1751155, _1751157, _1751159, _1751161, _1751163] : [c_List_Olist__all2(_1751155, _1751157, _1751159, _1751161, _1751163), -(c_List_Olist__all2(_1751155, _1751157, _1751159, hAPP(c_List_Orev(_1751155), _1751161), hAPP(c_List_Orev(_1751157), _1751163)))], (48170 ^ _782435) ^ [_1751272, _1751274, _1751276, _1751278, _1751280] : [-(hAPP(c_List_Ofoldl(_1751272, _1751274, _1751276, _1751278), _1751280) = c_List_Ofoldr(_1751274, _1751272, hAPP(c_COMBC(_1751272, _1751274, _1751272), _1751276), hAPP(c_List_Orev(_1751274), _1751280), _1751278))], (48172 ^ _782435) ^ [_1751329, _1751331, _1751333, _1751335, _1751337] : [-(c_List_Ofoldr(_1751329, _1751331, _1751333, _1751335, _1751337) = hAPP(c_List_Ofoldl(_1751331, _1751329, hAPP(c_COMBC(_1751329, _1751331, _1751331), _1751333), _1751337), hAPP(c_List_Orev(_1751329), _1751335)))], (48174 ^ _782435) ^ [_1751386, _1751388, _1751390] : [-(hAPP(c_List_Orev(_1751386), hAPP(hAPP(c_List_Olist_OCons(_1751386), _1751388), _1751390)) = hAPP(hAPP(c_List_Oappend(_1751386), hAPP(c_List_Orev(_1751386), _1751390)), hAPP(hAPP(c_List_Olist_OCons(_1751386), _1751388), c_List_Olist_ONil(_1751386))))], (48176 ^ _782435) ^ [_1751470, _1751472, _1751474, _1751476] : [hAPP(c_List_Orev(_1751470), _1751472) = hAPP(hAPP(c_List_Olist_OCons(_1751470), _1751474), _1751476), -(_1751472 = hAPP(hAPP(c_List_Oappend(_1751470), hAPP(c_List_Orev(_1751470), _1751476)), hAPP(hAPP(c_List_Olist_OCons(_1751470), _1751474), c_List_Olist_ONil(_1751470))))], (48182 ^ _782435) ^ [_1751619, _1751621, _1751623, _1751625] : [_1751621 = hAPP(hAPP(c_List_Oappend(_1751619), hAPP(c_List_Orev(_1751619), _1751625)), hAPP(hAPP(c_List_Olist_OCons(_1751619), _1751623), c_List_Olist_ONil(_1751619))), -(hAPP(c_List_Orev(_1751619), _1751621) = hAPP(hAPP(c_List_Olist_OCons(_1751619), _1751623), _1751625))], (48188 ^ _782435) ^ [_1751770, _1751772] : [-(_1751770 = c_List_Olist_ONil(_1751772)), -(c_List_Olast(_1751772, hAPP(c_List_Orev(_1751772), _1751770)) = hAPP(c_List_Ohd(_1751772), _1751770))], (48194 ^ _782435) ^ [_1751817, _1751819] : [-(_1751817 = c_List_Olist_ONil(_1751819)), -(hAPP(c_List_Ohd(_1751819), hAPP(c_List_Orev(_1751819), _1751817)) = c_List_Olast(_1751819, _1751817))], (48200 ^ _782435) ^ [_1751868, _1751870] : [-(c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1751868), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1751868))), c_List_Otranspose(_1751868, _1751870)))))], (48202 ^ _782435) ^ [_1751914, _1751916] : [-(hAPP(c_List_Orev(_1751914), _1751916) = hAPP(c_List_Ofoldl(tc_List_Olist(_1751914), _1751914, hAPP(c_COMBC(_1751914, tc_List_Olist(_1751914), tc_List_Olist(_1751914)), c_List_Olist_OCons(_1751914)), c_List_Olist_ONil(_1751914)), _1751916))], (48204 ^ _782435) ^ [_1751969, _1751971, _1751973] : [-(hAPP(c_List_Orev(_1751969), hAPP(hAPP(c_List_Odrop(_1751969), _1751971), _1751973)) = hAPP(hAPP(c_List_Otake(_1751969), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1751969)), _1751973)), _1751971)), hAPP(c_List_Orev(_1751969), _1751973)))], (48206 ^ _782435) ^ [_1752035, _1752037, _1752039] : [-(hAPP(c_List_Orev(_1752035), hAPP(hAPP(c_List_Otake(_1752035), _1752037), _1752039)) = hAPP(hAPP(c_List_Odrop(_1752035), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752035)), _1752039)), _1752037)), hAPP(c_List_Orev(_1752035), _1752039)))], (48208 ^ _782435) ^ [_1752101, _1752103, _1752105] : [-(hAPP(c_List_Orotate(_1752101, _1752103), hAPP(c_List_Orev(_1752101), _1752105)) = hAPP(c_List_Orev(_1752101), hAPP(c_List_Orotate(_1752101, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752101)), _1752105)), c_Divides_Odiv__class_Omod(tc_Nat_Onat, _1752103, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752101)), _1752105)))), _1752105)))], (48210 ^ _782435) ^ [_1752174, _1752176, _1752178] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752174), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752176)), _1752178))), -(hAPP(hAPP(c_List_Onth(_1752176), hAPP(c_List_Orev(_1752176), _1752178)), _1752174) = hAPP(hAPP(c_List_Onth(_1752176), _1752178), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752176)), _1752178)), hAPP(c_Nat_OSuc, _1752174))))], (48216 ^ _782435) ^ [_1752351, _1752353, _1752355, _1752357] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752351), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752353)), _1752355))), -(hAPP(c_List_Orev(_1752353), hAPP(hAPP(c_List_Olist__update(_1752353, _1752355), _1752351), _1752357)) = hAPP(hAPP(c_List_Olist__update(_1752353, hAPP(c_List_Orev(_1752353), _1752355)), 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(_1752353)), _1752355)), _1752351)), c_Groups_Oone__class_Oone(tc_Nat_Onat))), _1752357))], (48222 ^ _782435) ^ [_1752550, _1752552, _1752554, _1752556] : [class_Orderings_Olinorder(_1752550), c_List_Olinorder__class_Osorted(_1752550, hAPP(c_List_Orev(_1752550), _1752552)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1752554), _1752556)), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1752556), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1752550)), _1752552))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1752550), hAPP(hAPP(c_List_Onth(_1752550), _1752552), _1752556)), hAPP(hAPP(c_List_Onth(_1752550), _1752552), _1752554))))], (48240 ^ _782435) ^ [_1752887, _1752889, _1752891] : [class_Orderings_Olinorder(_1752887), c_List_Olinorder__class_Osorted(_1752887, hAPP(c_List_Orev(_1752887), _1752889)), 48247 ^ _782435 : [(48248 ^ _782435) ^ [] : [_1752889 = c_List_Olist_ONil(_1752887), -(c_List_Ofoldr(_1752887, _1752887, c_Orderings_Oord__class_Omax(_1752887), _1752889, _1752891) = _1752891)], (48254 ^ _782435) ^ [] : [-(_1752889 = c_List_Olist_ONil(_1752887)), -(c_List_Ofoldr(_1752887, _1752887, c_Orderings_Oord__class_Omax(_1752887), _1752889, _1752891) = hAPP(hAPP(c_Orderings_Oord__class_Omax(_1752887), hAPP(hAPP(c_List_Onth(_1752887), _1752889), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1752891))]]], (48260 ^ _782435) ^ [_1753201, _1753203] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753201), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753201))), _1753203))), 48263 ^ _782435 : [(48264 ^ _782435) ^ [] : [_1753203 = c_List_Olist_ONil(tc_List_Olist(_1753201)), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753201))), c_List_Otranspose(_1753201, _1753203)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (48270 ^ _782435) ^ [] : [-(_1753203 = c_List_Olist_ONil(tc_List_Olist(_1753201))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753201))), c_List_Otranspose(_1753201, _1753203)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753201)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753201)), _1753203), c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))]]], (48276 ^ _782435) ^ [_1753511, _1753513, _1753515] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753511), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753511))), _1753513))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753515), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753511))), _1753513))), -(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(_1753511))), hAPP(c_List_Ofilter(tc_List_Olist(_1753511), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_HOL_Obool, tc_List_Olist(_1753511)), hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1753515)), c_Nat_Osize__class_Osize(tc_List_Olist(_1753511)))), c_List_Otranspose(_1753511, _1753513))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1753511)), hAPP(hAPP(c_List_Onth(tc_List_Olist(_1753511)), _1753513), _1753515)))], (48286 ^ _782435) ^ [_1753820, _1753822] : [c_List_Olinorder__class_Osorted(tc_Nat_Onat, hAPP(c_List_Orev(tc_Nat_Onat), hAPP(hAPP(c_List_Omap(tc_List_Olist(_1753820), tc_Nat_Onat), c_Nat_Osize__class_Osize(tc_List_Olist(_1753820))), _1753822))), -(c_List_Otranspose(_1753820, c_List_Otranspose(_1753820, _1753822)) = c_List_OtakeWhile(tc_List_Olist(_1753820), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, tc_List_Olist(_1753820)), c_fNot), hAPP(hAPP(c_COMBC(tc_List_Olist(_1753820), tc_List_Olist(_1753820), tc_HOL_Obool), c_fequal), c_List_Olist_ONil(_1753820))), _1753822))], (48292 ^ _782435) ^ [] : [-(c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)))], (48294 ^ _782435) ^ [_1754031, _1754033, _1754035] : [class_Orderings_Olinorder(_1754031), c_List_Olinorder__class_Osorted(_1754031, _1754033), -(c_List_Olinorder__class_Osorted(_1754031, c_List_OtakeWhile(_1754031, _1754035, _1754033)))], (48304 ^ _782435) ^ [_1754170, _1754172, _1754174] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754170)), c_List_OtakeWhile(_1754170, _1754172, _1754174))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1754170)), _1754174))))], (48306 ^ _782435) ^ [_1754220, _1754222, _1754224, _1754226] : [hBOOL(hAPP(hAPP(c_member(_1754220), _1754222), hAPP(c_List_Oset(_1754220), c_List_OtakeWhile(_1754220, _1754224, _1754226)))), 48309 ^ _782435 : [(48310 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754220), _1754222), hAPP(c_List_Oset(_1754220), _1754226))))], (48312 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1754224, _1754222)))]]], (48324 ^ _782435) ^ [_1754601, _1754603, _1754605] : [48326 ^ _782435 : [(48327 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1754601), 48325 ^ [_1754601, _1754603, _1754605]), hAPP(c_List_Oset(_1754601), _1754605))))], (48329 ^ _782435) ^ [] : [hBOOL(hAPP(_1754603, 48325 ^ [_1754601, _1754603, _1754605]))]], -(c_List_OtakeWhile(_1754601, _1754603, _1754605) = _1754605)], (48314 ^ _782435) ^ [_1754405, _1754407, _1754409] : [c_List_OtakeWhile(_1754405, _1754407, _1754409) = _1754409, 48317 ^ _782435 : [(48318 ^ _782435) ^ [_1754492] : [hBOOL(hAPP(hAPP(c_member(_1754405), _1754492), hAPP(c_List_Oset(_1754405), _1754409))), -(hBOOL(hAPP(_1754407, _1754492)))]]], (48333 ^ _782435) ^ [_1754789, _1754791, _1754793, _1754795, _1754797] : [-(hAPP(hAPP(c_List_Ozip(_1754789, _1754791), c_List_OtakeWhile(_1754789, _1754793, _1754795)), _1754797) = c_List_OtakeWhile(tc_prod(_1754789, _1754791), hAPP(c_Fun_Ocomp(_1754789, tc_HOL_Obool, tc_prod(_1754789, _1754791), _1754793), c_Product__Type_Ofst(_1754789, _1754791)), hAPP(hAPP(c_List_Ozip(_1754789, _1754791), _1754795), _1754797)))], (48335 ^ _782435) ^ [_1754863, _1754865, _1754867, _1754869, _1754871] : [-(hAPP(hAPP(c_List_Ozip(_1754863, _1754865), _1754867), c_List_OtakeWhile(_1754865, _1754869, _1754871)) = c_List_OtakeWhile(tc_prod(_1754863, _1754865), hAPP(c_Fun_Ocomp(_1754865, tc_HOL_Obool, tc_prod(_1754863, _1754865), _1754869), c_Product__Type_Osnd(_1754863, _1754865)), hAPP(hAPP(c_List_Ozip(_1754863, _1754865), _1754867), _1754871)))], (48337 ^ _782435) ^ [_1754937, _1754939, _1754941, _1754943, _1754945] : [-(c_List_OtakeWhile(_1754937, _1754939, hAPP(hAPP(c_List_Omap(_1754941, _1754937), _1754943), _1754945)) = hAPP(hAPP(c_List_Omap(_1754941, _1754937), _1754943), c_List_OtakeWhile(_1754941, hAPP(c_Fun_Ocomp(_1754937, tc_HOL_Obool, _1754941, _1754939), _1754943), _1754945)))], (48339 ^ _782435) ^ [_1755002, _1755004, _1755006] : [hBOOL(hAPP(c_List_Odistinct(_1755002), _1755004)), -(hBOOL(hAPP(c_List_Odistinct(_1755002), c_List_OtakeWhile(_1755002, _1755006, _1755004))))], (48345 ^ _782435) ^ [_1755101, _1755103, _1755105, _1755107, _1755109] : [-(hBOOL(hAPP(_1755101, _1755103))), -(c_List_OtakeWhile(_1755105, _1755101, hAPP(hAPP(c_List_Oappend(_1755105), _1755107), hAPP(hAPP(c_List_Olist_OCons(_1755105), _1755103), _1755109))) = c_List_OtakeWhile(_1755105, _1755101, _1755107))], (48351 ^ _782435) ^ [_1755184, _1755186, _1755188, _1755190] : [hBOOL(hAPP(_1755184, _1755186)), -(c_List_OtakeWhile(_1755188, _1755184, hAPP(hAPP(c_List_Olist_OCons(_1755188), _1755186), _1755190)) = hAPP(hAPP(c_List_Olist_OCons(_1755188), _1755186), c_List_OtakeWhile(_1755188, _1755184, _1755190)))], (48357 ^ _782435) ^ [_1755311, _1755313, _1755315, _1755317] : [-(hBOOL(hAPP(_1755311, _1755313))), -(c_List_OtakeWhile(_1755315, _1755311, hAPP(hAPP(c_List_Olist_OCons(_1755315), _1755313), _1755317)) = c_List_Olist_ONil(_1755315))], (48363 ^ _782435) ^ [_1755369, _1755371, _1755373] : [-(c_List_OtakeWhile(_1755369, _1755371, _1755373) = hAPP(hAPP(c_List_Otake(_1755369), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755369)), c_List_OtakeWhile(_1755369, _1755371, _1755373))), _1755373))], (48365 ^ _782435) ^ [_1755419, _1755421] : [-(c_List_OtakeWhile(_1755419, _1755421, c_List_Olist_ONil(_1755419)) = c_List_Olist_ONil(_1755419))], (48367 ^ _782435) ^ [_1755452] : [-(c_List_Oreturn__list(_1755452) = hAPP(hAPP(c_List_Omap(tc_Int_Oint, tc_Nat_Onat), c_Int_Onat), _1755452))], (48369 ^ _782435) ^ [_1755480, _1755482, _1755484, _1755486, _1755488] : [hBOOL(hAPP(hAPP(c_member(_1755480), _1755482), hAPP(c_List_Oset(_1755480), _1755484))), -(hBOOL(hAPP(_1755486, _1755482))), -(c_List_OtakeWhile(_1755480, _1755486, hAPP(hAPP(c_List_Oappend(_1755480), _1755484), _1755488)) = c_List_OtakeWhile(_1755480, _1755486, _1755484))], (48379 ^ _782435) ^ [_1755638, _1755640, _1755642, _1755644] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1755638), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755640)), c_List_OtakeWhile(_1755640, _1755642, _1755644)))), -(hAPP(hAPP(c_List_Onth(_1755640), c_List_OtakeWhile(_1755640, _1755642, _1755644)), _1755638) = hAPP(hAPP(c_List_Onth(_1755640), _1755644), _1755638))], (48385 ^ _782435) ^ [_1755791, _1755793, _1755795] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755791)), c_List_OtakeWhile(_1755791, _1755793, _1755795))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755791)), _1755795))), hBOOL(hAPP(_1755793, hAPP(hAPP(c_List_Onth(_1755791), _1755795), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1755791)), c_List_OtakeWhile(_1755791, _1755793, _1755795)))))], (48391 ^ _782435) ^ [_1755958, _1755960] : [-(_1755958 = c_List_Olist_ONil(_1755960)), hBOOL(hAPP(c_List_Odistinct(_1755960), _1755958)), -(c_List_OtakeWhile(_1755960, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1755960), c_fNot), hAPP(hAPP(c_COMBC(_1755960, _1755960, tc_HOL_Obool), c_fequal), c_List_Olast(_1755960, _1755958))), _1755958) = c_List_Obutlast(_1755960, _1755958))], (48401 ^ _782435) ^ [_1756155, _1756157, _1756159, _1756161, _1756163] : [class_Orderings_Olinorder(_1756155), c_List_Olinorder__class_Osorted(_1756155, hAPP(c_List_Orev(_1756155), hAPP(hAPP(c_List_Omap(_1756157, _1756155), _1756159), _1756161))), -(hAPP(c_List_Ofilter(_1756157, hAPP(hAPP(c_COMBB(_1756155, tc_HOL_Obool, _1756157), hAPP(c_Orderings_Oord__class_Oless(_1756155), _1756163)), _1756159)), _1756161) = c_List_OtakeWhile(_1756157, hAPP(hAPP(c_COMBB(_1756155, tc_HOL_Obool, _1756157), hAPP(c_Orderings_Oord__class_Oless(_1756155), _1756163)), _1756159), _1756161))], (48411 ^ _782435) ^ [_1756402] : [c_List_Onat__list(_1756402), -(c_List_Oembed__list(c_List_Oreturn__list(_1756402)) = _1756402)], (48417 ^ _782435) ^ [_1756483, _1756485] : [-(hAPP(hAPP(c_List_Oappend(tc_Nat_Onat), _1756483), _1756485) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint), c_List_Oembed__list(_1756483)), c_List_Oembed__list(_1756485))))], (48419 ^ _782435) ^ [_1756526] : [-(c_List_Oembed__list(_1756526) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat, tc_Int_Oint), c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)), _1756526))], (48421 ^ _782435) ^ [_1756554, _1756556, _1756558] : [hBOOL(hAPP(c_List_Odistinct(_1756554), _1756556)), hBOOL(hAPP(hAPP(c_member(_1756554), _1756558), hAPP(c_List_Oset(_1756554), _1756556))), -(c_List_OtakeWhile(_1756554, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756554), c_fNot), hAPP(hAPP(c_COMBC(_1756554, _1756554, tc_HOL_Obool), c_fequal), _1756558)), hAPP(c_List_Orev(_1756554), _1756556)) = hAPP(c_List_Orev(_1756554), hAPP(c_List_Otl(_1756554), c_List_OdropWhile(_1756554, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756554), c_fNot), hAPP(hAPP(c_COMBC(_1756554, _1756554, tc_HOL_Obool), c_fequal), _1756558)), _1756556))))], (48431 ^ _782435) ^ [_1756845, _1756847, _1756849] : [hBOOL(hAPP(c_List_Odistinct(_1756845), _1756847)), hBOOL(hAPP(hAPP(c_member(_1756845), _1756849), hAPP(c_List_Oset(_1756845), _1756847))), -(c_List_OdropWhile(_1756845, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756845), c_fNot), hAPP(hAPP(c_COMBC(_1756845, _1756845, tc_HOL_Obool), c_fequal), _1756849)), hAPP(c_List_Orev(_1756845), _1756847)) = hAPP(hAPP(c_List_Olist_OCons(_1756845), _1756849), hAPP(c_List_Orev(_1756845), c_List_OtakeWhile(_1756845, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1756845), c_fNot), hAPP(hAPP(c_COMBC(_1756845, _1756845, tc_HOL_Obool), c_fequal), _1756849)), _1756847))))], (48441 ^ _782435) ^ [_1757142, _1757144, _1757146] : [-(hAPP(hAPP(c_List_Oappend(_1757142), c_List_OtakeWhile(_1757142, _1757144, _1757146)), c_List_OdropWhile(_1757142, _1757144, _1757146)) = _1757146)], (48443 ^ _782435) ^ [_1757185, _1757187, _1757189] : [class_Orderings_Olinorder(_1757185), c_List_Olinorder__class_Osorted(_1757185, _1757187), -(c_List_Olinorder__class_Osorted(_1757185, c_List_OdropWhile(_1757185, _1757189, _1757187)))], (48453 ^ _782435) ^ [_1757323, _1757325, _1757327] : [-(c_List_OdropWhile(_1757323, _1757325, _1757327) = c_List_Olist_ONil(_1757323)), hBOOL(hAPP(_1757325, hAPP(c_List_Ohd(_1757323), c_List_OdropWhile(_1757323, _1757325, _1757327))))], (48459 ^ _782435) ^ [_1757429, _1757431, _1757433] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757429)), c_List_OdropWhile(_1757429, _1757431, _1757433))), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1757429)), _1757433))))], (48471 ^ _782435) ^ [_1757697, _1757699, _1757701] : [48473 ^ _782435 : [(48474 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1757697), 48472 ^ [_1757697, _1757699, _1757701]), hAPP(c_List_Oset(_1757697), _1757701))))], (48476 ^ _782435) ^ [] : [hBOOL(hAPP(_1757699, 48472 ^ [_1757697, _1757699, _1757701]))]], -(c_List_OdropWhile(_1757697, _1757699, _1757701) = c_List_Olist_ONil(_1757697))], (48461 ^ _782435) ^ [_1757497, _1757499, _1757501] : [c_List_OdropWhile(_1757497, _1757499, _1757501) = c_List_Olist_ONil(_1757497), 48464 ^ _782435 : [(48465 ^ _782435) ^ [_1757588] : [hBOOL(hAPP(hAPP(c_member(_1757497), _1757588), hAPP(c_List_Oset(_1757497), _1757501))), -(hBOOL(hAPP(_1757499, _1757588)))]]], (48480 ^ _782435) ^ [_1757889, _1757891, _1757893] : [hBOOL(hAPP(c_List_Odistinct(_1757889), _1757891)), -(hBOOL(hAPP(c_List_Odistinct(_1757889), c_List_OdropWhile(_1757889, _1757893, _1757891))))], (48486 ^ _782435) ^ [_1758007, _1758009, _1758011, _1758013] : [hBOOL(hAPP(_1758007, _1758009)), -(c_List_OdropWhile(_1758011, _1758007, hAPP(hAPP(c_List_Olist_OCons(_1758011), _1758009), _1758013)) = c_List_OdropWhile(_1758011, _1758007, _1758013))], (48492 ^ _782435) ^ [_1758118, _1758120, _1758122, _1758124] : [-(hBOOL(hAPP(_1758118, _1758120))), -(c_List_OdropWhile(_1758122, _1758118, hAPP(hAPP(c_List_Olist_OCons(_1758122), _1758120), _1758124)) = hAPP(hAPP(c_List_Olist_OCons(_1758122), _1758120), _1758124))], (48498 ^ _782435) ^ [_1758182, _1758184] : [-(c_List_OdropWhile(_1758182, _1758184, c_List_Olist_ONil(_1758182)) = c_List_Olist_ONil(_1758182))], (48500 ^ _782435) ^ [_1758215, _1758217, _1758219, _1758221, _1758223] : [-(c_List_OdropWhile(_1758215, _1758217, hAPP(hAPP(c_List_Omap(_1758219, _1758215), _1758221), _1758223)) = hAPP(hAPP(c_List_Omap(_1758219, _1758215), _1758221), c_List_OdropWhile(_1758219, hAPP(c_Fun_Ocomp(_1758215, tc_HOL_Obool, _1758219, _1758217), _1758221), _1758223)))], (48502 ^ _782435) ^ [_1758280, _1758282, _1758284, _1758286, _1758288] : [hBOOL(hAPP(hAPP(c_member(_1758280), _1758282), hAPP(c_List_Oset(_1758280), _1758284))), -(hBOOL(hAPP(_1758286, _1758282))), -(c_List_OdropWhile(_1758280, _1758286, hAPP(hAPP(c_List_Oappend(_1758280), _1758284), _1758288)) = hAPP(hAPP(c_List_Oappend(_1758280), c_List_OdropWhile(_1758280, _1758286, _1758284)), _1758288))], (48512 ^ _782435) ^ [_1758478, _1758480, _1758482, _1758484, _1758486] : [c_List_OdropWhile(_1758478, _1758480, _1758482) = hAPP(hAPP(c_List_Olist_OCons(_1758478), _1758484), _1758486), 48515 ^ _782435 : [(48516 ^ _782435) ^ [] : [-(_1758482 = hAPP(hAPP(c_List_Oappend(_1758478), c_List_OtakeWhile(_1758478, _1758480, _1758482)), hAPP(hAPP(c_List_Olist_OCons(_1758478), _1758484), _1758486)))], (48518 ^ _782435) ^ [] : [hBOOL(hAPP(_1758480, _1758484))]]], (48520 ^ _782435) ^ [_1758659, _1758661, _1758663, _1758665, _1758667] : [-(c_List_OdropWhile(_1758659, _1758661, _1758663) = hAPP(hAPP(c_List_Olist_OCons(_1758659), _1758665), _1758667)), _1758663 = hAPP(hAPP(c_List_Oappend(_1758659), c_List_OtakeWhile(_1758659, _1758661, _1758663)), hAPP(hAPP(c_List_Olist_OCons(_1758659), _1758665), _1758667)), -(hBOOL(hAPP(_1758661, _1758665)))], (48530 ^ _782435) ^ [_1758873, _1758875, _1758877] : [-(c_List_OdropWhile(_1758873, _1758875, _1758877) = hAPP(hAPP(c_List_Odrop(_1758873), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758873)), c_List_OtakeWhile(_1758873, _1758875, _1758877))), _1758877))], (48532 ^ _782435) ^ [_1758923, _1758925, _1758927, _1758929] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1758923), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758925)), c_List_OdropWhile(_1758925, _1758927, _1758929)))), -(hAPP(hAPP(c_List_Onth(_1758925), c_List_OdropWhile(_1758925, _1758927, _1758929)), _1758923) = hAPP(hAPP(c_List_Onth(_1758925), _1758929), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1758923), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1758925)), c_List_OtakeWhile(_1758925, _1758927, _1758929)))))], (48538 ^ _782435) ^ [_1759110, _1759112, _1759114, _1759116, _1759118] : [class_Groups_Omonoid__add(_1759110), 48544 ^ _782435 : [(48545 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759112), 48543 ^ [_1759110, _1759112, _1759114, _1759116, _1759118]), hAPP(c_List_Oset(_1759112), _1759114))))], (48547 ^ _782435) ^ [] : [hBOOL(hAPP(_1759116, 48543 ^ [_1759110, _1759112, _1759114, _1759116, _1759118]))], (48549 ^ _782435) ^ [] : [hAPP(_1759118, 48543 ^ [_1759110, _1759112, _1759114, _1759116, _1759118]) = c_Groups_Ozero__class_Ozero(_1759110)]], -(hAPP(c_List_Omonoid__add__class_Olistsum(_1759110), hAPP(hAPP(c_List_Omap(_1759112, _1759110), _1759118), hAPP(c_List_Ofilter(_1759112, _1759116), _1759114))) = hAPP(c_List_Omonoid__add__class_Olistsum(_1759110), hAPP(hAPP(c_List_Omap(_1759112, _1759110), _1759118), _1759114)))], (48553 ^ _782435) ^ [_1759501, _1759503] : [class_Orderings_Olinorder(_1759501), 48560 ^ _782435 : [(48561 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), 48558 ^ [_1759501, _1759503]), 48559 ^ [_1759501, _1759503])))], (48563 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48559 ^ [_1759501, _1759503]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759501)), _1759503))))], (48565 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1759501), hAPP(hAPP(c_List_Onth(_1759501), _1759503), 48558 ^ [_1759501, _1759503])), hAPP(hAPP(c_List_Onth(_1759501), _1759503), 48559 ^ [_1759501, _1759503])))]], -(c_List_Olinorder__class_Osorted(_1759501, _1759503))], (48569 ^ _782435) ^ [_1759872, _1759874, _1759876] : [48571 ^ _782435 : [(48572 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1759872), 48570 ^ [_1759872, _1759874, _1759876]), hAPP(c_List_Oset(_1759872), c_List_OdropWhile(_1759872, _1759874, _1759876)))))], (48574 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1759874, 48570 ^ [_1759872, _1759874, _1759876])))]], -(c_List_OtakeWhile(_1759872, _1759874, _1759876) = hAPP(c_List_Ofilter(_1759872, _1759874), _1759876))], (48578 ^ _782435) ^ [_1759993, _1759995, _1759997, _1759999] : [48580 ^ _782435 : [(48581 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48579 ^ [_1759993, _1759995, _1759997, _1759999]), _1759993)))], (48583 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48579 ^ [_1759993, _1759995, _1759997, _1759999]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759995)), _1759997))))], (48585 ^ _782435) ^ [] : [hBOOL(hAPP(_1759999, hAPP(hAPP(c_List_Onth(_1759995), _1759997), 48579 ^ [_1759993, _1759995, _1759997, _1759999])))]], 48588 ^ _782435 : [(48589 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1759993), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1759995)), _1759997))))], (48591 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1759999, hAPP(hAPP(c_List_Onth(_1759995), _1759997), _1759993))))]], -(c_List_OtakeWhile(_1759995, _1759999, _1759997) = hAPP(hAPP(c_List_Otake(_1759995), _1759993), _1759997))], (48595 ^ _782435) ^ [_1760397, _1760399, _1760401, _1760403] : [48597 ^ _782435 : [(48598 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48596 ^ [_1760397, _1760399, _1760401, _1760403]), _1760397)))], (48600 ^ _782435) ^ [] : [hBOOL(hAPP(_1760399, hAPP(hAPP(c_List_Onth(_1760401), _1760403), 48596 ^ [_1760397, _1760399, _1760401, _1760403])))]], hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760397), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760401)), _1760403))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1760397), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1760401)), c_List_OtakeWhile(_1760401, _1760399, _1760403)))))], (48608 ^ _782435) ^ [_1760705, _1760707] : [class_Orderings_Olinorder(_1760705), 48611 ^ _782435 : [(48612 ^ _782435) ^ [] : [c_List_Olinorder__class_Osorted(_1760705, _1760707), -(_1760707 = c_List_Olist_ONil(_1760705)), 48621 ^ _782435 : [(48622 ^ _782435) ^ [] : [-(_1760707 = hAPP(hAPP(c_List_Olist_OCons(_1760705), 48620 ^ [_1760705, _1760707]), 48619 ^ [_1760705, _1760707]))], (48630 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760705, 48619 ^ [_1760705, _1760707]))], (48624 ^ _782435) ^ [_1761039] : [hBOOL(hAPP(hAPP(c_member(_1760705), _1761039), hAPP(c_List_Oset(_1760705), 48619 ^ [_1760705, _1760707]))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760705), 48620 ^ [_1760705, _1760707]), _1761039)))]]], (48632 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1760705, _1760707)), 48633 ^ _782435 : [(48634 ^ _782435) ^ [] : [_1760707 = c_List_Olist_ONil(_1760705)], (48636 ^ _782435) ^ [_1761265, _1761267] : [_1760707 = hAPP(hAPP(c_List_Olist_OCons(_1760705), _1761265), _1761267), 48642 ^ _782435 : [(48643 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1760705), 48641 ^ [_1760705, _1760707, _1761265, _1761267]), hAPP(c_List_Oset(_1760705), _1761267))))], (48645 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1760705), _1761265), 48641 ^ [_1760705, _1760707, _1761265, _1761267]))]], c_List_Olinorder__class_Osorted(_1760705, _1761267)]]]]], (48651 ^ _782435) ^ [_1761574, _1761576, _1761578, _1761580, _1761582] : [c_Fun_Oinj__on(_1761574, _1761576, _1761578, hAPP(hAPP(c_Set_Oinsert(_1761574), _1761580), hAPP(c_List_Oset(_1761574), _1761582))), -(hAPP(hAPP(c_List_Omap(_1761574, _1761576), _1761578), hAPP(c_List_OremoveAll(_1761574, _1761580), _1761582)) = hAPP(c_List_OremoveAll(_1761576, hAPP(_1761578, _1761580)), hAPP(hAPP(c_List_Omap(_1761574, _1761576), _1761578), _1761582)))], (48657 ^ _782435) ^ [_1761749, _1761751, _1761753] : [-(hBOOL(hAPP(hAPP(c_member(_1761749), _1761751), hAPP(c_List_Oset(_1761749), _1761753)))), -(c_List_Oinsert(_1761749, _1761751, _1761753) = hAPP(hAPP(c_List_Olist_OCons(_1761749), _1761751), _1761753))], (48663 ^ _782435) ^ [_1761811, _1761813, _1761815, _1761817] : [-(hAPP(c_List_OremoveAll(_1761811, _1761813), hAPP(hAPP(c_List_Oappend(_1761811), _1761815), _1761817)) = hAPP(hAPP(c_List_Oappend(_1761811), hAPP(c_List_OremoveAll(_1761811, _1761813), _1761815)), hAPP(c_List_OremoveAll(_1761811, _1761813), _1761817)))], (48665 ^ _782435) ^ [_1761874, _1761876, _1761878] : [-(c_List_Oinsert(_1761874, _1761876, c_List_Oremdups(_1761874, _1761878)) = c_List_Oremdups(_1761874, c_List_Oinsert(_1761874, _1761876, _1761878)))], (48667 ^ _782435) ^ [_1761915, _1761917] : [-(c_List_OremoveAll(_1761915, _1761917) = c_List_Ofilter(_1761915, hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1761915), c_fNot), hAPP(c_fequal, _1761917))))], (48669 ^ _782435) ^ [_1761955, _1761957, _1761959, _1761961] : [-(hBOOL(hAPP(_1761955, _1761957))), -(hAPP(c_List_OremoveAll(_1761959, _1761957), hAPP(c_List_Ofilter(_1761959, _1761955), _1761961)) = hAPP(c_List_Ofilter(_1761959, _1761955), _1761961))], (48675 ^ _782435) ^ [_1762015, _1762017, _1762019] : [hBOOL(hAPP(c_List_Odistinct(_1762015), _1762017)), -(hBOOL(hAPP(c_List_Odistinct(_1762015), c_List_Oinsert(_1762015, _1762019, _1762017))))], (48681 ^ _782435) ^ [_1762118, _1762120, _1762122] : [hBOOL(hAPP(c_List_Odistinct(_1762118), _1762120)), -(hBOOL(hAPP(c_List_Odistinct(_1762118), hAPP(c_List_OremoveAll(_1762118, _1762122), _1762120))))], (48687 ^ _782435) ^ [_1762240, _1762242, _1762244, _1762246] : [_1762240 = _1762242, -(hAPP(c_List_OremoveAll(_1762244, _1762240), hAPP(hAPP(c_List_Olist_OCons(_1762244), _1762242), _1762246)) = hAPP(c_List_OremoveAll(_1762244, _1762240), _1762246))], (48693 ^ _782435) ^ [_1762355, _1762357, _1762359, _1762361] : [-(_1762355 = _1762357), -(hAPP(c_List_OremoveAll(_1762359, _1762355), hAPP(hAPP(c_List_Olist_OCons(_1762359), _1762357), _1762361)) = hAPP(hAPP(c_List_Olist_OCons(_1762359), _1762357), hAPP(c_List_OremoveAll(_1762359, _1762355), _1762361)))], (48699 ^ _782435) ^ [_1762425, _1762427] : [-(hAPP(c_List_OremoveAll(_1762425, _1762427), c_List_Olist_ONil(_1762425)) = c_List_Olist_ONil(_1762425))], (48701 ^ _782435) ^ [_1762456, _1762458, _1762460] : [-(hBOOL(hAPP(hAPP(c_member(_1762456), _1762458), hAPP(c_List_Oset(_1762456), _1762460)))), -(hAPP(c_List_OremoveAll(_1762456, _1762458), _1762460) = _1762460)], (48707 ^ _782435) ^ [_1762512, _1762514, _1762516] : [hBOOL(hAPP(c_List_Odistinct(_1762512), _1762514)), -(c_List_Oremove1(_1762512, _1762516, _1762514) = hAPP(c_List_OremoveAll(_1762512, _1762516), _1762514))], (48713 ^ _782435) ^ [_1762619, _1762621, _1762623] : [hBOOL(hAPP(hAPP(c_member(_1762619), _1762621), hAPP(c_List_Oset(_1762619), _1762623))), -(c_List_Oinsert(_1762619, _1762621, _1762623) = _1762623)], (48719 ^ _782435) ^ [_1762730, _1762732, _1762734] : [-(hAPP(c_List_Oset(_1762730), c_List_Oinsert(_1762730, _1762732, _1762734)) = hAPP(hAPP(c_Set_Oinsert(_1762730), _1762732), hAPP(c_List_Oset(_1762730), _1762734)))], (48721 ^ _782435) ^ [_1762779, _1762781] : [-(c_List_Oinsert(_1762779, _1762781, c_List_Olist_ONil(_1762779)) = hAPP(hAPP(c_List_Olist_OCons(_1762779), _1762781), c_List_Olist_ONil(_1762779)))], (48723 ^ _782435) ^ [_1762820, _1762822, _1762824, _1762826, _1762828] : [c_Fun_Oinj__on(_1762820, _1762822, _1762824, c_Orderings_Otop__class_Otop(tc_fun(_1762820, tc_HOL_Obool))), -(hAPP(hAPP(c_List_Omap(_1762820, _1762822), _1762824), hAPP(c_List_OremoveAll(_1762820, _1762826), _1762828)) = hAPP(c_List_OremoveAll(_1762822, hAPP(_1762824, _1762826)), hAPP(hAPP(c_List_Omap(_1762820, _1762822), _1762824), _1762828)))], (48729 ^ _782435) ^ [_1762983, _1762985, _1762987] : [-(hAPP(c_List_Oset(_1762983), hAPP(c_List_OremoveAll(_1762983, _1762985), _1762987)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(_1762983, tc_HOL_Obool)), hAPP(c_List_Oset(_1762983), _1762987)), hAPP(hAPP(c_Set_Oinsert(_1762983), _1762985), c_Orderings_Obot__class_Obot(tc_fun(_1762983, tc_HOL_Obool)))))], (48731 ^ _782435) ^ [_1763062, _1763064, _1763066] : [hBOOL(hAPP(hAPP(c_member(_1763062), _1763064), hAPP(c_List_Oset(_1763062), _1763066))), -(c_List_Oinsert(_1763062, _1763064, _1763066) = _1763066)], (48737 ^ _782435) ^ [_1763167, _1763169, _1763171] : [-(hBOOL(hAPP(hAPP(c_member(_1763167), _1763169), hAPP(c_List_Oset(_1763167), _1763171)))), -(c_List_Oinsert(_1763167, _1763169, _1763171) = hAPP(hAPP(c_List_Olist_OCons(_1763167), _1763169), _1763171))], (48743 ^ _782435) ^ [_1763231, _1763233, _1763235, _1763237] : [-(c_List_Omaps(_1763231, _1763233, _1763235, _1763237) = c_List_Oconcat(_1763233, hAPP(hAPP(c_List_Omap(_1763231, tc_List_Olist(_1763233)), _1763235), _1763237)))], (48745 ^ _782435) ^ [_1763279, _1763281, _1763283, _1763285] : [-(c_List_Oconcat(_1763279, hAPP(hAPP(c_List_Omap(_1763281, tc_List_Olist(_1763279)), _1763283), _1763285)) = c_List_Omaps(_1763281, _1763279, _1763283, _1763285))], (48747 ^ _782435) ^ [_1763327, _1763329, _1763331] : [-(c_List_Omaps(_1763327, _1763329, _1763331, c_List_Olist_ONil(_1763327)) = c_List_Olist_ONil(_1763329))], (48749 ^ _782435) ^ [_1763363, _1763365, _1763367, _1763369, _1763371] : [-(c_List_Omaps(_1763363, _1763365, _1763367, hAPP(hAPP(c_List_Olist_OCons(_1763363), _1763369), _1763371)) = hAPP(hAPP(c_List_Oappend(_1763365), hAPP(_1763367, _1763369)), c_List_Omaps(_1763363, _1763365, _1763367, _1763371)))], (48751 ^ _782435) ^ [_1763423, _1763425] : [hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(_1763423)), _1763425)), 48757 ^ _782435 : [(48758 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763423)), 48756 ^ [_1763423, _1763425]), hAPP(c_List_Oset(tc_List_Olist(_1763423)), _1763425))))], (48760 ^ _782435) ^ [] : [hBOOL(hAPP(c_List_Odistinct(_1763423), 48756 ^ [_1763423, _1763425]))]], 48764 ^ _782435 : [(48765 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763423)), 48763 ^ [_1763423, _1763425]), hAPP(c_List_Oset(tc_List_Olist(_1763423)), _1763425))))], (48768 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1763423)), 48766 ^ [_1763423, _1763425]), hAPP(c_List_Oset(tc_List_Olist(_1763423)), _1763425))))], (48770 ^ _782435) ^ [] : [48763 ^ [_1763423, _1763425] = 48766 ^ [_1763423, _1763425]], (48772 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1763423, tc_HOL_Obool)), hAPP(c_List_Oset(_1763423), 48763 ^ [_1763423, _1763425])), hAPP(c_List_Oset(_1763423), 48766 ^ [_1763423, _1763425])) = c_Orderings_Obot__class_Obot(tc_fun(_1763423, tc_HOL_Obool))]], -(hBOOL(hAPP(c_List_Odistinct(_1763423), c_List_Oconcat(_1763423, _1763425))))], (48776 ^ _782435) ^ [_1764140, _1764142, _1764144, _1764146, _1764148] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), hAPP(_1764140, _1764142)), hAPP(_1764140, _1764144))), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764146, _1764146)), hAPP(hAPP(c_Product__Type_OPair(_1764146, _1764146), _1764142), _1764144)), c_List_Omeasures(_1764146, _1764148))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764146, _1764146)), hAPP(hAPP(c_Product__Type_OPair(_1764146, _1764146), _1764142), _1764144)), c_List_Omeasures(_1764146, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764146, tc_Nat_Onat)), _1764140), _1764148)))))], (48786 ^ _782435) ^ [_1764413, _1764415] : [-(c_Wellfounded_Owf(_1764413, c_List_Omeasures(_1764413, _1764415)))], (48788 ^ _782435) ^ [_1764456, _1764458, _1764460] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764456, _1764456)), hAPP(hAPP(c_Product__Type_OPair(_1764456, _1764456), _1764458), _1764460)), c_List_Omeasures(_1764456, c_List_Olist_ONil(tc_fun(_1764456, tc_Nat_Onat)))))], (48790 ^ _782435) ^ [_1764510, _1764512] : [-(c_List_Omeasures(_1764510, _1764512) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat), _1764510), c_List_Olex(tc_Nat_Onat, c_Wellfounded_Oless__than)), hAPP(hAPP(c_COMBC(_1764510, tc_List_Olist(tc_fun(_1764510, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1764510, tc_Nat_Onat), tc_Nat_Onat), tc_fun(tc_List_Olist(tc_fun(_1764510, tc_Nat_Onat)), tc_List_Olist(tc_Nat_Onat)), _1764510), c_List_Omap(tc_fun(_1764510, tc_Nat_Onat), tc_Nat_Onat)), hAPP(c_COMBC(tc_fun(_1764510, tc_Nat_Onat), _1764510, tc_Nat_Onat), c_COMBI(tc_fun(_1764510, tc_Nat_Onat))))), _1764512)))], (48792 ^ _782435) ^ [_1764631, _1764633, _1764635, _1764637, _1764639] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1764631, _1764631)), hAPP(hAPP(c_Product__Type_OPair(_1764631, _1764631), _1764633), _1764635)), c_List_Omeasures(_1764631, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764631, tc_Nat_Onat)), _1764637), _1764639)))), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764637, _1764633)), hAPP(_1764637, _1764635)))), 48799 ^ _782435 : [(48800 ^ _782435) ^ [] : [-(hAPP(_1764637, _1764633) = hAPP(_1764637, _1764635))], (48802 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764631, _1764631)), hAPP(hAPP(c_Product__Type_OPair(_1764631, _1764631), _1764633), _1764635)), c_List_Omeasures(_1764631, _1764639))))]]], (48804 ^ _782435) ^ [_1764910, _1764912, _1764914, _1764916, _1764918] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1764910, _1764910)), hAPP(hAPP(c_Product__Type_OPair(_1764910, _1764910), _1764912), _1764914)), c_List_Omeasures(_1764910, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1764910, tc_Nat_Onat)), _1764916), _1764918))))), 48805 ^ _782435 : [(48806 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1764916, _1764912)), hAPP(_1764916, _1764914)))], (48808 ^ _782435) ^ [] : [hAPP(_1764916, _1764912) = hAPP(_1764916, _1764914), hBOOL(hAPP(hAPP(c_member(tc_prod(_1764910, _1764910)), hAPP(hAPP(c_Product__Type_OPair(_1764910, _1764910), _1764912), _1764914)), c_List_Omeasures(_1764910, _1764918)))]]], (48816 ^ _782435) ^ [_1765233, _1765235, _1765237, _1765239, _1765241] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(_1765233, _1765235)), hAPP(_1765233, _1765237))), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1765239, _1765239)), hAPP(hAPP(c_Product__Type_OPair(_1765239, _1765239), _1765235), _1765237)), c_List_Omeasures(_1765239, hAPP(hAPP(c_List_Olist_OCons(tc_fun(_1765239, tc_Nat_Onat)), _1765233), _1765241)))))], (48822 ^ _782435) ^ [_1765404, _1765406, _1765408, _1765410, _1765412, _1765414, _1765416, _1765418] : [48824 ^ _782435 : [(48825 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1765404), 48823 ^ [_1765404, _1765406, _1765408, _1765410, _1765412, _1765414, _1765416, _1765418]), hAPP(c_List_Oset(_1765404), _1765406))))], (48827 ^ _782435) ^ [] : [hAPP(c_Fun_Ocomp(_1765408, _1765408, _1765410, hAPP(_1765412, 48823 ^ [_1765404, _1765406, _1765408, _1765410, _1765412, _1765414, _1765416, _1765418])), _1765414) = hAPP(c_Fun_Ocomp(_1765410, _1765408, _1765410, _1765414), hAPP(_1765416, 48823 ^ [_1765404, _1765406, _1765408, _1765410, _1765412, _1765414, _1765416, _1765418]))]], -(hAPP(c_List_Ofoldl(_1765408, _1765404, hAPP(c_COMBC(_1765404, _1765408, _1765408), _1765412), hAPP(_1765414, _1765418)), _1765406) = hAPP(_1765414, hAPP(c_List_Ofoldl(_1765410, _1765404, hAPP(c_COMBC(_1765404, _1765410, _1765410), _1765416), _1765418), _1765406)))], (48831 ^ _782435) ^ [_1765773, _1765775, _1765777, _1765779, _1765781] : [48832 ^ _782435 : [(48833 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765773)), hAPP(hAPP(c_List_Otake(_1765773), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765773)), _1765775)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765777)), _1765779))), _1765775)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765777)), hAPP(hAPP(c_List_Otake(_1765777), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765773)), _1765775)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765777)), _1765779))), _1765779)))], (48835 ^ _782435) ^ [] : [hBOOL(hAPP(_1765781, hAPP(hAPP(c_List_Ozip(_1765773, _1765777), hAPP(hAPP(c_List_Otake(_1765773), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765773)), _1765775)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765777)), _1765779))), _1765775)), hAPP(hAPP(c_List_Otake(_1765777), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765773)), _1765775)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1765777)), _1765779))), _1765779))))]], -(hBOOL(hAPP(_1765781, hAPP(hAPP(c_List_Ozip(_1765773, _1765777), _1765775), _1765779))))], (48839 ^ _782435) ^ [_1766185, _1766187, _1766189, _1766191] : [-(c_New__Random__Sequence_Opos__not__random__dseq(_1766185, _1766187, _1766189, _1766191) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(_1766185, _1766187), _1766189), _1766191)))], (48841 ^ _782435) ^ [_1766230, _1766232, _1766234, _1766236] : [48843 ^ _782435 : [(48844 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1766230), 48842 ^ [_1766230, _1766232, _1766234, _1766236]), hAPP(c_List_Oset(_1766230), _1766232))))], (48846 ^ _782435) ^ [] : [hBOOL(hAPP(_1766234, 48842 ^ [_1766230, _1766232, _1766234, _1766236]))]], -(c_List_OdropWhile(_1766230, _1766234, hAPP(hAPP(c_List_Oappend(_1766230), _1766232), _1766236)) = c_List_OdropWhile(_1766230, _1766234, _1766236))], (48850 ^ _782435) ^ [_1766448, _1766450, _1766452, _1766454, _1766456] : [hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766448)), _1766450) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766452)), _1766454), 48856 ^ _782435 : [(48857 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 48855 ^ [_1766448, _1766450, _1766452, _1766454, _1766456]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1766448)), _1766450))))], (48859 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1766456, hAPP(hAPP(c_List_Onth(_1766448), _1766450), 48855 ^ [_1766448, _1766450, _1766452, _1766454, _1766456])), hAPP(hAPP(c_List_Onth(_1766452), _1766454), 48855 ^ [_1766448, _1766450, _1766452, _1766454, _1766456])))]], -(c_List_Olist__all2(_1766448, _1766452, _1766456, _1766450, _1766454))], (48863 ^ _782435) ^ [_1766806, _1766808] : [class_Orderings_Olinorder(_1766806), hBOOL(hAPP(c_Finite__Set_Ofinite(_1766806), _1766808)), 48871 ^ _782435 : [(48872 ^ _782435) ^ [] : [-(hAPP(c_List_Oset(_1766806), 48870 ^ [_1766806, _1766808]) = _1766808)], (48874 ^ _782435) ^ [] : [-(c_List_Olinorder__class_Osorted(_1766806, 48870 ^ [_1766806, _1766808]))], (48876 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_List_Odistinct(_1766806), 48870 ^ [_1766806, _1766808])))], (48878 ^ _782435) ^ [_1767132] : [-(_1767132 = 48870 ^ [_1766806, _1766808]), hAPP(c_List_Oset(_1766806), _1767132) = _1766808, c_List_Olinorder__class_Osorted(_1766806, _1767132), hBOOL(hAPP(c_List_Odistinct(_1766806), _1767132))]]], (48892 ^ _782435) ^ [_1767363, _1767365, _1767367, _1767369] : [48894 ^ _782435 : [(48895 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767363), 48893 ^ [_1767363, _1767365, _1767367, _1767369]), hAPP(c_List_Oset(_1767363), _1767365))))], (48897 ^ _782435) ^ [] : [hBOOL(hAPP(_1767367, 48893 ^ [_1767363, _1767365, _1767367, _1767369]))]], -(c_List_OtakeWhile(_1767363, _1767367, hAPP(hAPP(c_List_Oappend(_1767363), _1767365), _1767369)) = hAPP(hAPP(c_List_Oappend(_1767363), _1767365), c_List_OtakeWhile(_1767363, _1767367, _1767369)))], (48901 ^ _782435) ^ [_1767597, _1767599, _1767601, _1767603, _1767605] : [class_Orderings_Olinorder(_1767597), 48907 ^ _782435 : [(48908 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1767599), 48906 ^ [_1767597, _1767599, _1767601, _1767603, _1767605]), hAPP(c_List_Oset(_1767599), _1767601))))], (48910 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1767597), hAPP(_1767603, _1767605)), hAPP(_1767603, 48906 ^ [_1767597, _1767599, _1767601, _1767603, _1767605])))]], -(hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(_1767599, _1767597, _1767603), _1767605), _1767601) = hAPP(hAPP(c_List_Olist_OCons(_1767599), _1767605), _1767601))], (48914 ^ _782435) ^ [_1767940, _1767942, _1767944, _1767946, _1767948] : [hAPP(hAPP(c_List_Olist_OCons(_1767940), _1767942), _1767944) = hAPP(c_List_Ofilter(_1767940, _1767946), _1767948), 48919 ^ _782435 : [(48920 ^ _782435) ^ [] : [-(_1767948 = hAPP(hAPP(c_List_Oappend(_1767940), 48917 ^ [_1767940, _1767942, _1767944, _1767946, _1767948]), hAPP(hAPP(c_List_Olist_OCons(_1767940), _1767942), 48918 ^ [_1767940, _1767942, _1767944, _1767946, _1767948])))], (48928 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1767946, _1767942)))], (48930 ^ _782435) ^ [] : [-(_1767944 = hAPP(c_List_Ofilter(_1767940, _1767946), 48918 ^ [_1767940, _1767942, _1767944, _1767946, _1767948]))], (48922 ^ _782435) ^ [_1768254] : [hBOOL(hAPP(hAPP(c_member(_1767940), _1768254), hAPP(c_List_Oset(_1767940), 48917 ^ [_1767940, _1767942, _1767944, _1767946, _1767948]))), hBOOL(hAPP(_1767946, _1768254))]]], (48932 ^ _782435) ^ [_1768458, _1768460, _1768462, _1768464, _1768466] : [-(hAPP(hAPP(c_List_Olist_OCons(_1768458), _1768460), _1768462) = hAPP(c_List_Ofilter(_1768458, _1768464), _1768466)), 48933 ^ _782435 : [(48934 ^ _782435) ^ [_1768586, _1768588] : [_1768466 = hAPP(hAPP(c_List_Oappend(_1768458), _1768588), hAPP(hAPP(c_List_Olist_OCons(_1768458), _1768460), _1768586)), 48940 ^ _782435 : [(48941 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1768458), 48939 ^ [_1768458, _1768460, _1768462, _1768464, _1768466, _1768586, _1768588]), hAPP(c_List_Oset(_1768458), _1768588))))], (48943 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1768464, 48939 ^ [_1768458, _1768460, _1768462, _1768464, _1768466, _1768586, _1768588])))]], hBOOL(hAPP(_1768464, _1768460)), _1768462 = hAPP(c_List_Ofilter(_1768458, _1768464), _1768586)]]], (48953 ^ _782435) ^ [_1769008, _1769010, _1769012, _1769014, _1769016] : [hAPP(c_List_Ofilter(_1769008, _1769010), _1769012) = hAPP(hAPP(c_List_Olist_OCons(_1769008), _1769014), _1769016), 48958 ^ _782435 : [(48959 ^ _782435) ^ [] : [-(_1769012 = hAPP(hAPP(c_List_Oappend(_1769008), 48956 ^ [_1769008, _1769010, _1769012, _1769014, _1769016]), hAPP(hAPP(c_List_Olist_OCons(_1769008), _1769014), 48957 ^ [_1769008, _1769010, _1769012, _1769014, _1769016])))], (48967 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1769010, _1769014)))], (48969 ^ _782435) ^ [] : [-(_1769016 = hAPP(c_List_Ofilter(_1769008, _1769010), 48957 ^ [_1769008, _1769010, _1769012, _1769014, _1769016]))], (48961 ^ _782435) ^ [_1769322] : [hBOOL(hAPP(hAPP(c_member(_1769008), _1769322), hAPP(c_List_Oset(_1769008), 48956 ^ [_1769008, _1769010, _1769012, _1769014, _1769016]))), hBOOL(hAPP(_1769010, _1769322))]]], (48971 ^ _782435) ^ [_1769526, _1769528, _1769530, _1769532, _1769534] : [-(hAPP(c_List_Ofilter(_1769526, _1769528), _1769530) = hAPP(hAPP(c_List_Olist_OCons(_1769526), _1769532), _1769534)), 48972 ^ _782435 : [(48973 ^ _782435) ^ [_1769654, _1769656] : [_1769530 = hAPP(hAPP(c_List_Oappend(_1769526), _1769656), hAPP(hAPP(c_List_Olist_OCons(_1769526), _1769532), _1769654)), 48979 ^ _782435 : [(48980 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1769526), 48978 ^ [_1769526, _1769528, _1769530, _1769532, _1769534, _1769654, _1769656]), hAPP(c_List_Oset(_1769526), _1769656))))], (48982 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1769528, 48978 ^ [_1769526, _1769528, _1769530, _1769532, _1769534, _1769654, _1769656])))]], hBOOL(hAPP(_1769528, _1769532)), _1769534 = hAPP(c_List_Ofilter(_1769526, _1769528), _1769654)]]], (48992 ^ _782435) ^ [_1770052, _1770054, _1770056, _1770058] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770052), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770054)), _1770056))), 48998 ^ _782435 : [(48999 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770054), 48997 ^ [_1770052, _1770054, _1770056, _1770058]), hAPP(c_List_Oset(_1770054), _1770056))))], (49001 ^ _782435) ^ [] : [hBOOL(hAPP(_1770058, 48997 ^ [_1770052, _1770054, _1770056, _1770058]))]], -(hBOOL(hAPP(_1770058, hAPP(hAPP(c_List_Onth(_1770054), _1770056), _1770052))))], (49005 ^ _782435) ^ [_1770338, _1770340, _1770342] : [class_Orderings_Olinorder(_1770338), 49011 ^ _782435 : [(49012 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1770338), 49010 ^ [_1770338, _1770340, _1770342]), hAPP(c_List_Oset(_1770338), _1770340))))], (49014 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1770338), _1770342), 49010 ^ [_1770338, _1770340, _1770342]))]], c_List_Olinorder__class_Osorted(_1770338, _1770340), -(c_List_Olinorder__class_Osorted(_1770338, hAPP(hAPP(c_List_Olist_OCons(_1770338), _1770342), _1770340)))], (49022 ^ _782435) ^ [_1770672, _1770674, _1770676] : [c_List_Olist__ex(_1770672, _1770674, _1770676), 49026 ^ _782435 : [(49027 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49025 ^ [_1770672, _1770674, _1770676]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770672)), _1770676))))], (49029 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1770674, hAPP(hAPP(c_List_Onth(_1770672), _1770676), 49025 ^ [_1770672, _1770674, _1770676]))))]]], (49031 ^ _782435) ^ [_1770842, _1770844, _1770846] : [-(c_List_Olist__ex(_1770842, _1770844, _1770846)), 49032 ^ _782435 : [(49033 ^ _782435) ^ [_1770907] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1770907), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1770842)), _1770846))), hBOOL(hAPP(_1770844, hAPP(hAPP(c_List_Onth(_1770842), _1770846), _1770907)))]]], (49041 ^ _782435) ^ [_1771080, _1771082, _1771084] : [hBOOL(hAPP(hAPP(c_member(_1771080), _1771082), hAPP(c_List_Oset(_1771080), _1771084))), -(_1771084 = hAPP(hAPP(c_List_Oappend(_1771080), 49044 ^ [_1771080, _1771082, _1771084]), hAPP(hAPP(c_List_Olist_OCons(_1771080), _1771082), 49045 ^ [_1771080, _1771082, _1771084])))], (49049 ^ _782435) ^ [_1771239, _1771241, _1771243] : [49050 ^ _782435 : [(49051 ^ _782435) ^ [_1771316, _1771318] : [_1771243 = hAPP(hAPP(c_List_Oappend(_1771239), _1771318), hAPP(hAPP(c_List_Olist_OCons(_1771239), _1771241), _1771316))]], -(hBOOL(hAPP(hAPP(c_member(_1771239), _1771241), hAPP(c_List_Oset(_1771239), _1771243))))], (49065 ^ _782435) ^ [_1771534, _1771536, _1771538, _1771540] : [49066 ^ _782435 : [(49067 ^ _782435) ^ [] : [hBOOL(hAPP(_1771536, _1771538))], (49069 ^ _782435) ^ [] : [c_List_Olist__ex(_1771534, _1771536, _1771540)]], -(c_List_Olist__ex(_1771534, _1771536, hAPP(hAPP(c_List_Olist_OCons(_1771534), _1771538), _1771540)))], (49055 ^ _782435) ^ [_1771420, _1771422, _1771424, _1771426] : [c_List_Olist__ex(_1771420, _1771422, hAPP(hAPP(c_List_Olist_OCons(_1771420), _1771424), _1771426)), -(hBOOL(hAPP(_1771422, _1771424))), -(c_List_Olist__ex(_1771420, _1771422, _1771426))], (49073 ^ _782435) ^ [_1771697, _1771699, _1771701] : [c_List_Olist__ex(_1771697, _1771699, hAPP(c_List_Orev(_1771697), _1771701)), -(c_List_Olist__ex(_1771697, _1771699, _1771701))], (49079 ^ _782435) ^ [_1771786, _1771788, _1771790] : [c_List_Olist__ex(_1771786, _1771788, _1771790), -(c_List_Olist__ex(_1771786, _1771788, hAPP(c_List_Orev(_1771786), _1771790)))], (49085 ^ _782435) ^ [_1771899, _1771901, _1771903] : [c_List_Olist__ex(_1771899, _1771901, _1771903), 49089 ^ _782435 : [(49090 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1771899), 49088 ^ [_1771899, _1771901, _1771903]), hAPP(c_List_Oset(_1771899), _1771903))))], (49092 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1771901, 49088 ^ [_1771899, _1771901, _1771903])))]]], (49094 ^ _782435) ^ [_1772053, _1772055, _1772057] : [-(c_List_Olist__ex(_1772053, _1772055, _1772057)), 49095 ^ _782435 : [(49096 ^ _782435) ^ [_1772110] : [hBOOL(hAPP(hAPP(c_member(_1772053), _1772110), hAPP(c_List_Oset(_1772053), _1772057))), hBOOL(hAPP(_1772055, _1772110))]]], (49114 ^ _782435) ^ [_1772382, _1772384, _1772386, _1772388] : [49115 ^ _782435 : [(49116 ^ _782435) ^ [] : [c_List_Olist__ex(_1772382, _1772384, _1772386)], (49118 ^ _782435) ^ [] : [c_List_Olist__ex(_1772382, _1772384, _1772388)]], -(c_List_Olist__ex(_1772382, _1772384, hAPP(hAPP(c_List_Oappend(_1772382), _1772386), _1772388)))], (49104 ^ _782435) ^ [_1772270, _1772272, _1772274, _1772276] : [c_List_Olist__ex(_1772270, _1772272, hAPP(hAPP(c_List_Oappend(_1772270), _1772274), _1772276)), -(c_List_Olist__ex(_1772270, _1772272, _1772274)), -(c_List_Olist__ex(_1772270, _1772272, _1772276))], (49122 ^ _782435) ^ [_1772537, _1772539] : [c_List_Olist__ex(_1772537, _1772539, c_List_Olist_ONil(_1772537))], (49124 ^ _782435) ^ [_1772583, _1772585, _1772587] : [hBOOL(hAPP(hAPP(c_member(_1772583), _1772585), hAPP(c_List_Oset(_1772583), _1772587))), 49129 ^ _782435 : [(49130 ^ _782435) ^ [] : [-(_1772587 = hAPP(hAPP(c_List_Oappend(_1772583), 49127 ^ [_1772583, _1772585, _1772587]), hAPP(hAPP(c_List_Olist_OCons(_1772583), _1772585), 49128 ^ [_1772583, _1772585, _1772587])))], (49132 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1772583), _1772585), hAPP(c_List_Oset(_1772583), 49127 ^ [_1772583, _1772585, _1772587])))]]], (49134 ^ _782435) ^ [_1772838, _1772840, _1772842] : [-(hBOOL(hAPP(hAPP(c_member(_1772838), _1772840), hAPP(c_List_Oset(_1772838), _1772842)))), 49135 ^ _782435 : [(49136 ^ _782435) ^ [_1772927] : [49137 ^ _782435 : [(49138 ^ _782435) ^ [_1773000] : [_1772842 = hAPP(hAPP(c_List_Oappend(_1772838), _1772927), hAPP(hAPP(c_List_Olist_OCons(_1772838), _1772840), _1773000))]], -(hBOOL(hAPP(hAPP(c_member(_1772838), _1772840), hAPP(c_List_Oset(_1772838), _1772927))))]]], (49144 ^ _782435) ^ [_1773139, _1773141, _1773143] : [hBOOL(hAPP(hAPP(c_member(_1773139), _1773141), hAPP(c_List_Oset(_1773139), _1773143))), 49149 ^ _782435 : [(49150 ^ _782435) ^ [] : [-(_1773143 = hAPP(hAPP(c_List_Oappend(_1773139), 49147 ^ [_1773139, _1773141, _1773143]), hAPP(hAPP(c_List_Olist_OCons(_1773139), _1773141), 49148 ^ [_1773139, _1773141, _1773143])))], (49152 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1773139), _1773141), hAPP(c_List_Oset(_1773139), 49148 ^ [_1773139, _1773141, _1773143])))]]], (49154 ^ _782435) ^ [_1773394, _1773396, _1773398] : [-(hBOOL(hAPP(hAPP(c_member(_1773394), _1773396), hAPP(c_List_Oset(_1773394), _1773398)))), 49155 ^ _782435 : [(49156 ^ _782435) ^ [_1773483, _1773485] : [_1773398 = hAPP(hAPP(c_List_Oappend(_1773394), _1773485), hAPP(hAPP(c_List_Olist_OCons(_1773394), _1773396), _1773483)), -(hBOOL(hAPP(hAPP(c_member(_1773394), _1773396), hAPP(c_List_Oset(_1773394), _1773483))))]]], (49174 ^ _782435) ^ [_1773898, _1773900, _1773902] : [49176 ^ _782435 : [(49177 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), 49175 ^ [_1773898, _1773900, _1773902]), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773898)), _1773902))))], (49179 ^ _782435) ^ [] : [hBOOL(hAPP(_1773900, hAPP(hAPP(c_List_Onth(_1773898), _1773902), 49175 ^ [_1773898, _1773900, _1773902])))]], -(c_List_Olist__all(_1773898, _1773900, _1773902))], (49164 ^ _782435) ^ [_1773684, _1773686, _1773688] : [c_List_Olist__all(_1773684, _1773686, _1773688), 49167 ^ _782435 : [(49168 ^ _782435) ^ [_1773773] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1773773), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1773684)), _1773688))), -(hBOOL(hAPP(_1773686, hAPP(hAPP(c_List_Onth(_1773684), _1773688), _1773773))))]]], (49183 ^ _782435) ^ [_1774106, _1774108, _1774110] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1774106), _1774108)), hBOOL(hAPP(_1774110, c_Orderings_Obot__class_Obot(tc_fun(_1774106, tc_HOL_Obool)))), 49194 ^ _782435 : [(49195 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1774106), 49193 ^ [_1774106, _1774108, _1774110])))], (49197 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(_1774106), 49192 ^ [_1774106, _1774108, _1774110]), 49193 ^ [_1774106, _1774108, _1774110]))], (49199 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1774110, 49193 ^ [_1774106, _1774108, _1774110])))], (49201 ^ _782435) ^ [] : [hBOOL(hAPP(_1774110, hAPP(hAPP(c_Set_Oinsert(_1774106), 49192 ^ [_1774106, _1774108, _1774110]), 49193 ^ [_1774106, _1774108, _1774110])))]], -(hBOOL(hAPP(_1774110, _1774108)))], (49205 ^ _782435) ^ [_1774614, _1774616, _1774618, _1774620] : [c_List_Olist__all(_1774614, _1774616, hAPP(hAPP(c_List_Olist_OCons(_1774614), _1774618), _1774620)), 49208 ^ _782435 : [(49209 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1774616, _1774618)))], (49211 ^ _782435) ^ [] : [-(c_List_Olist__all(_1774614, _1774616, _1774620))]]], (49213 ^ _782435) ^ [_1774741, _1774743, _1774745, _1774747] : [-(c_List_Olist__all(_1774741, _1774743, hAPP(hAPP(c_List_Olist_OCons(_1774741), _1774745), _1774747))), hBOOL(hAPP(_1774743, _1774745)), c_List_Olist__all(_1774741, _1774743, _1774747)], (49223 ^ _782435) ^ [_1774922, _1774924, _1774926] : [c_List_Olist__all(_1774922, _1774924, hAPP(c_List_Orev(_1774922), _1774926)), -(c_List_Olist__all(_1774922, _1774924, _1774926))], (49229 ^ _782435) ^ [_1775011, _1775013, _1775015] : [c_List_Olist__all(_1775011, _1775013, _1775015), -(c_List_Olist__all(_1775011, _1775013, hAPP(c_List_Orev(_1775011), _1775015)))], (49245 ^ _782435) ^ [_1775314, _1775316, _1775318] : [49247 ^ _782435 : [(49248 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775314), 49246 ^ [_1775314, _1775316, _1775318]), hAPP(c_List_Oset(_1775314), _1775318))))], (49250 ^ _782435) ^ [] : [hBOOL(hAPP(_1775316, 49246 ^ [_1775314, _1775316, _1775318]))]], -(c_List_Olist__all(_1775314, _1775316, _1775318))], (49235 ^ _782435) ^ [_1775124, _1775126, _1775128] : [c_List_Olist__all(_1775124, _1775126, _1775128), 49238 ^ _782435 : [(49239 ^ _782435) ^ [_1775205] : [hBOOL(hAPP(hAPP(c_member(_1775124), _1775205), hAPP(c_List_Oset(_1775124), _1775128))), -(hBOOL(hAPP(_1775126, _1775205)))]]], (49254 ^ _782435) ^ [_1775517, _1775519, _1775521, _1775523] : [c_List_Olist__all(_1775517, _1775519, hAPP(hAPP(c_List_Oappend(_1775517), _1775521), _1775523)), 49257 ^ _782435 : [(49258 ^ _782435) ^ [] : [-(c_List_Olist__all(_1775517, _1775519, _1775521))], (49260 ^ _782435) ^ [] : [-(c_List_Olist__all(_1775517, _1775519, _1775523))]]], (49262 ^ _782435) ^ [_1775642, _1775644, _1775646, _1775648] : [-(c_List_Olist__all(_1775642, _1775644, hAPP(hAPP(c_List_Oappend(_1775642), _1775646), _1775648))), c_List_Olist__all(_1775642, _1775644, _1775646), c_List_Olist__all(_1775642, _1775644, _1775648)], (49272 ^ _782435) ^ [_1775803, _1775805] : [-(c_List_Olist__all(_1775803, _1775805, c_List_Olist_ONil(_1775803)))], (49274 ^ _782435) ^ [_1775849, _1775851, _1775853] : [49276 ^ _782435 : [(49277 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1775849), 49275 ^ [_1775849, _1775851, _1775853]), hAPP(c_List_Oset(_1775849), _1775851))))], (49279 ^ _782435) ^ [] : [hBOOL(hAPP(_1775853, 49275 ^ [_1775849, _1775851, _1775853]))]], -(c_List_Olist__all(_1775849, _1775853, _1775851))], (49283 ^ _782435) ^ [_1776025, _1776027, _1776029] : [c_List_Olist__all(_1776025, _1776029, _1776027), 49286 ^ _782435 : [(49287 ^ _782435) ^ [_1776106] : [hBOOL(hAPP(hAPP(c_member(_1776025), _1776106), hAPP(c_List_Oset(_1776025), _1776027))), -(hBOOL(hAPP(_1776029, _1776106)))]]], (49303 ^ _782435) ^ [_1776429, _1776431, _1776433] : [49305 ^ _782435 : [(49306 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1776429), 49304 ^ [_1776429, _1776431, _1776433]), hAPP(c_List_Oset(_1776429), _1776433))))], (49308 ^ _782435) ^ [] : [hBOOL(hAPP(_1776431, 49304 ^ [_1776429, _1776431, _1776433]))]], -(c_List_Olist__all(_1776429, _1776431, _1776433))], (49293 ^ _782435) ^ [_1776239, _1776241, _1776243] : [c_List_Olist__all(_1776239, _1776241, _1776243), 49296 ^ _782435 : [(49297 ^ _782435) ^ [_1776320] : [hBOOL(hAPP(hAPP(c_member(_1776239), _1776320), hAPP(c_List_Oset(_1776239), _1776243))), -(hBOOL(hAPP(_1776241, _1776320)))]]], (49328 ^ _782435) ^ [_1776908, _1776910, _1776912, _1776914] : [-(c_List_Olist__ex1(_1776908, _1776910, hAPP(hAPP(c_List_Olist_OCons(_1776908), _1776912), _1776914))), 49331 ^ _782435 : [(49332 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1776910, _1776912)))], (49334 ^ _782435) ^ [] : [c_List_Olist__all(_1776908, hAPP(hAPP(c_COMBS(_1776908, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1776908), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1776908), c_fNot), _1776910))), hAPP(c_fequal, _1776912)), _1776914)]], 49335 ^ _782435 : [(49336 ^ _782435) ^ [] : [hBOOL(hAPP(_1776910, _1776912))], (49338 ^ _782435) ^ [] : [c_List_Olist__ex1(_1776908, _1776910, _1776914)]]], (49312 ^ _782435) ^ [_1776632, _1776634, _1776636, _1776638] : [c_List_Olist__ex1(_1776632, _1776634, hAPP(hAPP(c_List_Olist_OCons(_1776632), _1776636), _1776638)), 49315 ^ _782435 : [(49316 ^ _782435) ^ [] : [hBOOL(hAPP(_1776634, _1776636)), -(c_List_Olist__all(_1776632, hAPP(hAPP(c_COMBS(_1776632, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1776632), c_fdisj), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1776632), c_fNot), _1776634))), hAPP(c_fequal, _1776636)), _1776638))], (49322 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1776634, _1776636))), -(c_List_Olist__ex1(_1776632, _1776634, _1776638))]]], (49342 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1777246, _1777248] : [c_List_Olist__ex1(_1777246, _1777248, c_List_Olist_ONil(_1777246))], (49346 ^ _782435) ^ [_1777274, _1777276] : [-(c_FunDef_Ois__measure(_1777274, _1777276))], (49348 ^ _782435) ^ [_1777299, _1777301] : [-(c_FunDef_Ois__measure(_1777299, _1777301))], (49350 ^ _782435) ^ [_1777324, _1777326] : [-(c_FunDef_Ois__measure(_1777324, _1777326))], (49352 ^ _782435) ^ [_1777349] : [class_Nat_Osize(_1777349), -(c_FunDef_Ois__measure(_1777349, c_Nat_Osize__class_Osize(_1777349)))], (49358 ^ _782435) ^ [_1777426, _1777428, _1777430] : [c_FunDef_Ois__measure(_1777426, _1777428), -(c_FunDef_Ois__measure(tc_prod(_1777430, _1777426), hAPP(hAPP(c_COMBB(_1777426, tc_Nat_Onat, tc_prod(_1777430, _1777426)), _1777428), c_Product__Type_Osnd(_1777430, _1777426))))], (49364 ^ _782435) ^ [_1777543, _1777545, _1777547] : [c_FunDef_Ois__measure(_1777543, _1777545), -(c_FunDef_Ois__measure(tc_prod(_1777543, _1777547), hAPP(hAPP(c_COMBB(_1777543, tc_Nat_Onat, tc_prod(_1777543, _1777547)), _1777545), c_Product__Type_Ofst(_1777543, _1777547))))], (49370 ^ _782435) ^ [_1777678, _1777680, _1777682] : [c_List_Olist__ex1(_1777678, _1777680, _1777682), 49374 ^ _782435 : [(49375 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1777678), 49373 ^ [_1777678, _1777680, _1777682]), hAPP(c_List_Oset(_1777678), _1777682))))], (49377 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1777680, 49373 ^ [_1777678, _1777680, _1777682])))], (49379 ^ _782435) ^ [_1777924] : [-(_1777924 = 49373 ^ [_1777678, _1777680, _1777682]), hBOOL(hAPP(hAPP(c_member(_1777678), _1777924), hAPP(c_List_Oset(_1777678), _1777682))), hBOOL(hAPP(_1777680, _1777924))]]], (49389 ^ _782435) ^ [_1778111, _1778113, _1778115] : [-(c_List_Olist__ex1(_1778111, _1778113, _1778115)), 49390 ^ _782435 : [(49391 ^ _782435) ^ [_1778205] : [hBOOL(hAPP(hAPP(c_member(_1778111), _1778205), hAPP(c_List_Oset(_1778111), _1778115))), hBOOL(hAPP(_1778113, _1778205)), 49399 ^ _782435 : [(49400 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1778111), 49398 ^ [_1778111, _1778113, _1778115, _1778205]), hAPP(c_List_Oset(_1778111), _1778115))))], (49402 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1778113, 49398 ^ [_1778111, _1778113, _1778115, _1778205])))], (49404 ^ _782435) ^ [] : [49398 ^ [_1778111, _1778113, _1778115, _1778205] = _1778205]]]]], (49408 ^ _782435) ^ [] : [-(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 ^ _782435) ^ [_1778576, _1778578, _1778580, _1778582, _1778584] : [_1778576 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1778578, _1778580, _1778582, _1778584), _1778576) = c_Lazy__Sequence_Ohit__bound(_1778580))], (49416 ^ _782435) ^ [_1778673, _1778675, _1778677, _1778679, _1778681] : [-(_1778673 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Oneg__decr__bind(_1778675, _1778677, _1778679, _1778681), _1778673) = c_Lazy__Sequence_Ohb__bind(_1778675, _1778677, hAPP(_1778679, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1778673), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))), hAPP(hAPP(c_COMBC(_1778675, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1778677))), _1778681), _1778673)))], (49422 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49424 ^ _782435) ^ [] : [-(hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool), c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49426 ^ _782435) ^ [_1778789, _1778791, _1778793, _1778795, _1778797, _1778799, _1778801] : [-(c_New__Random__Sequence_Oneg__decr__bind(_1778789, _1778791, _1778793, _1778795, _1778797, _1778799, _1778801) = c_New__DSequence_Oneg__decr__bind(_1778789, _1778791, hAPP(hAPP(hAPP(_1778793, _1778797), _1778799), _1778801), hAPP(hAPP(c_COMBC(_1778789, 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(_1778791)))), hAPP(hAPP(c_COMBC(_1778789, 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(_1778791))))), hAPP(hAPP(c_COMBC(_1778789, 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(_1778791)))))), _1778795), _1778797)), _1778799)), _1778801)))], (49428 ^ _782435) ^ [_1778906, _1778908, _1778910, _1778912, _1778914] : [-(hAPP(c_New__DSequence_Oneg__bind(_1778906, _1778908, _1778910, _1778912), _1778914) = c_Lazy__Sequence_Ohb__bind(_1778906, _1778908, hAPP(_1778910, _1778914), hAPP(hAPP(c_COMBC(_1778906, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(_1778908))), _1778912), _1778914)))], (49430 ^ _782435) ^ [_1778967, _1778969, _1778971, _1778973, _1778975, _1778977, _1778979] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(_1778967, _1778969, _1778971, _1778973), _1778975), _1778977), _1778979) = c_New__DSequence_Oneg__bind(_1778967, _1778969, hAPP(hAPP(hAPP(_1778971, _1778975), _1778977), _1778979), hAPP(hAPP(c_COMBC(_1778967, 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(_1778969)))), hAPP(hAPP(c_COMBC(_1778967, 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(_1778969))))), hAPP(hAPP(c_COMBC(_1778967, 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(_1778969)))))), _1778973), _1778975)), _1778977)), _1778979)))], (49432 ^ _782435) ^ [_1779108, _1779110, _1779112, _1779114, _1779116] : [_1779108 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral), -(hAPP(c_New__DSequence_Opos__decr__bind(_1779110, _1779112, _1779114, _1779116), _1779108) = c_Lazy__Sequence_Oempty(_1779112))], (49438 ^ _782435) ^ [_1779205, _1779207, _1779209, _1779211, _1779213] : [-(_1779205 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)), -(hAPP(c_New__DSequence_Opos__decr__bind(_1779207, _1779209, _1779211, _1779213), _1779205) = hAPP(c_Lazy__Sequence_Obind(_1779207, _1779209, hAPP(_1779211, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1779205), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))), hAPP(hAPP(c_COMBC(_1779207, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779209)), _1779213), _1779205)))], (49444 ^ _782435) ^ [_1779285, _1779287, _1779289, _1779291, _1779293, _1779295, _1779297] : [-(c_New__Random__Sequence_Opos__decr__bind(_1779285, _1779287, _1779289, _1779291, _1779293, _1779295, _1779297) = c_New__DSequence_Opos__decr__bind(_1779285, _1779287, hAPP(hAPP(hAPP(_1779289, _1779293), _1779295), _1779297), hAPP(hAPP(c_COMBC(_1779285, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779287))), hAPP(hAPP(c_COMBC(_1779285, 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(_1779287)))), hAPP(hAPP(c_COMBC(_1779285, 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(_1779287))))), _1779291), _1779293)), _1779295)), _1779297)))], (49446 ^ _782435) ^ [_1779396, _1779398] : [-(hAPP(c_New__DSequence_Opos__empty(_1779396), _1779398) = c_Lazy__Sequence_Oempty(_1779396))], (49448 ^ _782435) ^ [_1779428, _1779430, _1779432, _1779434] : [-(c_New__Random__Sequence_Opos__empty(_1779428, _1779430, _1779432, _1779434) = c_New__DSequence_Opos__empty(_1779428))], (49450 ^ _782435) ^ [_1779464, _1779466, _1779468, _1779470, _1779472] : [-(hAPP(c_New__DSequence_Opos__bind(_1779464, _1779466, _1779468, _1779470), _1779472) = hAPP(c_Lazy__Sequence_Obind(_1779464, _1779466, hAPP(_1779468, _1779472)), hAPP(hAPP(c_COMBC(_1779464, tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779466)), _1779470), _1779472)))], (49452 ^ _782435) ^ [_1779525, _1779527, _1779529, _1779531, _1779533, _1779535, _1779537] : [-(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(_1779525, _1779527, _1779529, _1779531), _1779533), _1779535), _1779537) = c_New__DSequence_Opos__bind(_1779525, _1779527, hAPP(hAPP(hAPP(_1779529, _1779533), _1779535), _1779537), hAPP(hAPP(c_COMBC(_1779525, tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_Lazy__Sequence_Olazy__sequence(_1779527))), hAPP(hAPP(c_COMBC(_1779525, 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(_1779527)))), hAPP(hAPP(c_COMBC(_1779525, 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(_1779527))))), _1779531), _1779533)), _1779535)), _1779537)))], (49454 ^ _782435) ^ [_1779642, _1779644, _1779646, _1779648] : [-(c_New__Random__Sequence_Oneg__map(_1779642, _1779644, _1779646, _1779648) = c_New__Random__Sequence_Oneg__bind(_1779642, _1779644, _1779648, hAPP(c_Fun_Ocomp(_1779644, 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(_1779644)))))), _1779642, c_New__Random__Sequence_Oneg__single(_1779644)), _1779646)))], (49456 ^ _782435) ^ [_1779707, _1779709, _1779711, _1779713, _1779715] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(_1779707), _1779709), _1779711), _1779713), _1779715) = c_New__DSequence_Oneg__single(_1779707, _1779709))], (49458 ^ _782435) ^ [_1779755, _1779757, _1779759, _1779761] : [-(c_New__Random__Sequence_Opos__map(_1779755, _1779757, _1779759, _1779761) = c_New__Random__Sequence_Opos__bind(_1779755, _1779757, _1779761, hAPP(c_Fun_Ocomp(_1779757, 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(_1779757))))), _1779755, c_New__Random__Sequence_Opos__single(_1779757)), _1779759)))], (49460 ^ _782435) ^ [_1779818, _1779820, _1779822] : [-(hAPP(c_New__DSequence_Oneg__single(_1779818, _1779820), _1779822) = c_Lazy__Sequence_Ohb__single(_1779818, _1779820))], (49462 ^ _782435) ^ [_1779854, _1779856, _1779858, _1779860, _1779862] : [-(hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(_1779854), _1779856), _1779858), _1779860), _1779862) = c_New__DSequence_Opos__single(_1779854, _1779856))], (49464 ^ _782435) ^ [_1779902, _1779904, _1779906] : [-(hAPP(c_New__DSequence_Opos__single(_1779902, _1779904), _1779906) = hAPP(c_Lazy__Sequence_Osingle(_1779902), _1779904))], (49466 ^ _782435) ^ [_1779940, _1779942, _1779944] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779940)), c_List_Osplice(_1779940, _1779942, _1779944)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779940)), _1779942)), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1779940)), _1779944)))], (49468 ^ _782435) ^ [_1779998, _1780000, _1780002, _1780004, _1780006] : [-(c_List_Osplice(_1779998, hAPP(hAPP(c_List_Olist_OCons(_1779998), _1780000), _1780002), hAPP(hAPP(c_List_Olist_OCons(_1779998), _1780004), _1780006)) = hAPP(hAPP(c_List_Olist_OCons(_1779998), _1780000), hAPP(hAPP(c_List_Olist_OCons(_1779998), _1780004), c_List_Osplice(_1779998, _1780002, _1780006))))], (49470 ^ _782435) ^ [_1780069, _1780071] : [-(c_List_Osplice(_1780069, c_List_Olist_ONil(_1780069), _1780071) = _1780071)], (49472 ^ _782435) ^ [_1780100, _1780102] : [-(c_List_Osplice(_1780100, _1780102, c_List_Olist_ONil(_1780100)) = _1780102)], (49474 ^ _782435) ^ [_1780131, _1780133, _1780135] : [-(c_List_Osplice(_1780131, hAPP(hAPP(c_List_Olist_OCons(_1780131), _1780133), _1780135), c_List_Olist_ONil(_1780131)) = hAPP(hAPP(c_List_Olist_OCons(_1780131), _1780133), _1780135))], (49476 ^ _782435) ^ [_1780180, _1780182, _1780184, _1780186] : [-(c_Lazy__Sequence_Oproduct(_1780180, _1780182, _1780184, _1780186) = hAPP(c_Lazy__Sequence_Obind(_1780180, tc_prod(_1780180, _1780182), _1780184), hAPP(hAPP(c_COMBB(tc_fun(_1780182, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780180, _1780182))), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780180, _1780182)), _1780180), c_Lazy__Sequence_Obind(_1780182, tc_prod(_1780180, _1780182), _1780186)), hAPP(hAPP(c_COMBB(tc_fun(_1780182, tc_prod(_1780180, _1780182)), tc_fun(_1780182, tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780180, _1780182))), _1780180), hAPP(c_COMBB(tc_prod(_1780180, _1780182), tc_Lazy__Sequence_Olazy__sequence(tc_prod(_1780180, _1780182)), _1780182), c_Lazy__Sequence_Osingle(tc_prod(_1780180, _1780182)))), c_Product__Type_OPair(_1780180, _1780182)))))], (49478 ^ _782435) ^ [_1780301, _1780303, _1780305, _1780307] : [c_Fun_Obij__betw(_1780301, _1780303, _1780305, c_Orderings_Otop__class_Otop(tc_fun(_1780301, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1780303, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1780301, _1780303, _1780305), hAPP(c_Set_OCollect(_1780301), _1780307)) = hAPP(c_Set_OCollect(_1780303), hAPP(hAPP(c_COMBB(_1780301, tc_HOL_Obool, _1780303), _1780307), c_Hilbert__Choice_Oinv__into(_1780301, _1780303, c_Orderings_Otop__class_Otop(tc_fun(_1780301, tc_HOL_Obool)), _1780305))))], (49484 ^ _782435) ^ [_1780482, _1780484, _1780486, _1780488, _1780490, _1780492] : [c_Fun_Oinj__on(_1780482, _1780484, _1780486, _1780488), hBOOL(hAPP(hAPP(c_member(_1780482), _1780490), _1780488)), hAPP(_1780486, _1780490) = _1780492, -(hAPP(c_Hilbert__Choice_Oinv__into(_1780482, _1780484, _1780488, _1780486), _1780492) = _1780490)], (49498 ^ _782435) ^ [_1780727, _1780729, _1780731, _1780733, _1780735] : [c_Fun_Oinj__on(_1780727, _1780729, _1780731, _1780733), hBOOL(hAPP(hAPP(c_member(_1780727), _1780735), _1780733)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1780727, _1780729, _1780733, _1780731), hAPP(_1780731, _1780735)) = _1780735)], (49508 ^ _782435) ^ [_1780908, _1780910, _1780912, _1780914] : [c_Fun_Oinj__on(_1780908, _1780910, _1780912, c_Orderings_Otop__class_Otop(tc_fun(_1780908, tc_HOL_Obool))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1780908, _1780910, c_Orderings_Otop__class_Otop(tc_fun(_1780908, tc_HOL_Obool)), _1780912), hAPP(_1780912, _1780914)) = _1780914)], (49514 ^ _782435) ^ [_1781035, _1781037, _1781039, _1781041, _1781043] : [c_Fun_Oinj__on(_1781035, _1781037, _1781039, c_Orderings_Otop__class_Otop(tc_fun(_1781035, tc_HOL_Obool))), hAPP(_1781039, _1781041) = _1781043, -(hAPP(c_Hilbert__Choice_Oinv__into(_1781035, _1781037, c_Orderings_Otop__class_Otop(tc_fun(_1781035, tc_HOL_Obool)), _1781039), _1781043) = _1781041)], (49524 ^ _782435) ^ [_1781222, _1781224, _1781226, _1781228, _1781230] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1781222, _1781224, _1781226, _1781228), _1781230) = c_Hilbert__Choice_OEps(_1781222, hAPP(hAPP(c_COMBS(_1781222, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1781222), c_fconj), hAPP(hAPP(c_COMBC(_1781222, tc_fun(_1781222, tc_HOL_Obool), tc_HOL_Obool), c_member(_1781222)), _1781226))), hAPP(hAPP(c_COMBC(_1781222, _1781224, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1781224, tc_fun(_1781224, tc_HOL_Obool), _1781222), c_fequal), _1781228)), _1781230))))], (49526 ^ _782435) ^ [_1781322, _1781324, _1781326] : [c_Fun_Obij__betw(_1781322, _1781324, _1781326, c_Orderings_Otop__class_Otop(tc_fun(_1781322, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781324, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1781324, _1781322, c_Orderings_Otop__class_Otop(tc_fun(_1781324, tc_HOL_Obool)), c_Hilbert__Choice_Oinv__into(_1781322, _1781324, c_Orderings_Otop__class_Otop(tc_fun(_1781322, tc_HOL_Obool)), _1781326)) = _1781326)], (49532 ^ _782435) ^ [_1781467, _1781469, _1781471] : [c_Fun_Obij__betw(_1781467, _1781469, _1781471, c_Orderings_Otop__class_Otop(tc_fun(_1781467, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781469, tc_HOL_Obool))), -(c_Fun_Obij__betw(_1781469, _1781467, c_Hilbert__Choice_Oinv__into(_1781467, _1781469, c_Orderings_Otop__class_Otop(tc_fun(_1781467, tc_HOL_Obool)), _1781471), c_Orderings_Otop__class_Otop(tc_fun(_1781469, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1781467, tc_HOL_Obool))))], (49538 ^ _782435) ^ [_1781618, _1781620, _1781622, _1781624, _1781626] : [c_Fun_Obij__betw(_1781618, _1781620, _1781622, _1781624, _1781626), -(c_Fun_Obij__betw(_1781620, _1781618, c_Hilbert__Choice_Oinv__into(_1781618, _1781620, _1781624, _1781622), _1781626, _1781624))], (49544 ^ _782435) ^ [_1781723, _1781725, _1781727, _1781729, _1781731, _1781733] : [c_Fun_Obij__betw(_1781723, _1781725, _1781727, _1781729, _1781731), hBOOL(hAPP(hAPP(c_member(_1781723), _1781733), _1781729)), -(hAPP(c_Hilbert__Choice_Oinv__into(_1781725, _1781723, _1781731, c_Hilbert__Choice_Oinv__into(_1781723, _1781725, _1781729, _1781727)), _1781733) = hAPP(_1781727, _1781733))], (49554 ^ _782435) ^ [_1781920, _1781922, _1781924, _1781926, _1781928, _1781930] : [hAPP(c_Set_Oimage(_1781920, _1781922, _1781924), _1781926) = _1781928, hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1781922, tc_HOL_Obool)), _1781930), _1781928)), -(hAPP(c_Set_Oimage(_1781920, _1781922, _1781924), hAPP(c_Set_Oimage(_1781922, _1781920, c_Hilbert__Choice_Oinv__into(_1781920, _1781922, _1781926, _1781924)), _1781930)) = _1781930)], (49564 ^ _782435) ^ [_1782155, _1782157, _1782159] : [hAPP(c_Set_Oimage(_1782155, _1782157, _1782159), c_Orderings_Otop__class_Otop(tc_fun(_1782155, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782157, tc_HOL_Obool)), 49567 ^ _782435 : [(49568 ^ _782435) ^ [_1782266] : [-(hAPP(_1782159, hAPP(c_Hilbert__Choice_Oinv__into(_1782155, _1782157, c_Orderings_Otop__class_Otop(tc_fun(_1782155, tc_HOL_Obool)), _1782159), _1782266)) = _1782266)]]], (49570 ^ _782435) ^ [_1782305, _1782307, _1782309] : [hAPP(_1782309, hAPP(c_Hilbert__Choice_Oinv__into(_1782305, _1782307, c_Orderings_Otop__class_Otop(tc_fun(_1782305, tc_HOL_Obool)), _1782309), 49571 ^ [_1782305, _1782307, _1782309])) = 49571 ^ [_1782305, _1782307, _1782309], -(hAPP(c_Set_Oimage(_1782305, _1782307, _1782309), c_Orderings_Otop__class_Otop(tc_fun(_1782305, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782307, tc_HOL_Obool)))], (49577 ^ _782435) ^ [_1782505, _1782507, _1782509, _1782511] : [hAPP(c_Set_Oimage(_1782505, _1782507, _1782509), c_Orderings_Otop__class_Otop(tc_fun(_1782505, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782507, tc_HOL_Obool)), -(hAPP(_1782509, hAPP(c_Hilbert__Choice_Oinv__into(_1782505, _1782507, c_Orderings_Otop__class_Otop(tc_fun(_1782505, tc_HOL_Obool)), _1782509), _1782511)) = _1782511)], (49583 ^ _782435) ^ [_1782652, _1782654, _1782656, _1782658] : [hAPP(c_Set_Oimage(_1782652, _1782654, _1782656), c_Orderings_Otop__class_Otop(tc_fun(_1782652, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1782654, tc_HOL_Obool)), -(hAPP(c_Set_Oimage(_1782652, _1782654, _1782656), hAPP(c_Set_Oimage(_1782654, _1782652, c_Hilbert__Choice_Oinv__into(_1782652, _1782654, c_Orderings_Otop__class_Otop(tc_fun(_1782652, tc_HOL_Obool)), _1782656)), _1782658)) = _1782658)], (49589 ^ _782435) ^ [_1782815, _1782817, _1782819, _1782821, _1782823, _1782825] : [hAPP(c_Hilbert__Choice_Oinv__into(_1782815, _1782817, _1782819, _1782821), _1782823) = hAPP(c_Hilbert__Choice_Oinv__into(_1782815, _1782817, _1782819, _1782821), _1782825), hBOOL(hAPP(hAPP(c_member(_1782817), _1782823), hAPP(c_Set_Oimage(_1782815, _1782817, _1782821), _1782819))), hBOOL(hAPP(hAPP(c_member(_1782817), _1782825), hAPP(c_Set_Oimage(_1782815, _1782817, _1782821), _1782819))), -(_1782823 = _1782825)], (49603 ^ _782435) ^ [_1783108, _1783110, _1783112, _1783114, _1783116] : [hBOOL(hAPP(hAPP(c_member(_1783108), _1783110), hAPP(c_Set_Oimage(_1783112, _1783108, _1783114), _1783116))), -(hBOOL(hAPP(hAPP(c_member(_1783112), hAPP(c_Hilbert__Choice_Oinv__into(_1783112, _1783108, _1783116, _1783114), _1783110)), _1783116)))], (49609 ^ _782435) ^ [_1783249, _1783251, _1783253, _1783255, _1783257] : [hBOOL(hAPP(hAPP(c_member(_1783249), _1783251), hAPP(c_Set_Oimage(_1783253, _1783249, _1783255), _1783257))), -(hAPP(_1783255, hAPP(c_Hilbert__Choice_Oinv__into(_1783253, _1783249, _1783257, _1783255), _1783251)) = _1783251)], (49615 ^ _782435) ^ [_1783382] : [-(c_Hilbert__Choice_Oinv__into(_1783382, _1783382, c_Orderings_Otop__class_Otop(tc_fun(_1783382, tc_HOL_Obool)), c_Fun_Oid(_1783382)) = c_Fun_Oid(_1783382))], (49617 ^ _782435) ^ [_1783419, _1783421, _1783423, _1783425] : [-(hAPP(c_Hilbert__Choice_Oinv__into(_1783419, _1783421, c_Orderings_Otop__class_Otop(tc_fun(_1783419, tc_HOL_Obool)), _1783423), _1783425) = c_Hilbert__Choice_OEps(_1783419, hAPP(hAPP(c_COMBC(_1783419, _1783421, tc_HOL_Obool), hAPP(hAPP(c_COMBB(_1783421, tc_fun(_1783421, tc_HOL_Obool), _1783419), c_fequal), _1783423)), _1783425)))], (49619 ^ _782435) ^ [_1783487, _1783489, _1783491, _1783493, _1783495] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783487, tc_HOL_Obool)), _1783489), hAPP(c_Set_Oimage(_1783491, _1783487, _1783493), _1783495))), -(c_Fun_Oinj__on(_1783487, _1783491, c_Hilbert__Choice_Oinv__into(_1783491, _1783487, _1783495, _1783493), _1783489))], (49625 ^ _782435) ^ [_1783618, _1783620, _1783622, _1783624, _1783626] : [c_Fun_Oinj__on(_1783618, _1783620, _1783622, _1783624), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(_1783618, tc_HOL_Obool)), _1783626), _1783624)), -(hAPP(c_Set_Oimage(_1783620, _1783618, c_Hilbert__Choice_Oinv__into(_1783618, _1783620, _1783624, _1783622)), hAPP(c_Set_Oimage(_1783618, _1783620, _1783622), _1783626)) = _1783626)], (49635 ^ _782435) ^ [_1783821, _1783823, _1783825] : [c_Fun_Oinj__on(_1783821, _1783823, _1783825, c_Orderings_Otop__class_Otop(tc_fun(_1783821, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1783823, _1783821, c_Hilbert__Choice_Oinv__into(_1783821, _1783823, c_Orderings_Otop__class_Otop(tc_fun(_1783821, tc_HOL_Obool)), _1783825)), c_Orderings_Otop__class_Otop(tc_fun(_1783823, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1783821, tc_HOL_Obool)))], (49641 ^ _782435) ^ [_1783968, _1783970, _1783972, _1783974] : [c_Fun_Oinj__on(_1783968, _1783970, _1783972, c_Orderings_Otop__class_Otop(tc_fun(_1783968, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1783970, _1783968, c_Hilbert__Choice_Oinv__into(_1783968, _1783970, c_Orderings_Otop__class_Otop(tc_fun(_1783968, tc_HOL_Obool)), _1783972)), hAPP(c_Set_Oimage(_1783968, _1783970, _1783972), _1783974)) = _1783974)], (49647 ^ _782435) ^ [_1784111, _1784113, _1784115, _1784117] : [c_Fun_Oinj__on(_1784111, _1784113, _1784115, c_Orderings_Otop__class_Otop(tc_fun(_1784111, tc_HOL_Obool))), -(hAPP(c_Set_Oimage(_1784113, _1784111, c_Hilbert__Choice_Oinv__into(_1784111, _1784113, c_Orderings_Otop__class_Otop(tc_fun(_1784111, tc_HOL_Obool)), _1784115)), hAPP(c_Set_Oimage(_1784111, _1784113, _1784115), _1784117)) = _1784117)], (49653 ^ _782435) ^ [_1784254, _1784256, _1784258] : [hAPP(c_Set_Oimage(_1784254, _1784256, _1784258), c_Orderings_Otop__class_Otop(tc_fun(_1784254, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1784256, tc_HOL_Obool)), -(c_Fun_Oinj__on(_1784256, _1784254, c_Hilbert__Choice_Oinv__into(_1784254, _1784256, c_Orderings_Otop__class_Otop(tc_fun(_1784254, tc_HOL_Obool)), _1784258), c_Orderings_Otop__class_Otop(tc_fun(_1784256, tc_HOL_Obool))))], (49659 ^ _782435) ^ [_1784401, _1784403, _1784405, _1784407, _1784409] : [c_Fun_Oinj__on(_1784401, _1784403, _1784405, c_Orderings_Otop__class_Otop(tc_fun(_1784401, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1784403, _1784407, _1784401, hAPP(c_Fun_Ocomp(_1784401, _1784407, _1784403, _1784409), c_Hilbert__Choice_Oinv__into(_1784401, _1784403, c_Orderings_Otop__class_Otop(tc_fun(_1784401, tc_HOL_Obool)), _1784405))), _1784405) = _1784409)], (49665 ^ _782435) ^ [_1784550, _1784552, _1784554, _1784556, _1784558] : [c_Fun_Obij__betw(_1784550, _1784552, _1784554, c_Orderings_Otop__class_Otop(tc_fun(_1784550, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1784552, tc_HOL_Obool))), c_Fun_Obij__betw(_1784556, _1784550, _1784558, c_Orderings_Otop__class_Otop(tc_fun(_1784556, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1784550, tc_HOL_Obool))), -(c_Hilbert__Choice_Oinv__into(_1784556, _1784552, c_Orderings_Otop__class_Otop(tc_fun(_1784556, tc_HOL_Obool)), hAPP(c_Fun_Ocomp(_1784550, _1784552, _1784556, _1784554), _1784558)) = hAPP(c_Fun_Ocomp(_1784550, _1784556, _1784552, c_Hilbert__Choice_Oinv__into(_1784556, _1784550, c_Orderings_Otop__class_Otop(tc_fun(_1784556, tc_HOL_Obool)), _1784558)), c_Hilbert__Choice_Oinv__into(_1784550, _1784552, c_Orderings_Otop__class_Otop(tc_fun(_1784550, tc_HOL_Obool)), _1784554)))], (49675 ^ _782435) ^ [_1784835, _1784837, _1784839, _1784841, _1784843, _1784845, _1784847] : [c_Fun_Oinj__on(_1784835, _1784837, _1784839, hAPP(c_Set_Oimage(_1784841, _1784835, _1784843), _1784845)), c_Fun_Oinj__on(_1784841, _1784835, _1784843, _1784845), hBOOL(hAPP(hAPP(c_member(_1784837), _1784847), hAPP(c_Set_Oimage(_1784835, _1784837, _1784839), hAPP(c_Set_Oimage(_1784841, _1784835, _1784843), _1784845)))), -(hAPP(c_Hilbert__Choice_Oinv__into(_1784841, _1784837, _1784845, hAPP(c_Fun_Ocomp(_1784835, _1784837, _1784841, _1784839), _1784843)), _1784847) = hAPP(hAPP(c_Fun_Ocomp(_1784835, _1784841, _1784837, c_Hilbert__Choice_Oinv__into(_1784841, _1784835, _1784845, _1784843)), c_Hilbert__Choice_Oinv__into(_1784835, _1784837, hAPP(c_Set_Oimage(_1784841, _1784835, _1784843), _1784845), _1784839)), _1784847))], (49689 ^ _782435) ^ [_1785216, _1785218, _1785220] : [hAPP(c_Set_Oimage(_1785216, _1785218, _1785220), c_Orderings_Otop__class_Otop(tc_fun(_1785216, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785218, tc_HOL_Obool)), -(hAPP(c_Fun_Ocomp(_1785216, _1785218, _1785218, _1785220), c_Hilbert__Choice_Oinv__into(_1785216, _1785218, c_Orderings_Otop__class_Otop(tc_fun(_1785216, tc_HOL_Obool)), _1785220)) = c_Fun_Oid(_1785218))], (49695 ^ _782435) ^ [_1785365, _1785367, _1785369] : [hAPP(c_Fun_Ocomp(_1785365, _1785367, _1785367, _1785369), c_Hilbert__Choice_Oinv__into(_1785365, _1785367, c_Orderings_Otop__class_Otop(tc_fun(_1785365, tc_HOL_Obool)), _1785369)) = c_Fun_Oid(_1785367), -(hAPP(c_Set_Oimage(_1785365, _1785367, _1785369), c_Orderings_Otop__class_Otop(tc_fun(_1785365, tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(_1785367, tc_HOL_Obool)))], (49701 ^ _782435) ^ [_1785520, _1785522, _1785524] : [c_Fun_Oinj__on(_1785520, _1785522, _1785524, c_Orderings_Otop__class_Otop(tc_fun(_1785520, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785522, _1785520, _1785520, c_Hilbert__Choice_Oinv__into(_1785520, _1785522, c_Orderings_Otop__class_Otop(tc_fun(_1785520, tc_HOL_Obool)), _1785524)), _1785524) = c_Fun_Oid(_1785520))], (49707 ^ _782435) ^ [_1785671, _1785673, _1785675] : [c_Fun_Oinj__on(_1785671, _1785673, _1785675, c_Orderings_Otop__class_Otop(tc_fun(_1785671, tc_HOL_Obool))), -(hAPP(c_Fun_Ocomp(_1785673, _1785671, _1785671, c_Hilbert__Choice_Oinv__into(_1785671, _1785673, c_Orderings_Otop__class_Otop(tc_fun(_1785671, tc_HOL_Obool)), _1785675)), _1785675) = c_Fun_Oid(_1785671))], (49713 ^ _782435) ^ [_1785800, _1785802, _1785804] : [hAPP(c_Fun_Ocomp(_1785802, _1785800, _1785800, c_Hilbert__Choice_Oinv__into(_1785800, _1785802, c_Orderings_Otop__class_Otop(tc_fun(_1785800, tc_HOL_Obool)), _1785804)), _1785804) = c_Fun_Oid(_1785800), -(c_Fun_Oinj__on(_1785800, _1785802, _1785804, c_Orderings_Otop__class_Otop(tc_fun(_1785800, tc_HOL_Obool))))], (49719 ^ _782435) ^ [_1785935, _1785937, _1785939, _1785941] : [c_Fun_Obij__betw(_1785935, _1785937, _1785939, c_Orderings_Otop__class_Otop(tc_fun(_1785935, tc_HOL_Obool)), c_Orderings_Otop__class_Otop(tc_fun(_1785937, tc_HOL_Obool))), -(hAPP(c_Set_Ovimage(_1785935, _1785937, _1785939), _1785941) = hAPP(c_Set_Oimage(_1785937, _1785935, c_Hilbert__Choice_Oinv__into(_1785935, _1785937, c_Orderings_Otop__class_Otop(tc_fun(_1785935, tc_HOL_Obool)), _1785939)), _1785941))], (49725 ^ _782435) ^ [_1786090, _1786092, _1786094, _1786096, _1786098] : [c_Fun_Oinj__on(_1786090, _1786092, _1786094, c_Orderings_Otop__class_Otop(tc_fun(_1786090, tc_HOL_Obool))), 49731 ^ _782435 : [(49732 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1786092), 49730 ^ [_1786090, _1786092, _1786094, _1786096, _1786098]), hAPP(c_Set_Oimage(_1786090, _1786092, _1786094), c_Orderings_Otop__class_Otop(tc_fun(_1786090, tc_HOL_Obool))))))], (49734 ^ _782435) ^ [] : [hBOOL(hAPP(_1786096, hAPP(c_Hilbert__Choice_Oinv__into(_1786090, _1786092, c_Orderings_Otop__class_Otop(tc_fun(_1786090, tc_HOL_Obool)), _1786094), 49730 ^ [_1786090, _1786092, _1786094, _1786096, _1786098])))]], -(hBOOL(hAPP(_1786096, _1786098)))], (49738 ^ _782435) ^ [_1786416, _1786418] : [class_Lazy__Sequence_Osmall__lazy(_1786416), -(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786416), _1786418) = c_Lazy__Sequence_Oappend(tc_List_Olist(_1786416), hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(_1786416)), c_List_Olist_ONil(_1786416)), hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786416))), hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), c_Groups_Ozero__class_Ozero(tc_Int_Oint)), _1786418)), hAPP(c_Lazy__Sequence_Obind(tc_prod(_1786416, tc_List_Olist(_1786416)), tc_List_Olist(_1786416), c_Lazy__Sequence_Oproduct(_1786416, tc_List_Olist(_1786416), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786416, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786418), c_Groups_Oone__class_Oone(tc_Int_Oint))), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(_1786416), hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint), _1786418), c_Groups_Oone__class_Oone(tc_Int_Oint))))), hAPP(c_Product__Type_Oprod_Oprod__case(_1786416, tc_List_Olist(_1786416), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786416))), hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(_1786416), tc_List_Olist(_1786416)), tc_fun(tc_List_Olist(_1786416), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786416))), _1786416), hAPP(c_COMBB(tc_List_Olist(_1786416), tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(_1786416)), tc_List_Olist(_1786416)), c_Lazy__Sequence_Osingle(tc_List_Olist(_1786416)))), c_List_Olist_OCons(_1786416))))), c_Lazy__Sequence_Oempty(tc_List_Olist(_1786416)))))], (49744 ^ _782435) ^ [_1786777, _1786779, _1786781] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(_1786777, _1786779), _1786781) = c_Lazy__Sequence_Oproduct(_1786777, _1786779, c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786777, _1786781), c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(_1786779, _1786781))), class_Lazy__Sequence_Osmall__lazy(_1786777), class_Lazy__Sequence_Osmall__lazy(_1786779)], (49754 ^ _782435) ^ [_1786940, _1786942, _1786944, _1786946] : [-(hAPP(c_New__DSequence_Opos__union(_1786940, _1786942, _1786944), _1786946) = c_Lazy__Sequence_Oappend(_1786940, hAPP(_1786942, _1786946), hAPP(_1786944, _1786946)))], (49756 ^ _782435) ^ [_1787001, _1787003] : [c_Wellfounded_Oacyclic(_1787001, hAPP(c_Set_OCollect(tc_prod(_1787001, _1787001)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787001, _1787001, tc_HOL_Obool), c_Predicate_Oconversep(_1787001, _1787001, _1787003)))), -(c_Wellfounded_Oacyclic(_1787001, hAPP(c_Set_OCollect(tc_prod(_1787001, _1787001)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787001, _1787001, tc_HOL_Obool), _1787003))))], (49762 ^ _782435) ^ [_1787142, _1787144] : [c_Wellfounded_Oacyclic(_1787142, hAPP(c_Set_OCollect(tc_prod(_1787142, _1787142)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787142, _1787142, tc_HOL_Obool), _1787144))), -(c_Wellfounded_Oacyclic(_1787142, hAPP(c_Set_OCollect(tc_prod(_1787142, _1787142)), hAPP(c_Product__Type_Oprod_Oprod__case(_1787142, _1787142, tc_HOL_Obool), c_Predicate_Oconversep(_1787142, _1787142, _1787144)))))], (49768 ^ _782435) ^ [_1787289, _1787291, _1787293, _1787295] : [-(c_Predicate_Oconversep(_1787289, _1787291, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1787289, tc_fun(_1787291, tc_HOL_Obool))), _1787293), _1787295)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1787291, tc_fun(_1787289, tc_HOL_Obool))), c_Predicate_Oconversep(_1787289, _1787291, _1787293)), c_Predicate_Oconversep(_1787289, _1787291, _1787295)))], (49770 ^ _782435) ^ [_1787358] : [-(c_Predicate_Oconversep(_1787358, _1787358, c_fequal) = c_fequal)], (49772 ^ _782435) ^ [_1787385, _1787387, _1787389] : [-(c_Predicate_Oconversep(_1787385, _1787387, c_Predicate_Oconversep(_1787387, _1787385, _1787389)) = _1787389)], (49774 ^ _782435) ^ [_1787444, _1787446, _1787448, _1787450, _1787452] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787444, _1787446, _1787448), _1787450), _1787452)), -(hBOOL(hAPP(hAPP(_1787448, _1787452), _1787450)))], (49780 ^ _782435) ^ [_1787551, _1787553, _1787555, _1787557, _1787559] : [hBOOL(hAPP(hAPP(_1787555, _1787559), _1787557)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787551, _1787553, _1787555), _1787557), _1787559)))], (49786 ^ _782435) ^ [_1787688, _1787690, _1787692, _1787694, _1787696] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787688, _1787690, _1787692), _1787694), _1787696)), -(hBOOL(hAPP(hAPP(_1787692, _1787696), _1787694)))], (49792 ^ _782435) ^ [_1787795, _1787797, _1787799, _1787801, _1787803] : [hBOOL(hAPP(hAPP(_1787799, _1787803), _1787801)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787795, _1787797, _1787799), _1787801), _1787803)))], (49798 ^ _782435) ^ [_1787908, _1787910, _1787912, _1787914, _1787916] : [hBOOL(hAPP(hAPP(_1787908, _1787910), _1787912)), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1787914, _1787916, _1787908), _1787912), _1787910)))], (49804 ^ _782435) ^ [_1788019, _1788021, _1788023, _1788025, _1788027] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788019, _1788021, _1788023), _1788025), _1788027)), -(hBOOL(hAPP(hAPP(_1788023, _1788027), _1788025)))], (49810 ^ _782435) ^ [_1788148, _1788150, _1788152] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788148, _1788148, hAPP(hAPP(c_COMBB(tc_fun(_1788148, tc_HOL_Obool), tc_fun(_1788148, tc_HOL_Obool), _1788148), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788148), c_fNot)), c_fequal)), _1788150), _1788152)), _1788150 = _1788152], (49816 ^ _782435) ^ [_1788286, _1788288, _1788290] : [-(_1788288 = _1788290), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788286, _1788286, hAPP(hAPP(c_COMBB(tc_fun(_1788286, tc_HOL_Obool), tc_fun(_1788286, tc_HOL_Obool), _1788286), hAPP(c_COMBB(tc_HOL_Obool, tc_HOL_Obool, _1788286), c_fNot)), c_fequal)), _1788288), _1788290)))], (49822 ^ _782435) ^ [_1788358, _1788360, _1788362, _1788364, _1788366] : [-(c_Predicate_Oconversep(_1788358, _1788360, c_Predicate_Opred__comp(_1788358, _1788362, _1788360, _1788364, _1788366)) = c_Predicate_Opred__comp(_1788360, _1788362, _1788358, c_Predicate_Oconversep(_1788362, _1788360, _1788366), c_Predicate_Oconversep(_1788358, _1788362, _1788364)))], (49824 ^ _782435) ^ [_1788413, _1788415, _1788417, _1788419] : [-(c_Predicate_Oconversep(_1788413, _1788415, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788413, tc_fun(_1788415, tc_HOL_Obool))), _1788417), _1788419)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(_1788415, tc_fun(_1788413, tc_HOL_Obool))), c_Predicate_Oconversep(_1788413, _1788415, _1788417)), c_Predicate_Oconversep(_1788413, _1788415, _1788419)))], (49826 ^ _782435) ^ [_1788506, _1788508, _1788510, _1788512, _1788514] : [hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788506, _1788508, hAPP(hAPP(c_COMBC(_1788506, tc_fun(tc_prod(_1788506, _1788508), tc_HOL_Obool), tc_fun(_1788508, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788508, tc_fun(tc_fun(tc_prod(_1788506, _1788508), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1788506, _1788508), tc_HOL_Obool), tc_fun(_1788508, tc_HOL_Obool)), _1788506), c_COMBC(_1788508, tc_fun(tc_prod(_1788506, _1788508), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788508, tc_prod(_1788506, _1788508)), tc_fun(_1788508, tc_fun(tc_fun(tc_prod(_1788506, _1788508), tc_HOL_Obool), tc_HOL_Obool)), _1788506), hAPP(c_COMBB(tc_prod(_1788506, _1788508), tc_fun(tc_fun(tc_prod(_1788506, _1788508), tc_HOL_Obool), tc_HOL_Obool), _1788508), c_member(tc_prod(_1788506, _1788508)))), c_Product__Type_OPair(_1788506, _1788508)))), _1788510)), _1788512), _1788514)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1788508, _1788506)), hAPP(hAPP(c_Product__Type_OPair(_1788508, _1788506), _1788512), _1788514)), hAPP(c_Relation_Oconverse(_1788506, _1788508), _1788510))))], (49832 ^ _782435) ^ [_1788889, _1788891, _1788893, _1788895, _1788897] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1788891, _1788889)), hAPP(hAPP(c_Product__Type_OPair(_1788891, _1788889), _1788895), _1788897)), hAPP(c_Relation_Oconverse(_1788889, _1788891), _1788893))), -(hBOOL(hAPP(hAPP(c_Predicate_Oconversep(_1788889, _1788891, hAPP(hAPP(c_COMBC(_1788889, tc_fun(tc_prod(_1788889, _1788891), tc_HOL_Obool), tc_fun(_1788891, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788891, tc_fun(tc_fun(tc_prod(_1788889, _1788891), tc_HOL_Obool), tc_HOL_Obool)), tc_fun(tc_fun(tc_prod(_1788889, _1788891), tc_HOL_Obool), tc_fun(_1788891, tc_HOL_Obool)), _1788889), c_COMBC(_1788891, tc_fun(tc_prod(_1788889, _1788891), tc_HOL_Obool), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1788891, tc_prod(_1788889, _1788891)), tc_fun(_1788891, tc_fun(tc_fun(tc_prod(_1788889, _1788891), tc_HOL_Obool), tc_HOL_Obool)), _1788889), hAPP(c_COMBB(tc_prod(_1788889, _1788891), tc_fun(tc_fun(tc_prod(_1788889, _1788891), tc_HOL_Obool), tc_HOL_Obool), _1788891), c_member(tc_prod(_1788889, _1788891)))), c_Product__Type_OPair(_1788889, _1788891)))), _1788893)), _1788895), _1788897)))], (49838 ^ _782435) ^ [_1789278, _1789280, _1789282, _1789284, _1789286, _1789288] : [-(c_New__Random__Sequence_Opos__union(_1789278, _1789280, _1789282, _1789284, _1789286, _1789288) = c_New__DSequence_Opos__union(_1789278, hAPP(hAPP(hAPP(_1789280, _1789284), _1789286), _1789288), hAPP(hAPP(hAPP(_1789282, _1789284), _1789286), _1789288)))], (49840 ^ _782435) ^ [_1789349, _1789351] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789349), _1789351)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789349, _1789351) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (49846 ^ _782435) ^ [_1789436, _1789438] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789436), _1789438))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789436, _1789438) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789438), c_Lazy__Sequence_Osmall__lazy_H(_1789436, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789438), c_Groups_Oone__class_Oone(tc_Int_Oint)))))], (49852 ^ _782435) ^ [_1789498] : [-(c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint, _1789498) = c_Lazy__Sequence_Osmall__lazy_H(_1789498, hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint), _1789498)))], (49854 ^ _782435) ^ [_1789530, _1789532] : [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), _1789530), _1789532))), 49857 ^ _782435 : [(49858 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789530), _1789532)), -(c_Lazy__Sequence_Osmall__lazy_H(_1789530, _1789532) = c_Lazy__Sequence_Oempty(tc_Int_Oint))], (49864 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), _1789530), _1789532))), -(c_Lazy__Sequence_Osmall__lazy_H(_1789530, _1789532) = c_Lazy__Sequence_Oappend(tc_Int_Oint, hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint), _1789532), c_Lazy__Sequence_Osmall__lazy_H(_1789530, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), _1789532), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (49870 ^ _782435) ^ [_1789782, _1789784, _1789786] : [-(_1789782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Otl(_1789784), c_List_Oreplicate(_1789784, _1789782, _1789786)) = c_List_Oreplicate(_1789784, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1789782), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1789786))], (49876 ^ _782435) ^ [_1789839, _1789841, _1789843, _1789845, _1789847] : [-(hAPP(hAPP(c_List_Omap(_1789839, _1789841), _1789843), c_List_Oreplicate(_1789839, _1789845, _1789847)) = c_List_Oreplicate(_1789841, _1789845, hAPP(_1789843, _1789847)))], (49878 ^ _782435) ^ [_1789890, _1789892] : [-(c_List_Oreplicate(_1789890, c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1789892) = c_List_Olist_ONil(_1789890))], (49880 ^ _782435) ^ [_1789939, _1789941, _1789943] : [c_List_Olist_ONil(_1789939) = c_List_Oreplicate(_1789939, _1789941, _1789943), -(_1789941 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49886 ^ _782435) ^ [_1790026, _1790028, _1790030] : [_1790028 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Olist_ONil(_1790026) = c_List_Oreplicate(_1790026, _1790028, _1790030))], (49892 ^ _782435) ^ [_1790137, _1790139, _1790141] : [c_List_Oreplicate(_1790137, _1790139, _1790141) = c_List_Olist_ONil(_1790137), -(_1790139 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49898 ^ _782435) ^ [_1790224, _1790226, _1790228] : [_1790226 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(c_List_Oreplicate(_1790224, _1790226, _1790228) = c_List_Olist_ONil(_1790224))], (49904 ^ _782435) ^ [_1790317, _1790319] : [-(c_List_Oconcat(_1790317, c_List_Oreplicate(tc_List_Olist(_1790317), _1790319, c_List_Olist_ONil(_1790317))) = c_List_Olist_ONil(_1790317))], (49906 ^ _782435) ^ [_1790370, _1790372, _1790374, _1790376] : [hBOOL(hAPP(_1790370, _1790372)), -(hAPP(c_List_Ofilter(_1790374, _1790370), c_List_Oreplicate(_1790374, _1790376, _1790372)) = c_List_Oreplicate(_1790374, _1790376, _1790372))], (49912 ^ _782435) ^ [_1790477, _1790479, _1790481, _1790483] : [-(hBOOL(hAPP(_1790477, _1790479))), -(hAPP(c_List_Ofilter(_1790481, _1790477), c_List_Oreplicate(_1790481, _1790483, _1790479)) = c_List_Olist_ONil(_1790481))], (49918 ^ _782435) ^ [_1790533, _1790535, _1790537, _1790539] : [-(hAPP(hAPP(c_List_Oappend(_1790533), c_List_Oreplicate(_1790533, _1790535, _1790537)), c_List_Oreplicate(_1790533, _1790539, _1790537)) = hAPP(hAPP(c_List_Oappend(_1790533), c_List_Oreplicate(_1790533, _1790539, _1790537)), c_List_Oreplicate(_1790533, _1790535, _1790537)))], (49920 ^ _782435) ^ [_1790594, _1790596, _1790598, _1790600] : [-(c_List_Oreplicate(_1790594, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), _1790596), _1790598), _1790600) = hAPP(hAPP(c_List_Oappend(_1790594), c_List_Oreplicate(_1790594, _1790596, _1790600)), c_List_Oreplicate(_1790594, _1790598, _1790600)))], (49922 ^ _782435) ^ [_1790649, _1790651, _1790653, _1790655] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), _1790649), _1790651)), -(hAPP(hAPP(c_List_Onth(_1790653), c_List_Oreplicate(_1790653, _1790651, _1790655)), _1790649) = _1790655)], (49928 ^ _782435) ^ [_1790788, _1790790, _1790792, _1790794, _1790796] : [c_List_Oreplicate(_1790788, _1790790, _1790792) = c_List_Oreplicate(_1790788, _1790794, _1790796), 49931 ^ _782435 : [(49932 ^ _782435) ^ [] : [-(_1790790 = _1790794)], (49934 ^ _782435) ^ [] : [-(_1790790 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(_1790792 = _1790796)]]], (49940 ^ _782435) ^ [_1790924, _1790926, _1790928, _1790930, _1790932] : [-(c_List_Oreplicate(_1790924, _1790926, _1790928) = c_List_Oreplicate(_1790924, _1790930, _1790932)), _1790926 = _1790930, 49945 ^ _782435 : [(49946 ^ _782435) ^ [] : [_1790926 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (49948 ^ _782435) ^ [] : [_1790928 = _1790932]]], (49952 ^ _782435) ^ [_1791144, _1791146, _1791148, _1791150] : [49959 ^ _782435 : [(49960 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1791150, _1791148)))], (49962 ^ _782435) ^ [] : [_1791146 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 49953 ^ _782435 : [(49954 ^ _782435) ^ [_1791216] : [hBOOL(hAPP(hAPP(c_member(_1791144), _1791216), hAPP(c_List_Oset(_1791144), c_List_Oreplicate(_1791144, _1791146, _1791148)))), hBOOL(hAPP(_1791150, _1791216))]]], (49964 ^ _782435) ^ [_1791386, _1791388, _1791390, _1791392] : [49972 ^ _782435 : [(49973 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791386), 49971 ^ [_1791386, _1791388, _1791390, _1791392]), hAPP(c_List_Oset(_1791386), c_List_Oreplicate(_1791386, _1791388, _1791390)))))], (49975 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1791392, 49971 ^ [_1791386, _1791388, _1791390, _1791392])))]], hBOOL(hAPP(_1791392, _1791390)), -(_1791388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49977 ^ _782435) ^ [_1791642, _1791644, _1791646, _1791648] : [49979 ^ _782435 : [(49980 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1791642), 49978 ^ [_1791642, _1791644, _1791646, _1791648]), hAPP(c_List_Oset(_1791642), c_List_Oreplicate(_1791642, _1791644, _1791646)))))], (49982 ^ _782435) ^ [] : [hBOOL(hAPP(_1791648, 49978 ^ [_1791642, _1791644, _1791646, _1791648]))]], -(hBOOL(hAPP(_1791648, _1791646))), -(_1791644 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (49990 ^ _782435) ^ [_1791849, _1791851, _1791853, _1791855] : [49991 ^ _782435 : [(49992 ^ _782435) ^ [] : [hBOOL(hAPP(_1791855, _1791853))], (49994 ^ _782435) ^ [] : [_1791851 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]], 49995 ^ _782435 : [(49996 ^ _782435) ^ [_1791974] : [hBOOL(hAPP(hAPP(c_member(_1791849), _1791974), hAPP(c_List_Oset(_1791849), c_List_Oreplicate(_1791849, _1791851, _1791853)))), -(hBOOL(hAPP(_1791855, _1791974)))]]], (50002 ^ _782435) ^ [_1792101, _1792103, _1792105, _1792107, _1792109, _1792111] : [-(hAPP(hAPP(c_List_Ozip(_1792101, _1792103), c_List_Oreplicate(_1792101, _1792105, _1792107)), c_List_Oreplicate(_1792103, _1792109, _1792111)) = c_List_Oreplicate(tc_prod(_1792101, _1792103), hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792105), _1792109), hAPP(hAPP(c_Product__Type_OPair(_1792101, _1792103), _1792107), _1792111)))], (50004 ^ _782435) ^ [_1792173, _1792175, _1792177, _1792179] : [-(hAPP(hAPP(c_List_Odrop(_1792173), _1792175), c_List_Oreplicate(_1792173, _1792177, _1792179)) = c_List_Oreplicate(_1792173, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat), _1792177), _1792175), _1792179))], (50006 ^ _782435) ^ [_1792220, _1792222, _1792224] : [-(_1792220 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Ohd(_1792222), c_List_Oreplicate(_1792222, _1792220, _1792224)) = _1792224)], (50012 ^ _782435) ^ [_1792267, _1792269, _1792271, _1792273] : [-(hAPP(hAPP(c_List_Otake(_1792267), _1792269), c_List_Oreplicate(_1792267, _1792271, _1792273)) = c_List_Oreplicate(_1792267, hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat), _1792269), _1792271), _1792273))], (50014 ^ _782435) ^ [_1792314, _1792316, _1792318] : [-(_1792314 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(c_List_Olast(_1792316, c_List_Oreplicate(_1792316, _1792314, _1792318)) = _1792318)], (50020 ^ _782435) ^ [_1792359, _1792361, _1792363] : [-(hAPP(c_List_Orev(_1792359), c_List_Oreplicate(_1792359, _1792361, _1792363)) = c_List_Oreplicate(_1792359, _1792361, _1792363))], (50022 ^ _782435) ^ [_1792399, _1792401, _1792403] : [-(c_List_Oreplicate(_1792399, hAPP(c_Nat_OSuc, _1792401), _1792403) = hAPP(hAPP(c_List_Olist_OCons(_1792399), _1792403), c_List_Oreplicate(_1792399, _1792401, _1792403)))], (50024 ^ _782435) ^ [_1792445, _1792447, _1792449, _1792451] : [-(hAPP(hAPP(c_List_Oappend(_1792445), c_List_Oreplicate(_1792445, _1792447, _1792449)), hAPP(hAPP(c_List_Olist_OCons(_1792445), _1792449), _1792451)) = hAPP(hAPP(c_List_Olist_OCons(_1792445), _1792449), hAPP(hAPP(c_List_Oappend(_1792445), c_List_Oreplicate(_1792445, _1792447, _1792449)), _1792451)))], (50026 ^ _782435) ^ [_1792514, _1792516, _1792518, _1792520] : [-(hAPP(hAPP(c_List_Omap(_1792514, _1792516), hAPP(c_COMBK(_1792516, _1792514), _1792518)), _1792520) = c_List_Oreplicate(_1792516, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792514)), _1792520), _1792518))], (50028 ^ _782435) ^ [_1792569, _1792571, _1792573] : [-(hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792569)), c_List_Oreplicate(_1792569, _1792571, _1792573)) = _1792571)], (50030 ^ _782435) ^ [_1792607, _1792609, _1792611] : [-(c_List_Oreplicate(_1792607, hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1792607)), hAPP(c_List_Ofilter(_1792607, hAPP(c_fequal, _1792609)), _1792611)), _1792609) = hAPP(c_List_Ofilter(_1792607, hAPP(c_fequal, _1792609)), _1792611))], (50032 ^ _782435) ^ [_1792684, _1792686, _1792688, _1792690] : [hBOOL(hAPP(hAPP(c_member(_1792684), _1792686), hAPP(c_List_Oset(_1792684), c_List_Oreplicate(_1792684, _1792688, _1792690)))), 50035 ^ _782435 : [(50036 ^ _782435) ^ [] : [-(_1792686 = _1792690)], (50038 ^ _782435) ^ [] : [_1792688 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)]]], (50040 ^ _782435) ^ [_1792827, _1792829, _1792831, _1792833] : [-(hBOOL(hAPP(hAPP(c_member(_1792827), _1792829), hAPP(c_List_Oset(_1792827), c_List_Oreplicate(_1792827, _1792831, _1792833))))), _1792829 = _1792833, -(_1792831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50050 ^ _782435) ^ [_1793001, _1793003, _1793005] : [-(hAPP(hAPP(c_List_Oappend(_1793001), c_List_Oreplicate(_1793001, _1793003, _1793005)), hAPP(hAPP(c_List_Olist_OCons(_1793001), _1793005), c_List_Olist_ONil(_1793001))) = hAPP(hAPP(c_List_Olist_OCons(_1793001), _1793005), c_List_Oreplicate(_1793001, _1793003, _1793005)))], (50052 ^ _782435) ^ [_1793062, _1793064, _1793066] : [-(hAPP(hAPP(c_List_Omap(tc_Nat_Onat, _1793062), hAPP(c_COMBK(_1793062, tc_Nat_Onat), _1793064)), c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat), _1793066)) = c_List_Oreplicate(_1793062, _1793066, _1793064))], (50054 ^ _782435) ^ [_1793107, _1793109, _1793111] : [-(_1793107 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1793109), c_List_Oreplicate(_1793109, _1793107, _1793111)) = hAPP(hAPP(c_Set_Oinsert(_1793109), _1793111), c_Orderings_Obot__class_Obot(tc_fun(_1793109, tc_HOL_Obool))))], (50060 ^ _782435) ^ [_1793179, _1793181, _1793183] : [_1793179 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat), -(hAPP(c_List_Oset(_1793181), c_List_Oreplicate(_1793181, _1793179, _1793183)) = c_Orderings_Obot__class_Obot(tc_fun(_1793181, tc_HOL_Obool)))], (50066 ^ _782435) ^ [_1793280, _1793282, _1793284] : [-(_1793280 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hAPP(c_List_Oset(_1793282), c_List_Oreplicate(_1793282, _1793280, _1793284)) = hAPP(hAPP(c_Set_Oinsert(_1793282), _1793284), c_Orderings_Obot__class_Obot(tc_fun(_1793282, tc_HOL_Obool))))], (50072 ^ _782435) ^ [_1793342, _1793344, _1793346] : [-(hAPP(c_List_Oset(_1793342), c_List_Oreplicate(_1793342, hAPP(c_Nat_OSuc, _1793344), _1793346)) = hAPP(hAPP(c_Set_Oinsert(_1793342), _1793346), c_Orderings_Obot__class_Obot(tc_fun(_1793342, tc_HOL_Obool))))], (50074 ^ _782435) ^ [_1793394, _1793396, _1793398] : [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), _1793394), _1793396))), -(hBOOL(hAPP(hAPP(_1793398, _1793394), _1793396))), 50081 ^ _782435 : [(50082 ^ _782435) ^ [] : [-(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 ^ [_1793394, _1793396, _1793398]), 50080 ^ [_1793394, _1793396, _1793398]))))], (50090 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1793398, 50079 ^ [_1793394, _1793396, _1793398]), 50080 ^ [_1793394, _1793396, _1793398]))], (50084 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint), 50079 ^ [_1793394, _1793396, _1793398]), 50080 ^ [_1793394, _1793396, _1793398]))), -(hBOOL(hAPP(hAPP(_1793398, 50079 ^ [_1793394, _1793396, _1793398]), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint), 50080 ^ [_1793394, _1793396, _1793398]), c_Groups_Oone__class_Oone(tc_Int_Oint)))))]]], (50094 ^ _782435) ^ [_1793846, _1793848] : [-(c_Predicate_Opred__comp(_1793846, _1793846, _1793846, c_fequal, c_Predicate_Opred__comp(_1793846, _1793846, _1793846, _1793848, c_fequal)) = _1793848)], (50096 ^ _782435) ^ [_1793883, _1793885, _1793887] : [class_Fields_Olinordered__field(_1793883), 50102 ^ _782435 : [(50103 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(_1793883), c_Groups_Ozero__class_Ozero(_1793883)), 50101 ^ [_1793883, _1793885, _1793887])))], (50105 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793883), _1793885), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1793883), _1793887), 50101 ^ [_1793883, _1793885, _1793887])))]], -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(_1793883), _1793885), _1793887)))], (50109 ^ _782435) ^ [_1794161, _1794163, _1794165] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794161)), c_Lazy__Sequence_Olazy__sequence_OInsert(_1794161, _1794163, _1794165)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794161)), _1794165)), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50111 ^ _782435) ^ [_1794212, _1794214, _1794216, _1794218] : [-(c_Lazy__Sequence_Oappend(_1794212, c_Lazy__Sequence_Olazy__sequence_OInsert(_1794212, _1794214, _1794216), _1794218) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794212, _1794214, c_Lazy__Sequence_Oappend(_1794212, _1794216, _1794218)))], (50113 ^ _782435) ^ [_1794281, _1794283, _1794285, _1794287, _1794289] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1794281, _1794283, _1794285) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794281, _1794287, _1794289), 50116 ^ _782435 : [(50117 ^ _782435) ^ [] : [-(_1794283 = _1794287)], (50119 ^ _782435) ^ [] : [-(_1794285 = _1794289)]]], (50121 ^ _782435) ^ [_1794402, _1794404, _1794406, _1794408, _1794410] : [-(c_Lazy__Sequence_Olazy__sequence_OInsert(_1794402, _1794404, _1794406) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1794402, _1794408, _1794410)), _1794404 = _1794408, _1794406 = _1794410], (50131 ^ _782435) ^ [_1794561, _1794563, _1794565, _1794567] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794561, _1794563), c_Lazy__Sequence_Olazy__sequence_OInsert(_1794561, _1794565, _1794567)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1794563, _1794565)), hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794561, _1794563), _1794567))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50133 ^ _782435) ^ [_1794621, _1794623] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794621)), _1794623) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1794621, tc_Lazy__Sequence_Olazy__sequence(_1794621)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1794621, tc_Lazy__Sequence_Olazy__sequence(_1794621), tc_Nat_Onat), hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794621), tc_Nat_Onat), _1794621), hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1794621), 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(_1794621)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1794621)))), c_Groups_Oone__class_Oone(tc_Nat_Onat)))), hAPP(c_Lazy__Sequence_Oyield(_1794621), _1794623)))], (50135 ^ _782435) ^ [_1794717, _1794719, _1794721] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794717, _1794719), _1794721) = c_Option_Ooption_Ooption__case(tc_Nat_Onat, tc_prod(_1794717, tc_Lazy__Sequence_Olazy__sequence(_1794717)), c_Groups_Ozero__class_Ozero(tc_Nat_Onat), hAPP(c_Product__Type_Oprod_Oprod__case(_1794717, tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat), hAPP(hAPP(c_COMBC(_1794717, tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), tc_fun(tc_Nat_Onat, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat)), _1794717), c_COMBC(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat, tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_fun(tc_Nat_Onat, tc_Nat_Onat)), _1794717), hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_Lazy__Sequence_Olazy__sequence(_1794717)), c_Groups_Oplus__class_Oplus(tc_Nat_Onat))), hAPP(hAPP(c_COMBC(_1794717, tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat)), hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat, tc_Nat_Onat), tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat), tc_fun(tc_Lazy__Sequence_Olazy__sequence(_1794717), tc_Nat_Onat)), _1794717), c_COMBB(tc_Nat_Onat, tc_Nat_Onat, tc_Lazy__Sequence_Olazy__sequence(_1794717))), hAPP(hAPP(c_COMBB(tc_Nat_Onat, tc_fun(tc_Nat_Onat, tc_Nat_Onat), _1794717), c_Groups_Oplus__class_Oplus(tc_Nat_Onat)), _1794719))), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1794717, _1794719))))), c_Groups_Oone__class_Oone(tc_Nat_Onat))), hAPP(c_Lazy__Sequence_Oyield(_1794717), _1794721)))], (50137 ^ _782435) ^ [_1794910, _1794912, _1794914, _1794916, _1794918] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1794910, _1794912, _1794914, _1794916, _1794918) = c_Option_Ooption_Ooption__case(_1794910, tc_prod(_1794912, tc_Lazy__Sequence_Olazy__sequence(_1794912)), _1794914, hAPP(c_Product__Type_Oprod_Oprod__case(_1794912, tc_Lazy__Sequence_Olazy__sequence(_1794912), _1794910), _1794916), hAPP(c_Lazy__Sequence_Oyield(_1794912), _1794918)))], (50139 ^ _782435) ^ [_1794972] : [-(c_Lazy__Sequence_Oyieldn(_1794972) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(_1794972), _1794972, c_Lazy__Sequence_Oyield(_1794972)))], (50141 ^ _782435) ^ [_1795005, _1795007, _1795009, _1795011, _1795013, _1795015] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1795005, _1795007, _1795009, _1795011, c_Lazy__Sequence_Olazy__sequence_OInsert(_1795007, _1795013, _1795015)) = hAPP(hAPP(_1795011, _1795013), _1795015))], (50143 ^ _782435) ^ [_1795054, _1795056, _1795058, _1795060, _1795062] : [50145 ^ _782435 : [(50146 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1795054), 50144 ^ [_1795054, _1795056, _1795058, _1795060, _1795062]), _1795056)))], (50148 ^ _782435) ^ [] : [c_Relation_Orefl__on(_1795058, hAPP(_1795060, 50144 ^ [_1795054, _1795056, _1795058, _1795060, _1795062]), hAPP(_1795062, 50144 ^ [_1795054, _1795056, _1795058, _1795060, _1795062]))]], -(c_Relation_Orefl__on(_1795058, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1795054, tc_fun(_1795058, tc_HOL_Obool)), _1795056), _1795060), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1795054, tc_fun(tc_prod(_1795058, _1795058), tc_HOL_Obool)), _1795056), _1795062)))], (50152 ^ _782435) ^ [_1795340, _1795342, _1795344] : [hBOOL(hAPP(hAPP(c_member(_1795340), _1795342), hAPP(c_List_Oset(_1795340), _1795344))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1795340), _1795344), _1795342)))], (50158 ^ _782435) ^ [_1795453, _1795455, _1795457] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795453), _1795457), _1795455)), -(hBOOL(hAPP(hAPP(c_member(_1795453), _1795455), hAPP(c_List_Oset(_1795453), _1795457))))], (50174 ^ _782435) ^ [_1795727, _1795729, _1795731, _1795733] : [50175 ^ _782435 : [(50176 ^ _782435) ^ [] : [_1795729 = _1795733], (50178 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795727), _1795731), _1795733))]], -(hBOOL(hAPP(hAPP(c_List_Omember(_1795727), hAPP(hAPP(c_List_Olist_OCons(_1795727), _1795729), _1795731)), _1795733)))], (50164 ^ _782435) ^ [_1795593, _1795595, _1795597, _1795599] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795593), hAPP(hAPP(c_List_Olist_OCons(_1795593), _1795595), _1795597)), _1795599)), -(_1795595 = _1795599), -(hBOOL(hAPP(hAPP(c_List_Omember(_1795593), _1795597), _1795599)))], (50182 ^ _782435) ^ [_1795892] : [-(c_List_Omember(_1795892) = c_List_Oset(_1795892))], (50184 ^ _782435) ^ [_1795931, _1795933] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795931), c_List_Olist_ONil(_1795931)), _1795933))], (50186 ^ _782435) ^ [_1795983, _1795985, _1795987] : [hBOOL(hAPP(hAPP(c_List_Omember(_1795983), _1795985), _1795987)), -(hBOOL(hAPP(hAPP(c_member(_1795983), _1795987), hAPP(c_List_Oset(_1795983), _1795985))))], (50192 ^ _782435) ^ [_1796096, _1796098, _1796100] : [hBOOL(hAPP(hAPP(c_member(_1796096), _1796100), hAPP(c_List_Oset(_1796096), _1796098))), -(hBOOL(hAPP(hAPP(c_List_Omember(_1796096), _1796098), _1796100)))], (50198 ^ _782435) ^ [_1796215, _1796217, _1796219, _1796221, _1796223, _1796225] : [-(c_Nitpick_Opair__box_Opair__box__size(_1796215, _1796217, _1796219, _1796221, c_Nitpick_Opair__box_OPairBox(_1796215, _1796217, _1796223, _1796225)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), hAPP(_1796219, _1796223)), hAPP(_1796221, _1796225))), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))], (50200 ^ _782435) ^ [_1796295, _1796297, _1796299] : [c_List_Olist__ex1(_1796295, _1796297, _1796299), 50204 ^ _782435 : [(50205 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796295), 50203 ^ [_1796295, _1796297, _1796299]), hAPP(c_List_Oset(_1796295), _1796299))))], (50207 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1796297, 50203 ^ [_1796295, _1796297, _1796299])))], (50209 ^ _782435) ^ [_1796541] : [-(_1796541 = 50203 ^ [_1796295, _1796297, _1796299]), hBOOL(hAPP(hAPP(c_member(_1796295), _1796541), hAPP(c_List_Oset(_1796295), _1796299))), hBOOL(hAPP(_1796297, _1796541))]]], (50219 ^ _782435) ^ [_1796728, _1796730, _1796732] : [-(c_List_Olist__ex1(_1796728, _1796730, _1796732)), 50220 ^ _782435 : [(50221 ^ _782435) ^ [_1796822] : [hBOOL(hAPP(hAPP(c_member(_1796728), _1796822), hAPP(c_List_Oset(_1796728), _1796732))), hBOOL(hAPP(_1796730, _1796822)), 50229 ^ _782435 : [(50230 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1796728), 50228 ^ [_1796728, _1796730, _1796732, _1796822]), hAPP(c_List_Oset(_1796728), _1796732))))], (50232 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1796730, 50228 ^ [_1796728, _1796730, _1796732, _1796822])))], (50234 ^ _782435) ^ [] : [50228 ^ [_1796728, _1796730, _1796732, _1796822] = _1796822]]]]], (50238 ^ _782435) ^ [_1797184, _1797186, _1797188, _1797190, _1797192, _1797194] : [c_Nitpick_Opair__box_OPairBox(_1797184, _1797186, _1797188, _1797190) = c_Nitpick_Opair__box_OPairBox(_1797184, _1797186, _1797192, _1797194), 50241 ^ _782435 : [(50242 ^ _782435) ^ [] : [-(_1797188 = _1797192)], (50244 ^ _782435) ^ [] : [-(_1797190 = _1797194)]]], (50246 ^ _782435) ^ [_1797311, _1797313, _1797315, _1797317, _1797319, _1797321] : [-(c_Nitpick_Opair__box_OPairBox(_1797311, _1797313, _1797315, _1797317) = c_Nitpick_Opair__box_OPairBox(_1797311, _1797313, _1797319, _1797321)), _1797315 = _1797319, _1797317 = _1797321], (50256 ^ _782435) ^ [_1797478, _1797480, _1797482, _1797484] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(_1797478, _1797480)), c_Nitpick_Opair__box_OPairBox(_1797478, _1797480, _1797482, _1797484)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50258 ^ _782435) ^ [_1797520, _1797522, _1797524, _1797526, _1797528, _1797530] : [-(c_Nitpick_Opair__box_Opair__box__rec(_1797520, _1797522, _1797524, _1797526, c_Nitpick_Opair__box_OPairBox(_1797520, _1797522, _1797528, _1797530)) = hAPP(hAPP(_1797526, _1797528), _1797530))], (50260 ^ _782435) ^ [_1797570, _1797572, _1797574, _1797576, _1797578, _1797580] : [-(c_Nitpick_Opair__box_Opair__box__case(_1797570, _1797572, _1797574, _1797576, c_Nitpick_Opair__box_OPairBox(_1797570, _1797572, _1797578, _1797580)) = hAPP(hAPP(_1797576, _1797578), _1797580))], (50262 ^ _782435) ^ [_1797632, _1797634, _1797636] : [-(c_FunDef_OTHE__default(_1797634, _1797636, _1797632) = c_HOL_OThe(_1797634, _1797632)), 50263 ^ _782435 : [(50264 ^ _782435) ^ [_1797696] : [hBOOL(hAPP(_1797632, _1797696)), 50268 ^ _782435 : [(50269 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1797632, 50267 ^ [_1797632, _1797634, _1797636, _1797696])))], (50271 ^ _782435) ^ [] : [50267 ^ [_1797632, _1797634, _1797636, _1797696] = _1797696]]]]], (50275 ^ _782435) ^ [_1797890, _1797892, _1797894] : [-(c_FunDef_OTHE__default(_1797892, _1797894, _1797890) = _1797894), 50277 ^ _782435 : [(50278 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1797890, 50276 ^ [_1797890, _1797892, _1797894])))], (50280 ^ _782435) ^ [_1798012] : [hBOOL(hAPP(_1797890, _1798012)), -(_1798012 = 50276 ^ [_1797890, _1797892, _1797894])]]], (50288 ^ _782435) ^ [_1798151, _1798153, _1798155, _1798157] : [class_Groups_Ocomm__monoid__add(_1798151), hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(_1798153, tc_HOL_Obool)), _1798155)), 50298 ^ _782435 : [(50299 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798153, tc_HOL_Obool)), 50297 ^ [_1798151, _1798153, _1798155, _1798157]), _1798155)))], (50301 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1798153), 50297 ^ [_1798151, _1798153, _1798155, _1798157]))]], 50305 ^ _782435 : [(50306 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798153, tc_HOL_Obool)), 50304 ^ [_1798151, _1798153, _1798155, _1798157]), _1798155)))], (50309 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_fun(_1798153, tc_HOL_Obool)), 50307 ^ [_1798151, _1798153, _1798155, _1798157]), _1798155)))], (50311 ^ _782435) ^ [] : [50304 ^ [_1798151, _1798153, _1798155, _1798157] = 50307 ^ [_1798151, _1798153, _1798155, _1798157]], (50314 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798153), 50312 ^ [_1798151, _1798153, _1798155, _1798157]), 50304 ^ [_1798151, _1798153, _1798155, _1798157])))], (50316 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1798153), 50312 ^ [_1798151, _1798153, _1798155, _1798157]), 50307 ^ [_1798151, _1798153, _1798155, _1798157])))], (50318 ^ _782435) ^ [] : [hAPP(_1798157, 50312 ^ [_1798151, _1798153, _1798155, _1798157]) = c_Groups_Ozero__class_Ozero(_1798151)]], -(hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1798153, _1798151), _1798157), c_Complete__Lattice_OSup__class_OSup(tc_fun(_1798153, tc_HOL_Obool), _1798155)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(_1798153, tc_HOL_Obool), _1798151), hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(_1798153, _1798151), _1798157)), _1798155))], (50322 ^ _782435) ^ [_1799148, _1799150] : [hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(_1799148)), _1799150)), 50326 ^ _782435 : [(50327 ^ _782435) ^ [_1799249] : [hBOOL(hAPP(hAPP(c_member(tc_List_Olist(_1799148)), _1799249), _1799150)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(_1799148)), _1799249)), 50325 ^ [_1799148, _1799150])))]]], (50333 ^ _782435) ^ [_1799388] : [-(hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(_1799388)), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799388)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50335 ^ _782435) ^ [_1799435, _1799437, _1799439] : [c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799435) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1799435, _1799437, _1799439)], (50337 ^ _782435) ^ [_1799483, _1799485, _1799487] : [c_Lazy__Sequence_Olazy__sequence_OInsert(_1799483, _1799485, _1799487) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799483)], (50339 ^ _782435) ^ [_1799516, _1799518] : [-(c_Lazy__Sequence_Oappend(_1799516, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799516), _1799518) = _1799518)], (50341 ^ _782435) ^ [_1799547, _1799549, _1799551, _1799553] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(_1799547, _1799549, _1799551, _1799553, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799549)) = _1799551)], (50343 ^ _782435) ^ [_1799584, _1799586] : [-(hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(_1799584, _1799586), c_Lazy__Sequence_Olazy__sequence_OEmpty(_1799584)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat))], (50345 ^ _782435) ^ [_1799635, _1799637, _1799639] : [c_List_Olist__all(tc_Int_Oint, _1799635, c_List_Oupto(_1799637, _1799639)), -(c_List_Oall__interval__int(_1799635, _1799637, _1799639))], (50351 ^ _782435) ^ [_1799720, _1799722, _1799724] : [c_List_Oall__interval__int(_1799720, _1799722, _1799724), -(c_List_Olist__all(tc_Int_Oint, _1799720, c_List_Oupto(_1799722, _1799724)))], (50357 ^ _782435) ^ [_1799829, _1799831, _1799833] : [c_List_Olist__ex(tc_Int_Oint, _1799829, c_List_Oupto(_1799831, _1799833)), c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1799829), _1799831, _1799833)], (50363 ^ _782435) ^ [_1799919, _1799921, _1799923] : [-(c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Int_Oint, c_fNot), _1799919), _1799921, _1799923)), -(c_List_Olist__ex(tc_Int_Oint, _1799919, c_List_Oupto(_1799921, _1799923)))], (50379 ^ _782435) ^ [_1800166, _1800168, _1800170] : [50381 ^ _782435 : [(50382 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), 50380 ^ [_1800166, _1800168, _1800170]), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1800168, _1800170))))], (50384 ^ _782435) ^ [] : [hBOOL(hAPP(_1800166, 50380 ^ [_1800166, _1800168, _1800170]))]], -(c_List_Oall__interval__int(_1800166, _1800168, _1800170))], (50369 ^ _782435) ^ [_1799985, _1799987, _1799989] : [c_List_Oall__interval__int(_1799985, _1799987, _1799989), 50372 ^ _782435 : [(50373 ^ _782435) ^ [_1800063] : [hBOOL(hAPP(hAPP(c_member(tc_Int_Oint), _1800063), c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint, _1799987, _1799989))), -(hBOOL(hAPP(_1799985, _1800063)))]]], (50388 ^ _782435) ^ [_1800342, _1800344, _1800346, _1800348] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800342, _1800344, _1800346, c_Code__Numeral_OSuc__code__numeral(_1800348)) = hAPP(hAPP(_1800346, _1800348), c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800342, _1800344, _1800346, _1800348)))], (50390 ^ _782435) ^ [_1800404, _1800406, _1800408, _1800410] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1800404), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))), -(c_Random__Sequence_ORandom(_1800406, _1800408, _1800404, _1800410) = 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(_1800406)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1800406)))], (50396 ^ _782435) ^ [_1800535, _1800537, _1800539, _1800541] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral), _1800535), c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))), -(c_Random__Sequence_ORandom(_1800537, _1800539, _1800535, _1800541) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral), tc_prod(_1800537, 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(_1800537)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), hAPP(_1800539, _1800541)), 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(_1800537)))), 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(_1800537)))), 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(_1800537)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), tc_prod(_1800537, 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(_1800537)))), 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(_1800537)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))), c_Random__Sequence_ORandom(_1800537, _1800539, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral), _1800535), c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)), _1800541))), 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(_1800537)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800537))))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800537)))), 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(_1800537)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)))), tc_prod(_1800537, 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(_1800537)))), 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(_1800537)))), 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(_1800537))))), c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800537)))), 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(_1800537)))), tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800537)))), tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800537))))), tc_prod(_1800537, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Ounion(_1800537)), hAPP(hAPP(c_COMBB(_1800537, tc_fun(tc_Code__Numeral_Ocode__numeral, tc_fun(tc_HOL_Obool, tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(_1800537)))), tc_prod(_1800537, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))), c_DSequence_Osingle(_1800537)), c_Product__Type_Ofst(_1800537, tc_fun(tc_Product__Type_Ounit, tc_Code__Evaluation_Oterm))))))))], (50402 ^ _782435) ^ [_1800914, _1800916, _1800918] : [-(c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(_1800914, _1800916, _1800918, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = _1800916)], (50404 ^ _782435) ^ [_1800946, _1800948, _1800950] : [-(c_Random__Sequence_Oempty(_1800946, _1800948, _1800950) = 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(_1800946)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), c_DSequence_Oempty(_1800946)))], (50406 ^ _782435) ^ [_1800995, _1800997, _1800999, _1801001] : [-(hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(_1800995), _1800997), _1800999), _1801001) = 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(_1800995)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral)), hAPP(c_DSequence_Osingle(_1800995), _1800997)))], (50408 ^ _782435) ^ [_1801056, _1801058, _1801060, _1801062] : [-(c_Random__Sequence_Omap(_1801056, _1801058, _1801060, _1801062) = c_Random__Sequence_Obind(_1801056, _1801058, _1801062, hAPP(c_Fun_Ocomp(_1801058, 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(_1801058)))), tc_prod(tc_Code__Numeral_Ocode__numeral, tc_Code__Numeral_Ocode__numeral))))), _1801056, c_Random__Sequence_Osingle(_1801058)), _1801060)))], (50410 ^ _782435) ^ [_1801127, _1801129, _1801131, _1801133, _1801135, _1801137, _1801139] : [hBOOL(hAPP(hAPP(_1801127, hAPP(c_Product__Type_Osnd(_1801129, _1801131), _1801133)), hAPP(c_Product__Type_Ofst(_1801129, _1801131), _1801133))), 50417 ^ _782435 : [(50418 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1801127, 50416 ^ [_1801127, _1801129, _1801131, _1801133, _1801135, _1801137, _1801139]), 50415 ^ [_1801127, _1801129, _1801131, _1801133, _1801135, _1801137, _1801139])))], (50420 ^ _782435) ^ [] : [hBOOL(hAPP(_1801135, hAPP(hAPP(_1801137, 50415 ^ [_1801127, _1801129, _1801131, _1801133, _1801135, _1801137, _1801139]), 50416 ^ [_1801127, _1801129, _1801131, _1801133, _1801135, _1801137, _1801139])))]], -(hBOOL(hAPP(_1801135, hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(_1801129, _1801131, _1801139), _1801137), _1801133))))], (50424 ^ _782435) ^ [_1801524, _1801526, _1801528, _1801530] : [-(hAPP(c_Relation_OImage(_1801524, _1801526, hAPP(c_Set_OCollect(tc_prod(_1801524, _1801526)), hAPP(c_Product__Type_Oprod_Oprod__case(_1801524, _1801526, tc_HOL_Obool), _1801528))), _1801530) = hAPP(c_Set_OCollect(_1801526), hAPP(hAPP(c_COMBB(tc_fun(_1801524, tc_HOL_Obool), tc_HOL_Obool, _1801526), c_HOL_OEx(_1801524)), hAPP(hAPP(c_COMBB(tc_fun(_1801524, tc_HOL_Obool), tc_fun(_1801524, tc_HOL_Obool), _1801526), hAPP(c_COMBS(_1801524, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1801524), c_fconj), hAPP(hAPP(c_COMBC(_1801524, tc_fun(_1801524, tc_HOL_Obool), tc_HOL_Obool), c_member(_1801524)), _1801530)))), hAPP(c_COMBC(_1801524, _1801526, tc_HOL_Obool), _1801528)))))], (50426 ^ _782435) ^ [_1801650, _1801652, _1801654, _1801656, _1801658] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801650), tc_List_Olist(_1801650))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801650), tc_List_Olist(_1801650)), _1801652), _1801654)), c_List_Olexord(_1801650, _1801656))), hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801650), tc_List_Olist(_1801650))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801650), tc_List_Olist(_1801650)), _1801654), _1801658)), c_List_Olexord(_1801650, _1801656))), c_Relation_Otrans(_1801650, _1801656), -(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(_1801650), tc_List_Olist(_1801650))), hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(_1801650), tc_List_Olist(_1801650)), _1801652), _1801658)), c_List_Olexord(_1801650, _1801656))))], (50440 ^ _782435) ^ [] : [-(c_Relation_Otrans(tc_Nat_Onat, c_Wellfounded_Oless__than))], (50442 ^ _782435) ^ [_1802047, _1802049, _1802051, _1802053] : [c_Relation_Otrans(_1802047, _1802049), c_Relation_Otrans(_1802051, _1802053), -(c_Relation_Otrans(tc_prod(_1802047, _1802051), c_Wellfounded_Olex__prod(_1802047, _1802051, _1802049, _1802053)))], (50452 ^ _782435) ^ [_1802200, _1802202, _1802204, _1802206, _1802208] : [c_Relation_Otrans(_1802200, _1802202), hBOOL(hAPP(hAPP(c_member(tc_prod(_1802200, _1802200)), hAPP(hAPP(c_Product__Type_OPair(_1802200, _1802200), _1802204), _1802206)), _1802202)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1802200, _1802200)), hAPP(hAPP(c_Product__Type_OPair(_1802200, _1802200), _1802206), _1802208)), _1802202)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802200, _1802200)), hAPP(hAPP(c_Product__Type_OPair(_1802200, _1802200), _1802204), _1802208)), _1802202)))], (50480 ^ _782435) ^ [_1802970, _1802972] : [50483 ^ _782435 : [(50484 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802970, _1802970)), hAPP(hAPP(c_Product__Type_OPair(_1802970, _1802970), 50481 ^ [_1802970, _1802972]), 50482 ^ [_1802970, _1802972])), _1802972)))], (50487 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802970, _1802970)), hAPP(hAPP(c_Product__Type_OPair(_1802970, _1802970), 50482 ^ [_1802970, _1802972]), 50485 ^ [_1802970, _1802972])), _1802972)))], (50489 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802970, _1802970)), hAPP(hAPP(c_Product__Type_OPair(_1802970, _1802970), 50481 ^ [_1802970, _1802972]), 50485 ^ [_1802970, _1802972])), _1802972))]], -(c_Relation_Otrans(_1802970, _1802972))], (50466 ^ _782435) ^ [_1802528, _1802530] : [c_Relation_Otrans(_1802528, _1802530), 50469 ^ _782435 : [(50470 ^ _782435) ^ [_1802664, _1802666] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802528, _1802528)), hAPP(hAPP(c_Product__Type_OPair(_1802528, _1802528), _1802666), _1802664)), _1802530)), 50473 ^ _782435 : [(50474 ^ _782435) ^ [_1802807] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1802528, _1802528)), hAPP(hAPP(c_Product__Type_OPair(_1802528, _1802528), _1802664), _1802807)), _1802530)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1802528, _1802528)), hAPP(hAPP(c_Product__Type_OPair(_1802528, _1802528), _1802666), _1802807)), _1802530)))]]]]], (50493 ^ _782435) ^ [_1803390, _1803392, _1803394, _1803396] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803390, tc_fun(_1803392, tc_HOL_Obool)), _1803394), _1803396) = c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803392, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1803392, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1803390, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1803392, tc_HOL_Obool)), c_HOL_OEx(_1803390)), hAPP(hAPP(c_COMBB(tc_fun(_1803390, tc_HOL_Obool), tc_fun(_1803390, tc_HOL_Obool), tc_fun(_1803392, tc_HOL_Obool)), hAPP(c_COMBS(_1803390, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1803390), c_fconj), hAPP(hAPP(c_COMBC(_1803390, tc_fun(_1803390, tc_HOL_Obool), tc_HOL_Obool), c_member(_1803390)), _1803394)))), hAPP(hAPP(c_COMBC(tc_fun(_1803392, tc_HOL_Obool), tc_fun(_1803390, tc_fun(_1803392, tc_HOL_Obool)), tc_fun(_1803390, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803392, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803390, tc_fun(_1803392, tc_HOL_Obool)), tc_fun(_1803390, tc_HOL_Obool)), tc_fun(_1803392, tc_HOL_Obool)), c_COMBB(tc_fun(_1803392, tc_HOL_Obool), tc_HOL_Obool, _1803390)), c_fequal)), _1803396))))))], (50495 ^ _782435) ^ [_1803574, _1803576] : [-(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1803574, tc_HOL_Obool), _1803576) = hAPP(c_Set_OCollect(_1803574), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803574, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool, _1803574), c_HOL_OEx(tc_fun(_1803574, tc_HOL_Obool))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1803574, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1803574, tc_HOL_Obool), tc_HOL_Obool), _1803574), hAPP(c_COMBS(tc_fun(_1803574, 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(_1803574, tc_HOL_Obool)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1803574, tc_HOL_Obool), tc_fun(tc_fun(_1803574, tc_HOL_Obool), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1803574, tc_HOL_Obool))), _1803576)))), c_member(_1803574)))))], (50497 ^ _782435) ^ [_1803702, _1803704, _1803706, _1803708] : [c_Relation_Otrans(_1803702, _1803704), -(c_Relation_Otrans(_1803706, hAPP(hAPP(c_Relation_Oinv__image(_1803702, _1803706), _1803704), _1803708)))], (50503 ^ _782435) ^ [_1803801, _1803803] : [c_Relation_Otrans(_1803801, _1803803), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1803801, _1803801), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1803801, _1803801, _1803801), _1803803), _1803803)), _1803803)))], (50509 ^ _782435) ^ [_1803924] : [-(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1803924, tc_HOL_Obool) = c_Set_OBex(_1803924))], (50511 ^ _782435) ^ [_1803952, _1803954, _1803956] : [c_Relation_Otrans(_1803952, _1803954), c_Relation_Otrans(_1803952, _1803956), -(c_Relation_Otrans(_1803952, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1803952, _1803952), tc_HOL_Obool)), _1803954), _1803956)))], (50532 ^ _782435) ^ [_1804328, _1804330] : [50533 ^ _782435 : [(50534 ^ _782435) ^ [_1804394] : [hBOOL(hAPP(_1804330, _1804394))]], 50536 ^ _782435 : [(50537 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1804328), 50535 ^ [_1804328, _1804330]), c_Orderings_Otop__class_Otop(tc_fun(_1804328, tc_HOL_Obool)))))], (50539 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1804330, 50535 ^ [_1804328, _1804330])))]]], (50521 ^ _782435) ^ [_1804128, _1804130] : [-(hBOOL(hAPP(_1804130, 50528 ^ [_1804128, _1804130]))), 50522 ^ _782435 : [(50523 ^ _782435) ^ [_1804189] : [hBOOL(hAPP(hAPP(c_member(_1804128), _1804189), c_Orderings_Otop__class_Otop(tc_fun(_1804128, tc_HOL_Obool)))), hBOOL(hAPP(_1804130, _1804189))]]], (50541 ^ _782435) ^ [_1804497, _1804499] : [-(c_Relation_Otrans(_1804497, c_Transitive__Closure_Ortrancl(_1804497, _1804499)))], (50543 ^ _782435) ^ [_1804525, _1804527] : [c_Relation_Otrans(_1804525, _1804527), -(c_Relation_Otrans(tc_List_Olist(_1804525), c_List_Olexord(_1804525, _1804527)))], (50549 ^ _782435) ^ [_1804612] : [-(c_Relation_Otrans(tc_fun(_1804612, tc_HOL_Obool), c_Wellfounded_Ofinite__psubset(_1804612)))], (50551 ^ _782435) ^ [_1804640, _1804642] : [-(c_Relation_Otrans(_1804640, c_Relation_OId__on(_1804640, _1804642)))], (50553 ^ _782435) ^ [_1804668, _1804670] : [c_Relation_Otrans(_1804668, _1804670), -(c_Transitive__Closure_Otrancl(_1804668, _1804670) = _1804670)], (50559 ^ _782435) ^ [_1804751, _1804753] : [-(c_Relation_Otrans(_1804751, c_Transitive__Closure_Otrancl(_1804751, _1804753)))], (50561 ^ _782435) ^ [_1804779] : [-(c_Relation_Otrans(_1804779, c_Relation_OId(_1804779)))], (50563 ^ _782435) ^ [_1804819, _1804821] : [c_Relation_Otrans(_1804819, hAPP(c_Relation_Oconverse(_1804819, _1804819), _1804821)), -(c_Relation_Otrans(_1804819, _1804821))], (50569 ^ _782435) ^ [_1804904, _1804906] : [c_Relation_Otrans(_1804904, _1804906), -(c_Relation_Otrans(_1804904, hAPP(c_Relation_Oconverse(_1804904, _1804904), _1804906)))], (50575 ^ _782435) ^ [_1804995, _1804997] : [c_Relation_Otrans(_1804995, _1804997), -(c_Relation_Otrans(tc_List_Olist(_1804995), c_List_Olistrel(_1804995, _1804997)))], (50581 ^ _782435) ^ [_1805082, _1805084, _1805086] : [hBOOL(hAPP(hAPP(c_member(_1805084), _1805082), c_Orderings_Obot__class_Obot(tc_fun(_1805084, tc_HOL_Obool)))), hBOOL(hAPP(_1805086, _1805082))], (50587 ^ _782435) ^ [_1805188, _1805190, _1805192, _1805194] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805188), _1805190)), 50590 ^ _782435 : [(50601 ^ _782435) ^ [] : [50603 ^ _782435 : [(50604 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1805188), 50602 ^ [_1805188, _1805190, _1805192, _1805194]), _1805190)))], (50606 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805192), hAPP(c_Set_OCollect(_1805192), hAPP(hAPP(c_COMBC(_1805192, _1805188, tc_HOL_Obool), _1805194), 50602 ^ [_1805188, _1805190, _1805192, _1805194]))))]], -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805192), hAPP(c_Set_OCollect(_1805192), hAPP(hAPP(c_COMBB(tc_fun(_1805188, tc_HOL_Obool), tc_HOL_Obool, _1805192), c_HOL_OEx(_1805188)), hAPP(hAPP(c_COMBB(tc_fun(_1805188, tc_HOL_Obool), tc_fun(_1805188, tc_HOL_Obool), _1805192), hAPP(c_COMBS(_1805188, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805188), c_fconj), hAPP(hAPP(c_COMBC(_1805188, tc_fun(_1805188, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805188)), _1805190)))), _1805194))))))], (50591 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1805192), hAPP(c_Set_OCollect(_1805192), hAPP(hAPP(c_COMBB(tc_fun(_1805188, tc_HOL_Obool), tc_HOL_Obool, _1805192), c_HOL_OEx(_1805188)), hAPP(hAPP(c_COMBB(tc_fun(_1805188, tc_HOL_Obool), tc_fun(_1805188, tc_HOL_Obool), _1805192), hAPP(c_COMBS(_1805188, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1805188), c_fconj), hAPP(hAPP(c_COMBC(_1805188, tc_fun(_1805188, tc_HOL_Obool), tc_HOL_Obool), c_member(_1805188)), _1805190)))), _1805194))))), 50594 ^ _782435 : [(50595 ^ _782435) ^ [_1805496] : [hBOOL(hAPP(hAPP(c_member(_1805188), _1805496), _1805190)), -(hBOOL(hAPP(c_Finite__Set_Ofinite(_1805192), hAPP(c_Set_OCollect(_1805192), hAPP(hAPP(c_COMBC(_1805192, _1805188, tc_HOL_Obool), _1805194), _1805496)))))]]]]], (50610 ^ _782435) ^ [_1805892, _1805894] : [c_Relation_Otrans(_1805892, _1805894), -(c_Relation_Otrans(_1805892, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1805892, _1805892), tc_HOL_Obool)), _1805894), c_Relation_OId(_1805892))))], (50616 ^ _782435) ^ [_1806019, _1806021, _1806023] : [c_List_Olist__ex(_1806019, _1806021, _1806023), 50620 ^ _782435 : [(50621 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806019), 50619 ^ [_1806019, _1806021, _1806023]), hAPP(c_List_Oset(_1806019), _1806023))))], (50623 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1806021, 50619 ^ [_1806019, _1806021, _1806023])))]]], (50625 ^ _782435) ^ [_1806173, _1806175, _1806177] : [-(c_List_Olist__ex(_1806173, _1806175, _1806177)), 50626 ^ _782435 : [(50627 ^ _782435) ^ [_1806230] : [hBOOL(hAPP(hAPP(c_member(_1806173), _1806230), hAPP(c_List_Oset(_1806173), _1806177))), hBOOL(hAPP(_1806175, _1806230))]]], (50645 ^ _782435) ^ [_1806577, _1806579, _1806581] : [c_List_Olist__ex(_1806577, _1806581, _1806579), 50649 ^ _782435 : [(50650 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1806577), 50648 ^ [_1806577, _1806579, _1806581]), hAPP(c_List_Oset(_1806577), _1806579))))], (50652 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1806581, 50648 ^ [_1806577, _1806579, _1806581])))]]], (50635 ^ _782435) ^ [_1806387, _1806389, _1806391] : [-(c_List_Olist__ex(_1806387, _1806391, _1806389)), 50636 ^ _782435 : [(50637 ^ _782435) ^ [_1806444] : [hBOOL(hAPP(hAPP(c_member(_1806387), _1806444), hAPP(c_List_Oset(_1806387), _1806389))), hBOOL(hAPP(_1806391, _1806444))]]], (50654 ^ _782435) ^ [_1806737, _1806739, _1806741, _1806743] : [-(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(_1806737, tc_fun(_1806739, tc_HOL_Obool)), _1806741), _1806743) = c_Complete__Lattice_OInf__class_OInf(tc_fun(_1806739, tc_HOL_Obool), hAPP(c_Set_OCollect(tc_fun(_1806739, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806737, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1806739, tc_HOL_Obool)), c_HOL_OEx(_1806737)), hAPP(hAPP(c_COMBB(tc_fun(_1806737, tc_HOL_Obool), tc_fun(_1806737, tc_HOL_Obool), tc_fun(_1806739, tc_HOL_Obool)), hAPP(c_COMBS(_1806737, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1806737), c_fconj), hAPP(hAPP(c_COMBC(_1806737, tc_fun(_1806737, tc_HOL_Obool), tc_HOL_Obool), c_member(_1806737)), _1806741)))), hAPP(hAPP(c_COMBC(tc_fun(_1806739, tc_HOL_Obool), tc_fun(_1806737, tc_fun(_1806739, tc_HOL_Obool)), tc_fun(_1806737, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806739, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1806737, tc_fun(_1806739, tc_HOL_Obool)), tc_fun(_1806737, tc_HOL_Obool)), tc_fun(_1806739, tc_HOL_Obool)), c_COMBB(tc_fun(_1806739, tc_HOL_Obool), tc_HOL_Obool, _1806737)), c_fequal)), _1806743))))))], (50656 ^ _782435) ^ [_1806921, _1806923, _1806925, _1806927] : [class_Complete__Lattice_Ocomplete__lattice(_1806921), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1806923, _1806921), _1806925), _1806927) = c_Complete__Lattice_OSup__class_OSup(_1806921, hAPP(c_Set_OCollect(_1806921), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806923, _1806921), tc_HOL_Obool), tc_HOL_Obool, _1806921), c_HOL_OEx(tc_fun(_1806923, _1806921))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1806923, _1806921), tc_HOL_Obool), tc_fun(tc_fun(_1806923, _1806921), tc_HOL_Obool), _1806921), hAPP(c_COMBS(tc_fun(_1806923, _1806921), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1806923, _1806921)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1806923, _1806921), tc_fun(tc_fun(_1806923, _1806921), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1806923, _1806921))), _1806925)))), hAPP(hAPP(c_COMBC(_1806921, tc_fun(tc_fun(_1806923, _1806921), _1806921), tc_fun(tc_fun(_1806923, _1806921), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1806921, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1806923, _1806921), _1806921), tc_fun(tc_fun(_1806923, _1806921), tc_HOL_Obool)), _1806921), c_COMBB(_1806921, tc_HOL_Obool, tc_fun(_1806923, _1806921))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1806923, _1806921), _1806923, _1806921), c_COMBI(tc_fun(_1806923, _1806921))), _1806927)))))))], (50662 ^ _782435) ^ [_1807364, _1807366, _1807368, _1807370] : [class_Complete__Lattice_Ocomplete__lattice(_1807364), -(hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(_1807366, _1807364), _1807368), _1807370) = c_Complete__Lattice_OSup__class_OSup(_1807364, hAPP(c_Set_OCollect(_1807364), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807366, _1807364), tc_HOL_Obool), tc_HOL_Obool, _1807364), c_HOL_OEx(tc_fun(_1807366, _1807364))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807366, _1807364), tc_HOL_Obool), tc_fun(tc_fun(_1807366, _1807364), tc_HOL_Obool), _1807364), hAPP(c_COMBS(tc_fun(_1807366, _1807364), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1807366, _1807364)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1807366, _1807364), tc_fun(tc_fun(_1807366, _1807364), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1807366, _1807364))), _1807368)))), hAPP(hAPP(c_COMBC(_1807364, tc_fun(tc_fun(_1807366, _1807364), _1807364), tc_fun(tc_fun(_1807366, _1807364), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807364, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1807366, _1807364), _1807364), tc_fun(tc_fun(_1807366, _1807364), tc_HOL_Obool)), _1807364), c_COMBB(_1807364, tc_HOL_Obool, tc_fun(_1807366, _1807364))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1807366, _1807364), _1807366, _1807364), c_COMBI(tc_fun(_1807366, _1807364))), _1807370)))))))], (50668 ^ _782435) ^ [_1807807, _1807809, _1807811, _1807813] : [class_Complete__Lattice_Ocomplete__lattice(_1807807), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1807809, _1807807), _1807811), _1807813) = c_Complete__Lattice_OInf__class_OInf(_1807807, hAPP(c_Set_OCollect(_1807807), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807809, _1807807), tc_HOL_Obool), tc_HOL_Obool, _1807807), c_HOL_OEx(tc_fun(_1807809, _1807807))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1807809, _1807807), tc_HOL_Obool), tc_fun(tc_fun(_1807809, _1807807), tc_HOL_Obool), _1807807), hAPP(c_COMBS(tc_fun(_1807809, _1807807), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1807809, _1807807)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1807809, _1807807), tc_fun(tc_fun(_1807809, _1807807), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1807809, _1807807))), _1807811)))), hAPP(hAPP(c_COMBC(_1807807, tc_fun(tc_fun(_1807809, _1807807), _1807807), tc_fun(tc_fun(_1807809, _1807807), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1807807, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1807809, _1807807), _1807807), tc_fun(tc_fun(_1807809, _1807807), tc_HOL_Obool)), _1807807), c_COMBB(_1807807, tc_HOL_Obool, tc_fun(_1807809, _1807807))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1807809, _1807807), _1807809, _1807807), c_COMBI(tc_fun(_1807809, _1807807))), _1807813)))))))], (50674 ^ _782435) ^ [_1808250, _1808252, _1808254, _1808256] : [class_Complete__Lattice_Ocomplete__lattice(_1808250), -(hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(_1808252, _1808250), _1808254), _1808256) = c_Complete__Lattice_OInf__class_OInf(_1808250, hAPP(c_Set_OCollect(_1808250), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808252, _1808250), tc_HOL_Obool), tc_HOL_Obool, _1808250), c_HOL_OEx(tc_fun(_1808252, _1808250))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1808252, _1808250), tc_HOL_Obool), tc_fun(tc_fun(_1808252, _1808250), tc_HOL_Obool), _1808250), hAPP(c_COMBS(tc_fun(_1808252, _1808250), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1808252, _1808250)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1808252, _1808250), tc_fun(tc_fun(_1808252, _1808250), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1808252, _1808250))), _1808254)))), hAPP(hAPP(c_COMBC(_1808250, tc_fun(tc_fun(_1808252, _1808250), _1808250), tc_fun(tc_fun(_1808252, _1808250), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1808250, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1808252, _1808250), _1808250), tc_fun(tc_fun(_1808252, _1808250), tc_HOL_Obool)), _1808250), c_COMBB(_1808250, tc_HOL_Obool, tc_fun(_1808252, _1808250))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1808252, _1808250), _1808252, _1808250), c_COMBI(tc_fun(_1808252, _1808250))), _1808256)))))))], (50680 ^ _782435) ^ [_1808693, _1808695, _1808697, _1808699] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1808693), _1808695)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1808693), _1808697)), -(_1808697 = c_Orderings_Obot__class_Obot(tc_fun(_1808693, tc_HOL_Obool))), -(c_Wellfounded_Omax__extp(_1808693, _1808699, _1808695, _1808697)), 50694 ^ _782435 : [(50695 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1808693), 50693 ^ [_1808693, _1808695, _1808697, _1808699]), _1808695)))], (50697 ^ _782435) ^ [_1809038] : [hBOOL(hAPP(hAPP(c_member(_1808693), _1809038), _1808697)), hBOOL(hAPP(hAPP(_1808699, 50693 ^ [_1808693, _1808695, _1808697, _1808699]), _1809038))]]], (50705 ^ _782435) ^ [_1809219, _1809221] : [c_Predicate_Otransp(_1809219, _1809221), -(c_Relation_Otrans(_1809219, hAPP(c_Set_OCollect(tc_prod(_1809219, _1809219)), hAPP(c_Product__Type_Oprod_Oprod__case(_1809219, _1809219, tc_HOL_Obool), _1809221))))], (50711 ^ _782435) ^ [_1809322, _1809324] : [c_Relation_Otrans(_1809322, hAPP(c_Set_OCollect(tc_prod(_1809322, _1809322)), hAPP(c_Product__Type_Oprod_Oprod__case(_1809322, _1809322, tc_HOL_Obool), _1809324))), -(c_Predicate_Otransp(_1809322, _1809324))], (50717 ^ _782435) ^ [_1809431, _1809433, _1809435, _1809437, _1809439] : [c_Predicate_Otransp(_1809431, _1809433), hBOOL(hAPP(hAPP(_1809433, _1809435), _1809437)), hBOOL(hAPP(hAPP(_1809433, _1809437), _1809439)), -(hBOOL(hAPP(hAPP(_1809433, _1809435), _1809439)))], (50731 ^ _782435) ^ [_1809660, _1809662] : [c_Equiv__Relations_Oequivp(_1809660, _1809662), 50734 ^ _782435 : [(50735 ^ _782435) ^ [] : [-(c_Predicate_Oreflp(_1809660, _1809662))], (50737 ^ _782435) ^ [] : [-(c_Predicate_Osymp(_1809660, _1809662))], (50739 ^ _782435) ^ [] : [-(c_Predicate_Otransp(_1809660, _1809662))]]], (50741 ^ _782435) ^ [_1809791, _1809793] : [c_Predicate_Oreflp(_1809791, _1809793), c_Predicate_Osymp(_1809791, _1809793), c_Predicate_Otransp(_1809791, _1809793), -(c_Equiv__Relations_Oequivp(_1809791, _1809793))], (50755 ^ _782435) ^ [_1809972, _1809974, _1809976, _1809978] : [c_Predicate_Osymp(_1809972, _1809974), hBOOL(hAPP(hAPP(_1809974, _1809976), _1809978)), -(hBOOL(hAPP(hAPP(_1809974, _1809978), _1809976)))], (50765 ^ _782435) ^ [_1810144, _1810146] : [c_Equiv__Relations_Oequivp(_1810144, _1810146), 50768 ^ _782435 : [(50769 ^ _782435) ^ [] : [-(c_Predicate_Oreflp(_1810144, _1810146))], (50771 ^ _782435) ^ [] : [-(c_Predicate_Osymp(_1810144, _1810146))], (50773 ^ _782435) ^ [] : [-(c_Predicate_Otransp(_1810144, _1810146))]]], (50775 ^ _782435) ^ [_1810267, _1810269] : [-(c_Equiv__Relations_Oequivp(_1810267, _1810269)), c_Predicate_Oreflp(_1810267, _1810269), c_Predicate_Osymp(_1810267, _1810269), c_Predicate_Otransp(_1810267, _1810269)], (50789 ^ _782435) ^ [_1810471, _1810473, _1810475, _1810477] : [c_Wellfounded_Omax__extp(_1810471, _1810473, _1810475, _1810477), 50792 ^ _782435 : [(50793 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1810471), _1810475)))], (50795 ^ _782435) ^ [] : [-(hBOOL(hAPP(c_Finite__Set_Ofinite(_1810471), _1810477)))], (50797 ^ _782435) ^ [] : [_1810477 = c_Orderings_Obot__class_Obot(tc_fun(_1810471, tc_HOL_Obool))], (50799 ^ _782435) ^ [_1810687] : [hBOOL(hAPP(hAPP(c_member(_1810471), _1810687), _1810475)), 50803 ^ _782435 : [(50804 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810471), 50802 ^ [_1810471, _1810473, _1810475, _1810477, _1810687]), _1810477)))], (50806 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1810473, _1810687), 50802 ^ [_1810471, _1810473, _1810475, _1810477, _1810687])))]]]]], (50808 ^ _782435) ^ [_1810871, _1810873, _1810875, _1810877] : [-(c_Wellfounded_Omax__extp(_1810871, _1810873, _1810875, _1810877)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1810871), _1810875)), hBOOL(hAPP(c_Finite__Set_Ofinite(_1810871), _1810877)), -(_1810877 = c_Orderings_Obot__class_Obot(tc_fun(_1810871, tc_HOL_Obool))), 50822 ^ _782435 : [(50823 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1810871), 50821 ^ [_1810871, _1810873, _1810875, _1810877]), _1810875)))], (50825 ^ _782435) ^ [_1811216] : [hBOOL(hAPP(hAPP(c_member(_1810871), _1811216), _1810877)), hBOOL(hAPP(hAPP(_1810873, 50821 ^ [_1810871, _1810873, _1810875, _1810877]), _1811216))]]], (50833 ^ _782435) ^ [_1811384, _1811386] : [c_Relation_Otrans(_1811384, _1811386), c_Relation_Oantisym(_1811384, _1811386), -(c_Relation_Otrans(_1811384, hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(_1811384, _1811384), tc_HOL_Obool)), _1811386), c_Relation_OId(_1811384))))], (50843 ^ _782435) ^ [_1811545] : [-(c_Relation_Oantisym(_1811545, c_Orderings_Obot__class_Obot(tc_fun(tc_prod(_1811545, _1811545), tc_HOL_Obool))))], (50845 ^ _782435) ^ [_1811591, _1811593] : [c_Relation_Oantisym(_1811591, hAPP(c_Relation_Oconverse(_1811591, _1811591), _1811593)), -(c_Relation_Oantisym(_1811591, _1811593))], (50851 ^ _782435) ^ [_1811676, _1811678] : [c_Relation_Oantisym(_1811676, _1811678), -(c_Relation_Oantisym(_1811676, hAPP(c_Relation_Oconverse(_1811676, _1811676), _1811678)))], (50857 ^ _782435) ^ [_1811767] : [-(c_Relation_Oantisym(_1811767, c_Relation_OId(_1811767)))], (50859 ^ _782435) ^ [_1811792, _1811794] : [-(c_Relation_Oantisym(_1811792, c_Relation_OId__on(_1811792, _1811794)))], (50861 ^ _782435) ^ [_1811820, _1811822, _1811824] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1811820, _1811820), tc_HOL_Obool)), _1811822), _1811824)), c_Relation_Oantisym(_1811820, _1811824), -(c_Relation_Oantisym(_1811820, _1811822))], (50885 ^ _782435) ^ [_1812319, _1812321] : [50888 ^ _782435 : [(50889 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812319, _1812319)), hAPP(hAPP(c_Product__Type_OPair(_1812319, _1812319), 50886 ^ [_1812319, _1812321]), 50887 ^ [_1812319, _1812321])), _1812321)))], (50891 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1812319, _1812319)), hAPP(hAPP(c_Product__Type_OPair(_1812319, _1812319), 50887 ^ [_1812319, _1812321]), 50886 ^ [_1812319, _1812321])), _1812321)))], (50893 ^ _782435) ^ [] : [50886 ^ [_1812319, _1812321] = 50887 ^ [_1812319, _1812321]]], -(c_Relation_Oantisym(_1812319, _1812321))], (50871 ^ _782435) ^ [_1811994, _1811996] : [c_Relation_Oantisym(_1811994, _1811996), 50874 ^ _782435 : [(50875 ^ _782435) ^ [_1812106, _1812108] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1811994, _1811994)), hAPP(hAPP(c_Product__Type_OPair(_1811994, _1811994), _1812108), _1812106)), _1811996)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1811994, _1811994)), hAPP(hAPP(c_Product__Type_OPair(_1811994, _1811994), _1812106), _1812108)), _1811996)), -(_1812108 = _1812106)]]], (50897 ^ _782435) ^ [_1812640, _1812642, _1812644, _1812646] : [c_Relation_Oantisym(_1812640, _1812642), hBOOL(hAPP(hAPP(c_member(tc_prod(_1812640, _1812640)), hAPP(hAPP(c_Product__Type_OPair(_1812640, _1812640), _1812644), _1812646)), _1812642)), hBOOL(hAPP(hAPP(c_member(tc_prod(_1812640, _1812640)), hAPP(hAPP(c_Product__Type_OPair(_1812640, _1812640), _1812646), _1812644)), _1812642)), -(_1812644 = _1812646)], (50911 ^ _782435) ^ [_1812924, _1812926] : [c_Relation_Oantisym(_1812924, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1812924, _1812924), tc_HOL_Obool)), _1812926), c_Relation_OId(_1812924))), -(c_Relation_Oantisym(_1812924, _1812926))], (50917 ^ _782435) ^ [_1813029, _1813031] : [c_Relation_Oantisym(_1813029, _1813031), -(c_Relation_Oantisym(_1813029, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1813029, _1813029), tc_HOL_Obool)), _1813031), c_Relation_OId(_1813029))))], (50923 ^ _782435) ^ [_1813140, _1813142] : [c_Wellfounded_Oacyclic(_1813140, _1813142), -(c_Relation_Oantisym(_1813140, c_Transitive__Closure_Ortrancl(_1813140, _1813142)))], (50929 ^ _782435) ^ [_1813223, _1813225, _1813227, _1813229, _1813231, _1813233] : [-(c_Partial__Function_Ofun__lub(_1813223, _1813225, _1813227, _1813229, _1813231, _1813233) = hAPP(_1813229, hAPP(c_Set_OCollect(_1813223), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1813227, _1813223), tc_HOL_Obool), tc_HOL_Obool, _1813223), c_HOL_OEx(tc_fun(_1813227, _1813223))), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1813227, _1813223), tc_HOL_Obool), tc_fun(tc_fun(_1813227, _1813223), tc_HOL_Obool), _1813223), hAPP(c_COMBS(tc_fun(_1813227, _1813223), tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), tc_fun(_1813227, _1813223)), c_fconj), hAPP(hAPP(c_COMBC(tc_fun(_1813227, _1813223), tc_fun(tc_fun(_1813227, _1813223), tc_HOL_Obool), tc_HOL_Obool), c_member(tc_fun(_1813227, _1813223))), _1813231)))), hAPP(hAPP(c_COMBC(_1813223, tc_fun(tc_fun(_1813227, _1813223), _1813223), tc_fun(tc_fun(_1813227, _1813223), tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(_1813223, tc_HOL_Obool), tc_fun(tc_fun(tc_fun(_1813227, _1813223), _1813223), tc_fun(tc_fun(_1813227, _1813223), tc_HOL_Obool)), _1813223), c_COMBB(_1813223, tc_HOL_Obool, tc_fun(_1813227, _1813223))), c_fequal)), hAPP(hAPP(c_COMBC(tc_fun(_1813227, _1813223), _1813227, _1813223), c_COMBI(tc_fun(_1813227, _1813223))), _1813233)))))))], (50931 ^ _782435) ^ [_1813436, _1813438] : [c_Relation_Osym(_1813436, _1813438), c_Relation_Otrans(_1813436, _1813438), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(_1813436, _1813436), tc_HOL_Obool)), hAPP(hAPP(c_Relation_Orel__comp(_1813436, _1813436, _1813436), hAPP(c_Relation_Oconverse(_1813436, _1813436), _1813438)), _1813438)), _1813438)))], (50941 ^ _782435) ^ [_1813623, _1813625, _1813627, _1813629] : [c_Relation_Osym(_1813623, _1813625), hBOOL(hAPP(hAPP(c_member(tc_prod(_1813623, _1813623)), hAPP(hAPP(c_Product__Type_OPair(_1813623, _1813623), _1813627), _1813629)), _1813625)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813623, _1813623)), hAPP(hAPP(c_Product__Type_OPair(_1813623, _1813623), _1813629), _1813627)), _1813625)))], (50961 ^ _782435) ^ [_1814114, _1814116] : [50964 ^ _782435 : [(50965 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1814114, _1814114)), hAPP(hAPP(c_Product__Type_OPair(_1814114, _1814114), 50962 ^ [_1814114, _1814116]), 50963 ^ [_1814114, _1814116])), _1814116)))], (50967 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1814114, _1814114)), hAPP(hAPP(c_Product__Type_OPair(_1814114, _1814114), 50963 ^ [_1814114, _1814116]), 50962 ^ [_1814114, _1814116])), _1814116))]], -(c_Relation_Osym(_1814114, _1814116))], (50951 ^ _782435) ^ [_1813851, _1813853] : [c_Relation_Osym(_1813851, _1813853), 50954 ^ _782435 : [(50955 ^ _782435) ^ [_1813957, _1813959] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1813851, _1813851)), hAPP(hAPP(c_Product__Type_OPair(_1813851, _1813851), _1813959), _1813957)), _1813853)), -(hBOOL(hAPP(hAPP(c_member(tc_prod(_1813851, _1813851)), hAPP(hAPP(c_Product__Type_OPair(_1813851, _1813851), _1813957), _1813959)), _1813853)))]]], (50971 ^ _782435) ^ [_1814379, _1814381, _1814383, _1814385] : [c_Relation_Osym(_1814379, _1814381), -(c_Relation_Osym(_1814383, hAPP(hAPP(c_Relation_Oinv__image(_1814379, _1814383), _1814381), _1814385)))], (50977 ^ _782435) ^ [_1814478, _1814480] : [-(c_Relation_Osym(_1814478, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1814478, _1814478), tc_HOL_Obool)), _1814480), hAPP(c_Relation_Oconverse(_1814478, _1814478), _1814480))))], (50979 ^ _782435) ^ [_1814523, _1814525, _1814527] : [c_Relation_Osym(_1814523, _1814525), c_Relation_Osym(_1814523, _1814527), -(c_Relation_Osym(_1814523, hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(_1814523, _1814523), tc_HOL_Obool)), _1814525), _1814527)))], (50989 ^ _782435) ^ [_1814684, _1814686] : [c_Relation_Osym(_1814684, _1814686), -(c_Relation_Osym(_1814684, c_Transitive__Closure_Ortrancl(_1814684, _1814686)))], (50995 ^ _782435) ^ [_1814767, _1814769] : [-(c_Relation_Osym(_1814767, c_Relation_OId__on(_1814767, _1814769)))], (50997 ^ _782435) ^ [_1814795, _1814797] : [c_Relation_Osym(_1814795, _1814797), -(c_Relation_Osym(_1814795, c_Transitive__Closure_Otrancl(_1814795, _1814797)))], (51003 ^ _782435) ^ [_1814878, _1814880, _1814882] : [c_Relation_Osym(_1814878, _1814880), c_Relation_Osym(_1814878, _1814882), -(c_Relation_Osym(_1814878, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1814878, _1814878), tc_HOL_Obool)), _1814880), _1814882)))], (51013 ^ _782435) ^ [_1815039] : [-(c_Relation_Osym(_1815039, c_Relation_OId(_1815039)))], (51015 ^ _782435) ^ [_1815079, _1815081] : [c_Relation_Osym(_1815079, _1815081), -(hAPP(c_Relation_Oconverse(_1815079, _1815079), _1815081) = _1815081)], (51021 ^ _782435) ^ [_1815164, _1815166] : [hAPP(c_Relation_Oconverse(_1815164, _1815164), _1815166) = _1815166, -(c_Relation_Osym(_1815164, _1815166))], (51027 ^ _782435) ^ [_1815270, _1815272] : [c_Relation_Osym(_1815270, hAPP(c_Relation_Oconverse(_1815270, _1815270), _1815272)), -(c_Relation_Osym(_1815270, _1815272))], (51033 ^ _782435) ^ [_1815355, _1815357] : [c_Relation_Osym(_1815355, _1815357), -(c_Relation_Osym(_1815355, hAPP(c_Relation_Oconverse(_1815355, _1815355), _1815357)))], (51039 ^ _782435) ^ [_1815446, _1815448] : [c_Relation_Osym(_1815446, _1815448), -(c_Relation_Osym(tc_List_Olist(_1815446), c_List_Olistrel(_1815446, _1815448)))], (51045 ^ _782435) ^ [_1815533, _1815535] : [-(c_Relation_Osym(_1815533, hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(_1815533, _1815533), tc_HOL_Obool)), _1815535), hAPP(c_Relation_Oconverse(_1815533, _1815533), _1815535))))], (51047 ^ _782435) ^ [_1815596, _1815598, _1815600] : [c_Equiv__Relations_Oequiv(_1815596, _1815598, _1815600), 51050 ^ _782435 : [(51051 ^ _782435) ^ [] : [-(c_Relation_Orefl__on(_1815596, _1815598, _1815600))], (51053 ^ _782435) ^ [] : [-(c_Relation_Osym(_1815596, _1815600))], (51055 ^ _782435) ^ [] : [-(c_Relation_Otrans(_1815596, _1815600))]]], (51057 ^ _782435) ^ [_1815725, _1815727, _1815729] : [-(c_Equiv__Relations_Oequiv(_1815725, _1815727, _1815729)), c_Relation_Orefl__on(_1815725, _1815727, _1815729), c_Relation_Osym(_1815725, _1815729), c_Relation_Otrans(_1815725, _1815729)], (51071 ^ _782435) ^ [_1815918, _1815920, _1815922] : [c_Relation_Orefl__on(_1815918, _1815920, _1815922), c_Relation_Osym(_1815918, _1815922), c_Relation_Otrans(_1815918, _1815922), -(c_Equiv__Relations_Oequiv(_1815918, _1815920, _1815922))], (51085 ^ _782435) ^ [_1816109, _1816111, _1816113] : [c_Equiv__Relations_Oequiv(_1816109, _1816111, _1816113), 51088 ^ _782435 : [(51089 ^ _782435) ^ [] : [-(c_Relation_Orefl__on(_1816109, _1816111, _1816113))], (51091 ^ _782435) ^ [] : [-(c_Relation_Osym(_1816109, _1816113))], (51093 ^ _782435) ^ [] : [-(c_Relation_Otrans(_1816109, _1816113))]]], (51095 ^ _782435) ^ [_1816261, _1816263] : [c_Predicate_Osymp(_1816261, _1816263), -(c_Relation_Osym(_1816261, hAPP(c_Set_OCollect(tc_prod(_1816261, _1816261)), hAPP(c_Product__Type_Oprod_Oprod__case(_1816261, _1816261, tc_HOL_Obool), _1816263))))], (51101 ^ _782435) ^ [_1816364, _1816366] : [c_Relation_Osym(_1816364, hAPP(c_Set_OCollect(tc_prod(_1816364, _1816364)), hAPP(c_Product__Type_Oprod_Oprod__case(_1816364, _1816364, tc_HOL_Obool), _1816366))), -(c_Predicate_Osymp(_1816364, _1816366))], (51107 ^ _782435) ^ [_1816473, _1816475] : [51108 ^ _782435 : [(51109 ^ _782435) ^ [_1816529] : [hBOOL(hAPP(hAPP(_1816473, _1816529), _1816529))]], c_Predicate_Osymp(_1816475, _1816473), c_Predicate_Otransp(_1816475, _1816473), -(c_Equiv__Relations_Opart__equivp(_1816475, _1816473))], (51121 ^ _782435) ^ [_1816692, _1816694] : [c_Equiv__Relations_Opart__equivp(_1816692, _1816694), 51125 ^ _782435 : [(51126 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1816694, 51124 ^ [_1816692, _1816694]), 51124 ^ [_1816692, _1816694])))], (51128 ^ _782435) ^ [] : [-(c_Predicate_Osymp(_1816692, _1816694))], (51130 ^ _782435) ^ [] : [-(c_Predicate_Otransp(_1816692, _1816694))]]], (51132 ^ _782435) ^ [_1816844, _1816846] : [-(c_Equiv__Relations_Opart__equivp(_1816844, _1816846)), 51135 ^ _782435 : [(51136 ^ _782435) ^ [_1816921] : [hBOOL(hAPP(hAPP(_1816846, _1816921), _1816921))]], c_Predicate_Osymp(_1816844, _1816846), c_Predicate_Otransp(_1816844, _1816846)], (51146 ^ _782435) ^ [_1817050, _1817052, _1817054, _1817056, _1817058] : [c_Equiv__Relations_Opart__equivp(_1817050, _1817052), hBOOL(hAPP(hAPP(_1817052, _1817054), _1817056)), hBOOL(hAPP(hAPP(_1817052, _1817056), _1817058)), -(hBOOL(hAPP(hAPP(_1817052, _1817054), _1817058)))], (51160 ^ _782435) ^ [_1817279, _1817281, _1817283, _1817285] : [c_Equiv__Relations_Opart__equivp(_1817279, _1817281), hBOOL(hAPP(hAPP(_1817281, _1817283), _1817285)), -(hBOOL(hAPP(hAPP(_1817281, _1817285), _1817283)))], (51201 ^ _782435) ^ [_1818032, _1818034] : [-(c_Equiv__Relations_Opart__equivp(_1818032, _1818034)), 51204 ^ _782435 : [(51205 ^ _782435) ^ [_1818152] : [hBOOL(hAPP(hAPP(_1818034, _1818152), _1818152))]], 51222 ^ _782435 : [(51223 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1818034, 51206 ^ [_1818032, _1818034]), 51206 ^ [_1818032, _1818034])))], (51225 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1818034, 51207 ^ [_1818032, _1818034]), 51207 ^ [_1818032, _1818034])))], (51227 ^ _782435) ^ [] : [-(hAPP(_1818034, 51206 ^ [_1818032, _1818034]) = hAPP(_1818034, 51207 ^ [_1818032, _1818034]))], (51229 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1818034, 51206 ^ [_1818032, _1818034]), 51207 ^ [_1818032, _1818034]))]], 51210 ^ _782435 : [(51211 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1818034, 51206 ^ [_1818032, _1818034]), 51207 ^ [_1818032, _1818034])))], (51213 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1818034, 51206 ^ [_1818032, _1818034]), 51206 ^ [_1818032, _1818034])), hBOOL(hAPP(hAPP(_1818034, 51207 ^ [_1818032, _1818034]), 51207 ^ [_1818032, _1818034])), hAPP(_1818034, 51206 ^ [_1818032, _1818034]) = hAPP(_1818034, 51207 ^ [_1818032, _1818034])]]], (51170 ^ _782435) ^ [_1817451, _1817453] : [c_Equiv__Relations_Opart__equivp(_1817451, _1817453), 51174 ^ _782435 : [(51175 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1817453, 51173 ^ [_1817451, _1817453]), 51173 ^ [_1817451, _1817453])))], (51177 ^ _782435) ^ [_1817624, _1817626] : [hBOOL(hAPP(hAPP(_1817453, _1817626), _1817624)), 51180 ^ _782435 : [(51181 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1817453, _1817626), _1817626)))], (51183 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1817453, _1817624), _1817624)))], (51185 ^ _782435) ^ [] : [-(hAPP(_1817453, _1817626) = hAPP(_1817453, _1817624))]]], (51187 ^ _782435) ^ [_1817793, _1817795] : [-(hBOOL(hAPP(hAPP(_1817453, _1817795), _1817793))), hBOOL(hAPP(hAPP(_1817453, _1817795), _1817795)), hBOOL(hAPP(hAPP(_1817453, _1817793), _1817793)), hAPP(_1817453, _1817795) = hAPP(_1817453, _1817793)]]], (51233 ^ _782435) ^ [_1818700, _1818702] : [c_Equiv__Relations_Oequivp(_1818700, _1818702), -(c_Equiv__Relations_Opart__equivp(_1818700, _1818702))], (51239 ^ _782435) ^ [_1818777, _1818779] : [c_Equiv__Relations_Opart__equivp(_1818777, _1818779), 51243 ^ _782435 : [(51244 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1818779, 51242 ^ [_1818777, _1818779]), 51242 ^ [_1818777, _1818779])))], (51246 ^ _782435) ^ [] : [-(c_Predicate_Osymp(_1818777, _1818779))], (51248 ^ _782435) ^ [] : [-(c_Predicate_Otransp(_1818777, _1818779))]]], (51250 ^ _782435) ^ [_1818937, _1818939] : [c_Equiv__Relations_Opart__equivp(_1818937, _1818939), -(hBOOL(hAPP(hAPP(c_member(tc_fun(_1818937, tc_HOL_Obool)), 51253 ^ [_1818937, _1818939]), hAPP(hAPP(c_COMBB(tc_fun(_1818937, tc_HOL_Obool), tc_HOL_Obool, tc_fun(_1818937, tc_HOL_Obool)), c_HOL_OEx(_1818937)), hAPP(hAPP(c_COMBB(tc_fun(_1818937, tc_HOL_Obool), tc_fun(_1818937, tc_HOL_Obool), tc_fun(_1818937, tc_HOL_Obool)), hAPP(c_COMBS(_1818937, tc_HOL_Obool, tc_HOL_Obool), hAPP(hAPP(c_COMBB(tc_HOL_Obool, tc_fun(tc_HOL_Obool, tc_HOL_Obool), _1818937), c_fconj), hAPP(hAPP(c_COMBS(_1818937, _1818937, tc_HOL_Obool), _1818939), c_COMBI(_1818937))))), hAPP(hAPP(c_COMBC(tc_fun(_1818937, tc_HOL_Obool), tc_fun(_1818937, tc_fun(_1818937, tc_HOL_Obool)), tc_fun(_1818937, tc_HOL_Obool)), hAPP(hAPP(c_COMBB(tc_fun(tc_fun(_1818937, tc_HOL_Obool), tc_HOL_Obool), tc_fun(tc_fun(_1818937, tc_fun(_1818937, tc_HOL_Obool)), tc_fun(_1818937, tc_HOL_Obool)), tc_fun(_1818937, tc_HOL_Obool)), c_COMBB(tc_fun(_1818937, tc_HOL_Obool), tc_HOL_Obool, _1818937)), c_fequal)), _1818939))))))], (51257 ^ _782435) ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308] : [class_Groups_Ocomm__monoid__mult(_1819298), hBOOL(hAPP(c_Finite__Set_Ofinite(_1819300), _1819302)), 51267 ^ _782435 : [(51268 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819300), 51266 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308]), _1819302)))], (51270 ^ _782435) ^ [] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1819304), hAPP(_1819306, 51266 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308])))]], 51274 ^ _782435 : [(51275 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819300), 51273 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308]), _1819302)))], (51278 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1819300), 51276 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308]), _1819302)))], (51280 ^ _782435) ^ [] : [51273 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308] = 51276 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308]], (51282 ^ _782435) ^ [] : [hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(_1819304, tc_HOL_Obool)), hAPP(_1819306, 51273 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308])), hAPP(_1819306, 51276 ^ [_1819298, _1819300, _1819302, _1819304, _1819306, _1819308])) = c_Orderings_Obot__class_Obot(tc_fun(_1819304, tc_HOL_Obool))]], -(hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1819298, _1819304, c_Groups_Otimes__class_Otimes(_1819298)), _1819308), c_Groups_Oone__class_Oone(_1819298)), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1819300, tc_fun(_1819304, tc_HOL_Obool)), _1819302), _1819306)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(_1819298, _1819300, c_Groups_Otimes__class_Otimes(_1819298)), hAPP(hAPP(c_COMBB(tc_fun(_1819304, tc_HOL_Obool), _1819298, _1819300), hAPP(hAPP(c_Finite__Set_Ofold__image(_1819298, _1819304, c_Groups_Otimes__class_Otimes(_1819298)), _1819308), c_Groups_Oone__class_Oone(_1819298))), _1819306)), c_Groups_Oone__class_Oone(_1819298)), _1819302))], (51286 ^ _782435) ^ [_1820258] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1820258), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), -(_1820258 = hAPP(c_Code__Numeral_Onat__of, 51289 ^ [_1820258]))], (51293 ^ _782435) ^ [_1820363, _1820365] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1820363), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), hBOOL(hAPP(_1820365, hAPP(c_Code__Numeral_Onat__of, 51298 ^ [_1820363, _1820365]))), -(hBOOL(hAPP(_1820365, _1820363)))], (51305 ^ _782435) ^ [_1820543] : [-(_1820543 = hAPP(c_Code__Numeral_Oof__nat, 51303 ^ [_1820543]))], (51307 ^ _782435) ^ [_1820571] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51303 ^ [_1820571]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (51309 ^ _782435) ^ [_1820606, _1820608] : [51311 ^ _782435 : [(51312 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51310 ^ [_1820606, _1820608]), c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))))], (51314 ^ _782435) ^ [] : [hBOOL(hAPP(_1820606, hAPP(c_Code__Numeral_Oof__nat, 51310 ^ [_1820606, _1820608])))]], -(hBOOL(hAPP(_1820606, _1820608)))], (51318 ^ _782435) ^ [_1820775, _1820777, _1820779, _1820781] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1820775, _1820777, _1820779, _1820781, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1820777)) = _1820779)], (51320 ^ _782435) ^ [_1820812, _1820814, _1820816, _1820818, _1820820, _1820822] : [-(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1820812, _1820814, _1820816, _1820818, c_Lazy__Sequence_Olazy__sequence_OInsert(_1820814, _1820820, _1820822)) = hAPP(hAPP(hAPP(_1820818, _1820820), _1820822), c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(_1820812, _1820814, _1820816, _1820818, _1820822)))], (51322 ^ _782435) ^ [_1820870, _1820872, _1820874, _1820876] : [hBOOL(hAPP(_1820870, _1820872)), hBOOL(hAPP(_1820874, _1820876)), -(hBOOL(hAPP(_1820870, c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))), -(c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1820870) = hAPP(c_Nat_OSuc, c_Orderings_Oord__class_OLeast(tc_Nat_Onat, _1820874))), 51338 ^ _782435 : [(51339 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1820870, hAPP(c_Nat_OSuc, 51335 ^ [_1820870, _1820872, _1820874, _1820876]))))], (51341 ^ _782435) ^ [] : [hBOOL(hAPP(_1820874, 51335 ^ [_1820870, _1820872, _1820874, _1820876]))]], 51342 ^ _782435 : [(51343 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1820874, 51335 ^ [_1820870, _1820872, _1820874, _1820876])))], (51345 ^ _782435) ^ [] : [hBOOL(hAPP(_1820870, hAPP(c_Nat_OSuc, 51335 ^ [_1820870, _1820872, _1820874, _1820876])))]]], (51349 ^ _782435) ^ [_1821372, _1821374] : [hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1821372), _1821374)), -(c_Quickcheck_Obeyond(_1821372, _1821374) = _1821374)], (51355 ^ _782435) ^ [_1821459, _1821461] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral), _1821459), _1821461))), -(c_Quickcheck_Obeyond(_1821459, _1821461) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (51361 ^ _782435) ^ [_1821505] : [-(c_Quickcheck_Obeyond(_1821505, c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))], (51363 ^ _782435) ^ [_1821531, _1821533, _1821535, _1821537, _1821539, _1821541] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1821531, _1821533, _1821535, _1821537), _1821539), _1821541) = hAPP(_1821537, hAPP(hAPP(c_Product__Type_OPair(_1821531, _1821533), _1821539), _1821541)))], (51365 ^ _782435) ^ [_1821587, _1821589, _1821591, _1821593, _1821595] : [51367 ^ _782435 : [(51368 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1821587), 51366 ^ [_1821587, _1821589, _1821591, _1821593, _1821595]), _1821589)))], (51370 ^ _782435) ^ [] : [c_Relation_Orefl__on(_1821591, hAPP(_1821593, 51366 ^ [_1821587, _1821589, _1821591, _1821593, _1821595]), hAPP(_1821595, 51366 ^ [_1821587, _1821589, _1821591, _1821593, _1821595]))]], -(c_Relation_Orefl__on(_1821591, hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1821587, tc_fun(_1821591, tc_HOL_Obool)), _1821589), _1821593), hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(_1821587, tc_fun(tc_prod(_1821591, _1821591), tc_HOL_Obool)), _1821589), _1821595)))], (51374 ^ _782435) ^ [_1821855, _1821857, _1821859, _1821861, _1821863] : [hBOOL(hAPP(_1821855, hAPP(hAPP(c_Product__Type_OPair(_1821857, _1821859), _1821861), _1821863))), -(hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1821857, _1821859, tc_HOL_Obool, _1821855), _1821861), _1821863)))], (51380 ^ _782435) ^ [_1821980, _1821982, _1821984, _1821986] : [-(c_Product__Type_Ocurry(_1821980, _1821982, _1821984, hAPP(c_Product__Type_Oprod_Oprod__case(_1821980, _1821982, _1821984), _1821986)) = _1821986)], (51382 ^ _782435) ^ [_1822021, _1822023, _1822025, _1822027] : [-(hAPP(c_Product__Type_Oprod_Oprod__case(_1822021, _1822023, _1822025), c_Product__Type_Ocurry(_1822021, _1822023, _1822025, _1822027)) = _1822027)], (51384 ^ _782435) ^ [_1822062, _1822064, _1822066, _1822068, _1822070, _1822072] : [-(hAPP(hAPP(c_Product__Type_Ocurry(_1822062, _1822064, _1822066, _1822068), _1822070), _1822072) = hAPP(_1822068, hAPP(hAPP(c_Product__Type_OPair(_1822062, _1822064), _1822070), _1822072)))], (51386 ^ _782435) ^ [_1822118, _1822120, _1822122, _1822124, _1822126] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1822118, _1822120, tc_HOL_Obool, _1822122), _1822124), _1822126)), -(hBOOL(hAPP(_1822122, hAPP(hAPP(c_Product__Type_OPair(_1822118, _1822120), _1822124), _1822126))))], (51392 ^ _782435) ^ [_1822243, _1822245, _1822247, _1822249, _1822251] : [hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(_1822243, _1822245, tc_HOL_Obool, _1822247), _1822249), _1822251)), -(hBOOL(hAPP(_1822247, hAPP(hAPP(c_Product__Type_OPair(_1822243, _1822245), _1822249), _1822251))))], (51398 ^ _782435) ^ [_1822368, _1822370, _1822372] : [c_Equiv__Relations_Oequivp(_1822368, _1822370), 51401 ^ _782435 : [(51413 ^ _782435) ^ [] : [51414 ^ _782435 : [(51415 ^ _782435) ^ [_1822657] : [hBOOL(hAPP(_1822372, _1822657))]], 51417 ^ _782435 : [(51418 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1822368), 51416 ^ [_1822368, _1822370, _1822372]), c_Quotient_ORespects(_1822368, _1822370))))], (51420 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1822372, 51416 ^ [_1822368, _1822370, _1822372])))]]], (51402 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1822372, 51409 ^ [_1822368, _1822370, _1822372]))), 51403 ^ _782435 : [(51404 ^ _782435) ^ [_1822490] : [hBOOL(hAPP(hAPP(c_member(_1822368), _1822490), c_Quotient_ORespects(_1822368, _1822370))), hBOOL(hAPP(_1822372, _1822490))]]]]], (51422 ^ _782435) ^ [_1822766, _1822768, _1822770] : [hBOOL(hAPP(hAPP(c_member(tc_prod(_1822766, _1822766)), hAPP(hAPP(c_Product__Type_OPair(_1822766, _1822766), hAPP(_1822768, hAPP(c_Nat_OSuc, 51423 ^ [_1822766, _1822768, _1822770]))), hAPP(_1822768, 51423 ^ [_1822766, _1822768, _1822770]))), c_Transitive__Closure_Ortrancl(_1822766, _1822770))), c_Wellfounded_Owf(_1822766, c_Transitive__Closure_Otrancl(_1822766, _1822770)), 51431 ^ _782435 : [(51432 ^ _782435) ^ [_1823032] : [-(hAPP(_1822768, hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat), 51430 ^ [_1822766, _1822768, _1822770]), _1823032)) = hAPP(_1822768, 51430 ^ [_1822766, _1822768, _1822770]))]]], (51434 ^ _782435) ^ [_1823109, _1823111, _1823113] : [hBOOL(hAPP(hAPP(c_member(_1823109), _1823111), c_Quotient_ORespects(_1823109, _1823113))), -(hBOOL(hAPP(hAPP(_1823113, _1823111), _1823111)))], (51440 ^ _782435) ^ [_1823214, _1823216, _1823218] : [hBOOL(hAPP(hAPP(_1823218, _1823216), _1823216)), -(hBOOL(hAPP(hAPP(c_member(_1823214), _1823216), c_Quotient_ORespects(_1823214, _1823218))))], (51446 ^ _782435) ^ [_1823343, _1823345, _1823347] : [hBOOL(hAPP(c_Quotient_ORespects(_1823343, _1823345), _1823347)), -(hBOOL(hAPP(hAPP(_1823345, _1823347), _1823347)))], (51452 ^ _782435) ^ [_1823438, _1823440, _1823442] : [hBOOL(hAPP(hAPP(_1823440, _1823442), _1823442)), -(hBOOL(hAPP(c_Quotient_ORespects(_1823438, _1823440), _1823442)))], (51458 ^ _782435) ^ [_1823539, _1823541, _1823543, _1823545] : [c_Equiv__Relations_Oequivp(_1823539, _1823541), 51464 ^ _782435 : [(51465 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1823543, 51463 ^ [_1823539, _1823541, _1823543, _1823545])))], (51467 ^ _782435) ^ [] : [hBOOL(hAPP(_1823545, 51463 ^ [_1823539, _1823541, _1823543, _1823545]))]], 51470 ^ _782435 : [(51471 ^ _782435) ^ [_1823798] : [hBOOL(hAPP(_1823543, _1823798))]], 51473 ^ _782435 : [(51474 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1823539), 51472 ^ [_1823539, _1823541, _1823543, _1823545]), c_Quotient_ORespects(_1823539, _1823541))))], (51476 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1823545, 51472 ^ [_1823539, _1823541, _1823543, _1823545])))]]], (51478 ^ _782435) ^ [_1823911, _1823913, _1823915, _1823917] : [c_Equiv__Relations_Oequivp(_1823911, _1823913), -(c_Quotient_OBabs(_1823911, _1823915, c_Quotient_ORespects(_1823911, _1823913), _1823917) = _1823917)], (51484 ^ _782435) ^ [_1824008, _1824010, _1824012, _1824014, _1824016] : [hBOOL(hAPP(hAPP(c_member(_1824008), _1824010), _1824012)), -(hAPP(c_Quotient_OBabs(_1824008, _1824014, _1824012, _1824016), _1824010) = hAPP(_1824016, _1824010))], (51490 ^ _782435) ^ [_1824127, _1824129, _1824131, _1824133, _1824135, _1824137, _1824139] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824127, _1824129), tc_prod(_1824127, _1824129))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824127, _1824129), tc_prod(_1824127, _1824129)), hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), _1824131), _1824133)), hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), _1824135), _1824137))), c_Transitive__Closure_Ortrancl(tc_prod(_1824127, _1824129), _1824139))), -(hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), _1824131), _1824133) = hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), _1824135), _1824137)), 51499 ^ _782435 : [(51500 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824127, _1824129), tc_prod(_1824127, _1824129))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824127, _1824129), tc_prod(_1824127, _1824129)), hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), _1824131), _1824133)), hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), 51497 ^ [_1824127, _1824129, _1824131, _1824133, _1824135, _1824137, _1824139]), 51498 ^ [_1824127, _1824129, _1824131, _1824133, _1824135, _1824137, _1824139]))), _1824139)))], (51502 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824127, _1824129), tc_prod(_1824127, _1824129))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824127, _1824129), tc_prod(_1824127, _1824129)), hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), 51497 ^ [_1824127, _1824129, _1824131, _1824133, _1824135, _1824137, _1824139]), 51498 ^ [_1824127, _1824129, _1824131, _1824133, _1824135, _1824137, _1824139])), hAPP(hAPP(c_Product__Type_OPair(_1824127, _1824129), _1824135), _1824137))), c_Transitive__Closure_Ortrancl(tc_prod(_1824127, _1824129), _1824139))))]]], (51504 ^ _782435) ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824708, _1824710), tc_prod(_1824708, _1824710))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824708, _1824710), tc_prod(_1824708, _1824710)), hAPP(hAPP(c_Product__Type_OPair(_1824708, _1824710), _1824712), _1824714)), hAPP(hAPP(c_Product__Type_OPair(_1824708, _1824710), _1824716), _1824718))), c_Transitive__Closure_Ortrancl(tc_prod(_1824708, _1824710), _1824720))), hBOOL(hAPP(hAPP(_1824722, _1824716), _1824718)), 51517 ^ _782435 : [(51518 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824708, _1824710), tc_prod(_1824708, _1824710))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824708, _1824710), tc_prod(_1824708, _1824710)), hAPP(hAPP(c_Product__Type_OPair(_1824708, _1824710), 51513 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]), 51514 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722])), hAPP(hAPP(c_Product__Type_OPair(_1824708, _1824710), 51515 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]), 51516 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]))), _1824720)))], (51520 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1824708, _1824710), tc_prod(_1824708, _1824710))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1824708, _1824710), tc_prod(_1824708, _1824710)), hAPP(hAPP(c_Product__Type_OPair(_1824708, _1824710), 51515 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]), 51516 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722])), hAPP(hAPP(c_Product__Type_OPair(_1824708, _1824710), _1824716), _1824718))), c_Transitive__Closure_Ortrancl(tc_prod(_1824708, _1824710), _1824720))))], (51522 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1824722, 51515 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]), 51516 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722])))], (51524 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1824722, 51513 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]), 51514 ^ [_1824708, _1824710, _1824712, _1824714, _1824716, _1824718, _1824720, _1824722]))]], -(hBOOL(hAPP(hAPP(_1824722, _1824712), _1824714)))], (51528 ^ _782435) ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782] : [hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1825768, _1825770), tc_prod(_1825768, _1825770))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1825768, _1825770), tc_prod(_1825768, _1825770)), hAPP(hAPP(c_Product__Type_OPair(_1825768, _1825770), _1825772), _1825774)), hAPP(hAPP(c_Product__Type_OPair(_1825768, _1825770), _1825776), _1825778))), c_Transitive__Closure_Ortrancl(tc_prod(_1825768, _1825770), _1825780))), hBOOL(hAPP(hAPP(_1825782, _1825772), _1825774)), 51539 ^ _782435 : [(51540 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1825768, _1825770), tc_prod(_1825768, _1825770))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1825768, _1825770), tc_prod(_1825768, _1825770)), hAPP(hAPP(c_Product__Type_OPair(_1825768, _1825770), _1825772), _1825774)), hAPP(hAPP(c_Product__Type_OPair(_1825768, _1825770), 51537 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]), 51538 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]))), c_Transitive__Closure_Ortrancl(tc_prod(_1825768, _1825770), _1825780))))], (51544 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(_1825768, _1825770), tc_prod(_1825768, _1825770))), hAPP(hAPP(c_Product__Type_OPair(tc_prod(_1825768, _1825770), tc_prod(_1825768, _1825770)), hAPP(hAPP(c_Product__Type_OPair(_1825768, _1825770), 51537 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]), 51538 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782])), hAPP(hAPP(c_Product__Type_OPair(_1825768, _1825770), 51541 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]), 51542 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]))), _1825780)))], (51546 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(_1825782, 51537 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]), 51538 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782])))], (51548 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(_1825782, 51541 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]), 51542 ^ [_1825768, _1825770, _1825772, _1825774, _1825776, _1825778, _1825780, _1825782]))]], -(hBOOL(hAPP(hAPP(_1825782, _1825776), _1825778)))], (51552 ^ _782435) ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908] : [51555 ^ _782435 : [(51556 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1826898, _1826898)), hAPP(hAPP(c_Product__Type_OPair(_1826898, _1826898), 51553 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908]), 51554 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908])), _1826900)))], (51560 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1826902, _1826902)), hAPP(hAPP(c_Product__Type_OPair(_1826902, _1826902), 51557 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908]), 51558 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908])), _1826904)))], (51562 ^ _782435) ^ [] : [hAPP(hAPP(_1826906, 51553 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908]), 51557 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908]) = hAPP(hAPP(_1826906, 51554 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908]), 51558 ^ [_1826898, _1826900, _1826902, _1826904, _1826906, _1826908])]], -(c_Equiv__Relations_Ocongruent2(_1826898, _1826902, _1826908, _1826900, _1826904, _1826906))], (51566 ^ _782435) ^ [_1827462, _1827464, _1827466, _1827468] : [51569 ^ _782435 : [(51570 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_prod(_1827462, _1827462)), hAPP(hAPP(c_Product__Type_OPair(_1827462, _1827462), 51567 ^ [_1827462, _1827464, _1827466, _1827468]), 51568 ^ [_1827462, _1827464, _1827466, _1827468])), _1827464)))], (51572 ^ _782435) ^ [] : [hAPP(_1827466, 51567 ^ [_1827462, _1827464, _1827466, _1827468]) = hAPP(_1827466, 51568 ^ [_1827462, _1827464, _1827466, _1827468])]], -(c_Equiv__Relations_Ocongruent(_1827462, _1827468, _1827464, _1827466))], (51576 ^ _782435) ^ [_1827720, _1827722, _1827724] : [-(c_Lazy__Sequence_Oflat(_1827720, c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(_1827720), _1827722, _1827724)) = c_Lazy__Sequence_Oappend(_1827720, _1827722, c_Lazy__Sequence_Oflat(_1827720, _1827724)))], (51578 ^ _782435) ^ [_1827763] : [-(c_Lazy__Sequence_Oflat(_1827763, c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(_1827763))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1827763))], (51580 ^ _782435) ^ [_1827795, _1827797, _1827799, _1827801] : [-(hAPP(c_Lazy__Sequence_Obind(_1827795, _1827797, _1827799), _1827801) = c_Lazy__Sequence_Oflat(_1827797, c_Lazy__Sequence_Omap(_1827795, tc_Lazy__Sequence_Olazy__sequence(_1827797), _1827801, _1827799)))], (51592 ^ _782435) ^ [_1828046, _1828048, _1828050] : [51594 ^ _782435 : [(51595 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), 51593 ^ [_1828046, _1828048, _1828050]), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1828048), _1828050))))], (51597 ^ _782435) ^ [] : [hBOOL(hAPP(_1828046, 51593 ^ [_1828046, _1828048, _1828050]))]], -(c_List_Oall__interval__nat(_1828046, _1828048, _1828050))], (51582 ^ _782435) ^ [_1827859, _1827861, _1827863] : [c_List_Oall__interval__nat(_1827859, _1827861, _1827863), 51585 ^ _782435 : [(51586 ^ _782435) ^ [_1827939] : [hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat), _1827939), hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat, _1827861), _1827863))), -(hBOOL(hAPP(_1827859, _1827939)))]]], (51601 ^ _782435) ^ [_1828226, _1828228, _1828230, _1828232, _1828234] : [-(c_Lazy__Sequence_Omap(_1828226, _1828228, _1828230, c_Lazy__Sequence_Olazy__sequence_OInsert(_1828226, _1828232, _1828234)) = c_Lazy__Sequence_Olazy__sequence_OInsert(_1828228, hAPP(_1828230, _1828232), c_Lazy__Sequence_Omap(_1828226, _1828228, _1828230, _1828234)))], (51603 ^ _782435) ^ [_1828278, _1828280, _1828282] : [-(c_Lazy__Sequence_Omap(_1828278, _1828280, _1828282, c_Lazy__Sequence_Olazy__sequence_OEmpty(_1828278)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(_1828280))], (51605 ^ _782435) ^ [_1828332, _1828334, _1828336] : [c_List_Olist__all(tc_Nat_Onat, _1828332, c_List_Oupt(_1828334, _1828336)), -(c_List_Oall__interval__nat(_1828332, _1828334, _1828336))], (51611 ^ _782435) ^ [_1828417, _1828419, _1828421] : [c_List_Oall__interval__nat(_1828417, _1828419, _1828421), -(c_List_Olist__all(tc_Nat_Onat, _1828417, c_List_Oupt(_1828419, _1828421)))], (51617 ^ _782435) ^ [_1828526, _1828528, _1828530] : [c_List_Olist__ex(tc_Nat_Onat, _1828526, c_List_Oupt(_1828528, _1828530)), c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1828526), _1828528, _1828530)], (51623 ^ _782435) ^ [_1828616, _1828618, _1828620] : [-(c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool, tc_HOL_Obool, tc_Nat_Onat, c_fNot), _1828616), _1828618, _1828620)), -(c_List_Olist__ex(tc_Nat_Onat, _1828616, c_List_Oupt(_1828618, _1828620)))], (51629 ^ _782435) ^ [_1828664, _1828666, _1828668, _1828670, _1828672] : [-(c_New__DSequence_Opos__map(_1828664, _1828666, _1828668, _1828670, _1828672) = c_Lazy__Sequence_Omap(_1828664, _1828666, _1828668, hAPP(_1828670, _1828672)))], (51631 ^ _782435) ^ [_1828709, _1828711, _1828713, _1828715, _1828717, _1828719, _1828721, _1828723] : [c_Finite__Set_Ofolding__image(_1828709, _1828711, _1828713, _1828715, _1828717), hBOOL(hAPP(c_Finite__Set_Ofinite(_1828711), _1828719)), 51641 ^ _782435 : [(51642 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_member(_1828711), 51640 ^ [_1828709, _1828711, _1828713, _1828715, _1828717, _1828719, _1828721, _1828723]), _1828719)))], (51644 ^ _782435) ^ [] : [hAPP(_1828721, 51640 ^ [_1828709, _1828711, _1828713, _1828715, _1828717, _1828719, _1828721, _1828723]) = hAPP(_1828723, 51640 ^ [_1828709, _1828711, _1828713, _1828715, _1828717, _1828719, _1828721, _1828723])]], -(hAPP(hAPP(_1828717, _1828721), _1828719) = hAPP(hAPP(_1828717, _1828723), _1828719))], (51648 ^ _782435) ^ [_1829114, _1829116, _1829118] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1829114), _1829116)), hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat), _1829114), _1829118))), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat), c_Groups_Oone__class_Oone(tc_Nat_Onat)), _1829114)), -(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat), _1829116), _1829118)))], (51658 ^ _782435) ^ [_1829295, _1829297, _1829299] : [hBOOL(hAPP(c_Finite__Set_Ofinite(_1829295), _1829297)), -(_1829297 = c_Orderings_Obot__class_Obot(tc_fun(_1829295, tc_HOL_Obool))), -(hBOOL(hAPP(c_Finite__Set_Ofold1Set(_1829295, _1829299, _1829297), 51665 ^ [_1829295, _1829297, _1829299])))], (51669 ^ _782435) ^ [_1829433] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1829433), _1829433)))], (51671 ^ _782435) ^ [_1829461, _1829463] : [class_Rings_Ocomm__semiring__1(_1829461), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829461), _1829463), c_Groups_Ozero__class_Ozero(_1829461))))], (51677 ^ _782435) ^ [_1829554] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(c_Nat_OSuc, c_Groups_Ozero__class_Ozero(tc_Nat_Onat))), _1829554)))], (51679 ^ _782435) ^ [_1829579, _1829581, _1829583] : [class_Rings_Odvd(_1829579), class_Rings_Osemiring__0(_1829579), 51686 ^ _782435 : [(51687 ^ _782435) ^ [] : [51688 ^ _782435 : [(51689 ^ _782435) ^ [_1829771] : [hBOOL(hAPP(_1829581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829579), _1829583), _1829771)))]], 51691 ^ _782435 : [(51692 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829579), _1829583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829579), 51690 ^ [_1829579, _1829581, _1829583]), c_Groups_Ozero__class_Ozero(_1829579)))))], (51694 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1829581, 51690 ^ [_1829579, _1829581, _1829583])))]]], (51696 ^ _782435) ^ [] : [-(hBOOL(hAPP(_1829581, hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1829579), _1829583), 51703 ^ [_1829579, _1829581, _1829583])))), 51697 ^ _782435 : [(51698 ^ _782435) ^ [_1829908] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1829579), _1829583), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1829579), _1829908), c_Groups_Ozero__class_Ozero(_1829579)))), hBOOL(hAPP(_1829581, _1829908))]]]]], (51707 ^ _782435) ^ [_1830081, _1830083, _1830085] : [class_Divides_Osemiring__div(_1830081), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830081), _1830083), _1830085)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830081), _1830083), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830081), _1830085), _1830083)) = _1830085)], (51717 ^ _782435) ^ [_1830258, _1830260, _1830262, _1830264] : [class_Divides_Osemiring__div(_1830258), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830258), _1830260), _1830262)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830258), _1830264), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830258), _1830262), _1830260)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830258), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830258), _1830264), _1830262)), _1830260))], (51727 ^ _782435) ^ [_1830471, _1830473, _1830475] : [class_Divides_Osemiring__div(_1830471), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830471), _1830473), _1830475)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830471), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830471), _1830475), _1830473)), _1830473) = _1830475)], (51737 ^ _782435) ^ [_1830648, _1830650, _1830652, _1830654] : [class_Divides_Osemiring__div(_1830648), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830648), _1830650), _1830652)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830648), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830648), _1830652), _1830650)), _1830654) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830648), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830648), _1830652), _1830654)), _1830650))], (51747 ^ _782435) ^ [_1830861, _1830863, _1830865, _1830867, _1830869] : [class_Divides_Osemiring__div(_1830861), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830861), _1830863), _1830865)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1830861), _1830867), _1830869)), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830861), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830861), _1830865), _1830863)), hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830861), _1830869), _1830867)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1830861), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830861), _1830865), _1830869)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1830861), _1830863), _1830867)))], (51761 ^ _782435) ^ [_1831182, _1831184, _1831186, _1831188] : [class_Rings_Oidom(_1831182), 51764 ^ _782435 : [(51775 ^ _782435) ^ [] : [51776 ^ _782435 : [(51777 ^ _782435) ^ [] : [_1831184 = c_Groups_Ozero__class_Ozero(_1831182)], (51779 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831182), _1831186), _1831188))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831182), _1831184), _1831186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831182), _1831184), _1831188))))], (51765 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831182), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831182), _1831184), _1831186)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831182), _1831184), _1831188))), -(_1831184 = c_Groups_Ozero__class_Ozero(_1831182)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831182), _1831186), _1831188)))]]], (51783 ^ _782435) ^ [_1831540, _1831542, _1831544, _1831546] : [class_Rings_Oidom(_1831540), 51786 ^ _782435 : [(51797 ^ _782435) ^ [] : [51798 ^ _782435 : [(51799 ^ _782435) ^ [] : [_1831544 = c_Groups_Ozero__class_Ozero(_1831540)], (51801 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831540), _1831542), _1831546))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831540), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831540), _1831542), _1831544)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831540), _1831546), _1831544))))], (51787 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831540), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831540), _1831542), _1831544)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831540), _1831546), _1831544))), -(_1831544 = c_Groups_Ozero__class_Ozero(_1831540)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831540), _1831542), _1831546)))]]], (51805 ^ _782435) ^ [_1831898, _1831900, _1831902, _1831904] : [class_Rings_Ocomm__semiring__1(_1831898), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831898), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1831898), _1831900), _1831902)), _1831904)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1831898), _1831902), _1831904)))], (51815 ^ _782435) ^ [_1832077, _1832079, _1832081, _1832083] : [class_Rings_Ocomm__semiring__1(_1832077), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832077), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832077), _1832079), _1832081)), _1832083)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832077), _1832079), _1832083)))], (51825 ^ _782435) ^ [_1832256, _1832258, _1832260, _1832262] : [class_Rings_Odvd(_1832256), _1832258 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832256), _1832260), _1832262), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832256), _1832260), _1832258)))], (51835 ^ _782435) ^ [_1832421, _1832423, _1832425, _1832427, _1832429] : [class_Rings_Ocomm__semiring__1(_1832421), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832421), _1832423), _1832425)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832421), _1832427), _1832429)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832421), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832421), _1832423), _1832427)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832421), _1832425), _1832429))))], (51849 ^ _782435) ^ [_1832692, _1832694, _1832696, _1832698] : [class_Rings_Ocomm__semiring__1(_1832692), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832692), _1832694), _1832696)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832692), _1832694), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832692), _1832698), _1832696))))], (51859 ^ _782435) ^ [_1832871, _1832873, _1832875, _1832877] : [class_Rings_Ocomm__semiring__1(_1832871), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832871), _1832873), _1832875)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1832871), _1832873), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1832871), _1832875), _1832877))))], (51869 ^ _782435) ^ [_1833050, _1833052, _1833054] : [class_Rings_Ocomm__semiring__1(_1833050), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833050), _1833052), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833050), _1833054), _1833052))))], (51875 ^ _782435) ^ [_1833157, _1833159, _1833161] : [class_Rings_Ocomm__semiring__1(_1833157), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833157), _1833159), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833157), _1833159), _1833161))))], (51891 ^ _782435) ^ [_1833414, _1833416, _1833418] : [51892 ^ _782435 : [(51893 ^ _782435) ^ [] : [_1833414 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)], (51895 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833416), _1833418))]], -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833414), _1833416)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833414), _1833418))))], (51881 ^ _782435) ^ [_1833282, _1833284, _1833286] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833282), _1833284)), hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat), _1833282), _1833286))), -(_1833282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1833284), _1833286)))], (51899 ^ _782435) ^ [_1833577, _1833579, _1833581, _1833583] : [class_Rings_Ocomm__ring(_1833577), class_Rings_Odvd(_1833577), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833577), _1833579), _1833581)), 51910 ^ _782435 : [(51911 ^ _782435) ^ [_1833830, _1833832] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833577), _1833579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833577), _1833832), _1833583))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833577), _1833579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833577), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1833577), _1833832), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833577), _1833830), _1833581))), _1833583))))], (51917 ^ _782435) ^ [_1834003, _1834005] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833577), _1833579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833577), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1833577), _1834005), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1833577), _1834003), _1833581))), _1833583))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1833577), _1833579), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1833577), _1834005), _1833583))))]]], (51923 ^ _782435) ^ [_1834190, _1834192, _1834194, _1834196] : [class_Rings_Ocomm__ring(_1834190), class_Rings_Odvd(_1834190), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834190), _1834192), _1834194)), 51934 ^ _782435 : [(51935 ^ _782435) ^ [_1834443, _1834445] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834190), _1834192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834190), _1834445), _1834196))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834190), _1834192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834190), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1834190), _1834445), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834190), _1834443), _1834194))), _1834196))))], (51941 ^ _782435) ^ [_1834616, _1834618] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834190), _1834192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834190), hAPP(hAPP(c_Groups_Ominus__class_Ominus(_1834190), _1834618), hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834190), _1834616), _1834194))), _1834196))), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834190), _1834192), hAPP(hAPP(c_Groups_Oplus__class_Oplus(_1834190), _1834618), _1834196))))]]], (51947 ^ _782435) ^ [_1834803, _1834805, _1834807, _1834809, _1834811] : [class_Divides_Osemiring__div(_1834803), -(_1834805 = c_Groups_Ozero__class_Ozero(_1834803)), -(_1834807 = c_Groups_Ozero__class_Ozero(_1834803)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834803), _1834805), _1834809)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1834803), _1834807), _1834811)), 51966 ^ _782435 : [(51967 ^ _782435) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834803), _1834809), _1834805) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834803), _1834811), _1834807), -(hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834803), _1834809), _1834807) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834803), _1834805), _1834811))], (51973 ^ _782435) ^ [] : [hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834803), _1834809), _1834807) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1834803), _1834805), _1834811), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834803), _1834809), _1834805) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1834803), _1834811), _1834807))]]], (51979 ^ _782435) ^ [_1835396, _1835398, _1835400, _1835402] : [class_Divides_Osemiring__div(_1835396), -(_1835398 = c_Groups_Ozero__class_Ozero(_1835396)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(_1835396), _1835398), _1835400)), 51990 ^ _782435 : [(51991 ^ _782435) ^ [] : [hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1835396), _1835400), _1835398) = _1835402, -(_1835400 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835396), _1835402), _1835398))], (51997 ^ _782435) ^ [] : [_1835400 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(_1835396), _1835402), _1835398), -(hAPP(hAPP(c_Divides_Odiv__class_Odiv(_1835396), _1835400), _1835398) = _1835402)]]], (52003 ^ _782435) ^ [_1835812, _1835814, _1835816] : [c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835812, _1835814) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1835816), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))), 52006 ^ _782435 : [(52007 ^ _782435) ^ [] : [-(_1835812 = _1835814)], (52009 ^ _782435) ^ [] : [-(_1835814 = _1835816)]]], (52011 ^ _782435) ^ [_1835935, _1835937, _1835939] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1835935, _1835937) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1835939), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))), _1835935 = _1835937, _1835937 = _1835939], (52021 ^ _782435) ^ [_1836092] : [-(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836092, _1836092) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1836092), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52023 ^ _782435) ^ [_1836126, _1836128] : [_1836126 = _1836128, -(c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat, c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836126, _1836128) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat), _1836126), c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool))))], (52029 ^ _782435) ^ [_1836225, _1836227] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836225), _1836227)), -(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)))), _1836227, _1836225) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52035 ^ _782435) ^ [_1836324, _1836326] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836324), _1836326)), -(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)))), _1836326, _1836324) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52041 ^ _782435) ^ [_1836423, _1836425] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836423), _1836425)), -(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)))), _1836425, _1836423) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52057 ^ _782435) ^ [_1836696, _1836698] : [52058 ^ _782435 : [(52059 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836696), _1836698)))], (52061 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836698), _1836696))]], -(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)))), _1836696, _1836698) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52047 ^ _782435) ^ [_1836535, _1836537] : [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)))), _1836535, _1836537) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836535), _1836537)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836537), _1836535)))], (52075 ^ _782435) ^ [_1837020, _1837022] : [52076 ^ _782435 : [(52077 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837020), _1837022)))], (52079 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837022), _1837020))]], -(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)))), _1837020, _1837022) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)))], (52065 ^ _782435) ^ [_1836859, _1836861] : [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)))), _1836859, _1836861) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat, tc_HOL_Obool)), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836859), _1836861)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1836861), _1836859)))], (52093 ^ _782435) ^ [_1837344, _1837346] : [52094 ^ _782435 : [(52095 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837344), _1837346)))], (52097 ^ _782435) ^ [] : [hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837346), _1837344))]], -(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)))), _1837344, _1837346))], (52083 ^ _782435) ^ [_1837183, _1837185] : [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)))), _1837183, _1837185), hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837183), _1837185)), -(hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat), _1837185), _1837183)))], (52101 ^ _782435) ^ [] : [-(class_Lattices_Obounded__lattice(tc_HOL_Obool))], (52103 ^ _782435) ^ [_1837510, _1837512] : [class_Lattices_Obounded__lattice(_1837510), -(class_Lattices_Obounded__lattice(tc_fun(_1837512, _1837510)))], (52109 ^ _782435) ^ [_1837589, _1837591] : [class_Complete__Lattice_Ocomplete__lattice(_1837589), -(class_Complete__Lattice_Ocomplete__lattice(tc_fun(_1837591, _1837589)))], (52115 ^ _782435) ^ [_1837668, _1837670] : [class_Lattices_Obounded__lattice(_1837668), -(class_Lattices_Obounded__lattice__top(tc_fun(_1837670, _1837668)))], (52121 ^ _782435) ^ [_1837747, _1837749] : [class_Lattices_Obounded__lattice(_1837747), -(class_Lattices_Obounded__lattice__bot(tc_fun(_1837749, _1837747)))], (52127 ^ _782435) ^ [_1837826, _1837828] : [class_Lattices_Olattice(_1837826), -(class_Lattices_Osemilattice__sup(tc_fun(_1837828, _1837826)))], (52133 ^ _782435) ^ [_1837905, _1837907] : [class_Lattices_Olattice(_1837905), -(class_Lattices_Osemilattice__inf(tc_fun(_1837907, _1837905)))], (52139 ^ _782435) ^ [_1837984, _1837986] : [class_Lattices_Odistrib__lattice(_1837984), -(class_Lattices_Odistrib__lattice(tc_fun(_1837986, _1837984)))], (52145 ^ _782435) ^ [_1838063, _1838065] : [class_Lattices_Oboolean__algebra(_1838063), -(class_Lattices_Oboolean__algebra(tc_fun(_1838065, _1838063)))], (52151 ^ _782435) ^ [_1838142, _1838144] : [class_Orderings_Opreorder(_1838142), -(class_Orderings_Opreorder(tc_fun(_1838144, _1838142)))], (52157 ^ _782435) ^ [_1838221, _1838223] : [-(class_Finite__Set_Ofinite(tc_fun(_1838221, _1838223))), class_Finite__Set_Ofinite(_1838221), class_Finite__Set_Ofinite(_1838223)], (52167 ^ _782435) ^ [_1838350, _1838352] : [class_Lattices_Olattice(_1838350), -(class_Lattices_Olattice(tc_fun(_1838352, _1838350)))], (52173 ^ _782435) ^ [_1838429, _1838431] : [class_Orderings_Oorder(_1838429), -(class_Orderings_Oorder(tc_fun(_1838431, _1838429)))], (52179 ^ _782435) ^ [_1838508, _1838510] : [class_Orderings_Otop(_1838508), -(class_Orderings_Otop(tc_fun(_1838510, _1838508)))], (52185 ^ _782435) ^ [_1838587, _1838589] : [class_Orderings_Oord(_1838587), -(class_Orderings_Oord(tc_fun(_1838589, _1838587)))], (52191 ^ _782435) ^ [_1838666, _1838668] : [class_Orderings_Obot(_1838666), -(class_Orderings_Obot(tc_fun(_1838668, _1838666)))], (52197 ^ _782435) ^ [_1838745, _1838747] : [class_Groups_Ouminus(_1838745), -(class_Groups_Ouminus(tc_fun(_1838747, _1838745)))], (52203 ^ _782435) ^ [_1838824, _1838826] : [class_Groups_Ominus(_1838824), -(class_Groups_Ominus(tc_fun(_1838826, _1838824)))], (52209 ^ _782435) ^ [_1838903, _1838905] : [-(class_Enum_Oenum(tc_fun(_1838903, _1838905))), class_Enum_Oenum(_1838903), class_Enum_Oenum(_1838905)], (52219 ^ _782435) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint))], (52221 ^ _782435) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint))], (52223 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint))], (52225 ^ _782435) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint))], (52227 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint))], (52229 ^ _782435) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint))], (52231 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Int_Oint))], (52233 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint))], (52235 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint))], (52237 ^ _782435) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Int_Oint))], (52239 ^ _782435) ^ [] : [-(class_Groups_Olinordered__ab__group__add(tc_Int_Oint))], (52241 ^ _782435) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint))], (52243 ^ _782435) ^ [] : [-(class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint))], (52245 ^ _782435) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Int_Oint))], (52247 ^ _782435) ^ [] : [-(class_Rings_Olinordered__ring__strict(tc_Int_Oint))], (52249 ^ _782435) ^ [] : [-(class_Rings_Oring__no__zero__divisors(tc_Int_Oint))], (52251 ^ _782435) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Int_Oint))], (52253 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring__1(tc_Int_Oint))], (52255 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__group__add(tc_Int_Oint))], (52257 ^ _782435) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Int_Oint))], (52259 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Int_Oint))], (52261 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Int_Oint))], (52263 ^ _782435) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint))], (52265 ^ _782435) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Int_Oint))], (52267 ^ _782435) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Int_Oint))], (52269 ^ _782435) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Int_Oint))], (52271 ^ _782435) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Int_Oint))], (52273 ^ _782435) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Int_Oint))], (52275 ^ _782435) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Int_Oint))], (52277 ^ _782435) ^ [] : [-(class_Rings_Oordered__semiring(tc_Int_Oint))], (52279 ^ _782435) ^ [] : [-(class_Rings_Oordered__ring__abs(tc_Int_Oint))], (52281 ^ _782435) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Int_Oint))], (52283 ^ _782435) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Int_Oint))], (52285 ^ _782435) ^ [] : [-(class_Rings_Olinordered__ring(tc_Int_Oint))], (52287 ^ _782435) ^ [] : [-(class_Rings_Olinordered__idom(tc_Int_Oint))], (52289 ^ _782435) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Int_Oint))], (52291 ^ _782435) ^ [] : [-(class_Groups_Osemigroup__add(tc_Int_Oint))], (52293 ^ _782435) ^ [] : [-(class_Divides_Osemiring__div(tc_Int_Oint))], (52295 ^ _782435) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Int_Oint))], (52297 ^ _782435) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Int_Oint))], (52299 ^ _782435) ^ [] : [-(class_Groups_Oab__group__add(tc_Int_Oint))], (52301 ^ _782435) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Int_Oint))], (52303 ^ _782435) ^ [] : [-(class_Rings_Oordered__ring(tc_Int_Oint))], (52305 ^ _782435) ^ [] : [-(class_Orderings_Opreorder(tc_Int_Oint))], (52307 ^ _782435) ^ [] : [-(class_Orderings_Olinorder(tc_Int_Oint))], (52309 ^ _782435) ^ [] : [-(class_Groups_Omonoid__mult(tc_Int_Oint))], (52311 ^ _782435) ^ [] : [-(class_Rings_Ocomm__ring__1(tc_Int_Oint))], (52313 ^ _782435) ^ [] : [-(class_Groups_Omonoid__add(tc_Int_Oint))], (52315 ^ _782435) ^ [] : [-(class_Rings_Osemiring__1(tc_Int_Oint))], (52317 ^ _782435) ^ [] : [-(class_Rings_Osemiring__0(tc_Int_Oint))], (52319 ^ _782435) ^ [] : [-(class_Lattices_Olattice(tc_Int_Oint))], (52321 ^ _782435) ^ [] : [-(class_Groups_Ogroup__add(tc_Int_Oint))], (52323 ^ _782435) ^ [] : [-(class_Divides_Oring__div(tc_Int_Oint))], (52325 ^ _782435) ^ [] : [-(class_Rings_Omult__zero(tc_Int_Oint))], (52327 ^ _782435) ^ [] : [-(class_Rings_Ocomm__ring(tc_Int_Oint))], (52329 ^ _782435) ^ [] : [-(class_Orderings_Oorder(tc_Int_Oint))], (52331 ^ _782435) ^ [] : [-(class_Int_Oring__char__0(tc_Int_Oint))], (52333 ^ _782435) ^ [] : [-(class_Int_Onumber__ring(tc_Int_Oint))], (52335 ^ _782435) ^ [] : [-(class_Rings_Osemiring(tc_Int_Oint))], (52337 ^ _782435) ^ [] : [-(class_Orderings_Oord(tc_Int_Oint))], (52339 ^ _782435) ^ [] : [-(class_Groups_Ouminus(tc_Int_Oint))], (52341 ^ _782435) ^ [] : [-(class_Groups_Osgn__if(tc_Int_Oint))], (52343 ^ _782435) ^ [] : [-(class_Groups_Oabs__if(tc_Int_Oint))], (52345 ^ _782435) ^ [] : [-(class_Rings_Oring__1(tc_Int_Oint))], (52347 ^ _782435) ^ [] : [-(class_Groups_Ominus(tc_Int_Oint))], (52349 ^ _782435) ^ [] : [-(class_Power_Opower(tc_Int_Oint))], (52351 ^ _782435) ^ [] : [-(class_Groups_Ozero(tc_Int_Oint))], (52353 ^ _782435) ^ [] : [-(class_Rings_Oring(tc_Int_Oint))], (52355 ^ _782435) ^ [] : [-(class_Rings_Oidom(tc_Int_Oint))], (52357 ^ _782435) ^ [] : [-(class_Int_Onumber(tc_Int_Oint))], (52359 ^ _782435) ^ [] : [-(class_Groups_Oone(tc_Int_Oint))], (52361 ^ _782435) ^ [] : [-(class_Rings_Odvd(tc_Int_Oint))], (52363 ^ _782435) ^ [] : [-(class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat))], (52365 ^ _782435) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat))], (52367 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat))], (52369 ^ _782435) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat))], (52371 ^ _782435) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat))], (52373 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Nat_Onat))], (52375 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat))], (52377 ^ _782435) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat))], (52379 ^ _782435) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat))], (52381 ^ _782435) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Nat_Onat))], (52383 ^ _782435) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Nat_Onat))], (52385 ^ _782435) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Nat_Onat))], (52387 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Nat_Onat))], (52389 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Nat_Onat))], (52391 ^ _782435) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_Nat_Onat))], (52393 ^ _782435) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_Nat_Onat))], (52395 ^ _782435) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_Nat_Onat))], (52397 ^ _782435) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Nat_Onat))], (52399 ^ _782435) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Nat_Onat))], (52401 ^ _782435) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Nat_Onat))], (52403 ^ _782435) ^ [] : [-(class_Rings_Oordered__semiring(tc_Nat_Onat))], (52405 ^ _782435) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Nat_Onat))], (52407 ^ _782435) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Nat_Onat))], (52409 ^ _782435) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Nat_Onat))], (52411 ^ _782435) ^ [] : [-(class_Groups_Osemigroup__add(tc_Nat_Onat))], (52413 ^ _782435) ^ [] : [-(class_Divides_Osemiring__div(tc_Nat_Onat))], (52415 ^ _782435) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Nat_Onat))], (52417 ^ _782435) ^ [] : [-(class_Orderings_Owellorder(tc_Nat_Onat))], (52419 ^ _782435) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Nat_Onat))], (52421 ^ _782435) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Nat_Onat))], (52423 ^ _782435) ^ [] : [-(class_Orderings_Opreorder(tc_Nat_Onat))], (52425 ^ _782435) ^ [] : [-(class_Orderings_Olinorder(tc_Nat_Onat))], (52427 ^ _782435) ^ [] : [-(class_Groups_Omonoid__mult(tc_Nat_Onat))], (52429 ^ _782435) ^ [] : [-(class_Groups_Omonoid__add(tc_Nat_Onat))], (52431 ^ _782435) ^ [] : [-(class_Rings_Osemiring__1(tc_Nat_Onat))], (52433 ^ _782435) ^ [] : [-(class_Rings_Osemiring__0(tc_Nat_Onat))], (52435 ^ _782435) ^ [] : [-(class_Lattices_Olattice(tc_Nat_Onat))], (52437 ^ _782435) ^ [] : [-(class_Rings_Omult__zero(tc_Nat_Onat))], (52439 ^ _782435) ^ [] : [-(class_Orderings_Oorder(tc_Nat_Onat))], (52441 ^ _782435) ^ [] : [-(class_Rings_Osemiring(tc_Nat_Onat))], (52443 ^ _782435) ^ [] : [-(class_Orderings_Oord(tc_Nat_Onat))], (52445 ^ _782435) ^ [] : [-(class_Orderings_Obot(tc_Nat_Onat))], (52447 ^ _782435) ^ [] : [-(class_Groups_Ominus(tc_Nat_Onat))], (52449 ^ _782435) ^ [] : [-(class_Power_Opower(tc_Nat_Onat))], (52451 ^ _782435) ^ [] : [-(class_Groups_Ozero(tc_Nat_Onat))], (52453 ^ _782435) ^ [] : [-(class_Int_Onumber(tc_Nat_Onat))], (52455 ^ _782435) ^ [] : [-(class_Groups_Oone(tc_Nat_Onat))], (52457 ^ _782435) ^ [] : [-(class_Rings_Odvd(tc_Nat_Onat))], (52459 ^ _782435) ^ [] : [-(class_Nat_Osize(tc_Nat_Onat))], (52461 ^ _782435) ^ [] : [-(class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool))], (52463 ^ _782435) ^ [] : [-(class_Lattices_Obounded__lattice__top(tc_HOL_Obool))], (52465 ^ _782435) ^ [] : [-(class_Lattices_Obounded__lattice__bot(tc_HOL_Obool))], (52467 ^ _782435) ^ [] : [-(class_Lattices_Osemilattice__sup(tc_HOL_Obool))], (52469 ^ _782435) ^ [] : [-(class_Lattices_Osemilattice__inf(tc_HOL_Obool))], (52471 ^ _782435) ^ [] : [-(class_Lattices_Odistrib__lattice(tc_HOL_Obool))], (52473 ^ _782435) ^ [] : [-(class_Lattices_Oboolean__algebra(tc_HOL_Obool))], (52475 ^ _782435) ^ [] : [-(class_Orderings_Opreorder(tc_HOL_Obool))], (52477 ^ _782435) ^ [] : [-(class_Finite__Set_Ofinite(tc_HOL_Obool))], (52479 ^ _782435) ^ [] : [-(class_Lattices_Olattice(tc_HOL_Obool))], (52481 ^ _782435) ^ [] : [-(class_Orderings_Oorder(tc_HOL_Obool))], (52483 ^ _782435) ^ [] : [-(class_Orderings_Otop(tc_HOL_Obool))], (52485 ^ _782435) ^ [] : [-(class_Orderings_Oord(tc_HOL_Obool))], (52487 ^ _782435) ^ [] : [-(class_Orderings_Obot(tc_HOL_Obool))], (52489 ^ _782435) ^ [] : [-(class_Groups_Ouminus(tc_HOL_Obool))], (52491 ^ _782435) ^ [] : [-(class_Groups_Ominus(tc_HOL_Obool))], (52493 ^ _782435) ^ [] : [-(class_Enum_Oenum(tc_HOL_Obool))], (52495 ^ _782435) ^ [] : [-(class_Nat_Osize(tc_HOL_Obool))], (52497 ^ _782435) ^ [_1841534] : [class_Lazy__Sequence_Osmall__lazy(_1841534), -(class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(_1841534)))], (52503 ^ _782435) ^ [_1841609] : [-(class_Nat_Osize(tc_List_Olist(_1841609)))], (52505 ^ _782435) ^ [_1841633, _1841635] : [-(class_Finite__Set_Ofinite(tc_sum(_1841633, _1841635))), class_Finite__Set_Ofinite(_1841633), class_Finite__Set_Ofinite(_1841635)], (52515 ^ _782435) ^ [_1841762, _1841764] : [-(class_Enum_Oenum(tc_sum(_1841762, _1841764))), class_Enum_Oenum(_1841762), class_Enum_Oenum(_1841764)], (52525 ^ _782435) ^ [_1841891, _1841893] : [-(class_Nat_Osize(tc_sum(_1841891, _1841893)))], (52527 ^ _782435) ^ [_1841918] : [class_Finite__Set_Ofinite(_1841918), -(class_Finite__Set_Ofinite(tc_Option_Ooption(_1841918)))], (52533 ^ _782435) ^ [_1841993] : [class_Enum_Oenum(_1841993), -(class_Enum_Oenum(tc_Option_Ooption(_1841993)))], (52539 ^ _782435) ^ [_1842068] : [-(class_Nat_Osize(tc_Option_Ooption(_1842068)))], (52541 ^ _782435) ^ [_1842092, _1842094] : [-(class_Nat_Osize(tc_Nitpick_Opair__box(_1842092, _1842094)))], (52543 ^ _782435) ^ [_1842119, _1842121] : [-(class_Lazy__Sequence_Osmall__lazy(tc_prod(_1842119, _1842121))), class_Lazy__Sequence_Osmall__lazy(_1842119), class_Lazy__Sequence_Osmall__lazy(_1842121)], (52553 ^ _782435) ^ [_1842248, _1842250] : [-(class_Finite__Set_Ofinite(tc_prod(_1842248, _1842250))), class_Finite__Set_Ofinite(_1842248), class_Finite__Set_Ofinite(_1842250)], (52563 ^ _782435) ^ [_1842377, _1842379] : [-(class_Enum_Oenum(tc_prod(_1842377, _1842379))), class_Enum_Oenum(_1842377), class_Enum_Oenum(_1842379)], (52573 ^ _782435) ^ [_1842506, _1842508] : [-(class_Nat_Osize(tc_prod(_1842506, _1842508)))], (52575 ^ _782435) ^ [] : [-(class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit))], (52577 ^ _782435) ^ [] : [-(class_Finite__Set_Ofinite(tc_Product__Type_Ounit))], (52579 ^ _782435) ^ [] : [-(class_Enum_Oenum(tc_Product__Type_Ounit))], (52581 ^ _782435) ^ [] : [-(class_Nat_Osize(tc_Product__Type_Ounit))], (52583 ^ _782435) ^ [] : [-(class_Nat_Osize(tc_Code__Evaluation_Oterm))], (52585 ^ _782435) ^ [_1842623] : [-(class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(_1842623)))], (52587 ^ _782435) ^ [] : [-(class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52589 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral))], (52591 ^ _782435) ^ [] : [-(class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52593 ^ _782435) ^ [] : [-(class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52595 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral))], (52597 ^ _782435) ^ [] : [-(class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52599 ^ _782435) ^ [] : [-(class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52601 ^ _782435) ^ [] : [-(class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52603 ^ _782435) ^ [] : [-(class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral))], (52605 ^ _782435) ^ [] : [-(class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral))], (52607 ^ _782435) ^ [] : [-(class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52609 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52611 ^ _782435) ^ [] : [-(class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral))], (52613 ^ _782435) ^ [] : [-(class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral))], (52615 ^ _782435) ^ [] : [-(class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral))], (52617 ^ _782435) ^ [] : [-(class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral))], (52619 ^ _782435) ^ [] : [-(class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral))], (52621 ^ _782435) ^ [] : [-(class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral))], (52623 ^ _782435) ^ [] : [-(class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral))], (52625 ^ _782435) ^ [] : [-(class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral))], (52627 ^ _782435) ^ [] : [-(class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral))], (52629 ^ _782435) ^ [] : [-(class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral))], (52631 ^ _782435) ^ [] : [-(class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral))], (52633 ^ _782435) ^ [] : [-(class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral))], (52635 ^ _782435) ^ [] : [-(class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral))], (52637 ^ _782435) ^ [] : [-(class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral))], (52639 ^ _782435) ^ [] : [-(class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral))], (52641 ^ _782435) ^ [] : [-(class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral))], (52643 ^ _782435) ^ [] : [-(class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral))], (52645 ^ _782435) ^ [] : [-(class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral))], (52647 ^ _782435) ^ [] : [-(class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral))], (52649 ^ _782435) ^ [] : [-(class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral))], (52651 ^ _782435) ^ [] : [-(class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral))], (52653 ^ _782435) ^ [] : [-(class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral))], (52655 ^ _782435) ^ [] : [-(class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral))], (52657 ^ _782435) ^ [] : [-(class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral))], (52659 ^ _782435) ^ [] : [-(class_Power_Opower(tc_Code__Numeral_Ocode__numeral))], (52661 ^ _782435) ^ [] : [-(class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral))], (52663 ^ _782435) ^ [] : [-(class_Int_Onumber(tc_Code__Numeral_Ocode__numeral))], (52665 ^ _782435) ^ [] : [-(class_Groups_Oone(tc_Code__Numeral_Ocode__numeral))], (52667 ^ _782435) ^ [] : [-(class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral))], (52669 ^ _782435) ^ [] : [-(class_Nat_Osize(tc_Code__Numeral_Ocode__numeral))], (52671 ^ _782435) ^ [_1843403] : [-(class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(_1843403)))], (52673 ^ _782435) ^ [_1843427, _1843429] : [-(hAPP(c_COMBI(_1843427), _1843429) = _1843429)], (52675 ^ _782435) ^ [_1843457, _1843459, _1843461, _1843463] : [-(hAPP(hAPP(c_COMBK(_1843457, _1843459), _1843461), _1843463) = _1843461)], (52677 ^ _782435) ^ [_1843495, _1843497, _1843499, _1843501, _1843503, _1843505] : [-(hAPP(hAPP(hAPP(c_COMBB(_1843495, _1843497, _1843499), _1843501), _1843503), _1843505) = hAPP(_1843501, hAPP(_1843503, _1843505)))], (52679 ^ _782435) ^ [_1843547, _1843549, _1843551, _1843553, _1843555, _1843557] : [-(hAPP(hAPP(hAPP(c_COMBC(_1843547, _1843549, _1843551), _1843553), _1843555), _1843557) = hAPP(hAPP(_1843553, _1843557), _1843555))], (52681 ^ _782435) ^ [_1843599, _1843601, _1843603, _1843605, _1843607, _1843609] : [-(hAPP(hAPP(hAPP(c_COMBS(_1843599, _1843601, _1843603), _1843605), _1843607), _1843609) = hAPP(hAPP(_1843605, _1843609), hAPP(_1843607, _1843609)))], (52683 ^ _782435) ^ [_1843654, _1843656] : [hBOOL(hAPP(hAPP(c_fequal, _1843654), _1843656)), -(_1843654 = _1843656)], (52689 ^ _782435) ^ [_1843743, _1843745] : [_1843743 = _1843745, -(hBOOL(hAPP(hAPP(c_fequal, _1843743), _1843745)))], (52695 ^ _782435) ^ [] : [hBOOL(c_fFalse)], (52697 ^ _782435) ^ [] : [-(hBOOL(c_fTrue))], (52699 ^ _782435) ^ [_1843874] : [hBOOL(hAPP(c_fNot, _1843874)), hBOOL(_1843874)], (52705 ^ _782435) ^ [_1843950] : [-(hBOOL(_1843950)), -(hBOOL(hAPP(c_fNot, _1843950)))], (52711 ^ _782435) ^ [_1843985, _1843987] : [hBOOL(_1843985), hBOOL(_1843987), -(hBOOL(hAPP(hAPP(c_fconj, _1843985), _1843987)))], (52721 ^ _782435) ^ [_1844124, _1844126] : [hBOOL(hAPP(hAPP(c_fconj, _1844124), _1844126)), -(hBOOL(_1844124))], (52727 ^ _782435) ^ [_1844211, _1844213] : [hBOOL(hAPP(hAPP(c_fconj, _1844211), _1844213)), -(hBOOL(_1844213))], (52733 ^ _782435) ^ [_1844298, _1844300] : [hBOOL(_1844298), -(hBOOL(hAPP(hAPP(c_fdisj, _1844298), _1844300)))], (52739 ^ _782435) ^ [_1844385, _1844387] : [hBOOL(_1844385), -(hBOOL(hAPP(hAPP(c_fdisj, _1844387), _1844385)))], (52745 ^ _782435) ^ [_1844472, _1844474] : [hBOOL(hAPP(hAPP(c_fdisj, _1844472), _1844474)), -(hBOOL(_1844472)), -(hBOOL(_1844474))], (52755 ^ _782435) ^ [_1844566, _1844568] : [-(hBOOL(_1844566)), -(hBOOL(hAPP(hAPP(c_fimplies, _1844566), _1844568)))], (52761 ^ _782435) ^ [_1844606, _1844608] : [hBOOL(_1844606), -(hBOOL(hAPP(hAPP(c_fimplies, _1844608), _1844606)))], (52777 ^ _782435) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_G, v_ts_H))], (52779 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_ts_H)))], (52781 ^ _782435) ^ [] : [-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_G), v_Ga)))], (52783 ^ _782435) ^ [] : [-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts_H))], (52767 ^ _782435) ^ [_1844693, _1844695] : [hBOOL(hAPP(hAPP(c_fimplies, _1844693), _1844695)), hBOOL(_1844693), -(hBOOL(_1844695))]], input).
% 1.77/2.49  ncf('1',plain,[c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)],start(52785 ^ 0)).
% 1.77/2.49  ncf('1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts)), c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts_H), hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_ts_H))],extension(5757 ^ 1,bind([[_873442, _873444, _873446, _873448], [t_a, v_Ga, v_ts_H, v_ts]]))).
% 1.77/2.49  ncf('1.1.1',plain,[-(c_Hoare__Mirabelle_Ohoare__derivs(t_a, v_Ga, v_ts_H))],extension(52783 ^ 2)).
% 1.77/2.49  ncf('1.1.2',plain,[-(hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a), tc_HOL_Obool)), v_ts), v_ts_H)))],extension(52779 ^ 2)).
% 1.77/2.49  %-----------------------------------------------------
% 1.77/2.49  End of proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
%------------------------------------------------------------------------------